ALBERT

Description: We introduce a method for generating rational extensions of time-dependent potentials, such that the associated Schrödinger equation admits solutions in terms of exceptional orthogonal polynomials. Our method is applicable to position-dependent Schrödinger equations, as well as to their conventional counterparts for constant mass.

Description: In this paper, we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrödinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.

Description: We give an algorithm which produces a unique element of the Clifford group on n qubits ( C n ) from an integer 0 ≤ i 〈 C n (the number of elements in the group). The algorithm involves O ( n 3 ) operations and provides, in addition to a canonical mapping from the integers to group elements g , a factorization of g into a sequence of at most 4 n symplectic transvections. The algorithm can be used to efficiently select random elements of C n which are often useful in quantum information theory and quantum computation. We also give an algorithm for the inverse map, indexing a group element in time O ( n 3 ).

Description: In the present work, we redefine and generalize the action principle for dissipative systems proposed by Riewe by fixing the mathematical inconsistencies present in the original approach. In order to formulate a quadratic Lagrangian for non-conservative systems, the Lagrangian functions proposed depend on mixed integer order and fractional order derivatives. As examples, we formulate a quadratic Lagrangian for a particle under a frictional force proportional to the velocity and to the classical problem of an accelerated point charge.

Description: We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d -dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.

Description: A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G ( t ), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.

Description: Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length Len( K ) of a knot K indicates the minimum length necessary to construct K in the cubic lattice. Another important quantity in physical knot theory is the ropelength which is one of the knot energies measuring the complexity of knot conformation. The minimum ropelength Rop( K ) is the minimum length of an ideally flexible rope necessary to tie a given knot K . Much effort has been invested in the research project for finding upper bounds on both quantities in terms of the minimum crossing number c ( K ) of the knot. It is known that Len( K ) and Rop( K ) lie between O ( c ( K ) 3 4 ) and O( c ( K )[ln ( c ( K ))] 5 ), but unknown yet whether any family of knots has superlinear growth. In this paper, we focus on 2-bridge knots and links. Linear growth upper bounds on the minimum lattice length and minimum ropelength for nontrivial 2-bridge knots or links are presented as Len( K ) ⩽ 8 c ( K ) + 2 and Rop( K ) ⩽ 11.39 c ( K ) + 12.37.

Description: We construct a spectral triple for the C * -algebra of continuous functions on the space of p -adic integers by using a rooted tree obtained from coarse-grained approximation of the space, and the forward derivative on the tree. Additionally, we verify that our spectral triple satisfies the properties of a compact spectral metric space, and we show that the metric on the space of p -adic integers induced by the spectral triple is equivalent to the usual p -adic metric.

Description: We consider the 3-body problem in 3-dimensional spaces of nonzero constant Gaussian curvature and study the relationship between the masses of the Lagrangian relative equilibria, which are orbits that form a rigidly rotating equilateral triangle at all times. There are three classes of Lagrangian relative equilibria in 3-dimensional spaces of constant nonzero curvature: positive elliptic and positive elliptic-elliptic, on 3-spheres, and negative elliptic, on hyperbolic 3-spheres. We prove that all these Lagrangian relative equilibria exist only for equal values of the masses.

Description: In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius’ theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems.

Description: The possibility of predicting the droplet size distribution from the particle size distribution was investigated. For that purpose, suspensions of different types of materials were dried in a laboratory-scale spray drier. Drying of suspensions was performed with different sizes of two-fluid nozzles. Droplet size distribution was evaluated from the data obtained for spray drying of bismuth molybdate suspension. The method was validated experimentally with other tested materials. Investigated systems involve processes of drying, crystallization, and coating. The proposed methodology can be applied when nonagglomerated particles, spherical particles, or spherical agglomerates were obtained by spray drying. Spray drying is a unique drying process since formation of solid phase and drying occur simultaneously. Droplet size distribution produced by a two-fluid nozzle during spray drying of bismuth molybdate suspension was evaluated simply from the particle size distribution. The proposed methodology enables prediction of the particle size distribution obtained by spray drying.

Description: The influence of vibration parameters on the segregation phenomenon of a binary mixture in a vibration fluidized bed is investigated. Initially, the mixture composed of spherical balls with different densities but same diameter is in a perfect mixing state in the bed. The motion of particles is simulated based on the discrete element method. The effects of friction coefficient, vibration frequency, amplitudes, and gas velocity are analyzed. The coefficient of segregation to the degree of particle segregation is calculated for different operating conditions. The segregation degree in the vibration fluidized bed is found to be higher than that in the bed without vibration. The curve for the segregation degree exhibits a single peak value which represents the optimal segregation result. The impact of vibration on gas phase- and particle flow is not yet clarified due to the complex motion of particles in vibrated fluidized beds. Discrete particle simulation is used to investigate the segregation behavior of binary mixtures in a fluidized bed. The effect of vibration parameters and suitable operating conditions for segregation, particle distribution, and particle motion are evaluated.

Description: The effects of a turbulence-generating grid on fluid mixing and a passive chemical reaction are experimentally investigated in a liquid shear mixing layer under a nonpremixed condition. The grid is installed at three streamwise locations to find the optimal location to promote the chemical reaction. The results show that the grid generates disturbances at small scales that enhance fluid mixing and the chemical reaction. However, the turbulence intensity and mass diffusion in the mixing layers with the grid decrease rapidly and become even smaller than those in the mixing layer without the grid in a downstream region. Therefore, in the present study, the chemical production is maximized when the grid is installed at where the flow is turning to a developed mixing layer. Installation of a turbulence-generating grid is advantageous to promote fluid mixing and chemical reaction in a free shear flow in which the reactive fluids are introduced under a nonpremixed condition. Special attention is needed regarding the location of the grid to maximize the promotion effect since it could be better to install it in the downstream region rather than the upstream region.

Description: Bubble splitting in 2D gas-solid freely bubbling fluidized beds is experimentally investigated using digital image analysis. The quantitative results can be applied for the development of a new breakage model for bubbly fluidized beds, especially discrete bubble models. The variation of splitting frequency with bubble diameter, new resulting bubble volumes, positions, and also the assumptions of mass and momentum conservation for bubbles after breakage are studied in detail. Small bubbles are found to be more stable than large ones and nearly all mother bubbles split into two almost equally sized daughter bubbles. The momentum of gas bubbles in the vertical direction remains approximately constant after breakage, whereas that of bubbles in the horizontal direction changes with no clear trend. The effect of fluidizing gas velocity in breakage frequency is also examined. The behavior of gas bubbles plays a key role in heat- and mass-transfer operations in fluidized beds. Bubble splitting for Geldart B-type particles under varying conditions was investigated in a pseudo-2D gas-solid fluidized bed by digital image analysis. The quantitative results can facilitate the development of new breakage models for bubbly fluidized beds and are particularly relevant for discrete bubble modeling.

