bluuebunny/crossref_metadata_2025_split huggingface dataset:
Linear stability condition for explicit Runge–Kutta methods to solve the compressible Navier‐Stokes equations
Authors: Müller Bernhard 
Published: August 2005

AbstractA linear stability condition is dervied for explicit Runge–Kutta methods to solve the compressible Navier–Stokes equations by central second‐order finite‐difference and finite‐volume methods. The equations in non‐conservative form are simplified to quasilinear form, and the eigenvalues of the resulting coefficient matrices are determined for general co‐ordinates. Assuming a well‐posed Cauchy problem with constant coefficients, the von Neumann stability analysis yields sufficient stability conditions for viscous–inviscid operator‐splitting schemes. They have been applied in computational aerodynamics to solve the compressible Navier–Stokes equations by an unsplit explicit Runge–Kutta finite‐volume method.
Singular integral equations applied to free surface seepage from non‐linear channels
Authors: Oestreich Dieter 
Published: August 2005

AbstractThe problem of two‐dimensional seepage from a non‐linear channel through a homogeneous medium underlain at a finite depth by a drain will be considered. A new approach is given, transforming the seepage problem to a non‐linear singular integral equation for which the unique existence of the solution is proved. The free boundaries of the seepage region can be described explicitly.
An adapted Galerkin method for the resolution of Dirichlet and Neumann problems in a polygonal domain
Authors: Bourlard Maryse , Nicaise Serge , Paquet Luc 
Published: August 2005

AbstractThe Neumann problem for Laplace's equation in a polygonal domain is associated with the exterior Dirichlet problem obtained by requiring the continuity of the potential through the boundary. Then the solution is the simple layer potential of the charge q on the boundary. q is the solution of a Fredholm integral equation of the second kind that we solve by the Galerkin method. The charge q has a singular part due to the corners, so the optimal order of convergence is not reached with a uniform mesh. We restore this optimal order by grading the mesh adequately near the corners. The interior Dirichlet problem is solved analogously, by expressing the solution as a double layer potential.
A uniqueness condition for the polyharmonic equation in free space
Authors: Lesky P. 
Published: August 2005

AbstractConsider the polyharmonic wave equation ∂u + (− Δ)mu = f in ℝn × (0, ∞) with time‐independent right‐hand side. We study the asymptotic behaviour of u (x, t) as t → ∞ and show that u(x, t) either converges or increases with order tα or In t as t → ∞. In the first case we study the limit \documentclass{article}\pagestyle{empty}\begin{document}$ u_0 \left({\bf x} \right) \colone \mathop {\lim }\limits_{t \to \infty } \,u\left({{\bf x},t} \right) $\end{document} and give a uniqueness condition that characterizes u0 among the solutions of the polyharmonic equation ( − Δ)mu = f in ℝn. Furthermore we prove in the case 2m ⩾ n that the polyharmonic equation has a solution satisfying the uniqueness condition if and only if f is orthogonal to certain solutions of the homogeneous polyharmonic equation.
Junction between a 3‐D Stokes flow and a 2‐D thin film with pressure boundary conditions
Authors: Bayada G. , Chambat M. 
Published: August 2005

AbstractA 3‐D Stokes equation modelling the flow in the inlet region of a lubricated device is studied. Boundary conditions on both the pressure and the velocity are considered. The geometry induces that the flow region is divided into two parts: the first one is a thin gap with height ϵh, where a change of scale is performed, and the second one is a cavity whose dimensions are large with respect to ϵ. Two equivalent variational formulations are proposed and lead to accurate a priori estimates. The resulting asymptotic equation for the pressure in the thin gap is the currently used Reynolds equation, whose boundary conditions are obtained via the junction with the 3‐D cavity. Both hydrostatic and hydrodynamic cases are considered.
The three‐dimensional wigner‐poisson problem: Existence, uniqueness and approximation
Authors: Brezzi Franco , Markowich Peter A. 
Published: August 2005

AbstractWe prove the existence of a unique, global classical solution of the quantum Vlasov–Poisson problem posed on the phase space ℝ × ℝ. The proof is based on a reformulation of the quantum Vlasov–Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger‐Poisson problem is first analysed on a bounded domain in ℝ and the solution of the whole‐space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ℝ.
Dynamical shape control and the stabilization of non‐linear thin rods
Authors: Sokolowski J. , Sprekels J. 
Published: August 2005

