bluuebunny/crossref_metadata_2025 huggingface dataset:
A distributed implementation of the finite difference time‐domain (FDTD) method
Authors: Rodohan D. P. , Saunders S. R. , Glover R. J.
Published: August 2005

The finite difference time‐domain (FDTD) method is a well known numerical technique that has been used to solve electromagnetic boundary value problems. However, the method requires large computational resources to solve a problem, restricting its use on sequential computers to small problems.

This has led to the use of expensive supercomputers in the past to solve larger problems. In this paper we first discuss existing parallel implementations of the FDTD method. We then describe an approach to compute the FDTD equations based on distributed‐ memory computer architectures. Finally we evaluate a low‐cost parallel implementation of the FDTD method that runs on a network of Workstations, utilizing spare network capacity.
Structural Analysis of Lignin by Resonance Raman Spectroscopy
Authors: Barsberg Søren , Matousek Pavel , Towrie Mike
Published: August 2005

Summary: Resonance Raman (RR) spectroscopy, combined with Kerr gated fluorescence rejection in the time domain, has recently elucidated lignin structure with unique sensitivity and selectivity. This promises structural studies of fluorescent natural macromolecules, such as lignin, which were previously not possible. Such studies rely on an improved understanding of the RR spectral behavior of lignin, which is today scarcely understood. We explain for the first time this behavior by a semi‐empirical theory, and observe its pertinent features for lignin in vascular plants. We have used well‐defined oxidative treatments as means of probing lignin structural elements, and show that RR sensitivity and selectivity depend crucially on excitation wavelength. Through the theory we relate these results to basic structural aspects of lignin. Spectra obtained by blue light laser excitation (400 nm) are dominated by low redox potential syringyl lignin groups, whereas lower photon energy (500 nm) decreases the selectivity markedly. RR bands depend on molecular structure but also on molecular environment. Thus charge transfer donor‐acceptor interactions within lignin reduce the intensity of bands associated with electron rich moieties. New possibilities for basic and selective structural information on fluorescent natural materials, such as lignin, have thus appeared.

Raman scattering in relation to typical electronic state energies of lignin structures.

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Raman scattering in relation to typical electronic state energies of lignin structures.
Terminal and Penultimate Reactivity Ratios in Single‐Site Ethene/Propene Copolymerizations: Comparison of Kakugo and Direct Peak Methods
Authors: Karssenberg Frederik G. , Wang Bing , Friederichs Nic , Mathot Vincent B. F.
Published: August 2005

Summary: The original, first‐order Kakugo method is extended to find second‐order reactivity ratios of homogeneous catalysts in ethene/propene copolymerizations based on triad fractions. Subsequently, the first‐ and second‐order reactivity ratios of eight Si‐bridged C2‐symmetric ansa‐zirconocenes or hafnocenes, as obtained by the Direct Peak method, are used to compare with the Kakugo methods. From the results it is clear that the second‐order methods give better descriptions than the first‐order methods. Only the results of the second‐order Direct Peak method are statistically justified, reflecting reliabilities >99.5%. Though the Direct Peak method in all cases gives the most reliable reactivity ratios, the second‐order Kakugo method turns out to be a practical tool to find estimates.

Second‐order Kakugo method.

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Second‐order Kakugo method.
Modeling of Shape Memory Induction and Recovery in Heat‐Shrinkable Polymers
Authors: Morshedian Jalil , Khonakdar Hossein A. , Rasouli Sorour
Published: August 2005

Summary: A mechanical model was developed to describe qualitatively and quantitatively the stress‐strain‐time behavior of a prepared shape memory crosslinked polyethylene during hot stretching, stress relaxation under 200% strain at high temperature and strain recovery of the heat shrinkable polymer. The stress‐strain, the stress relaxation and the irrecoverable strain behavior of the model were established by driving the constitutive equation, which could qualitatively represent the behavior of the real material. By choosing significant values for the parameters of the proposed model, an excellent fit was obtained between the experimental behavior of the polymer and that predicted by the model. It was also revealed that the main source responsible for the imperfect recovery of the induced strain observed was the stress relaxation occurring during the stretch holding‐cooling time step.

Stress relaxation of crosslinked polyethylene under 200% strain at 160 °C.

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Stress relaxation of crosslinked polyethylene under 200% strain at 160 °C.
Very late‐onset Friedreich's ataxia with minimal GAA1 expansion mimicking multiple system atrophy of cerebellar type
Authors: Berciano José , Infante Jon , García Antonio , Polo José Miguel , Volpini Victor , Combarros Onofre
Published: August 2005

Very late‐onset Friedreich's ataxia (VLOFA) is characterized by symptomatic onset after 40 years of age and, usually, a benign phenotype. We describe a sporadic case with onset at 53 years of age and a novel VLOFA phenotype mimicking multiple system atrophy (MSA) of cerebellar type associated with minimal GAA1 expansion. We detected several atypical features for a diagnosis of MSA, which should alert to the possibility of an inherited ataxia. © 2005 Movement Disorder Society
Case of symptomatic propriospinal myoclonus evolving toward acute “myoclonic status”
Authors: Manconi Mauro , Sferrazza Barbara , Iannaccone Sandro , Massimo Antonio , Zucconi Marco , Ferini‐Strambi Luigi
Published: August 2005

