ALBERT

Description:    In the present work a general theoretical framework for coupled dimensionally-heterogeneous partial differential equations is developed. This is done by recasting the variational formulation in terms of coupling interface variables. In such a general setting we analyze existence and uniqueness of solutions for both the continuous problem and its finite dimensional approximation. This approach also allows the development of different iterative substructuring solution methodologies involving dimensionally-homogeneous subproblems. Numerical experiments are carried out to test our theoretical results. Content Type Journal Article Pages 1-37 DOI 10.1007/s00211-011-0387-y Authors Pablo J. Blanco, LNCC, Laboratório Nacional de Computação Científica, Av. Getúlio Vargas 333, Quitandinha, 25651-075 Petrópolis, Brazil Marco Discacciati, MATHICSE, Chair of Modelling and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland Alfio Quarteroni, MATHICSE, Chair of Modelling and Scientific Computing, Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator P consisting of finitely or countably many distributional operators P n , which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain appropriate full-space Green function G with respect to L :=  P * T P now becomes a conditionally positive function. In order to support this claim we ensure that the distributional adjoint operator P * of P is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space) associated with the Green function G can be embedded into or even be equivalent to a generalized Sobolev space. As an application, we take linear combinations of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant s f , X to data values sampled from an unknown generalized Sobolev function f at data sites located in some set X Ì \mathbb R d . We provide several examples, such as Matérn kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert spaces of well-known reproducing kernels are equivalent to a generalized Sobolev space. These examples further illustrate how we can rescale the Sobolev spaces by the vector distributional operator P . Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the “best” kernel function for kernel-based approximation methods. Content Type Journal Article Pages 1-27 DOI 10.1007/s00211-011-0391-2 Authors Gregory E. Fasshauer, Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA Qi Ye, Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We are concerned with the inverse problem for an eikonal equation of determining the speed function using observations of the arrival time on a fixed surface. This is formulated as an optimisation problem for a quadratic functional with the state equation being the eikonal equation coupled to the so-called Soner boundary condition. The state equation is discretised by a suitable finite difference scheme for which we obtain existence, uniqueness and an error bound. We set up an approximate optimisation problem and show that a subsequence of the discrete mimina converges to a solution of the continuous optimisation problem as the mesh size goes to zero. The derivative of the discrete functional is calculated with the help of an adjoint equation which can be solved efficiently by using fast marching techniques. Finally we describe some numerical results. Content Type Journal Article Pages 1-25 DOI 10.1007/s00211-011-0386-z Authors Klaus Deckelnick, Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany Charles M. Elliott, Mathematics Institute, University of Warwick, Coventry, CV4 7AL UK Vanessa Styles, Department of Mathematics, University of Sussex, Brighton, BN1 9RF UK Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: In the future, climate models predict an increase in global surface temperature and during winter a changing of precipitation from less snowfall to more raining. Without protective snow cover, freezing can be more intensive and can enter noticeably deeper into the soil with effects on C cycling and soil organic matter (SOM) dynamics. We removed the natural snow cover in a Norway spruce forest in the Fichtelgebirge Mts. during winter from late December 2005 until middle of February 2006 on three replicate plots. Hence, we induced soil frost to 15 cm depth (at a depth of 5 cm below surface up to –5°C) from January to April 2006, while the snow-covered control plots never reached temperatures 〈 0°C. Quantity and quality of SOM was followed by total organic C and biomarker analysis. While soil frost did not influence total organic-C and lignin concentrations, the decomposition of vanillyl monomers (Ac/Ad) V and the microbial-sugar concentrations decreased at the end of the frost period, these results confirm reduced SOM mineralization under frost. Soil microbial biomass was not affected by the frost event or recovered more quickly than the accumulation of microbial residues such as microbial sugars directly after the experiment. However, in the subsequent autumn, soil microbial biomass was significantly higher at the snow-removal (SR) treatments compared to the control despite lower CO 2 respiration. In addition, the water-stress indicator (PLFA [cy17:0 + cy19:0] / [16:1ω7c + 18:1ω7c]) increased. These results suggest that soil microbial respiration and therefore the activity was not closely related to soil microbial biomass but more strongly controlled by substrate availability and quality. The PLFA pattern indicates that fungi are more susceptible to soil frost than bacteria.

Description:    In this paper we construct polynomial lattice rules which have, in some sense, small gain coefficients using a component-by-component approach. The gain coefficients, as introduced by Owen, indicate to what degree the method improves upon Monte Carlo. We show that the variance of an estimator based on a scrambled polynomial lattice rule constructed component-by-component decays at a rate of N −(2 α +1)+ δ , for all δ  〉 0, assuming that the function under consideration has bounded variation of order α for some 0 〈 α ≤ 1, and where N denotes the number of quadrature points. An analogous result is obtained for Korobov polynomial lattice rules. It is also established that these rules are almost optimal for the function space considered in this paper. Furthermore, we discuss the implementation of the component-by-component approach and show how to reduce the computational cost associated with it. Finally, we present numerical results comparing scrambled polynomial lattice rules and scrambled digital nets. Content Type Journal Article Pages 1-27 DOI 10.1007/s00211-011-0385-0 Authors Jan Baldeaux, School of Mathematics, University of New South Wales, Sydney, 2052 Australia Josef Dick, School of Mathematics, University of New South Wales, Sydney, 2052 Australia Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    A procedure for the construction of robust, upper bounds for the error in the finite element approximation of singularly perturbed reaction–diffusion problems was presented in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999 ) which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem exactly and this fact was recognised in the above work where it was indicated that the limitation would be addressed in a subsequent article. We view the present work as fulfilling that promise and as completing the investigation begun in Ainsworth and Babuška (SIAM J Numer Anal 36(2):331–353, 1999 ) by removing the obligation to solve a local problem exactly. The resulting new estimator is indeed fully computable and the first to provide fully computable, robust upper bounds in the setting of singularly perturbed problems discretised by the finite element method. Content Type Journal Article Pages 1-25 DOI 10.1007/s00211-011-0384-1 Authors Mark Ainsworth, Department of Mathematics, Strathclyde University, 26 Richmond St., Glasgow, G1 1XH Scotland Tomáš Vejchodský, Institute of Mathematics, Academy of Sciences, Žitná 25, 115 67 Prague 1, Czech Republic Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We present a hierarchical a posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the error in the energy minimum is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. We even show that small oscillation implies a related saturation assumption. In addition, we prove efficiency and reliability of an a posteriori estimate of the discretization error and thereby cast some light on the theoretical understanding of previous hierarchical estimators. Finally, we illustrate our theoretical results by numerical computations. Content Type Journal Article Pages 1-25 DOI 10.1007/s00211-011-0364-5 Authors Qingsong Zou, Freie Universität Berlin, Berlin, Germany Andreas Veeser, Freie Universität Berlin, Berlin, Germany Ralf Kornhuber, Freie Universität Berlin, Berlin, Germany Carsten Gräser, Freie Universität Berlin, Berlin, Germany Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    In this article, we give a new rigorous condition number estimate of the finite element tearing and interconnecting (FETI) method and a variant thereof, all-floating FETI. We consider a scalar elliptic equation in a two- or three-dimensional domain with a highly heterogeneous (multiscale) diffusion coefficient. This coefficient is allowed to have large jumps not only across but also along subdomain interfaces and in the interior of the subdomains. In other words, the subdomain partitioning does not need to resolve any jumps in the coefficient. Under suitable assumptions, we derive bounds for the condition numbers of one-level and all-floating FETI that are robust with respect to strong variations in the contrast in the coefficient, and that are explicit in some geometric parameters associated with the coefficient variation. In particular, robustness holds for face, edge, and vertex islands in high-contrast media. As a central tool we prove and use new weighted Poincaré and discrete Sobolev type inequalities that are explicit in the weight. Our theoretical findings are confirmed in a series of numerical experiments. Content Type Journal Article Pages 1-45 DOI 10.1007/s00211-011-0359-2 Authors Clemens Pechstein, Institute of Computational Mathematics, Johannes Kepler University, Altenberger Str. 69, 4040 Linz, Austria Robert Scheichl, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We consider the Fourier analysis of multigrid methods (of Galerkin type) for symmetric positive definite and semi-positive definite linear systems arising from the discretization of scalar partial differential equations (PDEs). We relate the so-called smoothing factor to the actual two-grid convergence rate and also to the convergence rate of the V-cycle multigrid. We derive a two-sided bound that defines an interval containing both the two-grid and V-cycle convergence rate. This interval is narrow and away from 1 when both the smoothing factor and an additional parameter are small enough. Besides the smoothing factor, the convergence mainly depends on the angle between the range of the prolongation and the eigenvectors of the system matrix associated with small eigenvalues. Nice V-cycle convergence is guaranteed if the tangent of this angle has an upper bound proportional to the eigenvalue, whereas nice two-grid convergence requires a bound proportional to the square root of the eigenvalue. We also discuss the well-known rule which relates the order of the prolongation to that of the differential operator associated to the problem. We first define a frequency based order which in most cases amounts to the so-called high frequency order as defined in Hemker (J Comput Appl Math 32:423–429, 1990 ). We give a firmer basis to the related order rule by showing that, together with the requirement of having the smoothing factor away from one, it provides necessary and sufficient conditions for having the two-grid convergence rate away from 1. A stronger condition is further shown to be sufficient for optimal convergence with the V-cycle. The presented results apply to rigorous Fourier analysis for regular discrete PDEs, and also to local Fourier analysis via the discussion of semi-positive systems as may arise from the discretization of PDEs with periodic boundary conditions. Content Type Journal Article Pages 1-27 DOI 10.1007/s00211-011-0362-7 Authors Artem Napov, Service de Métrologie Nucléaire, Université Libre de Bruxelles (C.P. 165/84), 50, Av. F.D. Roosevelt, 1050 Brussels, Belgium Yvan Notay, Service de Métrologie Nucléaire, Université Libre de Bruxelles (C.P. 165/84), 50, Av. F.D. Roosevelt, 1050 Brussels, Belgium Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: Intensive land use may affect soil properties ( e.g., decreased soil organic matter [SOM] content) and, consequently, reduce crop yields considerably. One way of counteracting the loss of SOM and stimulating plant productivity could be the use of organic residues from agro-industrial processes as bioactive products. The present study was focused on the possible effects of phenol-containing organic substances derived from agro-industrial by-products on maize ( Zea mays L.) metabolism in a pot experiment. Plants were grown for 12 d in a nutrient solution in the absence (control) or in the presence of either a cellulosolitic dry apple hydrolyzate (AP) or a dry blueberry cool extract (BB) applied at two rates (0.1 and 1 mL L –1 ). Both products increased root and leaf biomass and led to higher concentrations of macronutrients in the plant tissue. AP and BB also had a positive impact on nitrogen (N) metabolism stimulating the activity and gene expression of phenylalanine ammonia-lyase, a key enzyme of the phenylpropanoid pathway. Furthermore, both products increased leaf concentrations of phenols (+ 28% and 49% for AP and BB, respectively) and flavonoids (+ 22% and 25% for AP and BB, respectively). From our results it can be assumed that residues from agro-industry may be successfully used as bioactive products in agriculture to increase plant yield and resistance to stress conditions.

Description:    Necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. Application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented. Content Type Journal Article Pages 1-31 DOI 10.1007/s00211-011-0372-5 Authors Jason S. Howell, Department of Mathematics, Clarkson University, Potsdam, NY 13676, USA Noel J. Walkington, Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: An agricultural use of reclaimed coal-mine spoil banks is limited to nonfood crop uses and provides potential for biofuel crops. Two high-biomass crops— Galega orientalis and Helianthus tuberosus —were cultivated in a greenhouse pot experiment conducted in sterilized and nonsterile spoil bank clay. We aimed (1) to determine the possibility of reducing the applied rate of organic amendments (thus decreasing the costs of spoil-bank reclamation) and (2) to assess whether the inoculation with arbuscular mycorrhizal fungi (AMF) can improve plant growth and biomass accumulation of bioenergy crops even in nonsterile soil containing naturally occurring AMF. The spoil substrate was either unamended or treated with a mixture of composted urban waste and ligno-cellulose at a rate corresponding to 40 t ha –1 . Three native AMF isolates or three isolates from the International Bank of Glomeromycota (BEG) originating from man-made ecosystems were used for inoculation. Generally, both plant species positively responded to both mycorrhizal inoculation and organic amendment. While G. orientalis did not show any preferences towards the AMF inoculum origin in the nonsterile soil, for H. tuberosus the specific combination of organic amendment and BEG isolates resulted in highest yields of shoot biomass. The study shows that the successful planting of both tested crops requires the organic amendment. However, its dosage can be substantially reduced. The effectiveness of mycorrhizal inoculation can vary for the combination of plant species and the origin of the applied AMF.

Description: Iodine is an essential element in the human diet, and iodine deficiency is a significant health problem. No attempts to increase iodine content in plant-derived food (biofortification) have so far been particularly effective. We studied iodine uptake in tomato ( Solanum lycopersicum L.) to evaluate whether it is possible to increase the iodine concentration in its fruits. Iodine translocation and storage inside tomato tissues were studied using radioactive iodine. Potassium iodide was also supplied at different concentrations to tomato plants to evaluate the resulting iodide concentration both in the vegetative tissues and the fruits. The results indicate that iodine was taken up better when supplied to the roots using hydroponically grown plants. However, a considerable amount of iodine was also stored after leaf treatment, suggesting that iodine transport through phloem also occurred. We found that tomato plants can tolerate high levels of iodine, stored both in the vegetative tissues and fruits at concentrations that are more than sufficient for the human diet. We conclude that tomato is an excellent crop for iodine-biofortification programs.

