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  • stability  (14)
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  • Physics  (18)
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  • Articles  (23)
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  • Springer  (23)
  • American Geophysical Union
  • American Institute of Physics (AIP)
  • American Physical Society
  • Blackwell Publishing Ltd
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  • 2000-2004
  • 1995-1999  (23)
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  • 1
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    Celestial mechanics and dynamical astronomy 67 (1997), S. 181-204 
    ISSN: 1572-9478
    Keywords: Hamiltonian systems ; symplectic mappings ; normal forms ; resonances ; stability ; three degrees of freedom
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional Hénon mapping is given.
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  • 2
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    Celestial mechanics and dynamical astronomy 69 (1997), S. 271-281 
    ISSN: 1572-9478
    Keywords: restricted three-body problem ; libration points ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied. It is found that L4,5 are unstable in the whole range 0 ≤ µ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable for 0 〈 µ 〈 µ0, where µ is the mass parameter and µ0 = 0.03852....
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  • 3
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    Celestial mechanics and dynamical astronomy 69 (1997), S. 317-330 
    ISSN: 1572-9478
    Keywords: artificial satellite ; Nekhoroshev's theory ; normal form ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the significance of long time stabilty predictions in the light of Nekhoroshev's theory by studying the orbits of artificial satellites. As a simplified model problem we consider the so-called J2problem for an earth's satellite, neglecting luni-solar perturbations and nonconservative effects. We consider a wide range of orbits, excluding those which are too close to the critical inclination. Most of the orbits turn out to be stable for times larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in Nekhoroshev's sense may be effective for physically realistic systems.
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  • 4
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    Archive of applied mechanics 67 (1997), S. 447-456 
    ISSN: 1432-0681
    Keywords: Key words rotation ; stability ; energy criterion ; variational analysis ; functional analysis ; eigenvalue problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Stability of a heavy rotating rod with a variable cross section is studied by energy method. Bifurcation points for the system of equilibrium equations are analyzed. It is shown that for the case when the rotation speed exceeds the critical one, the trivial solution ceases to be the minimizer of the potential energy, so that rod loses stability, according to the energy criteria. Also, a new estimate of the maximal rod deflection in the post-critical state is obtained.
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  • 5
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    Journal of statistical physics 88 (1997), S. 691-711 
    ISSN: 1572-9613
    Keywords: Quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; ground states ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We give strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions, but rather are generic in some regions of phase space. We show this by constructing classical lattice-gas models with translation-invariant finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.
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  • 6
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    Journal of intelligent and robotic systems 20 (1997), S. 131-155 
    ISSN: 1573-0409
    Keywords: robot adaptive control ; basis function-like networks ; stability ; discrete variable structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Stable neural network-based sampled-data indirect and direct adaptivecontrol approaches, which are the integration of a neural network (NN)approach and the adaptive implementation of the discrete variable structurecontrol, are developed in this paper for the trajectory tracking control ofa robot arm with unknown nonlinear dynamics. The robot arm is assumed tohave an upper and lower bound of its inertia matrix norm and its states areavailable for measurement. The discrete variable structure control servestwo purposes, i.e., one is to force the system states to be within the stateregion in which neural networks are used when the system goes out of neuralcontrol; and the other is to improve the tracking performance within the NNapproximation region. Main theory results for designing stable neuralnetwork-based sampled data indirect and direct adaptive controllers aregiven, and the extension of the proposed control approaches to the compositeadaptive control of a flexible-link robot is discussed. Finally, theeffectiveness of the proposed control approaches is illustrated throughsimulation studies.