Propriospinal myoclonus is a rare motor disorder consisting of involuntary spinal‐generated muscular jerks. Here, we report a severe and uncommon case of propriospinal myoclonus that appeared after a vertebral fracture of T11. In this patient, the polysomnographic investigation showed continuing focal myoclonic activity in axial muscles during stable sleep and an acute progression into a myoclonic “status” associated with respiratory failure and loss of consciousness. It is necessary to consider this severe progression and support it with prompt emergency maneuvers and adequate pharmacotherapy. © 2005 Movement Disorder Society
Frequent sequence variation at the ETM2 locus and its association with sporadic essential tremor in Korea
Authors: Kim Jeong‐Hyun , Cho Yoon‐Hee , Kim Jeong‐Kook , Park Yong‐Gou , Chang Jin Woo
Published: August 2005

Essential tremor (ET) is the most common but a complex neurological movement disorder. ET usually affects hands, but it may also affect head, neck, face, jaw, tongue, voice, trunk and, rarely, legs and feet. Although two susceptibility loci were identified on chromosome 2p24 (ETM2) and 3q13 (ETM1 or FET1), the exact transcript(s) has not been cloned. We analyzed unrelated Korean individuals with ET for a genetic association with three reported polymorphic loci (STS‐etm1240, STS‐etm1231, and STS‐etm1234) in a candidate region on chromosome 2p24.1. We investigated sequence polymorphisms at these three loci in 30 ET patients and 30 controls using polymerase chain reaction (PCR) amplification followed by sequence analysis. Eight different sequence variants (5 at etm1234, 2 at etm1240, and 1 at etm1231) were detected from 7 patients. Of interest, sequence variants were found only in classic ET patients but not in nonclassic ET patients and healthy individuals. Additionally, we also observed that a decrease in the number of short tandem repeats within etm1234 locus is more frequent in ET patients compared to controls. Our data thus support that ET development would be linked with the ETM2 locus and will facilitate the search for the ETM2 gene transcript. © 2005 Movement Disorder Society
Unilateral contact with adherence
Authors: Point Nelly
Published: August 2005

The dissipative adhesive properties of a viscoelastic solid are investigated. An approximate problem is considered and an existence theorem is proved. Numerical computations are presented.
A Hilbert space approach to maximum entropy reconstruction
Authors: Klaus Martin , Smith Robert T.
Published: August 2005

We examine here the problem of reconstructing an X‐ray attenuation function from measurements of its integrals. The approach that is taken is to maximize the difference of the entropy and the residual error in meeting the measurements. The solution of this optimization problem is constrained by requiring that the solution lie in a certain weakly compact subset of L2, to be determined by physical information.

We show that the constrained optimization problem is well‐posed: there exists a unique solution (even when the measured data are inconsistent) and the solution depends continuously on the measurements. In the course of proving this, we show that the entropy functional is continuous on L2. We further demonstrate that the solution of the optimization problem for a special case, must be piecewise constant.
Boundary value problems for static Maxwell's equations
Authors: Urbański P.
Published: August 2005

A generalized version of magnetostatics in differentiable manifolds is formulated. Different boundary value problems are treated as different representations of the same object as graphs of self‐adjoint mappings. The Hodge theorem for a domain with the local segment property is proved.
A dual method to the collocation method
Authors: Ruotsalainen K. , Saranen J.
Published: August 2005

In this article we consider methods which are related to the collocation method by interchanging the test and the trial spaces. Error estimates are derived. As a by‐product we obtain some extensions to the known convergence results for the collocation method.
Time‐periodic solutions of wave equations on ℝ1 and ℝ3
Authors: Smiley Michael W.
Published: August 2005

The classical Paiey‐Wiener theorem and Hilbert space methods are used to show the existence of time‐periodic solutions of the wave equation wtt−wrr+λw=h, 0 < r < + ∞, which are radially symmetric and have exponential decay as r → + ∞. This problem is obtained when considering a one‐dimensional or three‐dimensional problem, and should be thought of as a linearization of a semilinear problem in which the associated linear operator has point spectrum (− ∞, λ). When λ ⩽ 0 there is uniqueness, otherwise there is a non‐trivial finite‐dimensional null space. Estimates on w, wt, wr are obtained, which show that in either case there is a continuous correspondence h → w, where w is a uniquely characterized solution.
Initial boundary value problems in one‐dimensional non‐linear thermoelasticity
Authors: Racke Reinhard
Published: August 2005

The local existence of classical smooth solutions to the equations of homogeneous non‐linear thermoelasticity in one space dimension is proved for the physically reasonable Dirichlet boundary conditions for both bounded and unbounded domains assuming smooth data.
The optimal stability estimate for some ill‐posed Cauchy problems for a parabolic equation
Authors: Knabner Peter , Vessella Sergio
Published: August 2005