Description: Citrus established in calcareous soils can be affected by iron (Fe)-deficiency chlorosis which limits yield and the farmers' income. The degree of deficiency depends on the rootstock, but the resistance to Fe chlorosis still requires further investigation. To study physiological parameters of citrus rootstocks that could be used to evaluate resistance to Fe deficiency, plants of Troyer citrange ( Citrus sinensis L. Osb. × Poncitrus trifoliata L. Raf.), Carrizo citrange, Volkamer lemon ( Citrus volkameriana Ten. & Pasq.), alemow ( Citrus macrophylla Wester), and sour orange ( Citrus aurantium L.) were grown in nutrient solutions with 0, 5, 10, 15, or 20 μM Fe. For each rootstock, plant height, root and shoot dry weights, and concentration of Fe in the shoots and roots were measured at the end of the experiment. Chlorophyll (CHL) concentration was estimated throughout the experimental period using a portable CHL meter (SPAD-502) calibrated for each rootstock. At the end of the experiment, CHL fluorescence parameters were measured in each rootstock with a portable fluorimeter. Maximal and variable fluorescence values indicated that the photochemistry of Troyer was more affected by a low concentration of Fe in the nutrient solution than that of other rootstocks. To compare rootstocks, the absolute CHL concentration was converted into relative yield by employing a scaling divisor based on the maximum value of total CHL in plants without Fe-deficiency symptoms. Exponential models were developed to determine the minimum Fe concentration in nutrient solution required to maintain leaf CHL at 50% of the maximum CHL concentration (IC50). Models were also developed to assess the period of time the rootstocks were able to grow under Fe-stress conditions before they reached IC50. Volkamer lemon and sour orange needed the lowest Fe concentration (between 4 and 5 μM Fe) to maintain IC50, and Troyer citrange had the highest Fe requirement (14 μM Fe). Citrus macrophylla and Carrizo citrange required 7 and 9 μM of Fe, respectively. Similarly, Volkamer lemon and sour orange rootstocks withstood more days under total Fe depletion or with a low concentration of Fe (5 μM Fe in nutrient solution) until they reached IC50, compared to the other rootstocks. The approach used led to a classification of the rootstocks into three categories, regarding their internal tolerance to Fe chlorosis: resistance (sour orange and Volkamer lemon), intermediate resistance (C . macrophylla and Carrizo citrange), and reduced resistance (Troyer citrange).

Description: Trees interact in a complex manner with soils: they recycle and redistribute nutrients via many ecological pathways. Nutrient distribution via leaf litter is assumed to be of major importance. Beech is commonly known to have lower nutrient concentrations in its litter than other hardwood tree species occurring in Central Europe. We examined the influences of distribution of beech ( Fagus sylvatica L.), ash ( Fraxinus excelsior L.), lime ( Tilia cordata Mill. and T. platyphyllos Scop.), maple ( Acer spp. L.), and clay content on small-scale variability of pH and exchangeable Ca and Mg stocks in the mineral soil and of organic-C stocks in the forest floor in a near-natural, mature mixed deciduous forest in Central Germany. The soil is a Luvisol developed in loess over limestone. We found a positive effect of the proportion of beech on the organic-C stocks in the forest floor and a negative effect on soil pH and exchangeable Ca and Mg in the upper mineral soil (0 to 10 cm). The proportion of ash had a similar effect in the opposite direction, the other species did not show any such effect. The ecological impact of beech and ash on soil properties at a sample point was explained best by their respective proportion within a radius of 9 to 11 m. The proportion of the species based on tree volume within this radius was the best proxy to explain species effects. The clay content had a significant positive influence on soil pH and exchangeable Ca and Mg with similar effect sizes. Our results indicate that beech, in comparison to other co-occurring deciduous tree species, mainly ash, increased acidification at our site. This effect occurred on a small spatial scale and was probably driven by species-related differences in nutrient cycling via leaf litter. The distribution of beech and ash resulted not only in aboveground diversity of stand structures but also induced a distinct belowground diversity of the soil habitat.

Description: Several chemical and microbial properties of mine soils need to be measured for comprehensive assessment of the reclamation success. The objective of this study was to evaluate the ability of NIR spectroscopy to predict organic C (C org ), total N (N t ), and several microbial properties of mine soils reclaimed for forestry. Soils samples ( n = 154) were collected at two reclaimed areas in central and S Poland, and their spectra in the NIR region (including the visible range, 400–2500 nm) were recorded. A half of the samples was used to develop calibration equations, and another half was used for validation. The modified partial least squares regression was applied to build calibration equations using the whole spectrum (0 to 2nd derivative). The best predictions were obtained for C org and N t (ratio of standard deviation to standard error of prediction in the validation stage [RPD] = 3.4 and 4.1; the regressions coefficients [ a ] of linear regression [measured against predicted values] = 0.94 and 0.96; correlation coefficients [ r ] = 0.96 and 0.97, respectively). Very well predictive models applicable for quantitative measurements were obtained also for microbial biomass, basal respiration, and the activities of dehydrogenase and acid phosphatase (RPD = 2.3–2.5, a = 0.90–0.99, r = 0.90–0.92). Prediction of urease activity was slightly worse (RPD = 2.1, a = 0.88, r = 0.87) but sufficient for rough estimation. The obtained results indicated the ability of NIR spectroscopy to predict complex soil microbial properties. Therefore, application of this analytical method may improve the assessment of recovery of microbial functions in reclaimed post-mining barrens.

Description: Several algorithms exist for the calibration procedures of near-infrared spectra in soil-scientific studies, but the potential of a genetic algorithm (GA) for spectral feature selection and interpretation has not yet been sufficiently explored. Objectives were (1) to test the usefulness of near-infrared spectroscopy (NIRS) for a prediction of C and N from char and forest-floor Oa material in soils using either a partial least squares (PLS) method or a GA-PLS approach and (2) to discuss the mechanisms of GA feature selection for the examined constituents. Calibration and validation were carried out for measured reflectance spectra in the visible and near-IR region (400–2500 nm) on an existing set of 432 artificial mixtures of C-free soil, char (lignite, anthracite, charcoal, or a mixture of the three coals), and forest-floor Oa material. For all constituents (total C and N, C and N from all coals and from the Oa material, C derived from mixed coal, charcoal, lignite, and anthracite), the GA-PLS approach was superior over the full-spectrum PLS method. The RPD values (ratio of standard deviation of the laboratory results to standard error of prediction) ranged from 2.4 to 5.1 in the validation and indicated a better category of prediction for three constituents: “approximate quantitative” instead of a “distinction between high and low” for C derived from mixed coal and “good” instead of “approximate quantitative” for C and N derived from all coals. Overall, this study indicates that the approach using GA may have a greater potential than the PLS method in NIRS.

Description: Several genes in the aspen genome have been modified to generate stem wood with lower lignin content and an altered lignin composition. Lower lignin in wood reduces the time and energy required for pulping. Further, this modification can also increase the allocation of photosynthate to cellulose and total biomass production, potentially increasing CO 2 -sequestration capacity. However, widespread planting of trees with altered lignin content and composition could alter soil organic-C dynamics in complex ways. To further examine the effects of altered lignin biosynthesis on plant growth and accrual of soil organic C (SOC), we conducted a repeated greenhouse study with four lines of transgenic aspen ( Populus tremuloides Michx.) and one wild-type (control) aspen. Accrual of aspen-derived SOC was quantified by growing aspen trees (C3 plants) in C4 soil and measuring changes in the natural abundance of δ 13 C. We measured plant growth, biomass, and C content and combined these data with SOC measurements to create C budgets for the plant mesocosms. Lignin modifications resulted in differences in the accrual of aspen-derived SOC and total mesocosm C, primarily due to differences in biomass between genetically modified lines of aspen. One genetic alteration (low lignin, line 23) was able to perform similarly or better than the wild-type aspen (control, line 271) without altering SOC. Alterations in lignin structure (S : G ratios) had negative effects on biomass production and SOC formation. The addition of new (aspen-derived) SOC was proportional to the loss of existing SOC, evidence for a priming effect. The pool of new SOC was related to total plant biomass, suggesting that the effects of lignin modification on SOC are driven by changes in plant growth.

Description:    Recently, the format of TT tensors (Hackbusch and Kühn in J Fourier Anal Appl 15:706–722, 2009 ; Oseledets in SIAM J Sci Comput 2009 , submitted; Oseledets and Tyrtyshnikov in SIAM J Sci Comput 31:5, 2009 ; Oseledets and Tyrtyshnikov in Linear Algebra Appl 2009 , submitted) has turned out to be a promising new format for the approximation of solutions of high dimensional problems. In this paper, we prove some new results for the TT representation of a tensor U Î \mathbb R n 1 × ¼ × n d and for the manifold of tensors of TT-rank r . As a first result, we prove that the TT (or compression) ranks r i of a tensor U are unique and equal to the respective separation ranks of U if the components of the TT decomposition are required to fulfil a certain maximal rank condition. We then show that the set \mathbb T of TT tensors of fixed rank r locally forms an embedded manifold in \mathbb R n 1 × ¼ × n d , therefore preserving the essential theoretical properties of the Tucker format, but often showing an improved scaling behaviour. Extending a similar approach for matrices (Conte and Lubich in M2AN 44:759, 2010 ), we introduce certain gauge conditions to obtain a unique representation of the tangent space T U \mathbb T of \mathbb T and deduce a local parametrization of the TT manifold. The parametrisation of T U \mathbb T is often crucial for an algorithmic treatment of high-dimensional time-dependent PDEs and minimisation problems (Lubich in From quantum to classical molecular dynamics: reduced methods and numerical analysis, 2008 ). We conclude with remarks on those applications and present some numerical examples. Content Type Journal Article Pages 1-31 DOI 10.1007/s00211-011-0419-7 Authors Sebastian Holtz, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany Thorsten Rohwedder, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany Reinhold Schneider, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    Deckelnick and Dziuk (Math. Comput. 78(266):645–671, 2009 ) proved a stability bound for a continuous-in-time semidiscrete parametric finite element approximation of the elastic flow of closed curves in \mathbb R d , d ³ 2 . We extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in Barrett et al. (J Comput Phys 222(1): 441–462, 2007 ; SIAM J Sci Comput 31(1):225–253, 2008 ; IMA J Numer Anal 30(1):4–60, 2010 ), in particular an equidistribution mesh property. For this new approximation, we obtain also a stability bound for a continuous-in-time semidiscrete scheme. Apart from the isotropic situation, we also consider the case of an anisotropic elastic energy. In addition to the evolution of closed curves, we also consider the isotropic and anisotropic elastic flow of a single open curve in the plane and in higher codimension that satisfies various boundary conditions. Content Type Journal Article Pages 1-54 DOI 10.1007/s00211-011-0416-x Authors John W. Barrett, Department of Mathematics, Imperial College London, London, SW7 2AZ UK Harald Garcke, Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany Robert Nürnberg, Department of Mathematics, Imperial College London, London, SW7 2AZ UK Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We consider convergence analysis for a model reduction algorithm for a class of linear infinite dimensional systems. The algorithm computes an approximate balanced truncation of the system using solution snapshots of specific linear infinite dimensional differential equations. The algorithm is related to the proper orthogonal decomposition, and it was first proposed for systems of ordinary differential equations by Rowley (Int. J. Bifurc. Chaos Appl. Sci. Eng. 15(3):997–1013, 2005 ). For the convergence analysis, we consider the algorithm in terms of the Hankel operator of the system, rather than the product of the system Gramians as originally proposed by Rowley. For exponentially stable systems with bounded finite rank input and output operators, we prove that the balanced realization can be expressed in terms of balancing modes, which are related to the Hankel operator. The balancing modes are required to be smooth, and this can cause computational difficulties for PDE systems. We show how this smoothness requirement can be lessened for parabolic systems, and we also propose a variation of the algorithm that avoids the smoothness requirement for general systems. We prove entrywise convergence of the matrices in the approximate reduced order models in both cases, and present numerical results for two example PDE systems. Content Type Journal Article Pages 1-38 DOI 10.1007/s00211-011-0424-x Authors John R. Singler, Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We present and analyze subspace correction methods for the solution of variational inequalities of the second kind and apply these theoretical results to non smooth contact problems in linear elasticity with Tresca and non-local Coulomb friction. We introduce these methods in a reflexive Banach space, prove that they are globally convergent and give error estimates. In the context of finite element discretizations, where our methods turn out to be one- and two-level Schwarz methods, we specify their convergence rate and its dependence on the discretization parameters and conclude that our methods converge optimally. Transferring this results to frictional contact problems, we thus can overcome the mesh dependence of some fixed-point schemes which are commonly employed for contact problems with Coulomb friction. Content Type Journal Article Pages 1-27 DOI 10.1007/s00211-011-0423-y Authors L. Badea, Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania R. Krause, Institute of Computational Science, University of Lugano, via Giuseppe Buffi 13, 6900 Lugano, Switzerland Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: Wild barley ( Hordeum sp. ) germplasm is rich in genetic diversity and provides a treasure trove of useful genes for crop improvement. We carried out a comprehensive program combining short-term hydroponic screening via hematoxylin-staining of root-regrowth procedure and filter paper–based evaluation of diverse germplasm in response to Al/acid stress using 105 annual Tibetan wild barley and 45 cultivated barley genotypes. Root elongation among the 105 Tibetan wild barley genotypes varied significantly after Al exposure, ranging from 62.9% to 80.0% in variation coefficients and 4.35 to 4.45 in diversity index. These genotypic differences in Al resistance were fairly consistent in both the hydroponic and filter paper–based evaluations: XZ16, XZ166, and XZ113 were selected as Al-resistant genotypes, and XZ61, XZ45, and XZ98 as Al-sensitive wild genotypes. Furthermore, significantly lower Al concentrations in roots and shoots were detected in the three selected Al-resistant genotypes than in the three sensitive genotypes in the filter paper–based experiment. Meanwhile, XZ16 was the least affected by Al toxicity in regard to reduced SPAD value (chlorophyll meter readings), plant height, root length, dry biomass, tillers per plant, and chlorophyll fluorescence (Fv/Fm) in the long-term hydroponic experiment compared with the Al-resistant cultivated barley cv. Dayton, while XZ61 had the severest stress symptoms.