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  • 7
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    Journal of intelligent and robotic systems 19 (1997), S. 411-436 
    ISSN: 1573-0409
    Keywords: assembly planning ; stability ; robot ; forward ; operations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper presents an approach to sequence planning consisting in determining assembly sequences defined in terms of mating and non-mating operations and based on a dynamic expansion of the assembly tree obtained using a knowledge base management system. The planner considers the case of a single-robot assembly workcell. The use of stability and the detailed definition of sequences also by means of several non-mating operations are shown to be powerful instruments in the control of the tree expansion. Forward assembly planning has been chosen, in order to minimize the number of stability checks. Backtracking is avoided by combining precedence relations and stability analysis. Hard and soft constrains are introduced to drive the tree expansion. Hard constraints are precedence relations and stability analysis. All operations are associated to costs, which are used as soft constraints. The operation based approach enables one to manage even non-mating operations and to easily overcome the linearity constraint. Costs enable the planner to manage the association among tools and components. The first section of the paper concerns Stability Analysis that is subdivided into Static and Dynamic Stability Analysis. The former is mainly involved in analyzing gravity effects; the latter is mainly involved in evaluate inertia effects due to manipulation. Stability Analysis is implemented in a simplified form. Fundamental assumptions are: no rotational equilibrium condition is considered; for each reaction force only direction and versus, but not magnitude, are considered; friction is neglected. The second section discusses the structure of the planner and its implementation. The planner is a rule based system. Forward chaining and hypothetical reasoning are the inference strategies used. The knowledge base and the data base of the system are presented and the advantages obtained using a rule based system are discussed. The third section shows two planning examples, showing the performance of the system in a simple case and in an industrial test case, the assembly of a microwave branching filter composed of 26 components.
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  • 8
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    Boundary layer meteorology 83 (1997), S. 285-309 
    ISSN: 1573-1472
    Keywords: Adjoint ; Data assimilation ; Turbulence ; Complex terrain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract This paper describes an adjoint method for data assimilation intoupstream boundary conditions of numerical modelsusing optimal control theory. Mathematical formalisms are given along with the numerical implementation of the schemein a column model of the atmospheric boundary layer. The optimized mean and turbulence profiles are used as an upstream solutionin a model of turbulent flow in complex terrain. To contrast thiswith other methods, two solutions for flow over an isolatedhill are calculated, one with an optimized upstream solution andone with a simple surface-layer formulation for the upstream solution.These two solutions are compared to observations and analytical theory. The adjoint optimization method is shown to producesolutions of flow in complex terrain that are substantively differentat the two solutions, with the optimized solution giving more accurate results.
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  • 9
    ISSN: 1573-1472
    Keywords: Turbulence ; Canopies ; Temperature ramps ; Renewal models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Sensible heat, latent heat, and other scalar fluxes cannot be measuredwithin short dense canopies, e.g., straw mulches, with standard approachessuch as eddy correlation, Bowen ratio-energy balance, aerodynamic, andvariance methods. However, recently developed surface renewal models, thatare based on the fact that most of the turbulent transfer within and abovecanopies is associated with large-scale coherent eddies, which are evidentas ramp patterns in scalar time series, offer a feasible solution. Wepresent a new air renewal model that calculates sensible heat flux atdifferent heights within and above a canopy from the average cubictemperature structure function, sampled at a moderate rate, and measuredaverage friction velocity. The model is calibrated and tested with datameasured above and within a Douglas-fir forest and above a straw mulch andbare soil. We show that the model describes half-hour variations ofsensible heat flux very well, both within the canopy and roughnesssublayers and in the inertial sublayer, for stable and unstable atmosphericconditions. The combined empirical coefficient that appears in the modelhas an apparently universal value of about 0.4 for all surfaces andheights, which makes application of the model particularly simple. Themodel is used to predict daytime and nighttime sensible heat flux profileswithin the straw mulch and within a small bare opening in the mulch.
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  • 10
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    Boundary layer meteorology 84 (1997), S. 411-425 
    ISSN: 1573-1472
    Keywords: Trajectories ; Turbulence ; Dispersion ; Diffusion ; Numerical models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Among well-mixed multi-dimensional Lagrangian stochastic (LS) dispersion models, we observe that those in poorest agreement with observations produce ‘spiralling trajectories,’ with an associated reduction in dispersion. We therefore investigate statistics of increments dθ ' to the orientation θ'= arctan(W'/U') of the Lagrangian velocity-fluctuation vector – as a possible means to distinguish the better LS models within the well-mixed class. ‘Zero-spin’ models, having 〈 dθ'〉 = 0, are found to provide best agreement with observations. It is not clear however, whether imposition of the zero-spin property selects (in conjunction with the well-mixed condition) a unique model.