AbstractIn this paper we consider the problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well‐posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived. The theory applies to materials where the stress–strain relation is both non‐linear and non monotone, so that hysteresis effects arising from solid–solid phase transitions in the rod are included.
On the mildly degenerate Kirchhoff string
Authors: Arosio A. , Garavaldi S. 
Published: August 2005

AbstractLet us consider the Cauchy problem for the abstract evolution equation, which describes the Kirchhoff sring
u″ + m(〈Au, u〉) Au = 0, (t > 0),
Where ( )′ = d/dt, A is any symmetric isomorphism of a Hilbert space V into its (anti) dual V′ and m is a function of one real variable. Following physical considerations, we allow m(·) to be any non‐decreasing, non‐negative continuous function (a degenerate Kirchhoff string).We assume that the initial value u0 satisfies: m(〈Au0, u0〉)>0 (a mildly degenerate Kirchhoff string), that m is locally Lipschitz continuous in the open region where it does not vanish, and that m has a finite order of vanishing (e.g., m(ρ) = ργ, γ > 0).We establish the local well‐posedness of the Cauchy problem in the class D(Aα/2) × D(A(α−1)/2), For each α ⩾ 3/2. This improves the results of Medeiros and Miranda [15], Ebihara et al.[9] and a result of Yamada [27].We are not able to prove the global existence of the solution; however, we provide a lower estimate for the life span of the solution, which yields the almost global existence (AGE) in the case when m(ρ) = ργ (γ>0).
A uniqueness theorem in the dynamical theory of piezoelectricity
Authors: Morro A. , Straughan B. 
Published: August 2005

AbstractThe solution to the linearized equations of dynamical linear piezoelectricity is shown to be unique without requiring definiteness conditions in the elastic coefficients. Only continuity of the normal component of the electric displacement field across the boundary between the elastic body and free space is required. The proof employs a logarithmic convexity argument.
Diffraction by an acoustically transmissive or an electromagnetically dielectric half‐plane
Authors: Rawlins A. D. , Meister E. , Speck F. ‐O. 
Published: August 2005

AbstractThis work gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half‐plane. An approximate boundary condition is used that depends on the thickness of, and the material constants for, the half‐plane. A solution is obtained, by using the approximate boundary condition, for the problem of a line source field diffracted by a penetrable/dielectric half‐plane. The asymmetry of the approximate boundary condition results in a matrix Wiener–Hopf problem, which is solved explicitly.
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part I: Modelling of forces and torque, and theoretical prospects
Authors: Fuchs P. M. 
Published: August 2005

AbstractA model of the forces and the torque operating on a ball that is flying with rotation in the atmosphere of the Earth, and the resulting system of ordinary differential equations, are derived from mechanics and aerodynamics.The system of equations allows the theoretical aspects of the flight of a ball, such as the boundedness of its kinetic energy, the curvature of the orbit or the velocity function, to be investigated using certain transformations of the variables.The solutions of the corresponding ordinary or boundary value problems, computed numerically, are used to treat certain tasks in international ball games, for example, the maximum and minimum velocities of a volleyball service.
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part II: Theoretical aspects in the case of vertical angular frequency and applications
Authors: Fuchs P. M. 
Published: August 2005

AbstractIf a ball is viewed as a rigid body, its flight in the atmosphere can be described by a system of six ordinary differential equations, which has been derived in the first part of this paper.In this following second part, the theoretical aspects such as the curvature of the orbit and certain velocity functions will be investigated in the case of the vertical angular frequency of the rotating ball, in which the differential equations reduce to a planar dynamical system. This system turns out to be not explicity solvable.The solutions of the corresponding ordinary or boundary value problems. computed numerically, are used to treat certain problems in international ball games. for example, the maximum and minimum velocities of a volleyball service.
A trace theorem for solutions of linear partial differential equations
Authors: Bao Gang , Symes William W. 
Published: August 2005

AbstractIn this paper, we prove a trace regularity theorem for the solutions of general linear partial differential equations with smooth coefficients. Our result shows that by imposing additional microlocal smoothness along certain directions, the trace of the solution on a codimension‐one hypersuface will be just as regular as the solution itself. The proof is based on the Hörmander–Nirenberg pseudo‐differential cut‐off technique and a ‘fattening’ lemma, together with standard energy estimates.
The two‐dimensional Wigner–Poisson problem for an electron gas in the charge neutral case
Authors: Arnold Anton , Nier Francis 
Published: August 2005

