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  • 1995-1999  (526)
  • 1960-1964
  • 1996  (526)
  • Chemical Engineering  (437)
  • Numerical Methods and Modeling
  • Nuclear reactions
  • 1
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 15-31 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to Lp-Lq-estimates.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 2
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 217-233 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The mixed-Neumann problem for the non-linear wave equation □u-a(u)(∣∂tu)∣2-∣∇u∣2 = fε(z) is studied. The function fε(z) = ∑k∊Kfk(z,ε-1φk(z),ε), ε∊[0,1], K is finite, fk(z,θk,ε) are 2π-periodic with respect to θk. The existence of solution uε on a domain z = (t,x,y)∊[0,T]×∝+×∝d, d = 1 or 2, is proved when ε is sufficiently small; T does not depend on ε. By the non-linear geometric optics method the asymptotic (with respect to ε→0) solution ũ ε is constructed. The estimation for the rest ε2rε = uε-ũε is derived and the limit rε, ε→0, is studied.
    Materialart: Digitale Medien
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  • 3
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper analyses the Child-Langmuir asymptotics of the Vlasov-Poisson problem in cylindrical or spherical symmetry. The problem was stated in the first part of this paper [2]. We recall that the Child-Langmuir asymptotics concerns the boundary value problem for the Vlasov-Poisson system in the situation where the thermal energy of the injected particles at the boundary is small compared with the external applied bias.In the first part, we derived the set of estimates which allow us to pass to the limit in the asymptotic problem. In the present part, we analyse the limit (or ‘reduced’) problem, which leads us to a characterization of the limit or ‘Child-Langmuir’ current which flows through the system.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 4
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 341-361 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Lyapunov stability is analysed for a class of integro-differential equations with unbounded operator coefficients. These equations arise in the study of non-conservative stability problems for viscoelastic thin-walled elements of structures. Some sufficient stability conditions are derived by using the direct Lyapunov method. These conditions are formulated for arbitrary kernels of the Volterra integral operator in terms of norms of the operator coefficients. Employing these conditions the supersonic flutter of a viscoelastic panel is studied and explicit expressions for the critical gas velocity are derived. Dependence of the critical flow velocity on the material characteristics and compressive load is analysed numerically.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 381-400 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The equations describing the dynamics and steady states of a tubular reactor are studied in the region where an arbitrary number of steady-state solutions exist. The stability of these solutions is examined and their persistence for increases in the parameter values is determined. The physical implications of these solutions are examined.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 6
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 451-461 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We use the implicit function theorem to prove an existence of a heteroclinic orbit to a system of two non-linear second-order ODEs. The perturbation is carried out around infinite value of a ‘coupling parameter’. The form of the system which is considered in this paper is related to the system defining travelling wave solutions in a two temperature model of the laser sustained plasma.
    Materialart: Digitale Medien
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  • 7
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 897-907 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider a non-linear plate equation of Bernoulli-Euler type with a locally distributed damping term. Our main result asserts that if the damping is effective in a neighbourhood of the boundary then the energy decays exponentially. The method we use is a combination of multiplier techniques and of a compactness-uniqueness argument.
    Materialart: Digitale Medien
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  • 8
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 145-170 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Cauchy problem for the wave equation with power type non-linearity ±∣u∣σ*u and data in Hs+1(∝n)×Hs(∝n) is considered, where 0〈s〈(n/2)-1 and n≥3. Under the growth restriction σ*≤4/(n-2-2s) in many cases the existence of a local solution with u(t)∊Hs+1(∝n) is shown which is unique in a closely related class.
    Materialart: Digitale Medien
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  • 9
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 235-252 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The existence of global measure-valued solutions to the Euler equations describing the motion of an ideal compressible and heat conducting fluid is proved. The motion is considered in a bounded domain Ω⊂∝3 with impermeable boundary. The solution is a limit of an approximate solution obtained by adding the sixth-order elliptic operator in the equation of momentum.
    Materialart: Digitale Medien
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  • 10
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1017-1052 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A systematic way of ascribing values to integrals which diverge at infinity is described. For integrals with algebraic or logarithmic behaviour it is akin to Hadamard's finite part for integrands which have singularities at finite points. The power of the method is illustrated by examples of particular integrals and the convolution of distributions which are beyond the range of standard theory. Both one-dimensional and multi-dimensional integrals are included. The theory also enables the definition of products of distributions which are considered normally to be too singular for multiplication.
    Materialart: Digitale Medien
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  • 11
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1099-1120 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we consider a system of heat equations ut = Δu, vt = Δv in an unbounded domain Ω⊂∝N coupled through the Neumann boundary conditions uv = vp, vv = uq, where p〉0, q〉0, pq〉1 and ν is the exterior unit normal on ∂Ω. It is shown that for several types of domain there exists a critical exponent such that all of positive solutions blow up in a finite time in subcritical case (including the critical case) while there exist positive global solutions in the supercritical case if initial data are small.
    Materialart: Digitale Medien
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  • 12
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 363-374 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Periodic solutions of arbitrary period to semilinear partial differential equations of Zabusky or Boussinesq type are obtained. More generally, for a linear differential operator A(y,∂), the equation A(y,∂)u = (-1)∣γ∣∂γf(y,∂γu), y = (t,x)∊∝k×G is studied, where homogeneous boundary conditions on ∂G and periodicity conditions on t are imposed. The solutions are obtained by variational methods in anisotropic Sobolev spaces.