In this paper we consider the non‐characteristic Cauchy problem ut−a(x)uxx−b(x)ux−c(x)u = 0, x ∈ (0, l), t ∈ I, u(0, t) = φ(t), ux(0, t) = 0, t ∈ I, where I = ℝ or I = ℝ+ and u(x, 0) = 0, x ∈ [0, l], in the case I = ℝ+. Assuming an a priori bound for ‖u(l,.)‖, we derive the exact Hölder type dependence of on ‖u(x,.)‖ on ‖φ‖.
On the principles of limiting absorption and limit amplitude for a class of locally perturbed waveguides. Part 2: Time‐dependent theory
Authors: Morgenröther K. , Werner P.
Published: August 2005

In part 1

Math. meth. in the Appl. Sci, 10, 125–144 (1988).

we studied the principle of limiting absorption for local perturbations Ω of the n‐dimensional domain Ω0 = ℝn−1 × (0, π). In this second part we extend our investigations to the time‐dependent theory and show that absence of admissible standing waves implies the validity of the principle of limiting amplitude for every frequency ω≥0 if n ≠ 3 and for ω ≠ 2, 3,… if n = 3, respectively. In particular, the principle of limiting amplitude holds for every ω≥0 in the case n ≠ 3 and for every ω ≠ 2, 3,… in the case n = 3 if Ω≠Ω0 and ν·x′ ⩽0 on ∂Ω, where x′ = (x1,…, xn−1, 0) and ν is the normal unit vector on ∂Ω pointing into the complement of Ω This result stands in remarkable contrast to the fact that both principles are violated in the case of the unperturbed domain Ω0 at the frequencies ω = 1, 2,… if n⩽3. The question of the asymptotic behaviour of the solution as t→∞ for n = 3 and ω = 2, 3,… will be discussed in two subsequent papers.
A free boundary problem of biological interest
Authors: Colli Pierluigi , Visintin Augusto , Hadeler K. P.
Published: August 2005

During fertilization of certain echinoderms, a long actin‐filled tube is extended by the sperm towards the interior of the egg. This yields a parabolic free boundary problem, which differs from the classical one‐phase Stefan problem by the presence of a convective term in the partial differential equation, and because the equilibrium interface condition θ(s(t),t) = 0 is here replaced by a kinetic law s′(t) = vθ(s(t),t). This problem is set in variational form and the existence of a solution is proved by means of a Faedo–Galerkin approximation procedure.
Stability of linear systems of differential equations with variable structure and impulse effect
Authors: Milev N. V. , Bainov D. D. , Roach G. F.
Published: August 2005

In the present paper sufficient conditions for stability of the solutions of linear systems of differential equations with variable structure and impulse effect are found.
Threshold phenomena for the first initial boundary value problem of the FitzHugh–Nagumo equations
Authors: Weixi Shen , Roach G. F.
Published: August 2005

Under biologically reasonable assumptions the threshold phenomena for the first initial boundary value problem of FitzHugh–Nagumo equations is proved.
Existence and stability of travelling waves in fixed‐bed reactors
Authors: Knöpp Ulrich , Eckhaus W.
Published: August 2005

The model equations of the catalytic fixed‐bed reactor often possess solutions in the form of travelling wave fronts similar to the well‐known case of Fisher's equation. The mathematical investigation of these waves requires searching for solutions of singular boundary value problems in the phase plane or in the three‐dimensional phase space. In this paper necesary and sufficient conditions are derived which are to be satisfied by the model parameters and the propagation velocity of the wave front if wave solutions exist. Moreover, sufficient conditions for the asymptotic stability of these solutions are proved where the perturbations are supposed to belong to a certain weighted L2‐space. Finally, the connection between the initial distribution of the state variable and the velocity of the wave is discussed.
Properties of far‐field operators in acoustic scattering
Authors: Kirsch A. , Hsiao G. C.
Published: August 2005

The far‐field operator for an exterior boundary value problem for the Helmholtz equation maps the boundary data onto the far‐field pattern of the solution. This paper computes the L2‐adjoint of this operator for various choices of boundary conditions. In scattering theory the boundary data are given by the traces of plane waves. We characterize the closure of the span of the images of these plane waves under the far field operator.

Finally, the results are extended to more general topologies including Sobolev and Hölder norms.
Duality theorems in some overdetermined boundary value problems
Authors: Payne L. E. , Schaefer Philip W.
Published: August 2005

We consider several elliptic boundary value problems for which there is an overspecification of data on the boundary of the domain. After reformulating the problems in an equivalent integral form, we use the alternate integral formulation to deduce that if a solution exists, then the domain must be an N‐ball. Various Green's functions and classical boundary value problems of second, fourth and higher order are included among the problems considered here.
A constructive method for solving the displacement boundary‐value problem of elastostatics by use of global basis systems
Authors: Freeden Willi , Reuter Richard
Published: August 2005

In this paper we are concerned with the three‐dimensional homogeneous isotropic elastostatic boundary‐value problem. Global basis vector fields are shown to be constructive structures for approximating the solution. The theoretical tool is a regularity condition developed from the classical integral equation approach. The paper ends with some reflections on the practical computability and numerical applicability.
Continuous dependence on data for solutions of a conducting dusty gas model backwards in time
Authors: Calmelet‐Eluhu Colette , Crooke Philip
Published: August 2005