AbstractWe prove the global existence of a unique classical solution of the two‐dimensional Wigner–Poisson problem by a reformulation as a system of countably many Schrödinger equations coupled to a Poisson equation. The charge neutrality of the system implies the boundedness of the electrostatic potential in two dimensions, which is an important ingredient for the proof.
Solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $$\end{document}. Exact solutions of some partial differential equations in mechanics and physics
Authors: Abdel‐Gawad H. I. 
Published: August 2005

AbstractThe solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $\end{document}, for L̂ a linear operator are derived. Different forms for L̂ whether it is time independent or time dependent and self‐commutative (or not) at different times are considered separately. By using the results obtained, exact solutions of some partial differential equations are found for the first time.
Vacuum decay of non‐Abelian vortices
Authors: Yang Yisong 
Published: August 2005

AbstractThis note is a case study of a general SU(2) gauge vortex model where the two Higgs multiplets are in the adjoint representation of the gauge group and the Higgs potential energy density contains cross interaction terms The vacuum decay of finite‐energy solutions is proved and the existence of a non‐trivial solution is established. Moreover, for a special choice of the parameter region, the occurrence of a non‐linear desingularization phenomenon is observed.
Inversion of the Radon transform with incomplete data
Authors: Ramm A. G. 
Published: August 2005

AbstractThe Radon transform R(p, θ), θ∈Sn−1, p∈ℝ1, of a compactly supported function f(x) with support in a ball Ba of radius a centred at the origin is given for all \documentclass{article}\pagestyle{empty}\begin{document}$ \theta \in \mathop {S^{n - 1} }\limits^\tilde $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {S^{n - 1} }\limits^\tilde $\end{document} is an open set on Sn−1, and all p∈(− ∞, ∞), n≥2. An approximate formula is given to calculate f(x) from the given data.
Existence of solutions to some non‐linear thermoelastic systems with viscosity
Authors: Hoffmann K.‐H. , Zochowski A. 
Published: August 2005

AbstractIn this paper a non‐linear system of equations
magnified image
in a one‐dimensional domain is considered, where both the viscosity, v, and R are positive. The existence of solutions in the case of Neumann boundary conditions for θ and a polynomial form of p(θ, ϵ) is proved. When θ satisfies the Dirichlet boundary condition, the existence of solutions is obtained under additional assumptions limiting the growth of p(θ, ϵ) with respect to θ. In both cases the uniqueness of the solutions is also established.
Phase transition in binary systems and the binary alloy problem
Authors: Xie Weiqing 
Published: August 2005

AbstractIn this paper we consider a phase transition in binary systems describing the solidification of a dilute alloy in one space dimension, in which the equations of heat and mass transfer are coupled through the conditions at the free boundary. A kinetic condition is introduced to suggest a regularization of the model, which admits a unique solution, and to obtain the generalized solution of the dilute‐alloy problem under an additional assumption.
Wave equations with time‐dependent spatial operators of higher order
Authors: Lesky Peter 
Published: August 2005

AbstractWe study the initial‐boundary value problem for ∂t2u(t,x)+A(t)u(t,x)+B(t)∂tu(t,x)=f(t,x) on [0,T]×Ω(Ω⊂ℝn) with a homogeneous Dirichlet boundary condition; here A(t) denotes a family of uniformly strongly elliptic operators of order 2m, B(t) denotes a family of spatial differential operators of order less than or equal to m, and u is a scalar function. We prove the existence of a unique strong solution u. Furthermore, an energy estimate for u is given.
On the determination of the worst sampling error in a communication system for pulse‐amplitude‐modulated signals. I: The general model
Authors: Kerber Dirk 
Published: August 2005

AbstractWe present a mathematical model of a communication system perturbed by statistical sampling errors (timing jitter). The aim is to find an ‘optimal’ impulse response for the system, the optimization problem actually being a minimax problem. that is we put the model into a game‐theoretical framework. The basic game turns out to be a statistical game similar to those arising from estimation problems in statistics.Earlier results concerning least‐favourable sampling error distributions published by Krabs and Vogel are supplemented by estimations of the number of support points of the least‐favourable distribution.Furthermore, we state the existence of the saddle points of our game, which formerly has only been proved for some special cases. In the first part we treat the general situation, where one strategy set for the game—the set of all feasible impulse responses—forms a vector space with infinite dimension. In the second part we discuss the problem in the case that the impulse responses are restricted to a finite‐dimensional subspace of the whole infinite‐dimensional subspace.
Characterization of functions as radiation patterns in linear elasticity
Authors: Charalambopoulos Antonios , Kiriaki Kiriakie 
Published: August 2005