Description: For the application of microreactors in industrial processes, more scaling-up strategies are still required except of the original concept, the numbering-up. A more maneuverable and economic approach, combining both similarity-up and numbering-up, is introduced as an example for an innovative strategy. CFD simulation is also applied to assist analysis and optimization of fluid distribution. Based on this concept, named similarity-up + numbering-up + simulation, a pilot-plant microsieve dispersion minireactor used to proceed the reaction of cyclohexanecarboxylic acid and oleum is designed and tested experimentally. With the contribution of similarity-up, the treating capacity of the core unit is significantly increased. Ten parallel units are integrated to form a correspondingly enhanced capacity of the microreactor which exhibits low pressure drop, stable operating performance, and excellent main product selectivity. For industrial applications of microreactors, more flexible and economic scaling-up strategies are required. A scale-up approach for a microsieve dispersion reactor is proposed, combining similarity-up and numbering-up of the core unit with CFD simulation-based device structure optimization. Low fabrication cost, low pressure drop, and excellent main product selectivity can be achieved by this strategy.

Description: Multi-indexed Jacobi polynomials are defined by the Wronskian of four types of eigenfunctions of the Pöschl-Teller Hamiltonian. We give a correspondence between multi-indexed Jacobi polynomials and pairs of Maya diagrams, and we show that any multi-indexed Jacobi polynomial is essentially equal to some multi-indexed Jacobi polynomial of two types of eigenfunction. As an application, we show a Wronskian-type formula of some special eigenstates of the deformed Pöschl-Teller Hamiltonian.

Description: We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an observer can consistently quantify events and their relationships to one another. The result is a potential foundation for emergent space-time.

Description: We consider the scattering theory for discrete Schrödinger operators on Z d with long-range potentials. We prove the existence of modified wave operators constructed in terms of solutions of a Hamilton-Jacobi equation on the torus T d .

Description: Let A u t m H H ( H ) denote the set of all automorphisms of a monoidal Hopf algebra H with bijective antipode in the sense of Caenepeel and Goyvaerts [“Monoidal Hom-Hopf algebras,” Commun. Algebra39, 2216–2240 (2011)] and let G be a crossed product group A u t m H H ( H ) × A u t m H H ( H ) . The main aim of this paper is to provide new examples of braided T -category in the sense of Turaev [“Crossed group-categories,” Arabian J. Sci. Eng., Sect. C33(2C), 483–503 (2008)]. For this purpose, we first introduce a class of new categories MHYD H H ( A , B ) of ( A , B )-Yetter-Drinfeld Hom-modules with A , B ∈ A u t m H H ( H ) . Then we construct a category M H Y D ( H ) = { MHYD H H ( A , B ) } ( A , B ) ∈ G and show that such category forms a new braided T -category, generalizing the main constructions by Panaite and Staic [“Generalized (anti) Yetter-Drinfel'd modules as components of a braided T-category,” Isr. J. Math.158, 349–366 (2007)]. Finally, we compute an explicit new example of such braided T -categories.

Description: A new design of conjugated heat transfer in double-pass parallel-plate laminar countercurrent operations of power law fluids under wall isoflux was investigated experimentally and theoretically. The analytical solutions were obtained with a superposition model by introducing an eigenfunction expansion in terms of a power series for the homogeneous part and an asymptotic solution for the inhomogeneous part. The influence of the power law index on the average Nusselt numbers with the various design and operating parameters is also delineated. The theoretical predictions of the experimental results are represented graphically. The heat transfer performance was considerably improved when compared with a single-pass parallel-plate heat exchanger (without inserting a solid separator sheet). Suitable adjustments of the solid separator sheet position can effectively enhance the heat transfer efficiencies for such a recycling double-pass device, as compared with the efficiencies of single- and double-pass devices.

Description: The geometry of the Lie algebroid generalized tangent bundle of a generalized Lie algebroid is developed. Formulas of Ricci type and identities of Cartan and Bianchi type are presented. Introducing the notion of geodesic of a mechanical ρ , η -system with respect to a ( ρ , η )-spray, the Berwald ( ρ , η )-derivative operator, and its mixed curvature, we obtain main results to conceptualize the Weyl’s method in this general framework. Finally, we obtain two new results of Weyl type for the geometry of mechanical ρ , η -systems. In this way, it is proved that the projectively related sprays first have the same geodesics rather to an increasing parameter transformation and second their Berwald derivatives verify a respective relation.

Description: In this paper, we prove Anderson localization for the Klein-Gordon operator on the circle

Description: We generalize the idea of “extension of Hamiltonian systems”—developed in a series of previous articles—which allows the explicit construction of Hamiltonian systems with additional non-trivial polynomial first integrals of arbitrarily high degree, as well as the determination of new superintegrable systems from old ones. The present generalization, that we call “modified extension of Hamiltonian systems,” produces the third independent first integral for the (complete) Tremblay-Turbiner-Winternitz system, as well as for the caged anisotropic oscillator in dimension two.

Description: The Pöschl-Teller (PT) potential occupies a privileged place among the anharmonic oscillator potentials due to its applications from quantum mechanics to diatomic molecules. For this potential, a polynomial su (1, 1) algebra has been constructed previously. So far, the coherent states (CSs) associated with this algebra have never appeared. In this paper, we construct the coherent states of the Barut-Girardello coherent states (BG-CSs) type for the PT potentials, which have received less attention in the scientific literature. We obtain these CSs and demonstrate that they fulfil all conditions required by the coherent state. The Mandel parameter for the pure BG-CSs and Husimi’s and P-quasi distributions (for the mixed-thermal states) is also presented. Finally, the exponential form of the BG-CSs for the PT potential has been presented and enabled us to build Perelomov type CSs for the PT potential. We point out that the BG-CSs and the Perelomov type coherent states (PCSs) are related via Laplace transform.

Description: We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann’s Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.

Description: This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.

Description: The main result of this work is as follows: for arbitrary pairwise disjoint, finite intervals ( α j , β j ) ⊂ [0, ∞), j = 1, …, m , and for arbitrary n ≥ 2, we construct a family of periodic non-compact domains {Ω ε ⊂ℝ n } ε〉0 such that the spectrum of the Neumann Laplacian in Ω ε has at least m gaps when ε is small enough, moreover the first m gaps tend to the intervals ( α j , β j ) as ε → 0. The constructed domain Ω ε is obtained by removing from ℝ n a system of periodically distributed “trap-like” surfaces. The parameter ε characterizes the period of the domain Ω ε , also it is involved in a geometry of the removed surfaces.