A conducting dusty gas flow in the presence of a given applied magnetic field is modelled by an initial boundary value problem. The continuous dependence of solutions backward in time to this model is studied. The electric and induced magnetic fields are assumed to be negligible and the dust particles are non‐conducting. A uniqueness result is also derived.
Regularity of mixed boundary value problems in ℝ3and boundary element methods on graded meshes
Authors: Von Petersdorff T. , Stephan E. P.
Published: August 2005

The solution of the three‐dimensional mixed boundary value problem for the Laplacian in a polyhedral domain has special singular forms at corners and edges. A ‘tensor‐product’ decomposition of those singular forms along the edges is derived. We present a strongly elliptic system of boundary integral equations which is equivalent to the mixed boundary value problem. Regularity results for the solution of this system of integral equations are given which allow us to analyse the influence of graded meshes on the rate of convergence of the corresponding boundary element Galerkin solutions. We show that it suffices to refine the mesh only towards the edges of the surfaces to regain the optimal rate of convergence.
A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
Authors: Costabel Martin
Published: August 2005

Let u be a vector field on a bounded Lipschitz domain in ℝ3, and let u together with its divergence and curl be square integrable. If either the normal or the tangential component of u is square integrable over the boundary, then u belongs to the Sobolev space H1/2 on the domain. This result gives a simple explanation for known results on the compact embedding of the space of solutions of Maxwell's equations on Lipschitz domains into L2.
Non‐linear flexings in a periodically forced floating beam
Authors: Lazer A. C. , McKenna P. J.
Published: August 2005

This paper considers periodic flexing in a floating beam, in the presence of a small periodic forcing term. The beam is considered as a vibrating beam with the free‐end boundary condition, in the presence of an additional restoring force due to flotation, which becomes zero as soon as the beam lifts out of the water. The equation is therefore non‐linear. A theorem is proved which shows that in the presence of small periodic forcing terms, both small‐ and large‐amplitude solutions can exist. Numerical evidence is presented, which shows that the large‐amplitude solutions are stable over a wide range of frequency and amplitude, and suggests a cusp‐like surface for the multiple solutions.
A half‐space problem for a non‐linear Boltzmann equation arising in semiconductor statistics
Authors: Poupaud F.
Published: August 2005

In semiconductors the distributions of electrons satisfy a non‐linear Boltzmann–Vlasov equation. We consider the half‐space problem arising in the study of boundary layers when the mean free path tends to zero. We prove the existence and the uniqueness of the solution for any prescribed entering distribution. We establish that this solution tends towards a Fermi–Dirac distribution exponentially fast.
An artificial boundary condition for an advection–diffusion equation
Authors: Lohéac Jean‐Pierre
Published: August 2005

Consider the advection–diffusion equation: u1 + aux1 − vδu = 0 in ℝn × ℝ+ with initial data u0; the Support of u0 is contained in ℝ(x1 < 0) and a: ℝn → ℝ is positive. In order to approximate the full space solution by the solution of a problem in ℝ × ℝ+, we propose the artificial boundary condition: u1 + aux1 = 0 on ∑. We study this by means of a transmission problem: the error is an O(v2) for small values of the viscosity v.
Resonances in periodic media
Authors: Werner P.
Published: August 2005

We study the propagation of linear acoustic waves (a) in an infinite string with a periodic material distribution, (b) in an infinite cylinder with a meterial distribution that is periodic in the longitudinal direction and does not depend on the transverse coordinates. We assume that the wave field is generated by a time‐harmonic force distribution of frequency ω acting in a compact set. We show in both cases that resonances of order t1/2 occur for a discrete set of frequencies and that the solution is bounded as t→∞ for the remaining frequencies. In case (a) ω is a resonance frequency if and only if ω2 is a boundary point of one of the spectral bands of the corresponding spatial differential operator of Hill's type. A similar characterization of the resonance frequencies is given in case (b).
Optimal control of thermomechanical phase transitions in shape memory alloys: Necessary conditions of optimality
Authors: Brokate Martin , Sprekels Jürgen
Published: August 2005

The necessary conditions for the optimality of an optimal control problem associated with soiid–solid phase transitions in shape memory alloys are established.
Differential stability of solutions to parametric optimization problems
Authors: Rao Murali , Sokolowski Jan
Published: August 2005

A method for the differential stability of solutions to a class of solutions to a class of parametric optimization problem is prposed. Any solution of the parametric optimization problem is given as a fixed point of the metric projection onto the set of admissible coefficients. A new result on the differential stability of the metric projection in Sobolev space H2(Ω)onto a set of admissible parameters is obtained. The stability results with respect to perturbations of observations for the solutions to a coefficient estimation problem for a second‐order elliptic equation are derived.
Charge transport in semiconductors with degeneracy effects
Authors: Poupaud Frédéric , Schmeiser Christian
Published: August 2005

It has been a common procedure to derive a model for charge transport in degenerate semiconductor material by incorporating a Fermi–Dirac distribution into the classical drift–diffusion model. In this work a Boltzmann equation with a non‐linear collision term is considered. A new fluid dynamical model is derived by considering small perturbations of the thermal equilibrium. The analysis contains an existence and uniqueness proof for the Boltzmann equation, a justification of the perturbation argument and a study of initial boundary value problems for the new fluid dynamical model.
On a class of ill‐posed non‐linear integral equations arising in the interpretation of indirect measurements
Authors: Hofmann Bernd
Published: August 2005

