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  • Articles: DFG German National Licenses  (522)
  • 1995-1999  (522)
  • 1980-1984
  • 1996  (522)
  • Computational Chemistry and Molecular Modeling  (433)
  • Nuclear reactions
  • Numerical Methods and Modeling
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  • Articles: DFG German National Licenses  (522)
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  • 1995-1999  (522)
  • 1980-1984
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  • 1
    Electronic Resource
    Electronic Resource
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 15-31 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 4 Ill.
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  • 2
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 217-233 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 3
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 8 Ill.
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  • 4
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 341-361 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 5 Ill.
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  • 5
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 381-400 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 3 Ill.
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  • 6
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 451-461 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 7
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 897-907 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 8
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 145-170 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 9
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 235-252 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 10
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1017-1052 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 11
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1099-1120 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 12
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 363-374 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 401-424 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 6 Ill.
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  • 14
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 463-479 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 15
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 507-528 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 16
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 571-591 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 607-638 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 18
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 651-677 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 3 Ill.
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  • 19
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 187-215 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 2 Ill.
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  • 20
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 21
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 773-823 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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].
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  • 22
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 375-380 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 24
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 425-450 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 4 Ill.
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  • 25
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 959-976 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 991-1015 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1053-1072 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1091-1097 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 29
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1135-1140 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 30
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    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 31
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 857-881 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 32
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    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 33
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    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1409-1413 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1415-1431 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 35
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1445-1469 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 36
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 63-85 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 12 Ill.
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  • 37
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 171-185 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 39
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 639-649 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 40
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1-13 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 41
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 53-62 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 131-144 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 933-942 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 977-989 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 253-253 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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  • 46
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 33-51 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 1 Ill.
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    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Mathematical Methods in the Applied Sciences 19 (1996) 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 87-129 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 737-759 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
    Additional Material: 6 Tab.
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  • 51
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    Mathematical Methods in the Applied Sciences 19 (1996) 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 52
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 287-312 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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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    Mathematical Methods in the Applied Sciences 19 (1996), S. 883-896 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 909-931 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 55
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 481-505 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 555-569 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 57
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 593-605 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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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    Mathematical Methods in the Applied Sciences 19 (1996) 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Topics: Mathematics
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  • 59
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 699-716 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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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    Mathematical Methods in the Applied Sciences 19 (1996), S. 717-736 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 825-845 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1303-1316 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996) 
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    Mathematical Methods in the Applied Sciences 19 (1996) 
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    Keywords: Engineering ; Numerical Methods and Modeling
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 943-957 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996) 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1073-1090 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996) 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1141-1156 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1265-1277 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1317-1333 
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    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 72
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1397-1407 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: No Abstract
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  • 73
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1433-1444 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 74
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1471-1488 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 75
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    Mathematical Methods in the Applied Sciences 19 (1996), S. 1489-1507 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: 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.
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  • 76
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    Mathematical Methods in the Applied Sciences 19 (1996) 
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 77
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    International Journal of Quantum Chemistry 57 (1996), S. 63-71 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A new version of solutions in the form of an exponentially weighted power series is constructed for the two-dimensional circularly symmetric quartic oscillators, which reflects successfully the desired properties of the exact wave function. The regular series part is shown to be the solution of a transformed equation. The transformed equation is applicable to the one-dimensional problem as well. Moreover, the exact closed-form eigenfunctions of the harmonic oscillator can be reproduced as a special case of the present wave function. © 1996 John Wiley & Sons, Inc.
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  • 78
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    International Journal of Quantum Chemistry 57 (1996), S. 139-139 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 79
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    International Journal of Quantum Chemistry 57 (1996), S. 391-399 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The wave function of a system may be expanded in terms of eigenfunctions of the N -1 electron Hamiltonian times one-particle functions known as generalized overlap amplitudes (GOAS). The one-electron operator whose eigenfunctions are the GOAS is presented, without using an energy-dependent term as in the one-particle Green function or propagator approach. It is shown that this operator and the extended Koopmans' theorem (EKT) one-electron operator are of similar form, but perform complementary roles. The GOA operator begins with one-electron densities and total energies of N -1 electron states to generate the two-matrix and total energy of an N-electron state. The EKT operator begins with the two-matrix of an N-electron state to generate one-electron densities and ionization potentials (or approximations thereto) for N -1 electron states. However, whereas the EKT orbitals must be linearly independent, no such restriction applies to the GOAS. © 1996 John Wiley & Sons, Inc.