Description: In order to study emulsification phenomena, devices generating well-defined flow conditions are essential. Thus, emulsification of drop collectives under laminar shear flow is commonly performed in cylindrical Couette or Searle devices. In these devices, the flow conditions in the shear gap and in the volume underneath the rotor are often different, which can lead to inhomogeneous product properties and may complicate sample taking. Here, a novel cone-cone shear cell is presented to study emulsification processes. The flow inside the device is examined using numerical simulations. The numerical simulations indicate that simple shear flow is realized all over the sample volume in the cone-cone shear cell. The experimental results show that the drop breakup in the cone-cone shear cell is equivalent to the breakup under simple shear realized in the shear gap of a conventional device, i.e., the Searle device. Critical capillary numbers are calculated from the experimental data and show breakup behavior as predicted by single-drop experiments. Thus, the cone-cone shear cell proved to be suitable to study emulsification mechanisms in simple shear flow. Emulsion-based products are widely used in the food, chemical, and pharmaceutical industries. A novel cone-cone shear cell to study emulsification characteristics is described. The flow conditions inside the shear cell are validated via numerical simulations and experimental results.

Description: Hydrocracking of a bitumen-derived asphaltene over NiMo/ γ -Al 2 O 3 was investigated in a microbatch reactor at varying temperatures. The molar kinetics of asphaltene cracking reaction was examined by fitting the experimental data. Below a defined temperature, the molar reaction showed the first-order kinetic feature while at higher temperatures secondary reactions such as coke formation became significant, causing deviation of the reaction behavior from the proposed first-order kinetic model. Selectivity analysis proved that dominant products varied from gases to liquids to gases with increasing temperature, shifting the dominant reaction from C–S bonds cleavage to C–C bonds cleavage. Catalytic hydrocracking could be a proper choice for asphaltene upgrading but the reaction conditions still need to be optimized. Hydrocracking of a bitumen-derived asphaltene over a NiMo/ γ -Al 2 O 3 catalyst in a microbatch reactor at varying temperatures was analyzed. The molar kinetics of asphaltene cracking reaction was evaluated by fitting the experimental data.

Description: Two different types of metals (Cu and Ni) and the effect of CeO 2 addition to produce a CeO 2 -ZrO 2 co-supporter were investigated through the water-gas shift (WGS) reaction. It was found that the WGS activity could be enhanced with CeO 2 addition. At relatively high temperature, Ni-loaded catalysts exhibited higher CO conversion while Cu-loaded catalysts demonstrated better performance at low temperatures. The stability and yield of the CO 2 and H 2 products of the Cu catalysts were higher than those of the Ni catalysts. These results may be caused by an irreversible adsorption of CO on Ni and the reverse WGS reaction occurring on the Ni catalysts. In situ diffuse-reflection infrared Fourier transform spectroscopy data suggests that the WGS mechanism likely proceeded via formate species. The water-gas shift reaction (WGS), as an alternative way to produce H 2 and convert poisonous CO into CO 2 , was carried out using Cu and Ni loaded onto CeO 2 -ZrO 2 as catalysts. The Ni-loaded catalysts exhibited higher CO conversion at high temperature while the Cu-loaded catalysts performed better at low temperature. The WGS reaction was found to occur via the formation of formate species.

Description: Power ultrasound is applied for cooling crystallization to control and modify the particle size and crystal habit of an active pharmaceutical ingredient, phenacetin. Operating parameters including sonication intensity and duration, solution concentration, and cooling rate are studied and compared. With respect to mean particle size, the effect of sonication intensity is most significant. In addition, the crystal habit of recrystallized phenacetin is modified substantially and shows an elliptic shape. Recrystallized phenacetin also provides an enhanced dissolution rate compared with the original sample. These results prove that ultrasonic crystallization is an efficient tool for controlling the solid-state properties of an active pharmaceutical ingredient. Ultrasonic crystallization is a promising process for controlling the different stages of crystallization. Cooling crystallization applying power ultrasound is adopted for recrystallization of a nonsteroidal anti-inflammatory drug, phenacetin. The mean particle size can be managed by adjusting sonication intensity and duration. Phenacetin crystals with a regular crystal habit and an elliptic shape are obtained.

Description: In a variety of reactions in the chemical industry, eggshell catalysts with a thin active layer are applied; they are often crushed for laboratory testing. The destruction of the shell can be avoided by a special reactor design. The presented advanced TEMKIN reactor is a further development of the reactor system for testing eggshell catalysts on the laboratory scale published by Temkin and Kul'kova in 1969. It is suitable for kinetic studies and for the detailed investigation of deactivation processes, as shown on the example of selective hydrogenation of acetylene. The advanced TEMKIN reactor is well suitable for testing of uncrushed industrial eggshell catalysts because of its defined flow pattern and excellent mass and heat transport properties. Because of its simple and robust design, all technical requirements are fulfilled for a fast, competitive, and accurate optimization of prototypes as well as already established catalysts for industrial applications.

Description: A bench-scale submerged membrane bioreactor (SMBR) was employed to treat vegetable oil plant wastewater with complete sludge retention. Treatment performance and membrane fouling of the SMBR were investigated. The system stably removed high amounts of total organic carbon, oil, and ammonia from vegetable oil wastewater and reduced the chemical oxygen demand, demonstrating the great potential of the SMBR in removing pollutants. The membrane fouling layer was not only governed by deposition of organic substances composed of extracellular polymeric substances like proteins, polysaccharides etc., and oil substances but also by inorganic elements. Organic foulants coupled to inorganic precipitation enhanced the formation of a gel layer and triggered severe membrane fouling in the SMBR. Treatment and disposal of vegetable oil wastewaters (VOWs) represents one of the principal problems for vegetable oil producing countries. A bench-scale submerged membrane bioreactor was applied to treat VOWs with complete sludge retention. Treatment performance and membrane fouling were investigated. The experimental results demonstrated the great potential of this membrane bioreactor in removing pollutants.

Description: Adsorption processes are frequently applied to separate traces of hazardous and toxic substances from gas streams. Hence, knowledge of sorption characteristics of these substances on standard adsorbents is essential. Sorption of hexanal and acetaldehyde from a nitrogen gas stream in trace concentrations on activated carbon and ordered mesoporous carbon-based adsorbents (CMK) is studied. A magnetic suspension balance and an attached gaschromatograph-mass spectrometer were used to analyze the sorption process both gravimetrically and spectrometrically. Both types of adsorbents show a higher capacity for hexanal than acetaldehyde. The activated carbon exhibits considerable differences in regard to desorption of hexanal compared to the mesoporous CMK. Information on sorption characteristics of hazardous substances is essential to design separation processes. Adsorption and desorption of the toxic acetaldehyde and the intensely odorous hexanal on activated carbon and periodic mesoporous carbon were studied. Magnetic suspension balances were used to analyze the sorption processes. Both adsorbents exhibit a higher capacity for hexanal than acetaldehyde.