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  • 11
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    Boundary layer meteorology 85 (1997), S. 197-222 
    ISSN: 1573-1472
    Keywords: Turbulence ; Chemistry ; Closure ; Convective boundary layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯Θ, ¯w¯θ ¯θ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.
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  • 12
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    Acta mechanica Sinica 13 (1997), S. 366-376 
    ISSN: 1614-3116
    Keywords: vibro-impact ; stability ; multiplicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The coexisting periodic impacting motions and their multiplicity of a kind of dual component systems under harmonic excitation are analytically derived. The stability condition of a periodic impacting motion is given by analyzing the propagation of small, arbitrary perturbation from that motion. In numerical simulations, the periodic impacting motions are classified according to the system states before and after an impact. The numerical results show that there exist many types of vibro-impacts and the bifurcation of periodic vibro-impacts is not smooth.
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  • 13
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    Boundary layer meteorology 83 (1997), S. 43-73 
    ISSN: 1573-1472
    Keywords: Model evaluation ; Mesoscale ; Turbulence ; Dispersion ; Convective boundary layer ; Complex terrain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A prognostic three-dimensional mesoscale model has been developed andused in one- and two-dimensional modes to evaluate ten local turbulenceclosure schemes. The schemes ranged from first-order to the two-equationprognostic schemes. Predictions by the models were compared for aone-dimensional convective boundary layer using mixed layer scaling andmeasurements to interpret the results. Two-dimensional simulations were alsoperformed for a sea-breeze flow and for flow over a hill. The results showedthat for all of the models considered, minor differences were produced in themean meteorological fields and in the vertical scalar fluxes, but majordifferences were apparent in the velocity variances and dissipation rate.Predicted tracer concentrations were very sensitive to the turbulence modelformulation for dispersion from a point source in the convective boundarylayer, particularly for the prediction of maximum concentrations. Predictedtracer concentrations from a surface volume source for the two-dimensionalsimulations were similar for all models, although the degree of mixing in themorning growth period produced some differences. Generally, good results forthe mean meteorological fields can be obtained with first-order schemes, evenif they underpredict the magnitude of turbulence in the convective boundarylayer, and reasonable tracer concentrations can also be obtained with thesemodels provided near-source effects are not important. The two-equationprognostic models performed best for the prediction of turbulence in theconvective boundary layer.
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  • 14
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    Boundary layer meteorology 84 (1997), S. 1-22 
    ISSN: 1573-1472
    Keywords: Large-eddy simulation ; Turbulence ; Non-local closure ; Convective boundary layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Recently Frech and Mahrt proposed a closure scheme which includes alarge-scale stress term to represent the effects of non-local momentummixing in the convective boundary layer. Here large-eddy simulation (LES)datasets are used to evaluate the performance of this scheme across a rangeof stabilities between neutral and highly convective conditions, and as afunction of baroclinity. Generally the inclusion of the non-local term inthe closure model leads to results in better agreement with LES, althoughsome modifications to the model formulation are suggested.
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  • 15
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    Boundary layer meteorology 85 (1997), S. 35-52 
    ISSN: 1573-1472
    Keywords: Turbulence ; Atmospheric convective boundary layer ; Correlation function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A three-dimensional model for correlation functions and spectra in theatmospheric, convective boundary layer (CBL) is presented. The modelincludes vertical inhomogeneities introduced by eddy-blocking at the ground.By assuming the disturbance to the turbulent flow resulting from the groundblocking is irrotational, an equation is developed which allows one to writethe inhomogeneous, two-dimensional (2D) cross spectra for the blocked flowin terms of the 2D cross spectra for a homogeneous flow. VonKármán's energy spectrum then is used to determine thehomogeneous, 2D cross spectra. Although there are only two adjustableparameters in the model, the variance and a length scale, the model is shownto agree quite well with a diversity of previous results for the CBL.