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  • 80
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    International Journal of Quantum Chemistry 57 (1996), S. 959-970 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Interactions of DNA bases frequently involve the DNA base amino groups. In contrast to the empirical force fields, the ab initio calculations predict nonplanar DNA base amino groups. The same conclusion also follows from the density functional theory (DFT) calculations. Both local and nonlocal density approximations were used. Optimized geometries of two other molecules with nonplanar amino groups (aniline, formamidine) are presented for comparison. The influence of nonplanar DNA base amino groups on the conformational variability of DNA is discussed. © 1996 John Wiley & Sons, Inc.
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  • 81
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    International Journal of Quantum Chemistry 57 (1996), S. 943-948 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The conformational behavior and the stability of thiazolium and thiamin diphosphate (ThDP) adducts formed by the C2 addition of the substrates pyruvate and glyoxylate to the corresponding thiamin systems are investigated within the force-field version PIMM90 as well as the semiempirical AM1 and PM3 methods. Moreover, the reaction coordinate of the decarboxylation process of the adducts with respect to the C2α(SINGLEBOND)COO- bond are calculated by PM3 and AM1. The calculations on the key intermediates of the Breslow mechanism are performed in order to study the steric aspects of both substrate adducts that show a different pathway in the catalytic cycle. The alternative structural findings for the decarboxylation products are compared with first 6-31C* studies on the corresponding thiazolium model systems. Especially, the PM3 calculations show that the elimination of CO2 is favored if the arrangement of the carboxylate group is nearly perpendicular to the plane of the thiazolium ring. These results support the least-motion maximum-overlap mechanism in the enzymatic decarboxylation reaction, proposed by Kluger. The most stable conformers of the ThDP adducts and its decarboxylation products are characterized by V-like structures and the formation of a significant intramolecular hydrogen bonding under participation of the 4′-aminopyrimidine ring. © 1996 John Wiley & Sons, Inc.
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  • 82
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    International Journal of Quantum Chemistry 57 (1996), S. 971-974 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Ab initio calculations were performed on the tautomers and conformers of N-hydroxyurea using a 6-31G** basis set. The minimum-energy structures have been found and the importance of the intramolecular hydrogen bond as the stabilizing factor was pointed out. © 1996 John Wiley & Sons, Inc.
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  • 83
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    International Journal of Quantum Chemistry 57 (1996) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 84
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    International Journal of Quantum Chemistry 57 (1996), S. 985-1018 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 85
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    International Journal of Quantum Chemistry 57 (1996), S. 975-983 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Many biological processes are characterized by an essentially quantum dynamical event, such as electron or proton transfer, in a complex classical environment. To treat such processes properly by computer simulation, allowing nonadiabatic transitions involving excited states, we recently developed a density matrix evolution (DME) method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem, 97, 13464 (1993)] which simulates the dynamics of quantum systems embedded in a classical environment. The formalism of the method is presented and an overview of the applications ranging from collisions of a quantum harmonic oscillator with noble gas atoms to proton tunneling in a double-well hydrogen bond is given. The methodology for treatment of proton-transfer processes with inclusion of excited states is presented. Future application of the method on biologically interesting processes, such as proton transfer in enzymatic reactions, is discussed. © 1996 John Wiley & Sons, Inc.
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  • 86
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    International Journal of Quantum Chemistry 57 (1996), S. 1019-1031 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: For theoretical reasons, and on account of the development of a new interpolation technique, it is useful and important to examine the asymptotic behavior of the solution to the one-dimensional Hubbard model. In this article, it is shown how perturbative expansions for the energy can be developed in the asymptotic region of the relevant coupling for all the relevant excited states of cyclic polyene rings. © 1996 John Wiley & Sons, Inc.
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  • 87
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    International Journal of Quantum Chemistry 57 (1996), S. 1049-1055 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The simple BSSE-free SCF method (CHA/F) introduced in the previous parts of this series is extended to the case of three subsystems, which may be either three weakly interacting molecules or a bimolecular system described by using bond functions. The CHA/F formalism is formulated in a more transparent manner, indicating also a straightforward way for generalization to the case of an arbitrary number of subsystems. The illustrative calculations show the viability of using the CHA/F scheme for three-component systems. © 1996 John Wiley & Sons, Inc.