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  • 13
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 401-424 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi-Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is proved rigorously and error estimates are shown. We compute numerically static voltage-current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard drift-diffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 14
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 463-479 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A particles numerical method for incompressible fluid, based on a Hamiltonian formalism due to Oseledets [8], was recently introduced and exploited by Buttke [1]. Here we investigate the convergence of the solutions of such a particles system to the solutions of the incompressible Euler equation, and point out some features of the Hamiltonian formalism.
    Materialart: Digitale Medien
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  • 15
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 507-528 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Stokes problem-Δu+∇p = f, div u = g in Ω, u∣∂Ω = h is investigated for two-dimensional exterior domains Ω. By means of potential theory, existence, uniqueness and regularity results for weak solutions are proved in weighted Sobolev spaces with weights proportional to ∣x∣δ as ∣x∣→∞. For f = 0,g = 0, explicit decay formulas are obtained for the solutions u and p. Finally, the results are compared with the theory of r-generalized solutions, i.e. ∇u∊Lr.
    Materialart: Digitale Medien
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  • 16
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 571-591 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove global existence and uniqueness to the initial value problem for the coagulation-fragmentation equation for an unbounded coagulation kernel with possible linear growth at infinity and a fragmentation kernel from a very large class of unbounded functions. We show that the solutions satisfy the mass conservation law.
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  • 17
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 607-638 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study (a) acoustic waves generated by a time-harmonic force distribution and (b) the potential flow with prescribed velocity at infinity in an infinite cylinder Ω0 = Ω′×∝ with bounded cross-section Ω′⊂∝2 in the presence of m embedded obstacles B1,…,Bm. By using Green's function Gκ(x,y) of the Neumann problem for the reduced wave equation ΔU+κ2U = 0 in the unperturbed domain Ω0, both problems can be reduced to integral equations over the boundaries of the obstacles. The main properties of Gκ(x,y), which are required for this approach, are derived in the first part of this paper.
    Materialart: Digitale Medien
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  • 18
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 651-677 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The equations of the Hopfield network, without the constraint of symmetry, can have complex behaviours. Cottet borrowed techniques from particle methods to show that a class of such networks with symmetric, translation-invariant connection matrices may be approximated by a reaction-diffusion equation. This idea is extended to a wider class of network connections yielding a slightly more complex reaction-diffusion equation. It is also shown that the approximation holds rigorously only in certain spatial regions (even for Cottet's special case) but the small regions where it fails, namely within transition layers between regions of high and low activity, are not likely to be critical.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 19
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 187-215 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the self-adjoint operator governing the propagation of elastic waves in perturbed stratified media ∝3 with free boundary-interface conditions. In this paper we establish the limiting absorption principle for this self-adjoint operator in appropriate Hilbert space. The proof of the limiting absorption principle is based on the division theorem which is proved by means of eigenfunction expansions for the self-adjoint operator governing the propagation of elastic waves in unperturbed stratified media ∝3.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 20
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
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  • 21
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 773-823 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study initial and boundary value problems for the wave equation ∂2tu-Δu = fe-iωt with Dirichlet or Neumann boundary data in smooth domains Ω, which coincide with Ω0 = ∝2×(0,1) outside a sufficiently large sphere. The concept of a standing wave, introduced in [7], seems to be of special relevance. A standing wave of frequency ω is defined as a non-trivial solution U of the equation ΔU+ω2U = 0 in Ω, which satisfies on ∂Ω the prescribed boundary condition U = 0 or ∂U/∂n = 0, respectively, and a suitable condition at infinity. For instance, U(x) = sinπkx3 is a standing wave of frequency πk in the unperturbed domain Ω0 with Dirichlet boundary data. As shown in a series of joint papers with K. Morgenröther, u(x,t) is bounded as t→∞ if Ω does not admit standing waves of frequency ω. The main purpose of the present paper is the proof of the converse statement: If standing waves of frequency ω exist in Ω, then u(x,t) is unbounded as t→∞ for suitably chosen f∊C∞0(Ω). Thus the appearance of resonances is closely related to the presence of standing waves. The leading term of the asymptotic expansion of u(x,t) as t→∞ will be specified. In particular, it turns out that the resonance rate is either t or ln t. The rate t appears if and only if ω2 is an eigenvalue of the spatial operator, while the rate ln t can only occur if ω = πk. In the case of Neumann boundary data, U = 1 is a standing wave of frequency 0 for every local perturbation Ω of Ω0. The corresponding resonance has already been studied in [21].
    Materialart: Digitale Medien
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  • 22
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 375-380 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper an asymptotic result concerning the interface for some problems connected with radially symmetric non-linear diffusion is presented.