In this paper we consider a class of specific Urysohn integral equations for which the solutions are only determined with the exception of rearrangements of function values and associated arguments. As an alternative to Tikhonov's regularization method approximating minimum‐norm solutions for this ill‐posed class of inverse problems, a constrained least‐squares approach is presented. This approach is aimed at finding decreasing rearrangements serving as appropriate solution representatives. It is shown that the inverses of these decresing solutions solve a Fredholm linear integral equation of the first kind.
On the linear piezoelectricity of composite materials
Authors: Turbé N. , Maugin G. A.
Published: August 2005

From the equations of the linear piezoelectricity for a composite material with a periodic structure we derive the dynamical solution by means of Bloch expansion techniques. This expression techniques. This expression allows, as a limit case, a comparison with the homogenization method, and the macroscopic coefficients are also deduced.
Time decay of solutions of semilinear strongly damped generalized wave equations
Authors: Biler Piotr
Published: August 2005

We study the asymptotic behaviour in time of the solutions of dissipative perturbations of wave‐type equations in ℝN, utt + But + Au + G(u) = 0, with commuting positive operators A, B and a power like non‐linearity G(u). First we give some (pseudo) conformal invariants of the linear operator in the equation. This allows us to derive optimal decay rates for the solutions of the linearized problems. We then prove some decay estimates for the non‐linear problems using the tools of scattering theory and the aforementioned conformal invariants.
Generalized limiting absorption method and multidimensional inverse scattering theory
Authors: Weder Ricardo
Published: August 2005

We generalize the classical limiting absorption method. This generalization is applied to the study of the Faddeev–Lippmann–Schwinger equations in the Faddeev–Newton approach to multidimensional inverse scattering theory. In particular, we give a new proof, under more general conditions than were known previously, of the absence of exceptional points for small potentials and large values of the parameters, and on the existence of real exceptional points if there are complex ones, in particular for potentials that produce negative eigenvalues.
Wiener‐hopf equations for waves scattered by a system of parallel sommerfeld half‐planes
Authors: Meister E. , Rottbrand K.
Published: August 2005

A scalar time‐harmonic wave (governed by Helmholtz's equation) impinges on N semi‐infinite half‐planes. The scattered field is sought when first, second, and third‐kind boundary conditions or even general linear transmission conditions on the plates ∑m and their complementary parts ∑ are prescribed. Making use of the Fourier transform a representation formula for H1 (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)‐Wiener–Hopf (WH) system for jumps of the Dirichlet–and Neumann–Cauchy data across the semi‐infinite screens ∑m. The (2N × 2N)‐Fourier symbol matrix 𝔖𝒫 contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)‐symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑m.
On mathematical modelling of absorption and dispersion of seismic waves for low frequencies
Authors: Von Wolfersdorf L. , Rost L.
Published: August 2005

The problem of determining the dispersion and absorption of plane seismic waves by a given seismic quality factor is dealt with in the case that the quality factor tends to a positive limit as the frequency goes to zero.

General formulae are derived for the phase velocity and the attenuation coefficient by solving the corresponding Riemann–Hilbert problems for analytic functions in the upper half‐plane.
Green's contact functions for heat conduction of two half‐spaces and half‐planes with application to several boundary contact problems
Authors: Jentsch Lothar
Published: August 2005

Green's contact functions are constructed for two half‐spaces and two half‐planes for materials with different thermal conductivities. With the aid of these contact functions some bimetal problems are reduced to boundary integral equations along the outer boundary where only the boundary conditions are to be satisfied. The boundary integral operators are investigated in the plane case. They are Fredholm operators with index zero. The asymptotics of the density of the potentials, which depends on the material parameters and on the angles between the contact line and the outer boundary, is determined by the Mellin transform technique.
Time delay and finite differences for the non‐stationary non‐linear Navier–Stokes equations
Authors: Varnhorn Werner
Published: August 2005

In the present paper we use a time delay ϵ > 0 for an energy conserving approximation of the non‐linear term of the non‐stationary Navier–Stokes equations. We prove that the corresponding initial‐value problem (Nϵ) in smoothly bounded domains G ⊆ ℝ3 is well‐posed. We study a semidiscretized difference scheme for (Nϵ) and prove convergence to optimal order in the Sobolev space H2(G). Passing to the limit ϵ→0 we show that the sequence of stabilized solutions has an accumulation point such that it solves the Navier–Stokes problem (No) in a weak sense (Hopf).
Global solution to the Cauchy problem in non‐linear hyperbolic thermoelasticity
Authors: Gawinecki Jerzy
Published: August 2005

We prove the existence of global solutions for small data to the initial value problem for the non‐linear hyperbolic system of partial differential equations describing a thermoelastic medium in a three‐dimensional space under the assumption that the coefficients in the non‐linear terms are smooth functions of their arguments and behave like 0(∣η∣) for k0 ≥ 2 near the origin. The asymptotic behaviour of the solution as t → ∞ is also described.
Global existence of thermomechanical processes in non‐linear thin rods under velocity feedbacks
Authors: Sprekels Jürgen
Published: August 2005