Description: Simplified algebraic equations are derived to calculate directly the Brooks and Corey model parameters using data obtained from one-step outflow experiments and saturated hydraulic conductivity. The suggested method has been demonstrated only for horticultural substrates and is verified experimentally for four substrates with satisfactory agreement of the results.

Description: Fine roots from the soil archive of the Swedish National Forest Soil Inventory, collected in 1964, 1972, 1985, and 1998, were analyzed for 14 C contents. Two different methods of estimating residence time were compared. Residence time of root C was estimated to be 8 y using a steady state 1-pool model.

Description: Appropriate management of P from slurry can increase crop production and decrease nutrient loss to water bodies. The present study examined how the application of different size fractions of dairy slurry influenced the quantity and composition of P leached from grassland in a temperate climate. Soil blocks were amended (day 0 = start of the experiment) with either whole slurry (WS), the 〉 425 μm fraction (coarse slurry fraction, CSF), the 〈 45 μm slurry fraction (fine liquid slurry fraction, FLF), or not amended, i.e., the control soil (CON). Deionized water was added to the soil blocks to simulate six sequential rainfall events, equivalent to 250 mm (day 0.2, 1.2, 4.2, 11.2) or 500 mm of rainfall (day 18.2 and 25.2), with leachates collected the following day. The results showed that total dissolved P (TDP), dissolved reactive P (DRP), dissolved unreactive P (DUP), orthophosphate, phosphomonoester, and pyrophosphate concentrations generally decreased with the increasing number of simulated rain events. Total dissolved P was leached in the following order WS 〉 FLF ≈ CSF 〉 CON. Dissolved organic C was correlated with TDP, DRP, and DUP in leachates of all treatments. The highest concentrations of dissolved phosphomonoesters and pyrophosphate (147 μg P L –1 and 57 μg P L –1 , respectively) were detected using solution 31 P-NMR spectroscopy in the WS leachates. Overall, there were significant differences observed between slurry treatments ( e.g., relative contributions of inorganic P vs. organic P of dissolved P in leachates). Differences were independent from the rate at which slurry P was applied, because the highest dissolved P losses per unit of slurry P applied were measured in the FLF, i.e., the treatment that received the smallest amount of P. We conclude that the specific particle-size composition of applied slurry influences dissolved P losses from grassland systems. This information should be taken in account in farm-management approaches which aim to minimizing dissolved slurry P losses from grassland systems.

Description:    We discuss the full discretization of an elliptic optimal control problem with pointwise control and state constraints. We provide the first reliable a-posteriori error estimator that contains only computable quantities for this class of problems. Moreover, we show, that the error estimator converges to zero if one has convergence of the discrete solutions to the solution of the original problem. The theory is illustrated by numerical tests. Content Type Journal Article Pages 1-30 DOI 10.1007/s00211-011-0422-z Authors Arnd Rösch, Fakultät für Mathematik, Universität Duisburg-Essen, Forsthausweg 2, 47057 Duisburg, Germany Daniel Wachsmuth, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenbergerstraße 69, 4040 Linz, Austria Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this work, we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this parameter varies. Based on the concept of invariant pairs, a theoretically sound and reliable numerical continuation procedure is developed. Particular attention is paid to the situation when the procedure approaches a singularity, that is, when eigenvalues included in the invariant pair collide with other eigenvalues. For the real generic case, it is proven that such a singularity only occurs when two eigenvalues collide on the real axis. It is shown how this situation can be handled numerically by an appropriate expansion of the invariant pair. The viability of our continuation procedure is illustrated by a numerical example. Content Type Journal Article Pages 1-28 DOI 10.1007/s00211-011-0392-1 Authors Wolf-Jürgen Beyn, Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany Cedric Effenberger, Seminar for Applied Mathematics, D-MATH, ETH Zurich, Raemistrasse 101, 8092 Zurich, Switzerland Daniel Kressner, MATHICSE, EPF Lausanne, Station 8, 1015 Lausanne, Switzerland Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: Several methods are used for the extraction of soil solution. The objective of this study was to find out to what extent the different extraction methods yield complementary or equivalent information. Soil solutions were sampled once at 10 different forest sites in Germany, with 4 sampling points per site, using 5 different extraction methods. Concentrations of the major ions in the 1:2 extracts and the equilibrium soil-pore solutions (obtained from percolation of field-fresh soil cores) were generally lower than in desorption solutions, suction-cup solutions, and saturation extracts. Surprisingly, the latter three methods generally yielded equivalent results. However, possible systematic differences between these methods could have been masked by the high small-scale spatial variability within the sites.

Description: A standard and a high manganese (Mn) level (10 and 160 μM) were combined with a standard and a high zinc (Zn) level (4 and 64 μM) in the nutrient solution supplied to cucumber in closed-cycle hydroponic units to compensate for nutrient uptake. The concentrations of all nutrients except Mn and Zn were identical in all treatments. The objectives of the experiment were to establish critical Zn and Mn levels in both nutrient solutions and leaves of cucumber grown hydroponically, to assess the impact of gradual Zn and/or Mn accumulation in the external solution on nutrient uptake and gas exchange, and to find whether Mn and Zn have additive effects when the levels of both ions are excessively high in the root zone. The first symptoms of Mn and Zn toxicity appeared when the concentrations of Mn and Zn in the leaves of cucumber reached 900 and 450 mg kg –1 in the dry weight, respectively. Excessively high Mn or/and Zn concentrations in the leaves reduced the fruit biomass production due to decreases in the number of fruits per plant, as well as the net assimilation rate, stomatal conductance, and transpiration rate, but increased the intercellular CO 2 levels. Initially, the Mn or Zn concentrations in the recirculating nutrient solution increased rapidly but gradually stabilized to maximal levels, while the corresponding concentrations in the leaves constantly increased until the end of the experiment. The uptake of Mg, Ca, Fe, and Cu was negatively affected, while that of K and P remained unaffected by the external Mn and Zn levels. The combination of high Mn and Zn seems to have no additive effects on the parameters investigated.

Description: A pot experiment with wheat plants was carried out to study how late application of nitrogen (N) fertilizer affects the use of pre-anthesis N reserves during the grain-filling period. Increasing doses of N fertilizer were applied (0, 40, and 52 mg N plant –1 ), either in two amendments (growth stages GS20 and GS30, according to Zadoks scale) or in three amendments (GS20, GS30, and GS37). The experiment was arranged in a complete randomized three-block design with 129 plants per treatment. The plants were watered daily, harvested every 2 d between anthesis and maturity, and were separated into roots, leaf sheaths, leaf blades, and ears for further N determination. Grain N concentration improved due to a late N application in GS37 by 14% (higher N dose) and by 7% (further splitting the same N-fertilizer dose, respectively). The higher the N-fertilizer dose applied, the greater was the amount of pre-anthesis reserves in vegetative organs, these reserves became later available for remobilization. Although splitting the same N dose in three amendments did not increase the N reserves, these reserves were more efficiently remobilized allowing an improvement in grain N concentration. The fertilizer management did not change the temporary pattern of N accumulation in the ear, but did induce a change in the amount of N remobilized and in the contribution of each organ (root, leaf sheath, leaf blade) to this remobilization. Late N amendment allowed a greater N availability of leaf blades and ear N reserves (from 20% up to 26% and from 19% up to 22%, respectively) for remobilization towards the grain, decreasing the root contribution from 28% down to 15%, while the contribution of leaf sheaths was maintained around 35% irrespective of the N applied.

Description: Flooded rice ( Oryza sativa L.) may contain high arsenic (As) concentrations compared to other grain crops. For the development of measures to reduce the As concentration of rice grains, knowledge about the mobility of As within the rice plant is required. Therefore, to investigate the mobilization of As within the plant, rice was grown in nutrient solution and exposed to As either before flowering, after flowering, or continuously until maturity. Furthermore, rice was grown in four soils under greenhouse and field conditions and the time course of As accumulation in grains during the grain-filling period was investigated. When grown in nutrient solution, As removal at flowering did not reduce As concentrations in polished rice compared to plants supplied with As continuously or after flowering. Plants that received As only after flowering had the same As concentrations in shoot and bran as plants receiving As only before flowering. However, continuous As supply resulted in doubling of As concentrations in both plant parts. In contrast to grain and shoot, the As concentration in the root decreased after As removal compared to the treatments receiving As only after flowering or continuously. The observations indicate that As was mobilized from root or shoot to the grain and that it was accumulated in the grain, although it was not available in nutrient solution during the grain-filling period. In soil experiments, the 1000-grain weight increased up to 2 weeks before harvest in the field as well as in the greenhouse. The As concentration in rice grain was constant during the whole grain-filling period. It was at a similar level under field and greenhouse conditions, and its variation among soils was in the same order indicating that soil was the decisive factor for As concentration in grains. Our results suggest that temporary cultural measures during the cultivation period, for example drainage, might be ineffective because of the mobilization capacity within the rice plant. Moreover, harvest before final maturity of grains would not reduce the As concentration since it remained constant during the grain-filling period.

Description:    We analyze parabolic PDEs with certain type of weakly singular or degenerate time-dependent coefficients and prove existence and uniqueness of weak solutions in an appropriate sense. A localization of the PDEs to a bounded spatial domain is justified. For the numerical solution a space–time wavelet discretization is employed. An optimality result for the iterative solution of the arising systems can be obtained. Finally, applications to fractional Brownian motion models in option pricing are presented. Content Type Journal Article Pages 1-29 DOI 10.1007/s00211-011-0432-x Authors O. Reichmann, Rämistrasse 102, 8092 Zurich, Switzerland Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We study an implicit and discontinuous scheme for a non-local Hamilton–Jacobi equation modelling dislocation dynamics. For the evolution problem, we prove an a posteriori estimate of Crandall–Lions type for the error between continuous and discrete solutions. We deduce an a posteriori error estimate for the effective Hamiltonian associated to a stationary cell problem. In dimension one and under suitable assumptions, we also give improved a posteriori estimates. Numerical simulations are provided. Content Type Journal Article Pages 1-55 DOI 10.1007/s00211-011-0430-z Authors S. Cacace, Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Rome, Italy A. Chambolle, CMAP, Ecole Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex, France R. Monneau, CERMICS, Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: Recent studies indicate that soil soluble organic nitrogen (SON) plays an important regulatory role in the soil–plant N cycle. The aims of this study were to identify the vertical distribution of SON and its correlation with N mineralization, nitrification, and amidohydrolase activities, in a soil repeatedly amended with cow manure or chemical fertilizer. For this purpose, soil samples were collected from 0–20, 20–40, 40–60, 60–80, and 80–100 cm depths of a calcareous soil, which has been annually amended for 5 y with cow manure (CM) at two rates of 50 (CM 50 ) and 100 (CM 100 ) Mg CM ha –1 y –1 . Treatments with chemical fertilizer (CF) and a control (CT) were also included. Soluble organic N, N mineralization, nitrification rates, as well as L-glutaminase and L-asparaginase activities were determined. Both CM 50 and CM 100 enhanced SON content throughout the soil profile. Nitrogen-mineralization rate (N m ) was increased at the 0–20 cm depth of the CM 100 treatment and remained unaffected at the deeper depths. Nitrification rate (N n ) was significantly higher at the 0–60 cm depth of CM 100 compared to CF and CT. L-glutaminase and L-asparaginase activities were significantly increased at the 0–40 cm depth in both CM 50 and CM 100 compared to CF and CT. The amidohydrolase activities could not be detected below 40 cm, regardless of the fertilizer treatments. Our results suggest that SON makes a minor contribution to N mineralization in deep soil layers. It was also concluded that changes in the SON throughout the soil profile were not associated with changes in the N-transformation rates (N m and N n ) and amidohydrolase activities. While we conclude that SON is a major N pool in the whole profile of the manure applied soil further investigation is required to characterize SON and to investigate the bioavailability of SON for microbial activity in different soil depths.