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  • 23
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
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  • 24
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 425-450 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Van Roosbroeck's bipolar drift diffusion equations cover the qualitative behaviour of many semiconductor devices. The complexity of the model equations however prevents efficient implementations needed in circuit simulations. Under close-to-thermal-equilibrium biasing conditions (zero space charge assumption, low injection limit) the van Roosbroeck system can be replaced by a system of coupled non-linear Volterra integral equations of the second kind. Involving only the macroscopic quantities current, applied voltage and serial resistance this Volterra system can be handled with comparably little effort. Volterra integral equations models are formulated for a large class of semiconductor devices with abrupt pn-junctions. The model equations are made explicit for diodes, transistors and thyristors. A survey on various results concerning Volterra models describing the switching behaviour of pn-diodes is given. The integral equation model allows to recover all relevant properties of the voltage-current characteristics.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 25
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 959-976 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.
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  • 26
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 991-1015 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study a quasi-static incompressible flow of Bingham type with constituent law\[ \begin{array}{ll} T = p\left| {\cal E}u\right| ⁁{p-2}{\cal E}u+\beta \frac{{\cal E}u}{\left| {\cal E}u\right| } & \text{if }{\cal E}u\neq 0, \\ \left| T\right| \leq \beta & \text{if }{\cal E}u = 0, \end{array} \] T = p∣Eu∣p-2Eu+β Eu ∣Eu∣ if Eu≠0,∣T∣≤β if Eu = 0, where p≥2 and β〉0. Here Eu denotes the strain velocity and T the corresponding stress. The problem admits a variational formulation in the sense that the velocity field u minimizes the energy I(u) = ∫Ω∣Eu∣p+β∣Eu∣dx in the space {v∊H1,p(Ω,∝n): div v = 0} subject to appropriate boundary conditions. We then show smoothness of u on the set {x∊Ω: Eu≠0}.
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  • 27
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1053-1072 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we study an initial-boundary value problem for a system of phase-field equations arising from the Penrose-Fife approach to model the kinetics of phase transitions. In contrast to other recent works in the field, the correct form of the boundary condition for the temperature field is assumed which leads to additional difficulties in the mathematical treatment. It is demonstrated that global existence of strong solutions can be shown under essentially the same assumptions on the data as in the previous papers where a simplified boundary condition for the heat exchange with the surrounding medium has been used.
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  • 28
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1091-1097 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A numerical technique for determining the solution of the brachistochrone problem is presented. The brachistochrone problem is first formulated as a non-linear optimal control problem. Using Chebyshev nodes, we construct the Mth degree polynomial interpolation to approximate the state and the control variables. Application of this method results in the transformation of differential and integral expressions into some non-linear algebraic equations to which Newton-type methods can be applied. Simulation studies demonstrate computational advantages relative to existing methods in the literature.
    Zusätzliches Material: 3 Tab.
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  • 29
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1135-1140 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, following the ideas of Lax, we prove a blow-up result for a class of solutions of the equation φtt-φxx-φ2xφxx-φ3 = 0, corresponding, in certain cases, to the development of a singularity in the second derivatives of φ. These solutions solve locally (in time) the Cauchy problem for smooth initial data belonging to the uniformly local Sobolev spaces considered by Kato and by Majda.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
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  • 30
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
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  • 31
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 857-881 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the Stokes system with non-homogeneous Fourier boundary conditions depending on a parameter, in a domain with periodic inclusions of the size of the period. Following the values of this parameter, we obtain at the limit a Darcy's law, a Brinkmann type equation or a Stokes type equation.We also present a physical model to which the results apply. This model describes the flow of an incompressible viscous fluid through a porous medium under the action of an exterior electric field.
    Zusätzliches Material: 1 Ill.
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  • 32
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 33
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1409-1413 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We introduce a new identity satisfied by solutions of the Vlasov-Poisson system. It has the property that all quantities which appear have a definite sign, and this allows us to prove new results on the time decay of the solutions in the plasma physical case.
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  • 34
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1415-1431 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Dirac equation with a vector potential is considered using a biquaternionic formalism and boundary integral representations for its solutions are obtained. In order to characterize these solutions by a property of local approximability by linearization the corresponding notion of biquaternionic differentiability and its generalization in the sense of Bers (adapted to the spatial case) are given.
    Materialart: Digitale Medien
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  • 35
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1445-1469 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The three-dimensional mathematical problems of the interaction of an elastic and some scalar fields are investigated. It is assumed that the elastic structure under consideration is a bounded homogeneous anisotropic body occupying domain Ω¯+⊂∝3 and the physical scalar field is defined in the exterior domain Ω- = ∝3\Ω+. These two fields satisfy the governing equations in the corresponding domains together with the transmission conditions on the interface ∂Ω+. The problems are studied by the potential method and the existence and uniqueness theorems are proved.
    Materialart: Digitale Medien
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  • 36
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 63-85 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper is concerned with the effective numerical treatment of elliptic boundary value problems when the solutions contain singularities. The paper deals first with the theory of problems of this type in the context of weighted Sobolev spaces and covers problems in domains with conical vertices and non-intersecting edges, as well as polyhedral domains with Lipschitz boundaries. Finite element schemes on graded meshes for second-order problems in polygonal/polyhedral domains are then proposed for problems with the above singularities. These schemes exhibit optimal convergence rates with decreasing mesh size. Finally, we describe numerical experiments which demonstrate the efficiency of our technique in terms of ‘actual’ errors for specific (finite) mesh sizes in addition to the asymptotic rates of convergence.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
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  • 37
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 171-185 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: It is shown that the non-linear coagulation-fragmentation equation with constant kernels has a unique equilibrium solution. This equilibrium solution is given explicitly in terms of the initial data and the kernels. Weak L1 convergence of time-dependent solutions to the unique equilibrium is demonstrated via an invariance principle employing a suitable lower semicontinuous Lyapunov functional.