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  • 88
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    International Journal of Quantum Chemistry 57 (1996), S. 1033-1048 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: One is often led, in quantum mechanics, to a perturbative solution of an eigenvalue problem, which is defined by a given Hamiltonian. The perturbative series for the energy which results will be a function of a coupling constant which appears in the Hamiltonian. In this article, the perturbative series for the energy of a state of a cyclic polyene ring which are valid for the small and large coupling limit of the model are used to construct algebraic functions. These algebraic functions are defined in terms of polynomials which are given as a function of the energy variable and coupling parameter and can be solved to give the energy as a function of coupling. It is found that relatively small polynomials give very good agreement with the exact values and that the accuracy of the results increases rapidly as the degree of the polynomial increases. The final goal of this and subsequent articles is to study energy levels in PPP models of planar conjugated hydrocarbons. In this article, we test an interpolant technique on the case of the one-dimensional Hubbard model, where an exact solution can be obtained by solving a system of nonlinear equations. In the case of the Hubbard model, the correlation effects are overestimated. Therefore, if the technique works for the Hubbard model, it is reasonable to assume that the technique would work even better for the PPP model. © 1996 John Wiley & Sons, Inc.
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  • 89
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    International Journal of Quantum Chemistry 57 (1996), S. 1057-1066 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Ising, small-bipolaron (ISB) theory is a strong-coupling theory of cuprate superconductivity which is based on the negative-U, Hubbard Hamiltonian. Its ground state is composed of (small) bipolarons and (small-bipolaron) holes with a vibronically induced, bipolaron-hole exchange interaction, JBH, between them. The energy gap, Δ(0), is taken to be equal to the dissociation energy of a small bipolaron and which, since it is defined spectroscopically, is not an order parameter. The application of the Ising mean-field theory to the highly degenerate ground-state yields a second-order phase change with kTC/2 = JBH and a real order parameter, Ω(T), which is valid over the entire temperature range from zero to TC. Near TC, the Ising free-energy functional takes the same form as does the Landau. In the presence of an electromagnetic field, the Ising functional is a generalization of the Ginzburg-Landau functional which employs a complex order parameter and which is invariant under the electromagnetic gauge transformation. The breaking of the gauge invariance yields the London theory of superconductivity. © 1996 John Wiley & Sons, Inc.
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  • 90
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    International Journal of Quantum Chemistry 57 (1996), S. 1067-1076 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solvent shift of the π* ← n transition of acetone in water, acetonitrile, and tetrachloromethane was calculated in a combined quantum mechanical - classical mechanical approach, using both dielectric continuum and explicit, polarizable molecular solvent models. The explicit modeling of solvent polarizability allows for a separate analysis of electrostatic, induction, and dispersion contributions to the shifts. The calculations confirm the qualitative theories about the mechanisms behind the blue shift in polar solvents and the red shift in nonpolar solvents, the solvation of the ground state due to electrostatic interactions being preferential in the former, and favorable dispersion interaction with the excited state, in the latter case. Good quantitative agreement for the solvent shift between experiment (+1,700, +400, and -350 cm-1 in water, acetonitrile, and tetrachloromethane, respectively) and the explicit solvent model (+1,821, +922, and -381 cm-1) was reached through a modest Monte Carlo sampling of the solvent degrees of freedom. A consistent treatment of the solvent could only be realized in the molecular solvent model. The dielectric-only model needs reparameterization for each solvent. © 1996 John Wiley & Sons, Inc.
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  • 91
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    International Journal of Quantum Chemistry 57 (1996), S. 1097-1106 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In density functional theory (DFT), a many-electron problem for the electron density in atoms may be reduced, according to the Kohn-Sham scheme, to a one-electron problem. In the present work, a variational model is proposed which leads, within some assumptions, to the set of equations describing the change of the electron density ρ and energy ε during the ionization process. It is shown that the one-electron density contributions are not necessarily spherically symmetric, but assume the symmetry which depends upon the symmetry of the positive field. A few nonspherically symmetric potentials are studied in the present article. The nonlinear differential equation for density r is formulated and solved for Coulombic, Fues-Kratzer, and Hartmann potentials. The solutions and some particular examples are presented. © 1996 John Wiley & Sons, Inc.
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  • 92
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    International Journal of Quantum Chemistry 57 (1996), S. 1107-1114 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The cycloaddition reaction of FCH(double bond)C(double bond)O and NH2CH(double bond)NH leading to 2-azetidinone was studied theoretically at the level of RHF/6-31G and RHF/6-31G*. Two possible mechanisms via a gauche or trans intermediate were compared. The obtained results show that the reaction proceeds in a gauche manner much easier than in a trans one. © 1996 John Wiley & Sons, Inc.