Description: Due to energy crises and stricter environmental regulations, renewable energy sources like bio-methane produced by anaerobic digestion (biogas) become increasingly important. However, the application of slurries produced by biogas fermentation to agricultural land and subsequent ammonia emission may also create environmental risks to the atmosphere and to N-limited ecosystems. Evaluating ammonia loss from agricultural land by model simulation is an important tool of agricultural-systems analysis. The objective of this study was the systematical comparison of ammonia volatilization after application of two types of biogas slurries containing high amounts of energy crops in comparison with conventional animal slurries and to investigate the relative importance of factors affecting the emission process through an empirical model. A high number of ammonia-loss field measurements were carried out in the years 2007/08 in biogas cropping systems in N Germany. The study consisted of simultaneous measurement of NH 3 losses from animal and biogas slurries in multiple-plot field experiments with different N-fertilization levels. The derived empirical model for the calculation of NH 3 losses based on explanatory variables gave good predictions of ammonia emission for both biogas and pig slurries. The root mean square error ( RMSE ) and mean bias error ( MBE ) of the empirical model for validation data were 2.19 kg N ha –1 ( rRMSE 29%) and –1.19 kg N ha –1 , respectively. Biogas slurries produced highest NH 3 emissions compared to the two animal slurries. In view of the explanatory variables included in the model, total NH application rate, slurry type, temperature, precipitation, crop type, and leaf-area index were important for ammonia-volatilization losses.

Description:    We consider semi-discrete first-order finite difference schemes for a nonlinear degenerate convection–diffusion equations in one space dimension, and prove an L 1 error estimate. Precisely, we show that the L 1 loc difference between the approximate solution and the unique entropy solution converges at a rate O ( D x 1/11 ) , where D x is the spatial mesh size. If the diffusion is linear, we get the convergence rate O ( D x 1/2 ) , the point being that the O is independent of the size of the diffusion. Content Type Journal Article Pages 1-29 DOI 10.1007/s00211-011-0433-9 Authors K. H. Karlsen, Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, Oslo, 0316 Norway U. Koley, Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, Oslo, 0316 Norway N. H. Risebro, Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, Oslo, 0316 Norway Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We derive low-complexity matrix-free finite element algorithms for simplicial Bernstein polynomials on simplices. Our techniques, based on a sparse representation of differentiation and special block structure in the matrices evaluating B-form polynomials at warped Gauss points, apply to variable coefficient problems as well as constant coefficient ones, thus extending our results in Kirby (Numer Math, 2011 , in press). Content Type Journal Article Pages 1-19 DOI 10.1007/s00211-011-0431-y Authors Robert C. Kirby, Department of Mathematics and Statistics, Texas Tech University, PO Box 1042, Lubbock, TX 79409-1042, USA Kieu Tri Thinh, Department of Mathematics and Statistics, Texas Tech University, PO Box 1042, Lubbock, TX 79409-1042, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Algebraic Riccati Equations (MARE) XDX - AX - XB + C = 0 by which we mean the following conformally partitioned matrix ( ll B    - D - C    A ) is a nonsingular or an irreducible singular M -matrix. It is known that such an MARE has a unique minimal nonnegative solution F . It is proved that small relative perturbations to the entries of A , B , C , and D introduce small relative changes to the entries of the nonnegative solution F . Thus the smaller entries F do not suffer bigger relative errors than its larger entries, unlike the existing perturbation theory for (general) Algebraic Riccati Equations. We then discuss some minor but crucial implementation changes to three existing numerical methods so that they can be used to compute F as accurately as the input data deserve. Current study is based on a previous paper of the authors’ on M -matrix Sylvester equation for which D  = 0. Content Type Journal Article Pages 1-30 DOI 10.1007/s00211-011-0421-0 Authors Jungong Xue, School of Mathematical Science, Fudan University, Shanghai, 200433 People’s Republic of China Shufang Xu, School of Mathematical Sciences, Peking University, Beijing, 100871 People’s Republic of China Ren-Cang Li, Department of Mathematics, University of Texas at Arlington, Arlington, P.O. Box 19408, TX 76019, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    This paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Sylvester equation AX  +  XB  =  C by which we mean both A and B have positive diagonal entries and nonpositive off-diagonal entries and P = I m Ä A + B T Ä I n is a nonsingular M -matrix, and C is entrywise nonnegative. It is proved that small relative perturbations to the entries of A , B , and C introduce small relative errors to the entries of the solution X . Thus the smaller entries of X do not suffer bigger relative errors than its larger entries, unlikely the existing perturbation theory for (general) Sylvester equations. We then discuss some minor but crucial implementation changes to three existing numerical methods so that they can be used to compute X as accurately as the input data deserve. Content Type Journal Article Pages 1-32 DOI 10.1007/s00211-011-0420-1 Authors Jungong Xue, School of Mathematical Science, Fudan University, Shanghai, 200433 People’s Republic of China Shufang Xu, School of Mathematical Sciences, Peking University, Beijing, 100871 People’s Republic of China Ren-Cang Li, Department of Mathematics, University of Texas at Arlington, P.O. Box 19408, Arlington, TX 76019, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    In this paper we propose and analyse adaptive finite element methods for computing the band structure of 2D periodic photonic crystals. The problem can be reduced to the computation of the discrete spectra of each member of a family of periodic Hermitian eigenvalue problems on a unit cell, parametrised by a two-dimensional parameter - the quasimomentum. These eigenvalue problems involve non-coercive elliptic operators with generally discontinuous coefficients and are solved by adaptive finite elements. We propose an error estimator of residual type and show it is reliable and efficient for each eigenvalue problem in the family. In particular we prove that if the error estimator converges to zero then the distance of the computed eigenfunction from the true eigenspace also converges to zero and the computed eigenvalue converges to a true eigenvalue with double the rate. We also prove that if the distance of a computed sequence of approximate eigenfunctions from the true eigenspace approaches zero, then so must the error estimator. The results hold for eigenvalues of any multiplicity. We illustrate the benefits of the resulting adaptive method in practice, both for fully periodic structures and also for the computation of eigenvalues in the band gap of structures with defect, using the supercell method. Content Type Journal Article Pages 1-34 DOI 10.1007/s00211-011-0425-9 Authors S. Giani, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD UK I. G. Graham, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    In this paper, we discuss multiscale radial basis function collocation methods for solving certain elliptic partial differential equations on the unit sphere. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. Two variants of the collocation method are considered (sometimes called symmetric and unsymmetric, although here both are symmetric). A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. Content Type Journal Article Pages 1-27 DOI 10.1007/s00211-011-0428-6 Authors Q. T. Le Gia, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia I. H. Sloan, School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia H. Wendland, Mathematical Institute, University of Oxford, 24-29 St. Giles’, Oxford, OX1 3LB UK Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We study a class of numerical methods for a system of second-order SDE driven by a linear fast force generating high frequency oscillatory solutions. The proposed schemes permit the use of large step sizes, have uniform global error bounds in the position (i.e. independent of the large frequencies present in the SDE) and offer various additional properties. This new family of numerical integrators for SDE can be viewed as a stochastic generalisation of the trigonometric integrators for highly oscillatory deterministic problems. Content Type Journal Article Pages 1-29 DOI 10.1007/s00211-011-0426-8 Authors David Cohen, Mathematisches Institut, Universität Basel, 4051 Basel, Switzerland Magdalena Sigg, Mathematisches Institut, Universität Basel, 4051 Basel, Switzerland Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: Soil sulfur (S) partitioning among the various pools and changes in tropical pasture ecosystems remain poorly understood. Our study aimed to investigate the dynamics and distribution of soil S fractions in an 8-year-old signal grass ( Brachiaria decumbens Stapf.) pasture fertilized with nitrogen (N) and S. A factorial combination of two N rates (0 and 600 kg N ha –1 y –1 , as NH 4 NO 3 ) and two S rates (0 and 60 kg S ha –1 y –1 , as gypsum) were applied to signal grass pastures during 2 y. Cattle grazing was controlled during the experimental period. Organic S was the major S pool found in the tropical pasture soil, and represented 97% to 99% of total S content. Among the organic S fractions, residual S was the most abundant (42% to 67% of total S), followed by ester-bonded S (19% to 42%), and C-bonded S (11% to 19%). Plant-available inorganic SO 4 -S concentrations were very low, even for the treatments receiving S fertilizers. Low inorganic SO 4 -S stocks suggest that S losses may play a major role in S dynamics of sandy tropical soils. Nitrogen and S additions affected forage yield, S plant uptake, and organic S fractions in the soil. Among the various soil fractions, residual S showed the greatest changes in response to N and S fertilization. Soil organic S increased in plots fertilized with S following the residual S fraction increment (16.6% to 34.8%). Soils cultivated without N and S fertilization showed a decrease in all soil organic S fractions.

Description: A greenhouse pot experiment was carried out to investigate the effects of different P-fertilizer application forms (triple superphosphate [TSP], compost + TSP, TSP-enriched compost) on the growth of ryegrass and the soil microbial biomass. The fertilizers were applied at equivalent doses for all nutrients to a neutral Luvisol in comparison with an acidic Ferralsol. Fertilizer application led to significantly increased contents of microbial biomass C, N, and P. Furthermore, yields of shoot C and root C, and concentrations of P, Ca, Mg, K, Fe, and Mn in shoots and roots were significantly increased. These increases always followed the order TSP 〈 compost + TSP 〈 TSP-enriched compost. Sole TSP application led only to maximum concentrations of N and S. In the Ferralsol, TSP had only minimal positive effect on the P concentration of the grass shoots. The positive effect of TSP-enriched compost, i.e., incubating TSP together with compost for 24 h, did not differ between the neutral Luvisol and the acidic Ferralsol, i.e., the effect is independent of the soil type. Consequently, soluble inorganic P fertilizer should generally be mixed into an organic fertilizer before application to soil.

Description: The physical properties of a Luvisol derived from loess near Bonn, Germany, under different long-term fertilization treatments were examined. For the investigation of the impact of farmyard manure (FYM) on soil strength at the mesoscale (100 to 300 cm 3 soil cores), undisturbed samples were taken from two different depths (10 and 40 cm), either with no fertilization at all, with full mineral fertilization, with FYM only, and with both mineral and organic fertilization. We investigated hydraulic and mechanical parameters, namely precompression stress, pore-size distribution, saturated hydraulic and air conductivity, and calculated pore connectivity. Long-term organic fertilization resulted in significantly more and coarser pores which in addition were more conductant and mechanically stronger by trend. Mineral fertilization also increased pore volume by trend but not pore functionality. Mechanical strength generally increased with fertilization by trend, however, was reduced again when organic and mineral fertilization were combined. Nonetheless, FYM led to relatively higher soil strength as the FYM-treated plots with lower bulk density attained similar soil strength as the unfertilized but denser plots and thus supported the soil-improving impact of organic amendments. The subsoil physical properties were rather unaffected by fertilization, but were dominated by texture.

Description: Little is known about nutrient fluxes and nutrient-use efficiencies in urban and peri-urban agriculture (UPA) of rapidly expanding cities in developing countries. Therefore, horizontal flows of carbon (C), nitrogen (N), phosphorus (P), and potassium (K) as well as leaching losses of mineral N and P were measured over 2 years in three representative agricultural production systems of Kabul. These comprised 21 gardens and 18 fields dedicated to vegetable farming, cereal farming, and table-grape production (vineyards). Across sites (fields and gardens) biennial inputs averaged 375 kg N ha –1 , 155 kg P ha –1 , 145 kg K ha –1 , and 15 kg C ha –1 while with harvests 305 kg N ha –1 , 40 kg P ha –1 , 330 kg K ha –1 , and 7 kg C ha –1 were removed. In vegetable gardens, biennial net balances were 80 kg N ha –1 , 75 kg P ha –1 , –205 kg K ha –1 , and 4 kg C ha –1 , whereas in cereal farming biennial horizontal balances amounted to –155 kg N ha –1 , 20 kg P ha –1 , –355 kg K ha –1 , and 5 kg C ha –1 . In vineyards, corresponding values were 295 kg N ha –1 , 235 kg P ha –1 , 5 kg K ha –1 , and 3 kg C ha –1 . Annual leaching losses in two selected vegetable gardens varied from 70 to 205 kg N ha –1 and from 5 to 10 kg P ha –1 . Night soil and irrigation water were the major sources among the applied nutrient inputs in all studied farming systems, contributing on average 12% and 25% to total N, 22% and 12% to total P, 41% and 53% to total K, and 79% and 10% to total C, respectively. The results suggest that soils in extensive cereal fields are at risk of N and K depletion and in vegetable gardens of K depletion, while vineyards may be oversupplied with nutrients possibly contributing to groundwater contamination. This merits verification.