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  • 38
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 39
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 639-649 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the Cauchy problem for the damped Boussinesq equation governing long wave propagation in a viscous fluid of small depth. For the cases of one, two, and three space dimensions local in time existence and uniqueness of a solution is proved. We show that for discontinuous initial perturbations this solution is infinitely differentiable with respect to time t and space co-ordinates for t〉0 on a bounded time interval.
    Materialart: Digitale Medien
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  • 40
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1-13 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.
    Materialart: Digitale Medien
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  • 41
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 53-62 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the time evolution of the support of a positive vorticity for a non-viscous incompressible fluid evolving in ∝2-D, where D is a compact domain with smooth boundary. We bound its growth. In the same time we prove also that a fluid particle initially close to the origin cannot go fast away.
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  • 42
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 131-144 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The existence of global attractors of the periodic initial value problem for a coupled non-linear wave equation is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of uniform a priori estimates for time.
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  • 43
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 933-942 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This work proves global in time existence of large solutions for a quasistatic problem in non-linear viscoelasticity in the three-dimensional case. The basic idea is to apply the energy method for local in time solutions.
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  • 44
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 977-989 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A new approach to the boundary value problem for the classic Dirac equation is proposed. This approach is based on a recent version of the metaharmonic quaternionic analysis developed in [14-16]. In particular, the following problem is studied: when and how a given function on a surface can be extended to a time-harmonic spinor field.
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  • 45
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 253-253 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: No Abstract
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  • 46
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 33-51 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we generalize the abstract results of Mock and Marcowich [13, 12] for convergence of discrete Van Roosbroeck systems [12, 13, 17], to the case when the solutions are typically in W1,4-ε and not in H2. These conditions are verified on finite element discretizations. Error estimates are derived when the solution is unique. Due to the singularity at the flat angles, these estimates in the H1 norm are only O(h1/2). The techniques that are presented are broad and may be applied to other type of discretizations.
    Zusätzliches Material: 1 Ill.
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  • 47
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 48
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 49
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 87-129 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we employ concepts from Banach space geometry in order to examine the problem of approximating the optimal distributed control of vibrating media whose motion is governed by a wave equation with a 2n-order self-adjoint and positive-definite linear differential operator. We show that this geometrical approach, arrived at via duality theory, provides the exact framework in which the approximation problem must be placed in order to get the correct convergence results, for it is here that the necessary and sufficient conditions for the approximate norm or time minimal control can be fully developed. Using the theory of Asplund, we are also able to improve the traditional weak* convergence results for the more difficult case of L∞ controls. Finally, we consider certain numerical examples which help illustrate our theoretical results.
    Zusätzliches Material: 2 Ill.
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  • 50
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 737-759 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we continue the work of [1] and obtain a complete picture of asymptotic behavior and blow-up properties of solutions of a non-local Burgers' equation.
    Zusätzliches Material: 6 Tab.
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  • 51
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 52
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 287-312 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Child-Langmuir asymptotics of the Vlasov-Poisson system provides a model for vacuum diodes which operate under large biases. In these conditions the energy of the injected particles at the cathode is very small compared with the applied external bias. From the mathematical view point, this leads to an interesting and non-standard asymptotic problem for the Vlasov-Poisson equation, which has already been investigated in the one-dimensional Cartesian case, in [7]. The purpose of this paper is to extend the analysis to the cylindrically or spherically symmetric case. Surprisingly, the behaviour of the solutions of the model is somehow different than in the Cartesian case. This feature had not been noticed by the physicists before. Furthermore, the mathematical analysis is much more involved than in [7] because of the geometrical effects, and the techniques that are used are quite different. They mainly rely on the use of supersolutions in the spirit of [18, 19]. This work is divided in two parts. In this first part, we state the problem and establish the basic estimates which are needed for the asymptotic analysis.
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  • 53
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 883-896 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In the first section of this paper, some non-local boundary value problem for the polyharmonic equation in the plane is considered. This problem consists in determining solution of the polyharmonic equation satisfying some special non-local-type boundary condition on two curves. The existence theorem is proved. In the second section, an example for the case of the biharmonic equation is considered. In the third section, some non-local, non-linear problem of Riquier type is examined. The Riquier-type problem consists in determining the polyharmonic function in the plane whose value together with its successive Laplacians are prescribed on the boundary. The existence theorem is proved and an example for the case of the biharmonic equation is considered.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
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  • 54
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 909-931 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The paper deals with the Fourier-finite-element method (FFEM), which combines the approximate Fourier method with the finite-element method, and its application to Poisson-like equations -p̂Δ3û = f̂ in three-dimensional axisymmetric domains Ω^. Here, p^ is a piecewise constant coefficient having a jump at some axisymmetric interface. Special emphasis is given to estimates of the Fourier-finite-element error in the Sobolev space H1(Ω^), if the interface is smooth or if it meets the boundary of Ω^ at some edge. In general, the solution û contains a singularity at the interface, which is described by a tensor product representation and treated numerically by appropriate mesh grading in the meridian plane of Ω^. The rate of convergence of the combined approximation in H1(Ω^) is proved to be O(h+N-1) (h, N: the parameters of the finite-element- and Fourier-approximation, with h→0, N→∞). The theoretical results are confirmed by numerical experiments.