We study boundary velocity feedbacks to damp the transverse deflections of heat‐conducting thin rods with on‐linear stress‐strain relations that may be both non‐monotone and temperature dependent. It is shown at for suitable feedback laws global solutions exist.
Iterative continuous maximum‐likelihood reconstruction method
Authors: Mülthei H. N.
Published: August 2005

In this paper we continue our studying of the iterative maximum‐likelihood reconstruction method. We consider only the continuous case and show some convergence properties of the algorithm. In the discrete case convergence has already been proved. An example demonstrating divergence of the iterative method shows how to handle the continuous case.
Exponential attractors for non‐autonomous systems: Long‐time behaviour of vibrating beams
Authors: Feireisl Eduard
Published: August 2005

We introduce the concept of exponential attractor for non‐autonomous systems. Then we prove the existence and finite dimensionality of the attractor for the model equation magnified image where K and f are quasiperiodic in time.
Regularized inner products of distorted plane waves and near‐forward inverse scattering
Authors: Kurylev Yaroslav V.
Published: August 2005

Regularized inner products, r(s, e1, e2,) of the distorted plane waves fór the plasma wave equation uu − Δu + qu = 0 are introduced for potentials with compact support. The regularized inner product may be represented in terms of the far‐field pattern. The use of the WKB approximation shows that the behaviour of r as e2 → − e1 is closely related to the Radon transform of q. This observation indicates the possibility of finding the Radon transform of q in terms of r(s, e1, e2) and then of recovering q by means of the inverse Radon transform.
An extended equivariant branching theory
Authors: Allgower Eugene L. , Böhmer Klaus , Zhen Mei
Published: August 2005

Recent monographs and research articles have demonstrated that the highly complicated bifurcation structure, which usually arises in the presence of high symmetries, can often be systematically reduced with group theoretic concepts. Equivariant branching theorems and bifurcation subgroups have been the principle tools in this direction of investigation. The generalizations that we give allow the discussions of new classes of problems and the weakening of the usual hypotheses of absolute irreducibility of the group representation or of the appropriate subspaces. These extensions are illustrated in the case of a class of planar semilinear elliptic partial differential equations, which are usually treated as model problems in fluid mechanics and chemical reactions.
On the fundamental solutions of the operators of S. Timoshenko and R. D. Mindlin
Authors: Ortner Norbert , Wagner Peter
Published: August 2005

Our recent paper about some new fundamental solutions is complemented by a representation of the fundamental solution of certain evolution operators of fourth order in terms of a family of fundamental solutions of operators of second order. By applying this to the operators of vibrating beams and plates we deduce representations of their fundamental solutions as simple definite integrals over tabulated functions.
Numerical solution of a time‐like Cauchy problem for the wave equation
Authors: Klibanov Michael , Rakesh
Published: August 2005

Let D ⊂ ℝn be a bounded domain with piecewise‐smooth boundary, and q(x,t) a smooth function on D × [0, T]. Consider the time‐like Cauchy problem
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Given g, h for which the equation has a solution, we show how to approximate u(x,t) by solving a well posed fourth‐order elliptic partial differential equation (PDE). We use the method of quasi‐reversibility to construct the approximating PDE. We derive error estimates and present numerical results.
Abstract Besov space approach to the non‐stationary Navier–Stokes equations
Authors: Kobayashi Takayuki , Muramatu Tosinobu
Published: August 2005

The local existence, uniqueness and regularity of solutions of the initial‐value problem for non‐stationary Navier–Stokes equations are studied via abstract Besov spaces. The assumptions about Ω the initial data and the external force are improved on by rather simple proofs.
Inhomogeneous Timoshenko beam equations
Authors: Arosio Alberto , Panizzi Stefano , Paoli Maria Gabriella
Published: August 2005

The so‐called Timoshenko beam equation is a good linear model for the transverse vibrations of a homogeneous beam. Following the variational approach of Washizu, the governing equation is deduced in the case when the physical/geometrical parameters of the beam vary along its axis. The equation may not be studied by means of the iterated use of Fourier series. However, a convenient change of variables permits us to prove the well‐posedness of the associated Cauchy problem for a beam with sliding ends (the solution is intended in a mild sense). The proof is given in an abstract framework.
Analysis of the thermoelastic model of a plate with non‐linear shape memory alloy reinforcements
Authors: Hoffmann K.‐H. , Zochowski A.
Published: August 2005

In this paper we study the questions of the existence and uniqueness of the solutions for a thermoelastic system of equations magnified image magnified image in a two‐dimensional domain, where both the viscosity v and the rigidity D are positive. It seems that such a system has up to now been considered in a one‐dimensional setting only. The change of dimensions enforces the growth conditions with respect to θ and the additional regularity of the data. The existence of solutions in the case of the Neumann boundary conditions for θ and some weak regularity of data is proved. Under stronger regularity conditions the uniqueness is also established. The system has an interpretation as a plate reinforced by a shape memory alloy (SMA) wire mesh.
Dynamic MRI reconstruction as a moment problem
Authors: Zwaan M.
Published: August 2005