Description: Residues from biogas production contain essential plant nutrients such as nitrogen (N), phosphorus (P), and potassium (K) but also organic matter, and should be recycled in crop production. For efficient re-use as fertilizers, the availability of nutrients for crops and the effect of the residues on soil fertility need to be evaluated. Focusing on the element P, we compared effects of codigested slurry with dairy slurry, highly soluble mineral NPK fertilizer, and a control without any P supply (NK). Codigested slurry used in this experiment was based on anaerobic digestion of dairy slurry, maize silage, and wheat grain. The fertilizing effects were tested in an 8-week pot experiment on a sandy and a loamy soil using two crop species ( Zea mays L., Amaranthus cruentus L.). The plant P uptake was up to 64% greater in the slurry treatments than in the treatment without P. The effect of codigested slurry on P uptake was comparable to that of dairy slurry and mineral P. Plant N uptake from codigested slurry was lower than that from mineral N (NK, NPK), but tended to be higher than from dairy slurry. The water-soluble and double lactate–soluble P content of the soil was lower in the slurry treatments than in the mineral-P treatments and accompanied by higher contents of microbial-bound P. Differences between both organic fertilizers were detected for dehydrogenase activity which was up to 32% lower in soils fertilized with codigested slurry than it was in soils fertilized with dairy slurry. Our results indicate that codigestion of slurries in biogas plants does not substantially alter their fertilizer value as P and N sources for crops.

Description: The effect of different deficit-irrigation treatments on the dynamics of mineral nutrients in leaves of peach trees growing under Mediterranean conditions was studied. Treatments consisted of a control, continuous deficit irrigation, regulated deficit irrigation, and partial root drying. The dynamics of nutrients were unchanged by the water deficits, though the amount absorbed was slightly modified. The advantages of deficit-irrigation strategies with regard to water-use efficiency were accompanied by the absence of any harmful effect on leaf mineral nutrition.

Description: It has been suggested that short-term field experiments are not suitable for the quantitative assessment of cropping-systems impact on soil organic matter (SOM) levels in arable soils, as expectable temporal changes are very small compared to a large spatial variation of SOM background levels. However, applying an optimized sampling design based on repeated sampling in small plots, we were able to detect soil total carbon (STC) and nitrogen (STN) changes in the magnitude of ≈ 1% (STC) and ≈ 2% (STN) of background levels with only four replications, respectively. Gradually enlarging the sample size up to n = 24 did not considerably improve change detectability with STC, but with STN ( n = 15 allowing for the dection of ≈ 1% change of background levels). The common calculation of minimum detectable differences (MDD) based on a state analysis of SOM levels instead of repeated measurements considerably underestimated change detectability.

Description: Two experiments were conducted to study the effect of grafting on nitrogen-use efficiency (NUE) in mini-watermelon plants. In the first study, mini-watermelon plants ( Citrullus lanatus [Thumb.] Matsum. and Nakai cv. Minirossa) either ungrafted or grafted onto Macis, Vita ( Lagenaria siceraria [Mol.] Standl.), PS1313, and RP15 ( Cucurbita maxima Duchesne × Cucurbita moschata Duchesne) rootstocks grown in hydroponics were compared in terms of shoot dry biomass, leaf area, root-to-shoot ratio, SPAD index, shoot N uptake, and nitrate reductase (NR) activity 40 d after transplantation in response to nitrate concentration in the nutrient solution (0.5, 2.5, 5, 10, 15, or 20 mM of NO ). In the second experiment, the suitability of a selected rootstock with high NUE (Vita) to improve crop performance and NUE of grafted mini-watermelon plants was evaluated under field conditions. In the hydroponic experiment mini-watermelon grafted onto Vita rootstock needed the lowest nitrate concentration (1.31 mM of NO 3 ) in the nutrient solution to reach half maximum shoot dry weight. Total leaf area, SPAD index, and shoot N uptake increased in response to an increase of N concentration in the nutrient solution. At 2.5 mM NO , mini-watermelon grafted on either Vita or RP15 had the highest NR activity whereas no significant difference was observed at 10 mM NO . The open-field study indicated that increasing N-fertilization rates from 0 to 100 kg ha –1 improved total and marketable yields of mini-watermelon plants while decreasing NUE. When averaged over N levels, the marketable yield, NUE, N-uptake efficiency, and N-utilization efficiency were significantly higher by 39%, 38%, 21%, and 17%, respectively, in Minirossa grafted onto Vita compared to ungrafted Minirossa plants. Therefore, grafting mini-watermelon plants onto selected rootstocks can be used as a quick and effective method for improving productivity and NUE.

Description:    A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616–1625, 2010 ). Based on the concept of observers (also called Luenberger observers), this algorithm covers a large class of abstract evolution PDE’s. In this paper, we are concerned with the convergence analysis of this algorithm. More precisely, we provide a complete numerical analysis for semi-discrete (in space) and fully discrete approximations derived using finite elements in space and an implicit Euler method in time. The analysis is carried out for abstract Schrödinger and wave conservative systems with bounded observation (locally distributed). Content Type Journal Article Pages 1-37 DOI 10.1007/s00211-011-0408-x Authors Ghislain Haine, Université Henri Poincaré (Institut Élie Cartan), B.P. 70239, 54506 Vandoeuvre, France Karim Ramdani, INRIA Nancy Grand-Est (CORIDA), 615 rue du Jardin Botanique, 54600 Villers, France Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    In this paper, we propose some new residual-based a posteriori error estimators for the mortar finite element discretization of the second order elliptic equations with discontinuous coefficients. Reliability and efficiency of the estimators are given. Our analysis does not require any saturation assumptions and the mesh restrictions on the interface which are often needed in the literature. Numerical experiments are presented to confirm our theoretical analysis. Content Type Journal Article Pages 1-29 DOI 10.1007/s00211-011-0413-0 Authors Feng Wang, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100190 Beijing, China Xuejun Xu, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100190 Beijing, China Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    This paper presents adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method which departs from a well-understood selfadjoint problem. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contributions of the different error sources. The first algorithm balances the homotopy, discretization and approximation errors with respect to a fixed stepsize τ in the homotopy. The second algorithm combines the adaptive stepsize control for the homotopy with an adaptation in space that ensures an error below a fixed tolerance ε . The outcome of the analysis leads to the third algorithm which allows the complete adaptivity in space, homotopy stepsize as well as the iterative algebraic eigenvalue solver. All three algorithms are compared in numerical examples. Content Type Journal Article Pages 1-27 DOI 10.1007/s00211-011-0388-x Authors C. Carstensen, Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany J. Gedicke, Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany V. Mehrmann, Institut für Mathematik, MA 4-5, TU Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany A. Miedlar, Institut für Mathematik, MA 4-5, TU Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    Spherical t -designs are point sets X M ={ x 1 , ¼ , x M } Ì \mathbb S 2 which provide quadrature rules with equal weights for the sphere which are exact for polynomials up to degree t . In this paper we consider the problem of finding numerical spherical t -designs on the sphere \mathbb S 2 for high polynomial degree t Î \mathbb N . That is, we compute numerically local minimizers of a certain quadrature error A t ( X M ). The quadrature error A t was also used for a variational characterization of spherical t -designs by Sloan and Womersley (J Approx Theory 159:308–318, 2009 ). For the minimization problem we regard several nonlinear optimization methods on manifolds, like Newton and conjugate gradient methods. We show that by means of the nonequispaced fast spherical Fourier transforms we perform gradient and Hessian evaluations in O ( t 2 log t + M log 2 (1/ e )) arithmetic operations, where $${\varepsilon 〉0 }$$ is a prescribed accuracy. Using these methods we present numerical spherical t -designs for t ≤  1,000, even in the case M » \frac12 t 2 . Content Type Journal Article Pages 1-26 DOI 10.1007/s00211-011-0399-7 Authors Manuel Gräf, Faculty of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany Daniel Potts, Faculty of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: An evaluation of the factors determining the occurrence and the properties of soils with low permeability occurring in vast areas in S Portugal was carried out taking into account the terrain morphology and the geology of the region. This paper deals with the variation patterns of the physical and chemical characteristics of soils from several soil toposequences that occur under different gradient slopes and on different parent rocks. Spatial variation of soil properties mainly depends on the composition of their cation-exchange complex, as the role of other factors, such as the mineralogy of the clay fraction, were of minor importance. There is often a stronger increment of Na and/or Mg than of Ca with depth, causing a variable degree of sodicity in some of these soils, to which waterlogging tendency of their upper horizons is related. Though the occurrence of these features is determined by the nature of the parent rock, their degree of expression varies primarily according to the topographic position of soils. Therefore, a catenary distribution including nonsodic Cambisols or Luvisols in the hillcrests and Stagnic Solonetz or Sodic Luvisols or Sodic Stagnosols in the topographic lows is common. Such soil characteristics are of utmost importance for irrigation suitability and management of these soils, and for environmental impacts assessment, as the region is vulnerable to desertification.

Description: Oxisols cover ≈ 23% of the land surface in the tropics and are utilized extensively for agricultural purposes in the tropical countries. Under the variable input types of agricultural systems practiced locally, some of these soils still appear to have problems in terms of proper soil classification and subsequently hinder attempts to implement sustainable agro-management protocols. The definition for Oxisols in Soil Survey Staff (1999) indicates that additional input is still required to refine the definition in order to resolve some of the outstanding classification problems. Therefore, the objective of this study is to examine the properties of some Oxisols and closely related soils in order to evaluate the classification of these soils. Soils from Brazil, several countries in Africa, and Malaysia were used in this study. Field observations provided the first indication that some of the presently classified kandi-Alfisols and kandi-Ultisols were closer to Oxisols in terms of their properties. Water-retention differences and apparent CEC of the subsurface horizons also supported this idea. The types of extractable Fe oxides and external specific surface areas of the clay fractions showed that many kandic horizons have surface properties that are similar to the oxic horizons. Micromorphology indicated that the genetic transition from the argillic to the oxic involves a diminishing expression of the argillic. Properties, such as CEC, become dominant. The kandic horizon is therefore inferred as a transition to the oxic horizon. It is proposed that the Oxisols be keyed out based only on the presence of an oxic horizon and an iso–soil temperature regime. The presence of a kandic horizon will be reflected at lower levels in Oxisols. The Oxisols will now be exclusive to the intertropical belt with an iso–soil temperature regime. The geographic extend of the Oxisols would increase and that of kandi-Alfisols and Ultisols would decrease. A few kandi-Alfisols and Ultisols in the intertropical area will have low CEC which would fail the weatherable mineral contents. The kandic subgroups of some Alfisols and Ultisols will be transitional between the low (〈 16 cmol c [kg clay] –1 )- and high (〉 24 cmol c [kg clay] –1 )-activity clay soils. The proposed changes to classification will contribute to a better differentiation of the landscape units in the field. Testing of the proposed classification on some Malaysian soils showed that the new definition for Oxisols provides a better basis for the classification of the local soils and the development of meaningful soil-management groups for plantations.

Description: Variability in soil properties is a complication for fertilization, irrigation, and amendment application. However, only limited progress has been made in managing soil variability for uniform productivity and increased water-use efficiency. This study was designed to ameliorate the poor-productivity areas of the variable sandy soils in Florida citrus groves by using frequent small irrigations and applying organic and inorganic soil amendments. Two greenhouse experiments were set up with sorghum and radish as bioassay crops in a randomized complete block design (RCBD). The factors studied were two soil-productivity classes (very poor and very good), two water contents (50% and 100% of field capacity), two amendments (phosphatic clay and Fe humate), and two amendment rates (10 and 25 g kg –1 for sorghum and 50 and 100 g kg –1 for radish). Amendments applied at 50 and 100 g kg –1 increased the water-holding capacity (WHC) of poor soil by 2- to 6-fold, respectively. The lower rates (10 and 25 g kg –1 ) of amendments were not effective in enhancing sorghum growth. The higher rates (50 and 100 g kg –1 ) doubled the radish growth as compared to the control. The results indicate that rates greater than 50 g kg –1 of both amendments were effective in improving water retention and increasing productivity. Irrigation treatment of 100% of field capacity (FC) increased the sorghum and radish growth by about 2-fold as compared with the 50%–water content treatment. The results suggest that the root-zone water content should be maintained near FC by frequent small irrigations to enhance water availability in excessively drained sandy soils. In addition, application of soil amendments in the root zone can enhance the water retention of these soils. Furthermore, managing variable sandy soils with WHC-based irrigation can increase water uptake and crop production in the poor areas of the grove.

Description: A greenhouse experiment was conducted to evaluate the effects of humic substances extracted from composted sewage sludge on growth, phenological development, and photosynthetic activity of pepper ( Capsicum annuum L. cv. Piquillo) plants. Humic substances derived from composted sludge (HSS) were compared with those derived from leonardite (HSL). Two doses of both humic substances were assayed (200 and 500 mg C [L substrate] –1 ) and compared with a control (C). HSS showed higher nitrogen content and a higher percentage of aliphatic carbon, as well as a lower content of aromatic and phenolic carbon than HSL. HSS significantly increased plant dry-matter production (up to 560%), plant height (86%–151%), and leaf area (436%–1397%) during the early stages of pepper development. Net photosynthesis and stomatal conductance increased in the treatments with HSS (up to 48% and 63%, respectively) at the vegetative stage. In addition, HSS accelerated the phenological development of pepper plants, reducing significantly the number of days to flowering and ripening, which occurred 12 and 14 d earlier than in control plants, respectively. In general, the treatments with HSS and HSL did not markedly affect chlorophyll and nutrient concentrations in the leaves. At maturity, only small differences in total fruit yield, number of fruits per plant, and fruit size were observed between amended and control plants. The results suggest that the mechanisms through which HSS affected plant growth and development were not associated with an improved nutrient uptake. Although the identity of the growth-promoting factors remains to be found, the results suggest that they may be linked to the chemical structure of the humic substances.