    Zusätzliches Material: 5 Ill.
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  • 55
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 481-505 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman-Enskog procedure, introduced in [19], gives the error of order of ε2, uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion-type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker-Planck collision operator.
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  • 56
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 555-569 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A mathematical approach to the concept of shape of a submanifold M of a Euclidean space had previously been given by means of ‘measuring functions’ (e.g. diameter or volume) and of the derived ‘size functions’. This paper relates the study and the computation of any such size function to the structure of critical points of the associated measuring function.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 57
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 593-605 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on Clifford analysis. Applications to the quantum field theory are described.
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  • 58
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 59
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 699-716 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ∝3. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.
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  • 60
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 717-736 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider parabolic systems defined on cylindrical domains close to the threshold of instability, in which the Fourier modes with positive growth rates are concentrated at a non-zero critical wave number. In particular, we consider systems for which a so-called Ginzburg-Landau equation can be derived. Due to the presence of continuous spectrum, classical bifurcation theory is not available to describe bifurcating solutions. Thus, we consider a modified system with artificial spectral gap, which possesses an infinite-dimensional centre manifold. The amplitude equation on this manifold is called a generalized Ginzburg-Landau equation. From previous work [18] it is known that the Fourier modes are exponentially concentrated at integer multiples of the critical wave number. Hence, the error made by this modification is exponentially small in powers of the bifurcation parameter. The approximations obtained via the generalized Ginzburg-Landau equation are valid on a much longer time scale than those obtained by using the classical Ginzburg-Landau equation as an amplitude equation.
    Zusätzliches Material: 2 Ill.
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  • 61
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 825-845 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new class of solutions is obtained. Two-dimensional flows in channel are studied on the basis of exact solutions and analogy with the Carleman model. Explicit example of non-unique solution to a boundary value problem is given. Exact hydrodynamic equations are derived for the stationary Broadwell model. A role of the Navier-Stokes approximation is discussed in detail by comparison with these exact equations.
    Zusätzliches Material: 2 Ill.
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  • 62
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1303-1316 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The initial-boundary value problem in non-cylindrical domain for a semilinear hyperbolic system is investigated. A weak solution is constructed by the method of semidiscretization in time variable combining with variational calculus, when the time sections of domain has non-decreasing property.
    Materialart: Digitale Medien
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  • 63
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 64
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 65
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 943-957 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: When one end of an extensible beam whose ends are a fixed distance apart, is hinged while to other end a load is attached, the mathematical model describing the vibrations of the beam contains a non-linearity both in the partial differential equation as well as in the dynamical boundary condition. We introduce weak damping and consider the resulting boundary-value problem within the framework of the theories of B-evolutions and fractional powers of a closed pair of operators. This approach enables us to construct a unique weak solution which exhibits exponential decay by employing Faedo-Galerkin approximations.
    Materialart: Digitale Medien
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  • 66
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 67
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1073-1090 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We derive the low-frequency asymptotic expansion of the exterior boundary value problems in two dimensions for second-order elliptic system concerning the theory of elastostatics. As an application of our result, the rate of the local energy decay of solutions of the initial boundary value problem for the corresponding dynamical system is discussed.
    Materialart: Digitale Medien
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  • 68
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 69
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1141-1156 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper we investigate the properties of positive solutions for three non-local reaction-diffusion problems. The conditions on the existence and non-existence of global positive solutions are given. Moreover, we prove that the blow-up set is the whole region when the non-linearity occurs in the equation.
    Materialart: Digitale Medien
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  • 70
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1265-1277 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The existence of global weak solutions for coupled thermoelasticity with non-linear contact boundary conditions corresponding to the friction problem is considered. The time-continuous Galerkin method and a priori estimates obtained with Gronwall's inequality in connection with embedding theorems are applied to accomplish a straightforward generalization of one of the results proved by Martins and Oden 9.
    Materialart: Digitale Medien
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  • 71
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1317-1333 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We give new finite time blow-up results for the non-linear parabolic equations ut-Δu = up and ut-Δu+μ∣∇u∣q = up. We first establish an a priori bound in Lp+1 for the positive non-decreasing global solutions. As a consequence, we prove in particular that for the second equation on ∝N, with q = 2p/(p+1) and small μ〉0, blow-up can occur for any N≥1, p〉1, (N-2)p〈N+2 and without energy restriction on the initial data. Incidentally, we present a simple model in population dynamics involving this equation.
    Materialart: Digitale Medien
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  • 72
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1397-1407 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: No Abstract
    Materialart: Digitale Medien
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  • 73
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1433-1444 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The equations of motion for two-dimensional deformations of an incompressible elastoplastic material involve five equations, two equations expressing conservation of momentum, and three constitutive laws, which we take in the rate form, i.e. relating the stress rate to the strain rate. In hypoplasticity, the constitutive laws are homogeneous of degree one in the stress and strain rates. This property has the consequence that although the equations are not in conservation form, there is nonetheless a natural way to characterize planar shock waves. The Riemann problem is the initial value problem for plane waves, in which the initial data for stress and velocity consist of two constant vectors separated by a single discontinuity. The main result is that, under appropriate assumptions, the Riemann problem has a scale invariant piecewise constant solution. The issue of uniqueness is left unresolved. Indeed, we give an example satisfying the conditions for existence, for which there are many solutions. Using asymptotics, we show how solutions of the Riemann problem are approximated by smooth solutions of a system regularized by the addition of viscous terms that preserve the property of scale invariance.