Description: High-solids biomass slurries exhibit non-Newtonian behavior with a yield stress and require high power input for mixing. The goals were to determine the effect of scale and geometry on power number P 0 , and estimate the power for mixing a pretreated biomass slurry in a 3.8 million L hydrolysis reactor of conventional design. A lab-scale computational fluid dynamics model was validated against experimental data and then scaled up. A pitched-blade turbine and A310 hydrofoil were tested for various geometric arrangements. Flow was transitional; laminar and turbulence models resulted in equivalent P 0 which increased with scale. The ratio of impeller diameter to tank diameter affected P 0 for both impellers, but impeller clearance to tank diameter affected P 0 only for the A310. At least 2 MW is required to operate at this scale. High-solids biomass slurries are characterized by non-Newtonian behavior with a yield stress and high power input demand for mixing. A computational fluid dynamics model was developed to predict power requirements of non-Newtonian lignocellulosic slurry in an industrial-scale hydrolysis reactor with conventional mixing impellers. The lab-scale model was validated against experimental data and then scaled up.

Description: The effect of NaCl added in different quantities on thermodynamic properties, granulometric characteristics, and structure of glycine in a crystallization process was investigated. Solubilities of α - and γ -polymorphs in the presence of varying amounts of NaCl were analyzed. In order to examine the impact of the additive on granulometric properties of glycine, crystal morphology was examined by observing crystals under a scanning electron microscope. Crystal size distribution was determined by sieve analysis. By X-ray diffraction analysis, the critical concentration of NaCl at which the structure of glycine changed, could be defined. The purity of obtained polymorphs was confirmed by Fourier transform infrared spectroscopy. Interactions between additives and crystallizing phase influence crystallization processes. Batch-cooling crystallization of glycine with different amounts of added NaCl is described, causing changes in solubility, metastable zone width, supersaturation, final mass of crystals, granulometric properties, and structure. Process conditions for a conversion of α- into a γ- glycine structure are defined.

Description: Cryogenic air separation as the most important part of an integrated gasification combined cycle is a widely used operation unit for producing large quantities of high-purity oxygen and nitrogen. However, cryogenic distillation requires a large amount of energy due to the work needed to compress the air feed. An improved heat-integrated air separation column (HIASC) is proposed. The requirements of high-purity separation in the industrial cryogenic air separation process are achieved. An optimization model of the heat transfer coefficient ( UA ), a key parameter in column structure design and operation, is presented. The optimized UA value is obtained within the accepted value range reported in the international open literature, which ensures the practicability of the improved HIASC. An improved heat-integrated air separation column is proposed. With the new heat-integrated and thermally coupled structure, the pressure of the high-pressure column and the energy consumption decrease significantly compared with the conventional air separation column. The mathematic model and parameter analysis are presented. An optimization model for the heat transfer coefficient is proposed.

Description: Functional mesoporous Mo–SiO 2 materials were synthesized by a one-pot and facile room-temperature procedure, and characterized by X-ray diffraction, TEM, Raman spectroscopy, FT-IR, diffuse reflectance spectra, and BET analysis. The experimental results demonstrated that the mesoporous materials presented a high dispersion of molybdenum species and excellent catalytic activity for the removal of dibenzothiophene (DBT) without organic solvents as extractants. The catalytic performance on different sulfur-containing compounds was also investigated in detail. After recycling for eight times, the removal of the oxidation desulfurization system could still reach high values. GC-MS analysis detected the oxidation product of DBT. A mechanism was proposed for the absorptive oxidation process of sulfur compounds. The removal of sulfur compounds from petroleum is of utmost importance for stringent fuel specifications and environment pollution. Functional mesoporous Mo–SiO 2 materials were synthesized by a facile procedure and were characterized by a high dispersion of molybdenum species and excellent catalytic activity for the removal of dibenzothiophene under mild conditions without organic solvents as extractants.

Description: The level set method is combined with the concentration transformation method to solve the interphase mass transfer process. However, the artificial diffusion generated in the mass transfer convection term across the interface is inevitable, especially when large shape deformation is encountered at high Reynolds numbers. A semi-Lagrangian advection scheme is introduced to overcome this disadvantage. The methyl isobutyl ketone (MIBK)-acetic acid-water system is adopted to study the unsteady mass transport process accompanied with the Marangoni effect of a single deformable drop ascending in the infinite continuous phase. The predicted overall mass transfer coefficients agree with experimental data very well. The configuration of Marangoni convection is revealed and its effect on the interphase mass transfer process is investigated. The solute-induced Marangoni effect on an ascending drop driven by buoyancy is numerically simulated based on the level set method. The semi-Lagrangian convection scheme is introduced to eliminate the artificial diffusion. Compared with literature data, the present algorithm with the semi-Lagrangian convection scheme significantly suppressed the numerical diffusion and achieved much better predictions.

Description: The surface properties of solvent-based (SB) and water-based (WB) coatings and their impact on fouling during convective heat transfer of CaSO 4 solutions were investigated. Experiments demonstrated that the SB coatings had generally better non-adhesive characteristics, especially at higher values of the electron donor component since the deposits could easily be washed away. For the SB coatings, a longer induction period compared to those of untreated surfaces was observed and a significant reduction of the fouling rate could be achieved. Further analysis of surfaces revealed that SB coatings enhanced the acid-base repulsive force and thus reduced the deposit/solid adhesion energy. For the WB coatings, the Liftshitz-van der Waals attractive force plays a decisive role in the adhesion process due to the higher apolar component of the surface energy. Recent technological advances have given impetus in altering surface properties to mitigate fouling of heat transfer surfaces. The attempted coatings in this study demonstrated that they can extend the induction period of the fouling processes of CaSO 4 deposits by four times. This was but mostly due to their higher electron donor component of the surface energy compared to stainless-steel substrate.

Description: Ultrasonic hot embossing of polymers is an alternative to reduce fabrication costs of microreactors. An ultrasonic welding machine is used to melt a stack of thermoplastic foils and adapting them to a short-time milled aluminum mold showing the inversed design of the desired microfluidic cavities. Two micromixers were fabricated this way providing a low degree of axial dispersion and pressure loss. Stability analysis is successfully performed for a wide temperature range and high pressure. Mixing of colored aqueous solutions and neutralization reactions are implemented to both systems for defined volume flow rates and optically investigated via microscope. Reaction progress is automatically determined with a MATLAB script by reference to the consequential color change of the neutralization reaction with a color indicator. Typical mixing characteristics are identified for both mixers. Ultrasonic hot embossing of chemically resistant polymers as a simple and cost-effective fabrication method of microstructures and an optical analysis tool for tracing the progress of chemical reactions are introduced and evaluated. The simplicity of the fabrication method itself and good similarities of produced polymer micromixers with conventional ones made of other materials are pointed out.

Description: The existing screening and characterization systems for biocatalysts operate in batch mode, which could make catalyst selection and process development inaccurate when continuous operation mode is required in industry. A significant improvement of an innovative screening system based on miniaturized multiple membrane reactors formerly presented by the author is outlined, which enables continuous feeding of substrates and continuous removal of products. Although the presented screening system was originally designed for homogeneous enzymatic reactions, it can be used without further modifications for continuous catalysis with polymer-bound chemical catalysts or for quasi-homogeneous systems like reverse micelles. Currently available screening and characterization systems for biocatalysis are not sufficiently suitable for process description and scale-up of results to pilot- or full-scale reactors often operated in continuous mode. Hydrolysis of N -acetyl- L -methio-nine served as model reaction for an innovative continuous characterization system, implementing a precise dosing system.