This paper deals with some mathematical aspects of magnetic resonance imaging (MRI). MRI is used in diagnostic medicine to measure and display the cross section of, for example, a human organ. In this paper we formulate the MRI‐reconstruction problem and solve it aftèr restating it as a moment problem in a Hilbert space.
Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shell
Authors: Tan Nguyen Xuan
Published: August 2005

The purpose of this paper is to study bifurcation points of the equation T(v) = L(λ,v) + M(λ,v), (λ,v) ϵ Λ × D in Banach spaces, where for any fixed λ ϵ Λ, T, L(λ,·) are linear mappings and M(λ,·) is a nonlinear mapping of higher order, M(λ,0) = 0 for all λ ϵ Λ. We assume that λ is a characteristic value of the pair (T, L) such that the mapping T – L(λ,·) is Fredholm with nullity p and index s, p > s ⩾ 0. We shall find some sufficient conditions to show that (λ,0) is a bifurcation point of the above equation. The results obtained will be used to consider bifurcation points of the axisymmetric buckling of a thin spherical shell subjected to a uniform compressive force consisting of a pair of coupled non‐linear ordinary differential equations of second order.
Low Reynolds number deformation of compound drops in shear flow
Authors: Power Henry
Published: August 2005

The method developed by Rallison and Acrivos (1978) to solve the deformation of a single drop due to exterior shear flow for a small Reynolds number is extended to the problem of the deformation of a compound drop. The result is found in terms of a Fredholm integral equation of the second kind, which is shown to have a unique solution and the solution is given by means of a uniformly convergent Neumann series.
Finite deformation of an elasto‐plastic soil
Authors: Carter J. P. , Booker J. R. , Davis E. H.
Published: August 2005

Presented in this paper is a formulation and a numerical solution method for problems which involve finite deformations of an elasto‐plastic material. The governing equations are cast in rate form and the constitutive laws are formulated in a frame indifferent manner. Particular reference is made to the finite deformation of soil. Plastic failure is described by a general yield condition and plastic deformation by an arbitrary flow rule. Several examples are treated numerically.
Visco‐plastic behaviour during the excavation phase of a salt cavity
Authors: Fossum Arlo F.
Published: August 2005

The stress field and flow characteristics are studied for a cavity with the shape of a prolate spheroid in dome salt with emphasis given to the excavation phase. A semi‐empirical creep law is derived from thermodynamic principles and experimental results. In this paper, an elementary non‐linear form is used in the kinetic relation. A finite element solution procedure is discussed which incorporates the creep law, excavation sequence, and arbitrary non‐homogeneous initial stress field.
Stability analysis of a jointed beam
Authors: Chugh Ashok K.
Published: August 2005

A numerical step‐by‐step procedure, analogous to the ‘Initial Stress Method,’ is presented for the analysis of a single‐layer jointed rock beam subjected to gravity loads and in‐plane in situ formation pressure. The joints are permitted to open at locations where the flexural stresses exceed flexural strength. The material properties may be different for each rock block and joint. A detailed algorithm is given for the solution of the problem. The results of several analyses indicating the relative effects of initial formation pressure, transverse load, stiffness of the joint material, and joint spacing on the response of a jointed beam are presented. The convergence characteristics of the numerical procedure are included. The joint material is assumed to be ‘no‐tension’ type. Both the geometric and material non‐linear effects are considered.
A case study of the surface subsidence of the Polesine area
Authors: Schrefler B. A. , Lewis R. W. , Norris V. A.
Published: August 2005

The Polesine, a region in the northeast of Italy, has experienced considerable surface subsidence due to the withdrawal of water and gas from the underlying reservoir sediments. These settlements have been well documented and form the basis of a comparison study with a finite element consolidation model. It is shown that the model is capable of simulating the field behaviour during production and also after the closure of the wells.
The economic analysis of raft foundations
Authors: Wood L. A.
Published: August 2005

An approximate method, using a simplified soil model, for predicting the behaviour of raft foundations subjected to applied vertical forces and moments will be outlined. Results obtained for circular rafts of finite rigidity are compared with those obtained, from more rigorous solutions, by other authors. Satisfactory agreement is obtained for the surface settlements and raft bending moments over a wide range of soil inhomogeneity. Finally, the versatility of the method of analysis is illustrated for an unusual asymmetrical structure. Computed total and differential settlements are shown to be in reasonable agreement with measured values and those predicted by an independent plane strain finite element analysis.
A three‐dimensional deformation analysis of the Storvass dam
Authors: Martin H. L.
Published: August 2005

A three‐dimensional finite element program is used to analyse an 80 m high rockfill dam. An analysis is made of the deformed shape of the dam and the internal stresses and strains due to reservoir filling.
Associated and non‐associated constitutive relations for undrained behaviour of isotropic soft clays
Authors: Banerjee P. K. , Stipho A. S.
Published: August 2005