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  • 16
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    Boundary layer meteorology 83 (1997), S. 117-137 
    ISSN: 1573-1472
    Keywords: Reynolds averaging ; Turbulence ; Time series ; Cospectra ; Sampling error
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Geophysical variables are orthogonally decomposed by averaging timeseries using different averaging lengths, referred to as a (Haar)multiresolution decomposition. This simple and economic decomposition isassociated with cospectra that formally satisfy Reynolds averaging rules foreach averaging length. The multiresolution decomposition provides a naturalestimate of the random error in estimating a mean turbulent flux. The Fourierand multiresolution decompositions are compared using aircraft data fromBOREAS.
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  • 17
    ISSN: 1573-1472
    Keywords: Turbulence ; Canopies ; Temperature ramps ; Structure functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Air temperature time series within and above canopies reveal ramp patternsassociated with coherent eddies that are responsible for most of thevertical transport of sensible heat. Van Atta used a simple step-changeramp model to analyse the coherent part of air temperature structurefunctions. However, his ocean data, and our own measurements for aDouglas-fir forest, straw mulch, and bare soil, reveal that even withoutlinearization his model cannot account for the observed decrease of thecubic structure function for small time lag. We found that a ramp model inwhich the rapid change at the end of the ramp occurs in a finite microfronttime can describe this decrease very well, and predict at least relativemagnitudes of microfront times between different surfaces. Averagerecurrence time for ramps, determined by analysis of the cubic structurefunction with the new ramp model, agreed well with values determined usingthe Mexican Hat wavelet transform, except at lower levels within theforest. Ramp frequency above the forest and mulch scaled very well withwind speed at the canopy top divided by canopy height. Within the forest,ramp frequency did not vary systematically with height. This is inaccordance with the idea that large-scale canopy turbulence is mostlygenerated by instability of the mean canopy wind profile, similar to aplane mixing layer. The straw mulch and bare soil experiments uniquelyextend measurements of temperature structure functions and ramp frequencyto the smallest scales possible in the field.
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  • 18
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    Colloid & polymer science 275 (1997), S. 155-161 
    ISSN: 1435-1536
    Keywords: Key words HCO-10 ; vesicles ; encapsulation ; stability ; solubilization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  The characteristics of poly(oxyethylene) hydrogenated caster oil ether (HCO-10) vesicles were studied for the standpoints of encapsulation efficiency, stability, solubilization and permeability or barrier efficiency. The vesicles of 5% HCO-10 had 6.24% of calcein-entrapment efficiency and 240 nm of mean diameter. The stability of HCO-10 vesicle suspensions was dependent on their concentrations. In the vesicle suspensions of 10% HCO-10 or more, both the size of the vesicles and the fluidity of the suspensions obviously varied with incubation time, indicating that a flocculation occurred; whereas, the vesicle suspension of 5% HCO-10 was relatively stable. The solubilization process of HCO-10 vesicles by SDS was similar to that of EggPC liposomes. The rate constants for permeation of Cl ion and calcein were 2.46×10-3 s-1 and 5.79×10-5 s-1, respectively, suggesting that HCO-10 vesicles possessed some barrier potential for Cl ion and calcein although they were smaller than those of liposomes. Furthermore, the efflux of the solute such as calcein from HCO-10 vesicles was maximum at 37 °C, where the vesicle membrane was presumably destabilized by dehydration of EOs in HCO-10 molecules.
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  • 19
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    Colloid & polymer science 105 (1997), S. 38-40 
    ISSN: 1435-1536
    Keywords: α-haematite hydrosols ; stability ; urea ; ionic adsorption sequence ; water structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The effect of urea on the stability of α-haematite hydrosols in the presence of various monovalent ions was studied on each side of the pzc (pH 8.2) by measurements of the critical coagulation concentration (CCC) of the hydrosol. It was observed that for pHs lower than the pzc, the effect of urea depends strongly on the nature of coagulating ion and on the pH:The CCC values of IO 3 − increases with urea concentrations but those of ClO 4 − and Cl− decreases. For pHs higher than the pzc, an inversion of the cationic adsorption sequence was observed. This behavior is in a good agreement with the well-known action of urea on the structure of water and also with the general property of the α-haematite water interface.
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    Rheologica acta 36 (1997), S. 367-383 
    ISSN: 1435-1528
    Keywords: Viscoelastic flow ; arrays of cylinders ; stability ; porous media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (Wec), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above Wec which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above Wec a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplifieds spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.