    Materialart: Digitale Medien
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  • 74
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1471-1488 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We prove global existence of weak solutions of the drift diffusion model for semiconductors coupled with Maxwell's equations for the electromagnetic field by using a Galerkin method. The recombinations term for the density of electrons and holes may depend on the densities, the gradient of the densities and the electromagnetic field.
    Materialart: Digitale Medien
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  • 75
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1489-1507 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper concerns the well-posedness of the hydrodynamic model for semiconductor devices, a quasi-linear elliptic-parbolic-hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbolic equations are assumed to be well-posed in L2 sense. Maximally strictly dissipative boundary conditions for the hyperbolic equations satisfy the assumption of well-posedness in L2 sense. The well-posedness of the model under the boundary conditions is demonstrated.
    Materialart: Digitale Medien
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  • 76
    Digitale Medien
    Digitale Medien
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Schlagwort(e): Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 77
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 538-546 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Nuclear magnetic resonance (NMR) spin-lattice relaxation measurements are used to investigate pore structures and fluid phase distributions in porous media. A new method for estimating relaxation time distribution functions from measured relaxation data is presented using a B-spline basis to represent the distribution function and Tikhonov regularization to stabilize the estimation problem. Surface relaxivity, which is required to convert relaxation time distributions to pore-size distributions of fluid phase distributions at partial saturations, is determined using pore volume-to-surface-area ratios estimated by NMR diffusion measurements. This approach was validated by analyzing certain model porous media with known pore volume-to-surface-area ratios. The method is demonstrated by determining pore-size and fluid phase distributions of sandstone and carbonate samples, as well as by comparing the pore-size distributions of chalk samples obtained by this methodology with those estimated by mercury porosimetry.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
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  • 78
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 547-561 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Emulsion liquid membrane separation processes remain excessively vulnerable to one or more of four major problems. Difficulties lie in developing liquid membranes that combine high levels of both stability and permeability with acceptably low levels of swelling and ease of subsequent demulsification for membrane and solute recovery. This article provides a new technique for simultaneously overcoming the first three problems, while identifying physical indications that the proposed solution may have little adverse effect on the fourth problem (demulsification) and may even alleviate it. Numerous benefits of optimized conversion of the membrane phase into suitable non-Newtonian form are identified, their mechanisms outlined, and experimental verifications provided. These include increased stability, retained (or enhanced) permeability, reduced swelling, increased internal phase volume, and increased stirrer speeds. The highly favorable responsiveness of both aliphatic and aromatic membranes to the new technique is demonstrated.
    Zusätzliches Material: 18 Ill.
    Materialart: Digitale Medien
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  • 79
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996) 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 80
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 585-594 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A comprehensive equation of state was developed to represent the phase equilibria and volumetric properties of aqueous calcium chloride solutions at temperatures above 523 K. The equation consists of a reference part and a perturbation contribution. The reference function is developed from the statistical mechanical theory for mixtures of dipolar and quadrupolar hard spheres, which agrees well with the Monte Carlo simulation results. In this treatment, calcium chloride is described by the completely undissociated model. The empirical perturbation function is a truncated series of virial expansion terms. Thus, mixing rules are guided by those of virial coefficients, which are derived rigorously from statistical mechanics. The equation reproduces experimental saturated vapor pressures and volumetric data within experimental uncertainty for temperatures to 623 K. At higher temperatures, few and less accurate experimental data are available, but values of the saturated vapor pressures of the liquid have been reported and are represented satisfactorily.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
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  • 81
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 601-612 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A previously developed mathematical wetting model is generalized and applied to the following two closely related situations: the spreading of a liquid over a prewet solid surface and the receding contact-line motion with a microscopic residual film, remaining behind the contact line. An analytical expression for the velocity dependence of the dynamic contact angle is derived. Macroscopic characteristics (the dynamic contact angle and drag force) and the flow field corresponding to the spreading of a liquid over a wet solid surface differ considerably from those calculated for a dry surface. Under certain conditions the flow in the reference frame fixed with respect to the contact line has a region with closed streamlines. The region appears due to the flow-induced Marangoni effect, the reverse influence of the surface tension gradient along the liquid-solid interface caused by the flow on the flow, which gives rise to the gradient. The results are compared qualitatively with experimental data.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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  • 82
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 638-648 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The full Navier-Stokes equations were employed with a single-fluid model and a front tracking scheme to study a large cylindrical bubble in a free shear layer. A general formulation based on work by Auton et al. of the hydrodynamic forces on a finite Reynolds number large bubble in an unsteady, nonuniform and rotational flow was then used to investigate the effects of nonlinear spatial and temporal gradients on dispersion. The resulting bubble dispersion in the full Navier-Stokes solution significantly differ from that by a conventional bubble dynamic equation based on linear spatial gradients and quasi-steady flow. This was due to the adjunct forces not accounted for by such a formulation, which are related to regions of high nonuniformity and unsteadiness. These adjunct forces in the drag/lift direction were correlated with rapid variations of relative bubble velocity and high gradients of the liquid velocity.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 83