Description: The synthesis of n -butyl levulinate, one of the most important biodiesel additives, by catalytic esterification of biomass-derived levulinic acid (LA) with n -butanol over modified H-ZSM-5 (micro/meso-HZ-5) in a closed-batch system is reported for the first time. The optimization of the reaction conditions such as the reactant molar ratio, the catalyst loading, the reaction time and the temperature was performed in view to maximize the yield of n -butyl levulinate. Micro/meso-HZ-5 was found to be the most efficient catalyst, with 98 % yield of n -butyl levulinate and a reusability for six cycles, which is higher than reported in the literature. A possible catalytic mechanism for the esterification reaction is also proposed. A second-order pseudo-homogeneous model with R 2  〉 0.97 confirmed that the esterification reaction is performed in the kinetic regime due to the high activation energy of 23.84 kJ mol −1 . The modified zeolite catalyst H-ZSM-5 (micro/meso-HZ-5) was used as heterogeneous acid catalyst in the esterification of renewable levulinic acid with n -butanol to produce n -butyl levulinate in a closed system. Micro/meso-HZ-5 turned out to be an efficient catalyst with 98 % yield of n -butyl levulinate and high reusability.

Description: We consider the general open system problem of a charged quantum oscillator confined in a harmonic trap, whose frequency can be arbitrarily modulated in time, that interacts with both an incoherent quantized (blackbody) radiation field and with an arbitrary coherent laser field. We assume that the oscillator is initially in thermodynamic equilibrium with its environment, a non-factorized initial density matrix of the system and the environment, and that at t = 0 the modulation of the frequency, the coupling to the incoherent and the coherent radiation are switched on. The subsequent dynamics, induced by the presence of the blackbody radiation, the laser field, and the frequency modulation, is studied in the framework of the influence functional approach. This approach allows incorporating, in analytic closed formulae , the non-Markovian character of the oscillator-environment interaction at any temperature as well the non-Markovian character of the blackbody radiation and its zero-point fluctuations. Expressions for the time evolution of the covariance matrix elements of the quantum fluctuations and the reduced density-operator are obtained.

Description: We treat the N -particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q -boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A31, 6057–6071 (1998)] or the q -totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q -TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle's position at time t . To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys.279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.

Description: This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast ɛ Y -periodic conductivity. When the conductivity is bounded in L 1 and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ɛ −2 , the first Bloch eigenvalue converges as ɛ → 0 to a limit which preserves the second-order expansion with respect to the Bloch parameter. In dimension two the expansion of the limit can be improved until the fourth-order under the same hypotheses. On the contrary, in dimension three a fibers reinforced medium combined with a L 1 -unbounded conductivity leads us to a discontinuity of the limit first Bloch eigenvalue as the Bloch parameter tends to zero but remains not orthogonal to the direction of the fibers. Therefore, the high contrast conductivity of the microstructure induces an anomalous effect, since for a given low-contrast conductivity the first Bloch eigenvalue is known to be analytic with respect to the Bloch parameter around zero.

Description: We report a new class of hyperbolic asymmetric double-well whose bound state wavefunctions can be expressed in terms of confluent Heun functions. An analytic procedure is used to obtain the energy eigenvalues and the criterion for the potential to support bound states is discussed.

Description: Given a (smooth) action φ of a Lie group G on R d we construct a differential graded algebra whose Maurer–Cartan elements are in one-to-one correspondence with some class of deformations of the (induced) G -action on C ∞ ( R d ) [ [ ℏ ] ] . In the final part of this note we discuss the cohomological obstructions to the existence and to the uniqueness (in a sense to be clarified) of such deformations.

Description: Robot in Laboratory. Copyright: Max Tactic – Fotolia.com.

Description: In the present paper, we build a combinatorial invariant, called the “spectral monodromy” from the spectrum of a single (non-self-adjoint) h -pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h -pseudodifferential operators, given by S. Vu Ngoc [“Quantum monodromy in integrable systems,” Commun. Math. Phys.203(2), 465–479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat [“On global action-angle coordinates,” Commun. Pure Appl. Math.33(6), 687–706 (1980)].

Description: It is shown that three different Lax operators in the Dym hierarchy produce three generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component Korteweg de Vries (KdV) system. The first equation gives us known integrable two-component KdV system, while the second reduces to the known symmetrical two-component KdV equation. The last one reduces to the Drienfeld-Sokolov equation. This approach gives us new Lax representation for these equations.

Description: We study Killing tensors in the context of warped products and apply the results to the problem of orthogonal separation of the Hamilton-Jacobi equation. This work is motivated primarily by the case of spaces of constant curvature where warped products are abundant. We first characterize Killing tensors which have a natural algebraic decomposition in warped products. We then apply this result to show how one can obtain the Killing-Stäckel space (KS-space) for separable coordinate systems decomposable in warped products. This result in combination with Benenti's theory for constructing the KS-space of certain special separable coordinates can be used to obtain the KS-space for all orthogonal separable coordinates found by Kalnins and Miller in Riemannian spaces of constant curvature. Next we characterize when a natural Hamiltonian is separable in coordinates decomposable in a warped product by showing that the conditions originally given by Benenti can be reduced. Finally, we use this characterization and concircular tensors (a special type of torsionless conformal Killing tensor) to develop a general algorithm to determine when a natural Hamiltonian is separable in a special class of separable coordinates which include all orthogonal separable coordinates in spaces of constant curvature.

Description: We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.

Description: We study spectral asymptotics for a large class of differential operators on an open subset of R d with finite volume. This class includes the Dirichlet Laplacian, the fractional Laplacian, and also fractional differential operators with non-homogeneous symbols. Based on a sharp estimate for the sum of the eigenvalues we establish the first term of the semiclassical asymptotics. This generalizes Weyl's law for the Laplace operator.

Description: The present paper is devoted to the scattering theory of a class of continuum Schrödinger operators with deterministic sparse potentials. We first establish the limiting absorption principle for both modified free resolvents and modified perturbed resolvents. This actually is a weak form of the classical limiting absorption principle. We then prove the existence and completeness of local wave operators, which, in particular, imply the existence of wave operators. Under additional assumptions on the sparse potential, we prove the completeness of wave operators. In the context of continuum Schrödinger operators with sparse potentials, this paper gives the first proof of the completeness of wave operators.

Description: In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.

Description: We consider C -graded vertex algebras , which are vertex algebras V with a C -grading such that V is an admissible V -module generated by “lowest weight vectors.” We show that such vertex algebras have a “good” representation theory in the sense that there is a Zhu algebra A ( V ) and a bijection between simple admissible V -modules and simple A ( V )-modules. We also consider pseudo vertex operator algebras (PVOAs), which are C -graded vertex algebras with a conformal vector such that the homogeneous subspaces of V are generalized eigenspaces for L (0); essentially, these are VOAs that lack any semisimplicity or integrality assumptions on L (0). As a motivating example, we show that deformation of the conformal structure (conformal flow) of a strongly regular VOA (e.g., a lattice theory, or Wess-Zumino-Witten model) is a path in a space whose points are PVOAs.