Description: An accurate assessment of soil respiration is critical for understanding and predicting ecosystem responses to anthropogenic perturbation such as climate change, pollution, and agriculture. Infra-red gas analyzer (IRGA)–based field measurement is the most widely used technique for assessing soil-respiration flux rates. In this study, respiration rates obtained with two common IRGA systems (LI-COR 8100 and PP Systems EGM-4) were compared across three ecosystem types. Our results showed that both methods were highly comparable in their flux estimates, but the associated methodology used (notably the use or absence of a soil collar) resulted in greater uncertainty in flux rates and a greater degree of intrasite variation. Specifically, the use of collars significantly decreased the flux estimate for both IRGAs compared to the no-collar estimate. The disturbance caused by collar insertion was assumed to be a major factor in causing the differing flux estimates, with root and mycorrhizal severance likely being the main contributor. We conclude that the two IRGAs used in this study can be reliably compared for overall flux estimates but emphasis is needed to validate a common measurement methodology.

Description: Provision of appropriate fertilizer recommendations to smallholder farmers is becoming increasingly important, for reasons of food security, economic viability, and the need to maintain soil fertility. Oil palm is one of the most important crops in the humid tropics, but smallholder growers (〈 10 ha) typically have low yields, largely due to inadequate fertilizer inputs and/or incomplete harvesting. It is difficult to produce appropriate fertilizer recommendations for the smallholder growers, due to their large numbers and small farm sizes. In this work, we developed a way of transferring to smallholder growers the fertilizer recommendations that have been developed for nearby plantation fields using large fertilizer trials. The study site was in West New Britain Province, Papua New Guinea, and transfer of information was done using a geographic information system and maps of plantation fields, smallholder blocks, and soil types. The soil-map-unit descriptions were interpreted, and a unified classification system was derived. Then, fertilizer recommendations that had been made on a field-specific basis for the large plantations were allocated to soil types and thereby to individual smallholder blocks. In this way, block-specific fertilizer recommendations were made for more than 4000 individual smallholders. The procedures used were developed into a conceptual framework which is transferable to other regions. Recommendations can be updated as new information becomes available on smallholder block locations or plantation fertilizer recommendations.

Description: The efficacy of arbuscular mycorrhizae (AM) on nutrients, organic solutes, and antioxidant enzymes of wheat under salt stress was investigated and related to root colonization and plant productivity. The mycorrhizal inoculation increased N, P, K, Ca, and Mg uptake, soluble sugars, free amino acids, and proline accumulation, as well as peroxidase and catalase activities under saline conditions as compared to nonmycorrhizal plants. On the other hand, Na concentration was lower in mycorrhizal than in nonmycorrhizal plants grown under saline conditions. Arbuscular mycorrhizae protected wheat against the detrimental effects of salinity and stimulated its productivity. Hence, mycorrhizal colonization can play a vital role in the mitigation of the adverse effects of salinity by improving the wheat osmotic adjustment response, enhancing its defense system, and alleviating oxidative damage to cells. Arbuscular mycorrhizae are able to alter plant physiology in a way that empowers the plant to grow more efficiently on salt-affected lands.

Description:    The aim of this paper is to devise an adaptive timestep control in the contact-stabilized Newmark method ( ContacX ) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini’s condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact-stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example. Content Type Journal Article Pages 1-33 DOI 10.1007/s00211-011-0374-3 Authors Corinna Klapproth, Zuse Institute Berlin (ZIB), Takustrasse 7, 14195 Berlin-Dahlem, Germany Anton Schiela, Zuse Institute Berlin (ZIB), Takustrasse 7, 14195 Berlin-Dahlem, Germany Peter Deuflhard, Zuse Institute Berlin (ZIB), Takustrasse 7, 14195 Berlin-Dahlem, Germany Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    A conforming finite element method on polygonal meshes is reviewed which handles hanging nodes naturally. Trial functions are defined to fulfil the homogeneous PDE locally and they are treated by means of local boundary integral equations. Using a quasi-interpolation operator of Clément type a residual-based error estimate is obtained. This a posteriori estimator can be used to rate the accuracy of the approximation over polygonal elements or it can be applied to an adaptive BEM-based FEM. The numerical experiments confirm our results and show optimal convergence for the adaptive strategy on general meshes. Content Type Journal Article Pages 1-24 DOI 10.1007/s00211-011-0371-6 Authors Steffen Weißer, Department of Mathematics, Saarland University, 66041 Saarbrücken, Germany Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods. Content Type Journal Article Pages 1-28 DOI 10.1007/s00211-011-0363-6 Authors Georgios Akrivis, Department of Computer Science, University of Ioannina, 451 10 Ioannina, Greece Charalambos Makridakis, Department of Applied Mathematics, University of Crete, 71409 Heraklion-Crete, Greece Ricardo H. Nochetto, Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    In this paper we consider the issue of sliding motion in Filippov systems on the intersection of two or more surfaces. To this end, we propose an extension of the Filippov sliding vector field on manifolds of co-dimension p , with p  ≥ 2. Our model passes through the use of a multivalued sign function reformulation. To justify our proposal, we will restrict to cases where the sliding manifold is attractive. For the case of co-dimension p  = 2, we will distinguish between two types of attractive sliding manifold: “node-like” and “spiral-like”. The case of node-like attractive manifold will be further extended to the case of p  ≥ 3. Finally, we compare our model to other existing methodologies on some examples. Content Type Journal Article Pages 1-33 DOI 10.1007/s00211-011-0365-4 Authors Luca Dieci, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA Luciano Lopez, Dip. di Matematica, Universitá di Bari, Via Orabona 4, 70125 Bari, Italy Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    The extended Krylov subspace method has recently arisen as a competitive method for solving large-scale Lyapunov equations. Using the theoretical framework of orthogonal rational functions, in this paper we provide a general a priori error estimate when the known term has rank-one. Special cases, such as symmetric coefficient matrix, are also treated. Numerical experiments confirm the proved theoretical assertions. Content Type Journal Article Pages 1-20 DOI 10.1007/s00211-011-0366-3 Authors L. Knizhnerman, Central Geophysical Expedition, house 38, building 3, Narodnogo opolcheniya St., 123298 Moscow, Russia V. Simoncini, Dipartimento di Matematica, CIRSA, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Ravenna Italy Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    Domain decomposition methods for solving the coupled Stokes–Darcy system with the Beavers–Joseph interface condition are proposed and analyzed. Robin boundary conditions are used to decouple the Stokes and Darcy parts of the system. Then, parallel and serial domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence of the two methods is demonstrated and the results of computational experiments are presented to illustrate the convergence. Content Type Journal Article Pages 1-29 DOI 10.1007/s00211-011-0361-8 Authors Yanzhao Cao, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36830, USA Max Gunzburger, Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA Xiaoming He, Department of Scientific Computing, Florida State University, Tallahassee, FL 32306-4120, USA Xiaoming Wang, Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    This article is concerned with the analysis of semi-discrete-in-space and fully-discrete approximations of the null controllability (and controllability to the trajectories) for parabolic equations. We propose an abstract setting for space discretizations that potentially encompasses various numerical methods and we study how the controllability problems depend on the discretization parameters. For time discretization we use θ -schemes with q Î [\frac12,1] . For the proofs of controllability we rely on the strategy introduced by Lebeau and Robbiano (Comm Partial Differ Equ 20:335–356, 1995 ) for the null-controllability of the heat equation, which is based on a spectral inequality. We obtain relaxed uniform observability estimates in both the semi-discrete and fully-discrete frameworks, and associated uniform controllability properties. For the practical computation of the control functions we follow J.-L. Lions’ Hilbert Uniqueness Method strategy, exploiting the relaxed uniform observability estimate. Algorithms for the computation of the controls are proposed and analysed in the semi-discrete and fully-discrete cases. Additionally, we prove an error bound between the fully discrete and the semi-discrete control functions. This bound is however not uniform with respect to the space discretization. The theoretical results are illustrated through numerical experimentations. Content Type Journal Article Pages 1-61 DOI 10.1007/s00211-011-0368-1 Authors Franck Boyer, Aix-Marseille Université, Laboratoire d’Analyse Topologie Probabilités (LATP), CNRS UMR 6632, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13, France Florence Hubert, Aix-Marseille Université, Laboratoire d’Analyse Topologie Probabilités (LATP), CNRS UMR 6632, 39 rue F. Joliot-Curie, 13453 Marseille cedex 13, France Jérôme Le Rousseau, Laboratoire Mathématiques et Applications, Physique Mathématique d’Orléans, Université d’Orléans, CNRS UMR 6628, Fédération Denis-Poisson, FR CNRS 2964, B.P. 6759, 45067 Orléans cedex 2, France Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: Different procedures to investigate dissolved trace element concentration at the transition from unsaturated to saturated zone in soils were compared by concurrent sampling of soil solution and solid soil material in this zone. The in situ sampled soil solution from the percolated water was used to measure in situ concentrations, while solid soil material was used to measure concentrations at two liquid–solid ratios using batch experiments on 250 sample pairs. The liquid–solid ratios were 2 L kg –1 and 5 L kg –1 . At 5 L kg –1 , the ionic strength was adjusted with Ca(NO 3 ) 2 to a sample-specific value similar to in situ , while at 2 L kg –1 , the ionic strength was not adjusted. The extracted concentrations of most trace elements exhibited a statistically significant but weak correlation ( p value 〈 0.01) to the corresponding in situ concentrations. In the liquid–solid ratio of 2 L kg –1 extracts, Pb and Cr showed very poor comparability with the in situ equivalent. A likely cause was the enhanced dissolved-organic-C release in the extract due to the lower ionic strength compared to in situ conditions in combination with effects from drying and moistening soil samples. For the other elements, correlation increased in the order As 〈 Cu, Zn, Sb, Mo, V 〈 Cd, Ni, Co where adjustment of the ionic strength led to slightly better results. In addition to the element-specific shortcomings, it appeared that low concentration levels of in situ concentrations were generally underestimated by batch extraction methods. The liquid–solid ratio of 2 L kg –1 extracts could only be used as a method to predict exceedance of thresholds if a safety margin of approximately one order of magnitude higher than the thresholds was adopted. The ability of the batch-extraction methods to estimate in situ concentrations was equally limited.

Description: Tonoplast Na + /H + antiporters increase the salt resistance of various plant species, but very little is known about the role of these antiporters in the salt resistance of trees. Understanding the physiological responses of plants to salinity stress is of paramount importance in examining the salt resistance of transgenic plants. In this study, the wild-type poplar (WT; Populus × euramericana var. Neva) and its transgenic varieties (TR) that overexpress the AtNHX1 gene were exposed to various seawater concentrations (0%, 10%, 20%, and 30%) for 30 d to determine the effects of seawater on seedling growth, ion content, and photosynthetic productivity. Results show that TR plants grew much better than WT under saline conditions. Differences between WT and TR in most parameters were significant after 30 d exposure to 20% and 30% seawater concentrations. The dry weight of TR was higher than that of WT for each seawater treatment. Transgenic variety was able to maintain higher photosynthetic ability than WT upon exposure to salinity and maintained higher K + concentrations and K + : Na + ratio but had less Cl – compared with WT. This suggests that AtNHX1 has a critical role in the regulation of K + homeostasis, which in turn affects plant K + nutrition and salt resistance.

Description: Recent studies have documented adverse affects of urea on the establishment and growth of aerobic rice when applied at seeding. The following experiments were conducted to examine the relative importance of ammonia and nitrite (NO ) toxicities as mechanisms contributing to poor germination and early growth of aerobic rice. Soil was collected from an experiment in the Philippines where aerobic rice was grown continuously for 7 years. Subsamples of the soil were: (1) pretreated with sulfuric acid (0.5 M H 2 SO 4 added at 75 mL kg –1 ), (2) oven-heated at 120°C for 12 h, or (3) left untreated. In a greenhouse study N was applied to the untreated, acidified, and oven-heated soils as either urea or ammonium sulfate (0.0 or 0.3 g N kg –1 ). Plant height, root length, total biomass, and number of seminal roots were evaluated after 10 d. Microdiffusion incubations were used to assess the effects of soil pretreatment, N source, and N rate (0, 0.5, 1.0, 1.5 g N kg –1 ) on ammonia (NH 3 ) volatilization and germination. Nitrite incubations were conducted to establish a critical level for NO toxicity and measure the extractable NO and germination trends as affected by soil pretreatment, N source, and N rate. On untreated soil, urea reduced early growth and germination while ammonium sulfate caused no adverse effects. Progressively higher rates of urea increased NH 3 volatilization and inhibited germination, while oven-heating and acidification minimized the adverse effects. All treatment combinations (soil pretreatment, N source, N rate) had extractable NO levels below the critical level of 0.2 g N kg –1 , suggesting that ammonia and not NO toxicity was the principal cause of inhibition. Since the risk of NH 3 toxicity is highest just following urea hydrolysis, strategies to optimize the timing and placement of urea should be considered.