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 623-637 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The evolution of a film with insoluble surfactant on a wavy horizontal wall differs from flow without surfactant (the way it usually is studied) in that the film passes through different stages. The first stage is as if the surfactant were absent. Once the surface tension gradient - induced by the nonuniform surfactant concentration adsorbed at the free surface - starts resisting the flow effectively, the evolution enters a transitional stage. A final stage is reached once the free surface becomes rigid due to the surface-tension gradient (high elasticity limit) or becomes virtually leveled before the surface-tension gradient is released (low elasticity limit). The velocity profile through the film changes with time, sol fluid is depleted or accumulated at different strata in the film as the flow evolves. The velocity profile and resulting deformations throughout the film can be influenced significantly by the viscosity distribution or stratification, which occurs, for example, when multiple layers of different viscosity are coated simultaneously. A model and applications for the leveling of such a film are presented. The evolution is described in general terms for a film of uniform viscosity and for a film of two discrete layers of different viscosity. Then the three limiting cases are established. For two of these limits, the effect on the exponential decay rate of the flow and the deformation of the different strata or layers is examined when the viscosity is changed in an infinitesimally thin layer or stratum, and in a layer of finite thickness in films of two and three discrete layers.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
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  • 84
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 809-819 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A general theory for the adsorption of self-associating molecules in microporous structures is developed. The approach is similar to the “chemical” interpretation of nonideality of vapor and liquid phases. The theory displays Type 5 isotherm behavior and can explain Types 1 and 5 transition. Isothermal data are represented by only three parameters: Henry's law constant, saturation capacity, and reaction constant for “cluster” formation in the micropores. When isotherms at different temperatures are available, the theory can be used with five temperature-independent parameters to describe the entire phase behavior including the heat of adsorption. Water adsorption on activated carbon, the most common display of Type 5 behavior, is used to test the theory. Analysis of several data sets indicates that the theory can closely correlate data, provide physically meaningful parameter values in line with carbon properties, and it is highly effective in correlating temperature variation. The reaction enthalpy for water dimerization in the carbon micropores is lower than that in vapor phase. This preliminary conclusion with the theory needs to be supported with more accurate data when available.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
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  • 85
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 820-828 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The new application of nuclear magnetic resonance imaging (MRI) techniques for characterizing fractures and flow in fractured media is investigated. Specifically, a relaxation-weighted imaging technique is used for selectively highlighting either fracture or porous matrix regions. Many advantages over conventional spin-density MRI techniques for characterizing fractured media are demonstrated. Its use to speed image acquisition is also demonstrated. In addition, a multislice profile imaging technique is used to investigate imbibition and drainage displacement experiments in fractured porous media. These images demonstrate that the fractures can have profound effects on the fluid distributions in multiphase flow.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
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  • 86
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 829-836 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Many living organisms store iron in solid form, Fe(III), as a crystal in the inner cavity of the ferritin molecule. When iron is needed for biosynthesis, a reducing agent reduces Fe(III) into the soluble form Fe2+ released by ferritin. Crystallization and release processes are reversible, and their rates evolve in an identical way as a function of the number n of iron atoms in the molecule. The rate increases with n, showing a maximum value when n is approximately 1,300, and then stabilizes for the highest values of n, which can reach 4,500. On the other hand, plotting the amount of released iron as a function of time gives curves with a sigmoid shape. The proposed model was based on the theoretical description of different steps involved in crystal growth inside the protein shell: several independent crystals grow freely at the inner protein wall, and then a distribution function takes into account possible overlapping of different crystallite clusters, whose further growth is limited by diminution of the available space inside the cavity. The kinetics derived was then used to calculate the release curve as a function of time. Solving the system of differential mass-balance equations was simplified by describing the ferritin population as a large discrete distribution of species. The model fully fitted and explained the variation in the crystallization rate with n, and the sigmoid shape of the release curve as a function of time obtained experimentally in a thin-layer electrochemical cell.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 87
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 837-849 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A new group-contribution lattice-fluid equation of state (GCLF-EOS), which is capable of predicting the equilibrium properties of polymer-solvent solutions, was developed by modifying the original GCLF-EOS of High and Danner. The GCLF-EOS is a group-contribution form of the Panayiotou-Vera equation of state based on the lattice-hole theory. Group contributions for the interaction energy and reference volume were developed based only on the saturated vapor pressure and liquid densities of low molecular weight compounds. For a mixture, a binary interaction parameter was introduced into the mixing rules. Group contributions for the binary interaction parameter were developed from the binary vapor-liquid equilibria of low molecular weight compounds. This modified GCLF-EOS model gives excellent predictions of solvent activity coefficients both at infinite dilution and at finite concentrations. It is significantly better than the original GCLF-EOS model in its prediction capability. The only input required for the model is the structure of the molecules in terms of their functional groups. No other pure component or mixture properties of the polymer or solvent are needed.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
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  • 88