Description: Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor.44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pure Appl. Math.14, 187 (1961)].

Description: Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. Introducing first an attractive Dirac-comb potential, i.e., Dirac comb with strength − g ( g 〉 0), in the space-fractional Schrödinger equation we show that the problem of obtaining eigenenergies of a system with N Dirac-δ wells can be reduced to a problem of obtaining the eigenvalues of an N × N matrix. As an illustration we use the present matrix formulation to derive expressions satisfied by the bound-state energies of N = 1, 2, 3 delta wells. We also obtain the corresponding wave functions and express them in terms of Fox's H -function.

Description: Let F α ( C ) be the Hilbert space generated by the orthonormal basis e n α , ν ( z ) = ( 2 ν π ) 1 / 4 e ν 2 z 2 e − π 2 ν ( n + α ) 2 + 2 i π ( n + α ) z ; n ∈ N where ν 〉 0 and α are real numbers, this space is a particular case of (Γ, χ)-theta Fock-Bargmann spaces recently constructed by Ghanmi-Intissar [J. Math. Phys.54, 063514 (2013)]. In the present work, we consider on F α ( C ) the weight shift operator M defined by M e n α , ν = ω n e n + 1 α , ν , n ∈ N where ω n = c α , ν e 2 π ν n and c α , ν = e π ν + 2 α and we show the chaoticity of the operator H p = M p D p + 1 ; p = 0 , 1 , 2 , . . . where D is adjoint of M .

Description: This paper is devoted to a scalar conservation law with a linear flux function involving discontinuous coefficients. It is clear that the delta standing wave should be introduced into the Riemann solution in some nonclassical situation. In order to study the formation of delta standing wave, we consider a regularization of the discontinuous coefficient with the Helmholtz mollifier and then obtain a regularized system which depends on a regularization parameter ɛ 〉 0. The regularization mechanism is a nonlinear bending of characteristic curves that prevents their finite-time intersection. It is proved rigorously that the solutions of regularized system converge to the delta standing wave solution in the ɛ → 0 limit. Compared with the classical method of vanishing viscosity, here it is clear to see how the delta standing wave forms naturally along the characteristics.

Description: An elliptic equation that arises from a cosmic string model with the action of the Born-Infeld nonlinear electromagnetism, is considered. We classify and establish the uniqueness of radially symmetric solutions.

Description: We show a new lower bound on the H ̇ 3 2 T 3 norm of a possible blow-up solution to the Navier-Stokes equation, and also comment on the extension of this result to the whole space. This estimate can be seen as a natural limiting result for Leray's blow-up estimates in L p R 3 , 3 〈 p 〈 ∞. We also show a lower bound on the blow-up rate of a possible blow-up solution of the Navier-Stokes equation in H ̇ 5 2 T 3 , and give the corresponding extension to the case of the whole space.

Description: The quantum graph having the form of branching strips with hexagonal (honeycomb) structure is considered. The Hamiltonian is determined as free 1D Schrödinger operator on each edge and some “boundary” conditions at each vertex. We obtain the conditions ensuring the point spectrum's existence for the Schrödinger operator of the system and relations that give us the eigenvalues.

Description: Multi-time wave functions are wave functions that have a time variable for every particle, such as ϕ ( t 1 , x 1 , ... , t N , x N ) . They arise as a relativistic analog of the wave functions of quantum mechanics but can be applied also in quantum field theory. The evolution of a wave function with N time variables is governed by N Schrödinger equations, one for each time variable. These Schrödinger equations can be inconsistent with each other, i.e., they can fail to possess a joint solution for every initial condition; in fact, the N Hamiltonians need to satisfy a certain commutator condition in order to be consistent. While this condition is automatically satisfied for non-interacting particles, it is a challenge to set up consistent multi-time equations with interaction. We prove for a wide class of multi-time Schrödinger equations that the presence of interaction potentials (given by multiplication operators) leads to inconsistency. We conclude that interaction has to be implemented instead by creation and annihilation of particles, which, in fact, can be done consistently [S. Petrat and R. Tumulka, “Multi-time wave functions for quantum field theory,” Ann. Physics (to be published)]. We also prove the following result: When a cut-off length δ 〉 0 is introduced (in the sense that the multi-time wave function is defined only on a certain set of spacelike configurations, thereby breaking Lorentz invariance), then the multi-time Schrödinger equations with interaction potentials of range δ are consistent; however, in the desired limit δ → 0 of removing the cut-off, the resulting multi-time equations are interaction-free, which supports the conclusion expressed in the title.

Description: In a recent paper, Jaradat et al. [J. Math. Phys.53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl.272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr.72, 119 (2005)].

Description: In this paper, we study the dependence on initial data of solutions to the incompressible Euler equations in Besov spaces. We show that for s 〉 n / p + 1, p ∈ (1, ∞), and r ∈ [1, ∞], the solution map u 0 ↦ u is Hölder continuous in Besov space B p , r s equipped with weaker topology. When the space variable x is taken to be periodic, we obtain a family of explicit periodic solutions. Furthermore, we prove that for any s ∈ R and 1 ⩽ r ⩽ ∞, the solution map is not globally uniformly continuous in B 2 , r s ( T n ) , which extends some results of Himonas and Misiołek [Commun. Math. Phys.296(1), 285–301 (2010)].

Description: We study the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary channel acting on a d -level quantum system can be uniquely identified among all other channels (unitary or otherwise) with only O ( d 2 ) interactive observables, as opposed to the O ( d 4 ) required for tomography of arbitrary channels. This result generalizes to the problem of identifying channels with at most q Kraus operators, and slight improvements can be obtained if we wish to identify such a channel only among unital channels or among other channels with q Kraus operators. These results are proven via explicit construction of large subspaces of Hermitian matrices with various conditions on rank, eigenvalues, and partial trace. Our constructions are built upon various forms of totally nonsingular matrices.

Description: Starting from well-known expressions for the T -matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.

Description: Explicit solutions for the wave equations associated to the Dirac, Euler operators and the harmonic oscillator are given.

Description: A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves.

Description: Considering successive extensions of primary translationally shape invariant potentials, we enlarge the Krein-Adler theorem to mixed chains of state adding and state-deleting Darboux-Bäcklund transformations. It allows us to establish novel bilinear Wronskian and determinantal identities for classical orthogonal polynomials.

Description: In this paper we investigate the properties of a delayed bistable system under the effect of multiplicative noise. We first prove the existence and uniqueness of the positive solution and show that its moments are uniformly bounded. Then, we study stochastic dynamics of the solution in long time, the lower and upper bounds for the paths and an estimate for the average value are provided.