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  • 93
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    International Journal of Quantum Chemistry 57 (1996), S. 1077-1096 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The role of the asymptotic behavior of approximating sequences of electron densities ρn(r) in the calculation of one-electron properties is studied. Rigorous mathematical results in the frame of Hilbert spaces are used to prove the following facts: (i) Both the L2 convergence of wave functions ψn and the E convergence of the corresponding energies En guarantee the correctness of the limiting procedure limn→x ∫Ω s((overline)x(/overline)|ψn|2 d(overline)x(/overline) = ∫Ω s((overline)x(/overline))|ψ|2 d(overline)x(/overline) for the most frequently used operators s(x), Ω being any bounded region of the n-particle configuration space R3N; and (ii) the uniform boundedness of the sequence {ρn} together with both the L2 and E convergencies is sufficient to guarantee the correctness of the limiting procedure limn→x ∫∞0 s(r)ρnr2dr = ∫x0 s(r)ρr2 dr for most one-electron operators s(r) including the power moment operators rk which, for large k, are representative of the class of operators not relatively form-bounded by the Hamiltonian. The mathematical concept of uniform boundedness is used to give a characterization of the capability of {ρn} to reproduce the asymptotic behavior of the true electron density ρ and it is shown by means of numerical examples how a sequence {ρn} that does not reproduce the correct asymptotic behavior is not uniformly bounded and can give divergent expectation values of one-electron operators s(r) not relatively form-bounded by the Hamiltonian. © 1996 John Wiley & Sons, Inc.
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    International Journal of Quantum Chemistry 57 (1996), S. 1115-1119 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We performed electronic ab initio calculations of ion clusters simulating a piece of ionic crystal. Our main interest here is to estimate the (direct) energy band gap from the cluster energy levels. The model consists of a central cation surrounded by four shells of ions, with additional point charges embedding the cluster. We present results for the series of alkali halides with rock-salt structure. © 1996 John Wiley & Sons, Inc.
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  • 95
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 96
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    International Journal of Quantum Chemistry 57 (1996), S. 1133-1133 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    International Journal of Quantum Chemistry 57 (1996), S. 1131-1131 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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  • 98
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    International Journal of Quantum Chemistry 57 (1996), S. 1121-1129 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report on an isolated cluster approach to determine local electronic structures of TiO2 surfaces before and after formation of intrinsic defects, i.e., oxygen vacancies, at different crystallographic sites. In particular, isolated oxygen vacancies at bridging sites, isolated oxygen vacancies at in-plane sites and aggregated oxygen vacancies at bridging sites have been treated which lead to changes in the coordination of the adjacent Ti atoms. We find that electronic band gap states are only formed in the presence of fourfold coordinated Ti surface atoms. © 1996 John Wiley & Sons, Inc.
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  • 99
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    International Journal of Quantum Chemistry 58 (1996), S. 3-10 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The quantum dynamics of prototypical three-level metastable system under external perturbations, both time-independent and time-dependent, are studied numerically as well as analytically. The regular Rabi oscillations generated in the system under a monochromatic perturbation are shown to develop additional features when the system has a metastable state. The autocorrelation function of ψ(t) reveals nondecaying, almost quasiperiodic, behavior in such systems. The Rabi oscillations turn more complex when a bichromatic perturbation with two incommensurate frequencies is allowed to interact with the three-level system, irrespective of the presence or absence of a metastable state. A rapid decay in the autocorrelation function of the wavefunction [ψ(t)] is observed in such cases. © 1996 Wiley & Sons, Inc.
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  • 100
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    International Journal of Quantum Chemistry 58 (1996), S. 11-21 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The present knowledge of the monotonicity properties of the spherically averaged electron density ρ(r) and its derivatives, which comes mostly from Roothan-Hartree-Fock calculations, is reviewed and extended to all Hartree-Fock ground-state atoms from hydrogen (Z = 1) to uranium (Z = 92). In looking for electron functions with universal (i.e., valid in the whole periodic table) monotonicity properties, it is found that there exist positive values of α so that the function go(r; α) = ρ(r)/rα is convex, and g1(r;α) = -ρ′(r)/rα is not only monotonically decreasing from the origin but also convex. This is, however, not the case for the function g2(r; α) = ρ′(r)/rα. Additionally, the conditions which specify values for β such that the function gn(r; β) = (-1) ′ρ(n)(r)/rβ is logarithmically convex are obtained and numerically calculated for n = 0,1 in all neutral atoms below uranium. The last property is used to obtain inequalities of general validity involving three radial expectation values which generalize all the similar ones known to date, as well as other relationships among these quantities and the values of the electron density and its derivatives at the nucleus. © 1996 John Wiley & Sons, Inc.
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