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 249-258 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Ion-selective electrodes were used to measure the activity coefficients at 298.2 K of individual ions in aqueous solutions of NaCl and NaBr up to of 5 molal and of KCl up to 4 molal. The mean ionic activity coefficients of NaCl, NaBr, and KCl, obtained from the values of the activity coefficients of the individual ions, show good agreement with values reported in the literature. The experimental results show that the activity coefficients are different for the anion and the cation in an aqueous solution of a single electrolyte and that, as expected from the ion-ion and ion-solvent interactions, the activity coefficient of an ion depends on the nature of its counterion. A modified form of the Pitzer's model, which distinguishes between the activity coefficients of the anion and the cation, was used to correlate the experimental results.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 89
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 850-860 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Cartilage constructs were grown using isolated chondrocytes and biodegradable polymer scaffolds made of fibrous polyglycolic acid in the form of 1-cm-dia × 5-mm-thick discs. The scaffolds were seeded in a mixed cell suspension and cultured for up to 8 weeks under static or mixed tissue culture conditions in petri dishes and spinner flasks. Turbulent mixing significantly improved the biochemical compositions and altered morphologies of the cartilage constructs, which were the thickest ones cultured to date in vitro. Constructs from mixed cultures were more regular in shape and contained up to 70% more cells, 60% more sulfated glycosaminoglycan, and 125% more total collagen when compared to constructs from static cultures. Mixing also induced the formation of an outer capsule with multiple layers of elongated cells and collagen fibrils around the inner tissue phase, while statically grown constructs consisted of round cells embedded in cartilaginous matrix. Mixing during cell seeding and tissue culture is thus an important parameter for the cultivation of tissue-engineered cartilage in a range of sizes, shapes and compositions for a variety of clinical applications (e.g., fibrous cartilage for reconstructive surgery or articular cartilage for joint resurfacing).
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 90
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 876-883 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A solid-state carbon monoxide sensor was fabricated using a 9% yttria-stabilized zirconia (YSZ) disc sandwiched between two platinum thin-film electrodes. One of the electrodes was coated with a thin layer of 7 CuO · 10 ZnO · 3 Al2O3 catalyst. The sensor showed limiting current behavior at an applied voltage between 0.5 and 1.2 V. Linear response was observed with carbon monoxide in a nitrogen-oxygen mixture at high temperature and limiting current conditions. The linear carbon monoxide concentration range increased with increase in the operating temperature and its sensitivity increased from 2.437 mA · atm-1 CO at 1,023 K to 10.771 at 1,093 K. These characteristics were adequately described by the proposed mathematical model relating the response to the rate processes occurring in the catalyst layer and in the electrochemical cell under limiting current conditions. The model showed that effective sensing and high sensitivity are best obtained using a catalyst with high catalytic activity toward the test solute and proper design and fabrication of the sensor to ensure its high diffusivity in the catalyst.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 91
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 889-891 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 92
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 892-895 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 93
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 884-888 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 94
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 896-900 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 95
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996) 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 96
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 910-920 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: New data on the variation of the diffusion coefficient with concentration in binary nonideal liquid mixtures are presented. The diffusion coefficients were measured with laser holography with an improved analysis procedure and are primarily in systems that form two liquid phases. The results show that for such systems the diffusion coefficient is constant if a chemical-potential driving force is used. If, however, the miscibility gap is wide, the Schreiner equation (Schreiner, 1922) is shown to be more accurate than relations that consider the variation of viscosity. Cluster theories developed for diffusion behavior near critical points were found to explain the data well only in water-organic systems on the water-rich side.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 97
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 277-284 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 98
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 285-289 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 99
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 1041-1068 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The study of spatial structures in heterogeneous reactors is a challenging academic topic, revealing patterns that differ from those known to exist in reaction-diffusion systems exposed to uniform conditions, as well as a practical problem that should affect design and operation procedures of commercial reactors like the catalytic convertor. Experimental observations and mathematical models of spatiotemporal patterns in high-pressure catalytic reactors are reviewed. Patterns in high-pressure reactors, in which thermal effects provide the positive feedback, as well as the long-range communication, usually emerge due to global interaction. Patterns are classified comprehensively by considering reactors of increasing degree of complexity: a wire or ribbon exposed to uniform conditions, a globally coupled catalyst in a mixed reactor or in a control loop, and a fixed bed in which interaction by convection occurs only in one direction. Catalytic wires are not expected to exhibit sustained patterns in the absence of global interaction. Global interactions by external control or gas-phase coupling are shown experimentally and analytically to induce a rich plethora of patterns. Complex motions were simulated to occur due to the interaction of convection, conduction and reaction in a fixed-bed; only a few of these patterns were experimentally observed. Directions for future research are suggested.
    Zusätzliches Material: 26 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 100
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 42 (1996), S. 1088-1094 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The ignited state is associated with a thin reaction zone and a steep temperature gradient ahead of the front. The stability of this front is analyzed for small radial and azimuthal perturbations. The near-equidiffusional assumption is made, and the deviation of the Lewis number from unity is considered as the bifurcation parameter. The analysis shows that the planar front becomes unstable at Lewis numbers above unity after a Hopf bifurcation. The oscillatory front collapses into hot spots or rings which oscillate around the axial axis. For Lewis numbers less than one, a steady-state cellular front structure is found.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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