Description: We examine a class of discrete Painlevé equations which present a strong asymmetry. These equations can be written as a system of two equations, the right-hand-sides of which do not have the same functional form. We limit here our investigation to two canonical families of the Quispel-Roberts-Thompson (QRT) classification both of which lead to difference equations. Several new integrable discrete systems are identified.

Description: Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys.137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common use of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.

Description: A magnetic field is defined by the property that its divergence is zero in a three-dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to study the magnetic flow associated with the Killing magnetic field in a three-dimensional oriented Riemann manifold, ( M 3 , g ). And then, we investigate the trajectories of the magnetic fields called as N-magnetic and B-magnetic curves.

Description: Polyethersulfone (PES) was blended with poly( D,L -lactide) (PDLLA) to prepare asymmetric membranes using the phase inversion method. The effects of the blend ratios and poly(ethylene glycol) (PEG) as additive on the membrane structure, properties, and performance were investigated. The membranes were characterized by contact angle determination, scanning electron microscopy, porosity measurement, thermogravimetric analysis, degradation tests in compost, and dynamic tests for pure water flux and bakery product wastewater treatment. PES and PEG slightly reduced the membrane contact angle. Increasing the PDLLA concentration in the blend membranes enhanced the membrane degradation in compost and also the membrane porosity. The permeate flux of the membranes was improved, but the rejection of pollution indices did not change noticeably. Porous membranes have been widely applied in the fields of dialysis, clarification, and purification. The composition of membranes prepared by blending polyethersulfone with poly( D,L -lactide) (PDLLA) affected their characteristics. Increases in the concentrations of PDLLA and the additive poly(ethylene glycol) led to more porous structures, causing higher fluxes.

Description: We show that the range of applicability of the change of representation formula derived by Bravetti et al. [J. Math. Phys.54, 033513 (2013)] is very narrow and extend it to include all physical applications, particularly, applications to black hole thermodynamics, cosmology, and fluid thermodynamics.

Description: The separation efficiency of a pilot-scale zigzag apparatus is investigated numerically using computational fluid dynamics simulations and discrete particle modeling in a coupled manner. The effects of various process variables, like particle size and air flow velocity, and of turbulence models were analyzed. The resulting changes concerning the process performance expressed by separation function and sharpness are discussed. Moreover, the residence time distribution was found to differ for fine and coarse particle discharges. Small particles are easily carried away by the fluid and respond immediately to almost every change in flow velocity. Therefore, they are affected by vortices, which increase their residence times compared to bigger particles. Zigzag air classifiers are superior to simple sieves for the separation of particles and are used in many industrial processes. The separation efficiency of a pilot-scale zigzag apparatus is studied using combined computational fluid dynamics simulations and discrete particle modeling. The process performance is discussed with respect to the chosen modeling approach and the operating conditions.

Description: Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by Heisenberg. Here we prove such relations for the case of two canonically conjugate observables like position and momentum, and establish a close connection with the more familiar preparation uncertainty relations constraining the sharpness of the distributions of the two observables in the same state. Both sets of relations are generalized to means of order α rather than the usual quadratic means, and we show that the optimal constants are the same for preparation and for measurement uncertainty. The constants are determined numerically and compared with some bounds in the literature. In both cases, the near-saturation of the inequalities entails that the state (resp. observable) is uniformly close to a minimizing one.

Description: Blow-up behavior of positive solutions of a semi-linear parabolic system arising from thermal explosion, which subject to the homogenous Dirichlet boundary conditions, is investigated. In particular, sufficient conditions for the solutions to blow up are obtained.

Description: We study the three-dimensional magnetohydrodynamics system and obtain its regularity criteria in terms of only two velocity vector field components eliminating the condition on the third component completely. The proof consists of a new decomposition of the four nonlinear terms of the system and estimating a component of the magnetic vector field in terms of the same component of the velocity vector field. This result may be seen as a component reduction result of many previous works [C. He and Z. Xin, “On the regularity of weak solutions to the magnetohydrodynamic equations ,” J. Differ. Equ.213(2), 234–254 (2005); Y. Zhou, “Remarks on regularities for the 3D MHD equations ,” Discrete Contin. Dyn. Syst.12(5), 881–886 (2005)].

Description: In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A k is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of ( PZS ) 4 space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.

Description: We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.

Description: We present the geometric formulation of gravity based on the mathematical structure of a Lie Algebroid. We show that this framework provides the geometrical setting to describe the gauge propriety of gravity.

Description: In order to observe the impact of different water compositions on sludge dewaterability, assessments of floc sizes using a particle size analyzer and of sludge dewaterability based on the capillary suction time (CST) test were carried out. Synthetic raw water had small floc sizes, and synthetic domestic wastewater had both larger median floc sizes and a better correlation between sludge dewaterability and median floc sizes. The floc size distribution results showed that synthetic raw water is associated with a narrow particle size distribution. In comparison, synthetic domestic wastewater produced a wider distribution. However, the CST values were similar for both waters. Compared to synthetic wastewater, natural wastewater had the largest distribution with generally larger particle sizes. In order to observe the impact of different water compositions on sludge dewaterability, assessments of floc sizes and sludge dewaterability tests were carried out. The particle distribution results show that synthetic raw water is associated with a very narrow range of particles. In comparison, synthetic domestic wastewater produced a larger distribution. The capillary suction times were similar.

Description: The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency ω, evaluation of the electric field using this Green's function exhibits numerical instability. In this short note, we provide an alternative approach which is immune from this low-frequency breakdown as ω → 0. Our approach is based on the generalized Debye source representation of Maxwell fields. Using this formulation, the electric and magnetic fields gracefully decouple in the static limit, a behavior similar to that of the classical Lorenz-Debye-Mie representation of Maxwell fields in spherical geometries. We derive extensions of both the generalized Deybe source and Lorenz-Debye-Mie representations to planar geometries, as well as provide equations for the solution of scattering from a perfectly conducting half-space and in layered media using a Sommerfeld-like approach. These formulas are stable as ω tends to zero, and offer alternatives to the electric field dyadic Green's function.

Description: The direct-ignition technology of an entrained-flow coal-water slurry gasifier with hot-oxygen burner (HOB) is presented. Experimental tests were carried out using diesel oil and coal-water slurry in a bench-scale entrained-flow opposed multi-burner (OMB) gasifier. Using a CCD camera equipped with high-temperature endoscope, flame images inside the gasifier were recorded and subsequently processed. The results show that the HOB diesel flame is more stable than the normal two-channel burner flame typically used. Entrained-flow coal-water slurry gasifiers can start up using the HOB directly without a higher preheated wall temperature. An HOB can potentially save gasifier preheating time and operation costs and enables a wide range of future applications. Entrained-flow gasification offers one of the cleanest ways to obtain energy from coal. The direct-ignition technology of an entrained-flow coal-water slurry gasifier with a new type of hot-oxygen burner (HOB) was extensively studied to prove the feasibility of the gasifier startup with this setup. The HOB permits to effectively decrease the gasifier preheating time and the system operation costs.