Incremental theory of plasticity has been used to derive associated and non‐associated stress–strain relations for analysing the undrained stress‐strain response of isotropic normally and lightly overconsolidated clays. A series of comparisons between the theoretical stress‐strain‐pore pressure response and laboratory test results for 3 in. × 6 in. samples of very high degree of repeatability and reproduceability have been described. From these comparisons it can be seen that both the associated and, non‐associated Cam clay models appear to give consistently the best correlations between the theoretical results and the experimental observations.
The response of a deep rigid anchor due to undrained elastic deformations of the surrounding soil medium
Authors: Selvadurai A. P. S.
Published: August 2005

The equations governing the undrained linear elastic behaviour of a saturated soil are formally similar to the equations governing slow of an incompressible Newtonian viscous fluid. This principle of equivalence can then be effectively employed to obtain the load‐deflection reiationship for a deep rigid anchor with the shape of a solid of revolution which is embedded in bonded contact with an unbounded incompressible elastic medium. It is found that the load‐deflection relationship for the deep rigid anchor can be directly recovered from the expression for the drag induced on an impermeable object with the same size and shape as the anchor, which is appropriately placed in a slow viscous flow region of uniform velocity.
Slipping strip analysis of reinforced earth
Authors: Naylor D. J. , Richards H.
Published: August 2005

Reinforced earth in plane strain is idealized as a homogeneous material with the strips attached to the elastic soil matirx by a conceptual shear zone. A ‘no‐slip’ finite element model is derived by assigning a large shear modulus to the shear zone. Relaxation of this modulus using a tangential stiffness algorithm in conjunction with a Mohr–Coulomb strip‐slip criterion allows slipping to be simulated.

The finite element formulation is validated and the finite element discretization assessed by comparisons against exact solutions for a simple test problem.

An idealized reinforced earth wall example is used to demonstrate the feasibility of the method and to answer the question: ‘is slipping significant?’ The method is shown to be potentially useful, and slipping is shown to be significant.
Non‐linear seismic response and liquefaction
Authors: Zienkiewicz O. C. , Chang C. T. , Hinton E.
Published: August 2005

The essential cause of the growth of pore pressure during cyclic loading is identified as an ‘autogenous’ shrinkage or densification of the solid phase of the soil and this is related to a strain path parameter. Introduction of this ‘shrinkage’ coupled with an elasto‐plastic behaviour of the soil skeleton allows a full non‐linear dynamic analysis to be conducted up to the point of structural failure for any earthquake input. Explicit time marching procedures are used. The procedure outlined is applicable to all problems of complex geometry and for conditions of undrained or partially drained behaviour at a moderate computational cost.
A numerical solution of an irrigation flowfield
Authors: Bruch John C.
Published: August 2005

Two‐dimensional seepage from an array of triangular channels into permeable soil underlain at a finite depth by a drain has been solved by using the Baiocchi method. The use of this approach allowed a simple formulation of the seepage problem through extension of the solution region to an a priori known region. The new problem was treated numerically by using the S.O.R. method combined with projection. This technique proved to be very accurate when compared with analytical results and efficient from a computer programming standpoint.
Analytical studies of pile wandering during installation
Authors: Burgess I. W.
Published: August 2005

In a previous paper it was established with very simple assumptions that piles might undergo a directional instability during placement, of a type more usually found in aerodynamic problems. The study is here extended to piles driven into soils whose shear strength and lateral reaction modulus can vary with depth. The analysis consists of a parametric study of the effect of linear variation of the soil parameters with depth on the critical lengths for instability, and a comparison of site evidence with the critical lengths obtained from a stepwise‐constant representation of the variation of soil parameters with depth. The theory is shown to give very reasonable estimates of the depths at which major deviation starts, although there is a pressingneed for more detailed site and laboratory data.
The analysis of finite elasto‐plastic consolidation
Authors: Carter J. P. , Booker J. R. , Small J. C.
Published: August 2005

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto‐plastic soil subject to finite deformations. The soil is assumed to be a two‐phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto‐plastic skeleton which obeys a Morh–Coulomb yield criterion and a non‐associated flow law.
Observed and predicted test pile behaviour
Authors: Ottaviani Mario , Marchetti Silvano
Published: August 2005

The results obtained from a loading test on a bored, cast‐in‐place pile instrumented with six pairs of load cells at different levels are compared with the results obtained from a non‐linear finite element analysis based on the geotechnical parameters of the cohesive soils in which the pile was bored.

Settlements computed using deformability parameters obtained by a standard laboratory test were much larger than the measured settlements. Satisfactory results are instead obtained assuming Ei=1000cu and cα=cu.

The distribution of the vertical stresses within the pile and of the shear stresses in the soil adjacent to the pile obtained by the numerical analysis are compared with the measured values.

A fair agreement is found at loads below failure but differences between experimental and computed values are found at loads close to failure.
An algorithm and a modular subroutine for the CAP model
Authors: Sandler I. S. , Rubin D.
Published: August 2005

A cap model algorithm and the associated FORTRAN subroutine, CAP, are presented. The algorithm lends itself to a wide range of soil and rock cap models, and can easily be incorporated into most dynamic codes. The routine permits the user to obtain flexibility with respect to changes in functional forms and parameters with minor coding changes.