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  • 21
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    Rheologica acta 36 (1997), S. 367-383 
    ISSN: 1435-1528
    Keywords: Key words Viscoelastic flow ; arrays of cylinders ; stability ; porous media
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Low Reynolds number flow of Newtonian and viscoelastic Boger fluids past periodic square arrays of cylinders with a porosity of 0.45 and 0.86 has been studied. Pressure drop measurements along the flow direction as a function of flow rate as well as flow visualization has been performed to investigate the effect of fluid elasticity on stability of this class of flows. It has been shown that below a critical Weissenberg number (We c ), the flow in both porosity cells is a two-dimensional steady flow, however, pressure fluctuations appear above We c which is 2.95±0.25 for the 0.45 porosity cell and 0.95±0.08 for the higher porosity cell. Specifically, in the low porosity cell as the Weissenberg number is increased above We c a transition between a steady two-dimensional to a transient three-dimensional flow occurs. However, in the high porosity cell a transition between a steady two-dimensional to a steady three-dimensional flow consisting of periodic cellular structures along the length of the cylinder in the space between the first and the second cylinder occurs while past the second cylinder another transition to a transient three-dimensional flow occurs giving rise to time- dependent cellular structures of various wavelengths along the length of the cylinder. Overall, the experiments indicate that viscoelastic flow past periodic arrays of cylinders of various porosities is susceptible to purely elastic instabilities. Moreover, the instability observed in lower porosity cells where a vortex is present between the cylinders in the base flow is amplified spatially, that is energy from the mean flow is continuously transferred to the disturbance flow along the flow direction. This instability gives rise to a rapid increase in flow resistance. In higher porosity cells where a vortex between the cylinders is not present in the base flow, the energy associated with the disturbance flow is not greatly changed along the flow direction past the second cylinder. In addition, it has been shown that in both flow cells the instability is a sensitive function of the relaxation time of the fluid. Hence, the instability in this class of flows is a strong function of the base flow kinematics (i.e., curvature of streamlines near solid surfaces), We and the relaxation time of the fluid.
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  • 22
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    Journal of statistical physics 87 (1997), S. 1145-1164 
    ISSN: 1572-9613
    Keywords: Fisher-Kolmogorov equation ; traveling fronts ; fixed points ; population dynamics ; bifurcations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The one-dimensional reaction-diffusion equations for the process (D) $$A + B \to 2A,B + C \to 2B,C + A \to 2C$$ are extended to include the counteracting reactions (R) $$A + 2B \to 3B,B + 2C \to 3C,C + 2A \to 3A$$ which have a reaction rate α relative to the direct process (D). This process can be seen as a three-component version of the reaction which is described by the Fisher-Kolmogorov equation. The fixed points of the equations are studied as a function of α. It is shown that the equations admit solutions which consist of a series of traveling fronts. Other solutions exist which are traveling periodic waves. A very remarkable fact is that for these waves exact expressions can be constructed.
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  • 23
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    Journal of elasticity 48 (1997), S. 218-239 
    ISSN: 1573-2681
    Keywords: stability ; nonlinear elasticity ; Mooney-Rivlin material ; incompressible material ; thick-walled tube
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The problem of instability of a hyperelastic, thick-walled cylindrical tube was first studied by Wilkes [1] in 1955. The solution was formulated within the framework of the theory of small deformations superimposed on large homogeneous deformations for the general class of incompressible, isotropic materials; and results for axially symmetrical buckling were obtained for the neo-Hookean material. The solution involves a certain quadratic equation whose characteristic roots depend on the material response functions. For the neo-Hookean material these roots always are positive. In fact, here we show for the more general Mooney–Rivlin material that these roots always are positive, provided the empirical inequalities hold. In a recent study [2] of this problem for a class of internally constrained compressible materials, it is observed that these characteristic roots may be real-valued, pure imaginary, or complex-valued. The similarity of the analytical structure of the two problems, however, is most striking; and this similarity leads one to question possible complex-valued solutions for the incompressible case. Some remarks on this issue will be presented and some new results will be reported, including additional results for both the neo-Hookean and Mooney–Rivlin materials.
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