Description: Different approaches were analyzed to combine the tuneable micropore structure of carbide-derived carbons with a foam-like secondary porosity. The resulting structured catalyst supports were characterized in detail and applied in the model reaction of ethene hydrogenation. Preparation methods studied were dip-coating using polytetrafluoroethylene as binder on cellular metal structures, a chemical vapor deposition coating of the metal structures with thin carbide layers and subsequent conversion to carbide-derived carbon, and the partial or full conversion of carbide foams to carbon/carbide composites. For the binder method, optimal parameters for stable slurry preparation as well as for calcination of the slurry were obtained. It could further be demonstrated that the conversion of carbide foams into carbon/carbide composites leads to an appreciation between decreasing mechanical strength and increasing specific surface area. Structured catalysts are advantageous to conventional fixed-bed systems. Carbide-derived carbons with tuneable microporous structure were combined with a foamlike catalyst structure. The three preparation methods studied resulted in highly active catalysts. Optimal conditions for the easy-to-apply dip-coating method to stabilize the slurry for successful coating were determined and evaluated.

Description: An opposed multi-burner (OMB) entrained-flow gasifier with coal water slurry feeding is developed by the East China University of Science and Technology. A 3D model is employed to numerically simulate the gas flow field, motion of char particles, and distributions of temperature and gaseous components in an OMB gasifier and in a conceptual two-stage gasifier modified from the OMB gasifier (TS-OMB gasifier). Results show that the TS-OMB gasifier produces higher concentration and productivity of the effective gases (CO+H 2 ) with a slightly higher carbon conversion than the OMB gasifier. The reasons for the differences between these two types of gasifier are discussed by means of numerical simulation. This information is valuable for guiding the design of an advanced OMB gasifier. With an increasing demand for syngas, entrained-flow gasifiers for coal conversion are installed at the fastest pace due to advantages such as low pollutant emission. Simulations of the gas component distribution, amongst other key factors, in an opposed multi-burner (OMB) gasifier and modified two-stage OMB gasifier were compared. The results are valuable for future design of an advanced OMB gasifier.

Description: We consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type (PT) in the frame of the observer crossing the horizon can be different from that formally obtained in the usual (but singular in the horizon limit) frame of an observer on a circular orbit. We call this entity the boosted Petrov type (BPT), as the corresponding frame is obtained by a singular boost from the regular one. The PT off-horizon can be more general than PT on-horizon and that can be more general than the BPT on horizon. This is valid for all regular metrics, irrespective of the extremality of the horizon. We analyze and classify the possible relations between the three characteristics and discuss the nature and features of the underlying singular boost. The three Petrov types can be the same only for space-times of PT D and O off-horizon. The mutual alignment of principal null directions and the generator in the vicinity of the horizon is studied in detail. As an example, we also analyze a special class of metrics with utra-extremal horizons (for which the regularity conditions look different from the general case) and compare their off-horizon and on-horizon algebraic structure in both frames.

Description: This paper presents a simple but nontrivial generalization of Abel's mechanical problem, based on the extended isochronicity condition and the superposition principle. There are two primary aims. The first one is to reveal the linear relation between the transit-time T and the travel-length X hidden behind the isochronicity problem that is usually discussed in terms of the nonlinear equation of motion d 2 X d t 2 + d U d X = 0 with U ( X ) being an unknown potential. Second, the isochronicity condition is extended for the possible Abel-transform approach to designing the isochronous trajectories of charged particles in spectrometers and/or accelerators for time-resolving experiments. Our approach is based on the integral formula for the oscillatory motion by Landau and Lifshitz [Mechanics (Pergamon, Oxford, 1976), pp. 27–29]. The same formula is used to treat the non-periodic motion that is driven by U ( X ). Specifically, this unknown potential is determined by the (linear) Abel transform X ( U ) ∝  A [ T ( E )], where X ( U ) is the inverse function of U ( X ), A = ( 1 / π ) ∫ 0 E d U / E − U is the so-called Abel operator, and T ( E ) is the prescribed transit-time for a particle with energy E to spend in the region of interest. Based on this Abel-transform approach, we have introduced the extended isochronicity condition: typically, τ = T A ( E ) + T N ( E ) where τ is a constant period, T A ( E ) is the transit-time in the Abel type [A-type] region spanning X 〉 0 and T N ( E ) is that in the Non-Abel type [N-type] region covering X 〈 0. As for the A-type region in X 〉 0, the unknown inverse function X A ( U ) is determined from T A ( E ) via the Abel-transform relation X A ( U ) ∝  A [ T A ( E )]. In contrast, the N-type region in X 〈 0 does not ensure this linear relation: the region is covered with a predetermined potential U N ( X ) of some arbitrary choice, not necessarily obeying the Abel-transform relation. In discussing the isochronicity problem, there has been no attempt of N-type regions that are practically of full use for the charged-particle spectrometers and/or accelerators. In this Abel-transform approach, the superposition principle simplifies the derivation of X A ( U ) satisfying the extended isochronicity condition. Although the extended isochronicity condition inevitably discards the low-energy particles, there is no problem for handling accelerated particles because they do not involve the small-amplitude oscillations around the potential minimum. We present analytic examples of X A ( U ) that are instructive. In Appendix B , Urabe's criterion is interpreted in the time domain, using the Abel-transform approach.

Description: A symmetry in quantum mechanics is described by the projective representations of a Lie symmetry group that transforms between physical quantum states such that the square of the modulus of the states is invariant. The Heisenberg commutation relations that are fundamental to quantum mechanics must be valid in all of these physical states. This paper shows that the maximal quantum symmetry group, whose projective representations preserve the Heisenberg commutation relations in this manner, is the inhomogeneous symplectic group. The projective representations are equivalent to the unitary representations of the central extension of the inhomogeneous symplectic group. This centrally extended group is the semidirect product of the cover of the symplectic group and the Weyl-Heisenberg group. Its unitary irreducible representations are computed explicitly using the Mackey representation theorems for semidirect product groups.

Description: Let M n be an n × n real (resp. complex) Wigner matrix and U n Λ n U n * be its spectral decomposition. Set ( y 1 , y 2 ⋯ , y n ) T = U n * x , where x = ( x 1 , x 2 , ⋅⋅⋅, x n ) T is a real (resp. complex) unit vector. Under the assumption that the elements of M n have 4 matching moments with those of GOE (resp. GUE), we show that the process X n ( t ) = β n 2 ∑ i = 1 ⌊ n t ⌋ ( | y i | 2 − 1 n ) converges weakly to the Brownian bridge for any x satisfying ‖ x ‖ ∞ → 0 as n → ∞, where β = 1 for the real case and β = 2 for the complex case. Such a result indicates that the orthogonal (resp. unitary) matrices with columns being the eigenvectors of Wigner matrices are asymptotically Haar distributed on the orthogonal (resp. unitary) group from a certain perspective.