Description: Soil structure affects all soil functions especially those related to physical and biological processes. On the other hand, soil structure itself is directly affected by these agents. Hence, soil structure—from single pores to the pedon scale—is expected to reflect the capacity of soil to deliver ecosystem functions. We analyzed soil structure including its seasonal dynamics for two plots within the long-term fertilization experiment in Bad Lauchstädt (Germany). The different plots received very different amounts of mineral and organic fertilizers over a period of 106 y. The quantification of structural properties includes pore-size distribution and pore connectivity obtained by X-ray microtomography. We present a methodological approach for image analysis that allows to combine samples of different size and resolution to cover pores within one order of magnitude in diameter. The results for the different plots obtained in spring and summer are compared. We found that the enormous difference in energy input only affects the structure of the topsoil (Ap horizon) towards a higher porosity and pore-network connectivity and in terms of an increased resilience after tillage. However, the structural properties of the subsoil below the plowed horizon (Ah horizon) are not affected. We hypothesize that the structure of the subsoil reflects soil formation over much longer time scales, it allows for an increased turnover of soil organic matter, and it is rather stable at the time scale of the fertilization experiment.

Description: The organic matter supply can promote the dispersal and activity of applied plant growth–promoting rhizobacteria (PGPR), but the complementary effect of organic fertilization and PGPR application on the turnover of P is scarcely known. The effects of the application of two PGPR strains ( Pseudomonas fluorescens strain DR54 and Enterobacter radicincitans sp. nov. strain DSM 16656) alone and in combination with organic fertilization (cattle manure and biowaste compost) on growth and P uptake of maize ( Zea mays L.) and oilseed rape ( Brassica napus L.) were investigated under semi–field conditions. Furthermore, P pools and phosphatase activities in soil and the arbuscular mycorrhizal–fungi colonization of maize roots were examined. The organic-fertilizer amendments increased the growth and P uptake of both plant species and the soil P pools. The application of the E. radicincitans strain increased P uptake of oilseed rape when no organic fertilizer was added. Furthermore, the application of both bacterial strains increased the activities of phosphatases under both plant species. Here, the effect of the PGPR application even exceeded the effect of organic fertilization. The magnitude of this effect varied between the different fertilizing treatments and between the two bacterial strains. Phosphatase activities were increased to the greatest extent after application of P. fluorescens in the unfertilized soil. Under rape increases of 52% for acid phosphatase activities (ACP), 103% for alkaline phosphatase activities (ALP), and 133% for phosphodiesterase (PDE) were observed therewith. In the unfertilized soil, the application of P. fluorescens also resulted in a strong increase of the arbuscular mycorrhizal colonization of maize. We conclude that application of PGPR can promote the P mobilization and supply of crops in P-deficient soils, however, in combination with organic fertilization these effects might be masked by a general improved P supply of the crops. Interactive effects of applied bacterial strains and organic fertilization depend on the sort of organic fertilizer and crop species used.

Description: To ensure high yield and quality in organic vegetable production, crops often require additional fertilizer applied during the season. Due to the risk of contamination of edible plant products from slurry, plant-based fertilizers may be used as an alternative. The purpose of our work was to develop mobile green manures with specific high nutrient concentrations ( e.g., nitrogen [N], sulfur [S], and phosphorus [P]) that are released quickly after soil incorporation and that are easy to handle during storage and application. To distinguish from traditional green manures that are grown to improve soil fertility, the term “mobile green manures” is used for green-manure crops that are harvested in one field and then moved as a whole and used as fertilizer in other fields. To further investigate mobile-green-manure crops for use as efficient fertilizers, pot and field experiments were conducted with cauliflower ( Brassica oleracea botrytis ) and kale ( Brassica oleracea sabellica ) supplied with organic matter consisting of a wide range of plant species with varying nutrient concentrations. Further, field experiments were conducted with leek ( Allium porrum ) and celery ( Apium graveolens dulce ) supplied with increasing amounts of organic matter consisting of fresh, ensiled, or dried green manures. Results show that garden sorrel ( Rumex acetosa ), dyer's woad ( Isatis tinctoria ), and fodder radish ( Raphanus sativus ) harvested with a high leaf-to-stem ratio resulted in high P concentration, and cruciferous crops in high S concentration. Dyer's woad, salad burnet ( Sanguisorba minor ), and stinging nettle ( Urtica dioica ) showed high boron (B) concentration, whereas species such as dandelion ( Taraxacum officinale ), chicory ( Cichorium intybus ), and garden sorrel showed high potassium (K) concentration. Green manures with high P and S concentrations increased the nutrient uptake and yield of pot-grown cauliflower and kale. Field experiments showed that the production of cauliflower and kale decreased when the carbon-to-nitrogen (C : N) ratio of applied green manure increased. In kale, for example, application of 160 kg N ha –1 in early harvested lucerne ( Medicago sativa ) with a C : N ratio of 10 resulted in the highest kale production whereas application of an equal amount of N in late harvested lucerne with a C : N ratio of 20 produced 34% less. Differences in vegetable production were not due to the amount of N applied, but to the N availability. Field experiments with fresh, ensiled, or dry green manure applied to leek and celery showed that the C : N ratio has to be low to get a fast response. Further, these field experiments demonstrate the importance of green manures, which can be stored and are easy to handle during transport, crop application, and soil incorporation. It is concluded that it is possible to produce green manures with high concentrations of S, P, K, and B, and low C : N ratios and that these properties have a great impact on the value of the green manure for vegetable production.

Description: Splash cups have long been successfully used for both the quantification of kinetic energy of rainfall and the detachability of soil particles by rainfall impact, the so-called “splash erosion”. Measurements of kinetic energy, however, have been difficult to operate in the field especially in remote areas, on steep slopes, and in forests since boundary conditions need to be controlled precisely. This paper introduces a new splash cup based on Ellison's archetype that reliably and accurately measures kinetic energy as a function of sand loss under a large variety of conditions. The Tübingen splash cup (T splash cup) is relatively easy to operate under harsh field conditions, and it can be used in experimental designs with a large number of plots and replications at reasonably low costs. The cup is constructed from plastic laboratory flasks and plastic pipes from water-supply equipments. The unit sand is held by a removable carrier system that can easily be replaced in the field. The splash cups have been calibrated in combination with a laser distrometer using a linear regression function with r 2 = 0.98. They measure kinetic energy over a wide range of rainfall intensities from 0.6 to 40 L m –2 h –1 . Kinetic energy per area varies between 10 and 250 J m –2 . Two years of field test measurements in a subtropical forest ecosystem in China proved the reliability, durability, and usability of our new splash cups and allowed detecting differences in kinetic energy between different tree species and biodiversity levels.

Description:    In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided. Content Type Journal Article Pages 1-28 DOI 10.1007/s00211-011-0373-4 Authors Alfio Quarteroni, CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne EPFL, Station 8, 1015 Lausanne, Switzerland Ricardo Ruiz-Baier, CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne EPFL, Station 8, 1015 Lausanne, Switzerland Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description:    In this paper, we propose a palindromic quadratization approach, transforming a palindromic matrix polynomial of even degree to a palindromic quadratic pencil. Based on the ( S + S - 1 ) -transform and Patel’s algorithm, the structure-preserving algorithm can then be applied to solve the corresponding palindromic quadratic eigenvalue problem. Numerical experiments show that the relative residuals for eigenpairs of palindromic polynomial eigenvalue problems computed by palindromic quadratized eigenvalue problems are better than those via palindromic linearized eigenvalue problems or polyeig in MATLAB. Content Type Journal Article Pages 1-23 DOI 10.1007/s00211-011-0370-7 Authors Tsung-Ming Huang, Department of Mathematics, National Taiwan Normal University, Taipei, 116 Taiwan Wen-Wei Lin, Department of Mathematics, National Taiwan University, Taipei, 106 Taiwan Wei-Shuo Su, Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 300 Taiwan Journal Numerische Mathematik Online ISSN 0945-3245 Print ISSN 0029-599X

Description: A multivariate statistical approach based on a large data set of abiotic and biotic variables was used to classify four contrasting-land-use soils. Soil samples were collected at increasing depth from a calcareous agricultural soil, a temperate upland grassland soil, a moderately acidic agricultural soil, and an acidic pine forest soil. Analytical investigations were carried out by using a combination of conventional physical, chemical, and biochemical methods coupled with denaturing gradient gel electrophoresis (DGGE) community fingerprinting of PCR-amplified 16S rRNA gene-coding fragments from soil-extracted total-community DNA. The data set of soil physical, chemical, and biochemical variables was reduced in dimensionality by means of a principal-component-analysis (PCA) procedure. Compositional shifts in soil bacterial-community structure were analyzed through a clustering algorithm that allowed identifying six main bacterial-community clusters. DGGE fingerprinting clusters were further analyzed by discriminant analysis (DA) using extracted PCA components as explanatory variables. Soil organic matter–related pools (TOC, TN) and functionally related active pools (microbial biomass C and N, K 2 SO 4 -extractable C) significantly decreased with soil depth, and resulted statistically linked to one other and positively related to enzymatic activities (acid phosphatase, arylsulfatase, β-glucosidase, dehydrogenase, hydrolysis of fluorescein diacetate) and silt content. Besides organic-C gradients, pedogenetic-driven physico-chemical properties, and possibly soil thermal and moisture regimes seemed to play a key role in regulating size and energetic ecophysiological status of soil microbial communities. DGGE analysis showed that contrasting horizons were conducive to the dominance of particular bacterial ribotypes. DA revealed that the bacterial-community structure was mainly influenced by organic matter–related variables (TOC, TN, CEC, C flush , N flush , Extr-C), chemical properties such as pH, CaCO 3 , and EC, together with textural properties. Results indicate that, beyond land use or plant cover, pedogenetic-driven physico-chemical conditions changing with soil type and depth are the key factors regulating microbial size and activity, and determining the genetic structure of bacterial community.

Description: Sulfonamides are the second most used antibiotic class in veterinary medicine and applied to livestock to treat bacterial infections. Subsequently, they are spread onto agricultural soils together with the contaminated manure used as fertilizer. Both manure and antibiotics affect the soil microbial community. However, the influence of different liquid manure loads on effects of antibiotics to soil microorganisms is not well understood. Therefore, we performed a microcosm experiment for up to 32 d to clarify whether the function and structure of the soil microbial community is differently affected by interactions of manure and the antibiotic sulfadiazine (SDZ). To this end selected concentrations of pig liquid manure (0, 20, 40, 80 g kg –1 ) and SDZ (0, 10, 100 mg kg –1 ) were combined. We hypothesized that incremental manure amendment might reduce the effect of SDZ in soils, due to an increasing sorption capacity of SDZ to organic compounds. Clear dose-dependent effects of SDZ on microbial biomass and PLFA pattern were determined, and SDZ effects interacted with the liquid manure application rate. Soil microbial biomass increased with incremental liquid manure addition, whereas this effect was absent in the presence of additional SDZ. However, activities of enzymes such as urease and protease were only slightly affected and basal respiration was not affected by SDZ application, while differences mostly depended on the concentration of liquid manure. These results illustrated that the microbial biomass and structural composition react more sensitive to SDZ contamination than functional processes. Furthermore, effects disproportionally increased with incremental liquid manure addition, although extractable amounts of SDZ declined with increasing liquid manure application.

Description: The present investigation was aimed to analyze influence of earthworm culture on nutritive status, microbial population, and enzymatic activities of composts prepared by utilizing different plant wastes. Vermicomposts were prepared from different types of leaves litter of horticulture and forest plant species by modified vermicomposting process at a farm unit. Initial thermophilic decomposition of waste load using cow-dung slurry was done in the separate beds. The culture of Eisenia fetida was used for vermicomposting in specially designed vermibeds at the farm unit. The physico-chemical characteristics, enzyme activities (oxido-reductases and hydrolases), and microbial population (bacteria, fungi, free-living nitrogen-fixing bacteria, actinomycetes, Bacillus, Pseudomonas , phosphate-solubilizing bacteria and fungi) of vermicomposts were found significantly higher ( p 〈 0.05) than those of control (without earthworm inoculum). The study quantified significant contributions of earthworm culture to physico-chemical, enzymatic, and microbiological properties of vermicompost and confirmed superior fertilization potential of vermicompost for organic farming. The agronomic utility of vermicompost was assessed on yellow mustard plant in a pot experiment. Pot soil was amended with different ratios (5%, 10%, 20%) of vermicompost and normal compost (without earthworm inoculum). Effects of these amendments on the growth of Brassica comprestis L. were studied. The significant differences ( p 〈 0.05) in the growth of plant were observed among vermicompost-, compost-amended soil, and control. Vermicompost increased the root and shoot lengths, numbers of branches and leaves per plant, fresh and dry weights per plant, numbers of pods and flowers, and biochemical properties of plant leaf significantly, especially in 20% amendment. These results proved better fertilization potential of vermicompost over non-earthworm-inoculated compost.

Description: Experiments to evaluate the effect of in-season calcium (Ca) sprays on late-season peach ( Prunus persica L. Batsch cv. Calrico) were carried out for a 2-year period. Calcium formulations (0.5% and 1.0% in 2008 and only 0.5% tested in 2009) supplied either as CaCl 2 or Ca propionate in combination with two or three adjuvants (0.05% of the nonionic surfactants Tween 20 and Break Thru, and 0.5% carboxymethylcellulose, CMC) were sprayed four to five times over the growing season. Peach mesocarp and endocarp Ca concentrations were determined on a 15-day basis from the beginning of May until the end of June. Further tissue analyses were performed at harvest. A decreasing trend in fruit Ca concentrations over the growing season was always observed regardless of the Ca treatments. Both in 2008 and 2009, significant tissue Ca increments associated with the application of Ca-containing sprays in combination with adjuvants were only observed in June, which may be coincident with the period of pit hardening. In 2008, both at harvest and after cold storage, the total soluble-solids concentration (° Brix) of fruits supplied with Ca propionate (0.5% and 1.0% Ca) was always lower as compared to the rest of treatments. The application of multiple Ca-containing sprays increased firmness at harvest and after cold storage, especially when CaCl 2 was the active ingredient used. Supplying the adjuvants Tween 20 and CMC increased fruit acidity both at harvest and after cold storage. Evaluation of the development of physiological disorders after cold storage (2 weeks at 0°C) indicated a lower susceptibility of Ca-treated fruits to internal browning. Fruits treated with multiple CaCl 2 -, CMC-, and Break Thru®-containing sprays during the growing season were significantly less prone to the development of chilling injuries as compared to untreated peaches.

Description: Recent literature confirmed that P fractions in soil are controlled by land use. However, differences in intensity of the same type of land use have received less attention although management intensity plays a crucial role in determining nutrient supply in soil. The objective of our work was to assess the influence of land-use intensity (LUI) on P fractions in soil. In the “Biodiversity Exploratories”, grassland and forest sites in Germany were selected in three regions (Schorfheide-Chorin, Hainich-Dün, Schwäbische Alb). In spring 2008, we sampled topsoil of 241 experimental plots. The plots included unfertilized and fertilized meadows, pastures, and mown pastures and near-natural to intensively used forests. Land-use intensity was classified according to the extent of annual biomass removal. We used the sequential extraction method of Hedley et al. (1982) to characterize P partitioning in soil. In summary, total P (TP) concentrations in soil were lowest at Schorfheide-Chorin (62–952 mg kg –1 ) followed by the Hainich-Dün (230–1631 mg kg –1 ) and the Schwäbische Alb (205–1838 mg kg –1 ). Differences between grassland and forest sites were mainly attributable to pH. The pH value was the most important factor among several soil properties explaining P partitioning in soil. For grassland, at pH values ≈ 6.5, the application of lime-containing fertilizer increased P availability in soil while effects of organic or mineral P fertilizers were negligible and related to the low application rates (〈 12 kg ha –1 ). Land-use intensity contributed up to 10% of the variation in the contribution of NaOH-P i to TP concentrations (ANOVA, Type I). In the Schwäbische Alb grassland soils, elevated LUI resulted in low NaOH-P i concentrations in soil which was probably caused by reduced sorption. Our findings highlight the importance of LUI as a control of P fractions in soil.

Description: This study explored the influence of 10 annual forage legumes belonging to the Lathyrus and Vicia genera on wet aggregate stability (WAS) and dispersion ratio (DR) indices of a clay soil. Five Lathyrus and five Vicia species were sown in autumn. Seed-to-seed and row-to-row distance was maintained at 5 cm and 20 cm, respectively. The experiment was planned in a randomized block design with three replications. After 90 d following seed harvest, soil cores were collected from two depths (0–15, 15–30 cm) in each plot and WAS and DR were determined. Annual forage legumes increased WAS of the soil but decreased the DR index. The WAS and DR values were affected at level of p 〈 0.001 by genus, species, and soil depth. Values of WAS and DR of the control plots without plant on the average were found to be 44.5% and 9.3% for 0–15 cm, and 41.2% and 10.1% for 15–30 cm, respectively. For 0–15 cm depth, the highest WAS (77.7%) and the lowest DR (6.4%) values were found in L. sphaericus L. (wild) plots. For 15–30 cm depth, the highest WAS value (62.6%) was obtained in L. annuus L. (wild) plots and the lowest DR value (6.7%) was in L. sativus L. (Gurbuz-2001) plots.

Description: A major challenge in sustainable crop management is to ensure adequate P supply for crops, while minimizing losses of P that could negatively impact water quality. The objective of the present study was to investigate the effects of long-term applications of different levels of mineral fertilizers and farmyard manure on (1) the availability of P, (2) the relationship between soil C, N, and P, and (3) the distribution of inorganic and organic P in size fractions obtained by wet sieving. Soil samples were taken from the top 20 cm of a long-term (29 y) fertilization trial on a sandy Cambisol near Darmstadt, SW Germany. Plant-available P, determined with the CAL method, was little affected by fertilization treatment ( p 〈 0.05) and was low to optimal. The concentration of inorganic and organic P extracted with a NaOH-EDTA solution (P NaOH-EDTA ) averaged about 350 mg (kg dry soil) –1 , with 42% being in the organic form (P o ). Manure application tended to increase soil C, N, and P o concentrations by 8%, 9%, and 5.6%, respectively. Across all treatments, the C : N : P o ratio was 100 : 9.5 : 2 and was not significantly affected by the fertilization treatments. Aggregate formation was weak due to the low clay and organic-matter content of the soil, and the fractions 〉 53 μm consisted predominantly of sand grains. The different fertilization treatments had little effect on the distribution of size fractions and their C, N, and P contents. In the fractions 〉 53 μm, P NaOH-EDTA ranged between 200 and 300 mg kg –1 , while it reached 1260 mg kg –1 in the fraction 〈 53 μm. Less than one third of P NaOH-EDTA was present as P o in the fractions 〉 53 μm, while P o accounted for 70% of P NaOH-EDTA in the smallest fraction (〈 53 μm). Therefore, 16% and 28% of P NaOH-EDTA and P o , respectively, were associated with the smallest fraction, even though this fraction accounted for 〈 5% of the soil mass. Therefore, runoff may cause higher P losses than the soil P content suggests in this sandy soil with a weak aggregate formation. Overall, the results indicate that manure and mineral fertilizer had similar effects on soil P fractions.

Description: The aim of this study was to evaluate the interaction between yield levels of nonleguminous crops and soil organic matter (SOM) under the specific conditions of organic and conventional farming, respectively, and to identify implications for SOM management in arable farming considering the farming system (organic vs. conventional). For that purpose, correlations between yield levels of nonlegume crops and actual SOM level (C org , N t , C hwe , N hwe ) as well as SOM-level development were examined including primary data from selected treatments of seven long-term field experiments in Germany and Switzerland. Yield levels of nonlegume crops were positively correlated with SOM levels, but the correlation was significant only under conditions of organic farming, and not with conventional farming treatments. While absolute SOM levels had a positive impact on yield levels of nonlegumes, the yield levels of nonlegumes and SOM-level development over time correlated negatively. Due to an increased demand of N from SOM mineralization, higher yield levels of nonlegumes obviously indicate an increased demand for OM supply to maintain SOM levels. Since this observation is highly significant for farming without mineral-N fertilization but not for farming with such fertilization, we conclude that the demand of SOM-level maintenance or enhancement and thus adequate SOM management is highly relevant for crop production in organic farming both from an agronomical and ecological point of view. Under conventional management, the agronomic relevance of SOM with regard to nutrient supply is much lower than under organic management. However, it has to be considered that we excluded other possible benefits of SOM in our survey that may be highly relevant for conventional farming as well.

Description: Maize ( Zea mays L.) is an important crop in central Thailand where fallow is widely practiced and farmers are interested in crop rotation and beneficial soil biota. A pot experiment using a Typic Paleustult (topsoil + subsoil) from the National Corn and Sorghum Research Centre, Nakhonratchasima Province, Thailand was undertaken over three successive crops to evaluate effects of agronomic practices on populations of arbuscular mycorrhizal (AM) fungi and to determine whether reintroduction of a local Glomus was beneficial to maintain maize yield. The three crops and their treatments were: (1) preceding crop: maize grown in all pots; (2) subexperiment 1: agronomic practices [maize, fallow ± soil disturbance, fallow with solarization, non–AM host (cabbage)]; and (3) subexperiment 2: maize ± Glomus sp. 3 at three rates of P fertilization (0, 33, 92 kg P ha –1 ). The AM-fungal community was established under the preceding crop. In subexperiment 1, the three fallow treatments decreased (30%–40%) the total AM spore number in the topsoil whereas there was no change under maize or cabbage. Glomus , the dominant genus, showed sensitivity to fallow. In subexperiment 2, inoculation with Glomus sp. 3 enhanced total AM spore number and root colonization when applied following the three fallow treatments. Furthermore, inoculation promoted grain yield; at nil P following fallow ± soil disturbance, at 33 kg P ha –1 following fallow without soil disturbance, and following solarization. Two treatments, maize following maize and maize following cabbage, did not respond to inoculation with Glomus sp. 3. Overall, the results suggest that reintroduction of Glomus sp. 3, a local AM fungus in this soil, may overcome negative effects of fallow and promote effectiveness of P fertilizer. Further work is needed to evaluate the benefits of other indigenous AM species that persist under modern fertilization practices.

Description: A few studies have shown that amine compounds ( e.g., hydroxylamine) can be co-metabolically introduced into the reaction pathway of denitrification. During this microbial process, the N atom of the amine species is bound to a N atom of nitrite. In case of hydroxylamine, this concomitant reaction ultimately results in the formation of hybrid N 2 O. Due to its co-metabolic character the process has been termed co-denitrification. Hybrid N 2 O production during co-denitrification has been proven to occur in prokaryotic ( e.g., Pseudomonas sp. ) as well as eukaryotic ( e.g., Fusarium sp. ) species. Many of them are already well-known as common denitrifiers. However, until now no clear evidence has been provided to show that N 2 O production by co-denitrification really takes place in a soil. In the present study, a formation of hybrid N 2 O was revealed by an adapted 15 N-tracer model, when both hydroxylamine and 15 N-nitrate were applied (mol ratio 10:1) to an anaerobically incubated soil suspension from a Haplic Chernozem. The presence of hybrid N 2 O was also indicated by a novel characteristic factor ( R binom ) developed for a hybrid-N-N-gas detection. By contrast, no hybrid N 2 O was found when either an autoclaved soil suspension, only nitrate or only hydroxylamine was used. Thus, it appears that hybrid-N 2 O formation occurred due to co-denitrification of hydroxylamine. Hence, this is the first study which demonstrates hybrid-N 2 O production by co-denitrification beyond a microbial species level. The 15 N-tracer model revealed that under the given experimental conditions N 2 O production by co-denitrification prevailed against N 2 O from denitrification and abiotic hydroxylamine decomposition. In addition, a formation of hybrid N 2 was also calculated by the model. However, the experimental results lead to the conclusion that it was most likely caused by a reduction of hybrid N 2 O due to conventional denitrification.

Description: The subcellular distribution and chemical forms of different heavy metals in rice are correlated with their bio-toxicity. An experiment was conducted to investigate the subcellular distribution and chemical forms of chromium (Cr) in two rice genotypes ( Oryza sativa L. cv. Xiushui 113 and cv. Dan K5) differing in Cr accumulation, to understand the mechanisms of Cr toxicity and resistance in rice plants. The results show that Cr in the roots of rice plants exposed to Cr stress was mainly localized in cell walls, whereas Cr in leaves and stems was mainly present in both cell walls and vacuoles, suggesting that both compartments act as important protective barriers against Cr toxicity in rice plants. Although Cr ions in all plant tissues exist predominantly in the forms extracted by 80% ethanol and distilled water, the amount of Cr in the chemical forms extracted by 2% HAc, 0.6 M HCl, and in residues was significantly increased under the highest Cr level (100 μM Cr) compared to the plants grown under lower Cr levels. These results indicate that excess Cr accumulated in rice plants under Cr stress is bound to undissolved or low-bioavailable compounds, such as undissolved phosphate and oxalate, being beneficial for rice plants to alleviate Cr toxicity. In addition, under the highest Cr level (100 μM), Dan K5 had a higher percentage of Cr in the chemical forms extracted by 2% HAc, 0.6 M HCl, and in residues compared to Xiushui 113 in both stems and leaves, indicating that more Cr ions in shoots of Dan K5 were bound to undissolved or low-bioavailable compounds, in comparison with those of Xiushui 113. It is evident that the low bioavailability of Cr in the shoots of Dan K5 is related to a high Cr accumulation.

Description: Crops grown in seleniferous soil may accumulate selenium (Se) to levels considered highly toxic for animal and human consumption. Furthermore, higher Se content in plant tissues leads to considerable deterioration in product quality. Application of organic amendments plays an important role in improving soil physical, chemical, and biological conditions and influencing nutrient availability. A field trial was conducted to evaluate the effect of organic amendments, namely poultry manure (PM), sugar cane press mud (SCPM), and farmyard manure (FYM), on Se uptake and grain quality of wheat and oilseed rape grown on a seleniferous soil in Punjab, India. Selenium accumulation by wheat and oilseed rape grains decreased significantly (75%–95%) with the application of PM and SCPM, while FYM application resulted in a significant decrease (23%) only in case of wheat grains. The amount of Se associated with seed proteins varied in proportion to its uptake under different treatments. Quality of wheat grains improved considerably with respect to total soluble sugars, reducing sugars, starch, lipids, and sulfur concentrations only after application of SCPM and PM. Treating a Se-contaminated soil with organic amendments significantly increased the oil concentration and changed the proportion of various fatty acids in rape grains. It is concluded that applying organic amendments to Se-contaminated soils can alleviate the deleterious effects of Se and restore the nutritional quality of grains.