AbstractIn this paper a necessary and sufficient condition for a pair of vector functions to be radiation patterns is presented. More precisely, it is proved that two vector functions, the first in the radial direction and the second in the tangential one, are radiation patterns if and only if there are two entire harmonic vector functions whose radial and tangential projections, respectively, are identical with the previous functions on the unit sphere and whose L2‐norm over a sphere of radius R is a function of exponential type in the variable R.
A stability analysis for semilinear Neumann problems with concave non‐linearities
Authors: Bandle C. , Brauner C. M. , Schmidt‐Lainé C. 
Published: August 2005

AbstractThis paper is concerned with non‐linear parabolic problems. This particular type of probiem arose from the study of the instability of transverse detonation waves in channels. A fairly complete account of the equilibrium states is given. A global approach is adopted for the upper and lower solutions and the energy estimates. Finally, the invariant manifolds that describe the asymptotic behaviour of the solutions near the equilibrium states are discussed.
High‐frequency asymptotics in inverse scattering by ellipsoids
Authors: Arnaoudov Yani , Dassios George , Georgiev Vladimir 
Published: August 2005

AbstractA triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High‐frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high‐frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non‐zero‐measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.
Behaviour of mushy regions under the action of a volumetric heat source
Authors: Andreucci Daniele 
Published: August 2005

AbstractIn this paper we consider solutions to Stefan problems in spatial dimensions N ⩾ 1. We find the necessary conditions on the heat source for the appearance of a ‘mushy region’ (i.e. a region where the temperature coincides identically with the temperature of the change of phase) inside a purely liquid (or solid) phase. For sources depending on energy such conditions are connected only with the local behaviour of the source near the energy level corresponding to the beginning of the change or phase. Both weak and smooth solutions are considered; in the latter case the behaviour of the solution at the free boundary is investigated in detail.
Initial‐boundary value problems for non‐linear equations of generalized thermoelasticity and elasticity
Authors: Chrzęszczyk Andrzej 
Published: August 2005

AbstractWe formulate a local existence theorem for the initial‐boundary value problems of generalized thermoelasticity and classical elasticity. We present a unified approach to such boundary conditions as, for example, the boundary condition of traction, pressure or place combined with the boundary condition of heat flux or temperature.
Cramér–Rao bounds for three‐point decomposition of water and fat
Authors: Pineda Angel R. , Reeder Scott B. , Wen Zhifei , Pelc Norbert J. 
Published: August 2005

AbstractThe noise analysis for three‐point decomposition of water and fat was extended to account for the uncertainty in the field map. This generalization leads to a nonlinear estimation problem. The Crámer–Rao bound (CRB) was used to study the variance of the estimates of the magnitude, phase, and field map by computing the maximum effective number of signals averaged (NSA) for any choice of echo time shifts. The analysis shows that the noise properties of the reconstructed magnitude, phase, and field map depend not only on the choice of echo time shifts but also on the amount of fat and water in each voxel and their alignment at the echo. The choice of echo time shifts for spin‐echo, spoiled gradient echo, and steady‐state free precession imaging techniques were optimized using the CRB. The noise analysis for the magnitude explains rough interfaces seen clinically in the boundary of fat and water with source images obtained symmetrically about the spin‐echo. It also provides a solution by choosing appropriate echo time shifts (−π/6 + πk, π/2 + πk, 7π/6 + πk), with k an integer. With this choice of echo time shifts it is possible to achieve the maximum NSA uniformly across all fat:water ratios. The optimization is also carried out for the estimation of phase and field map. These theoretical results were verified using Monte Carlo simulations with a newly developed nonlinear least‐squares reconstruction algorithm that achieves the CRB. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Iterative decomposition of water and fat with echo asymmetry and least‐squares estimation (IDEAL): Application with fast spin‐echo imaging
Authors: Reeder Scott B. , Pineda Angel R. , Wen Zhifei , Shimakawa Ann , Yu Huanzhou , Brittain Jean H. , Gold Garry E. , Beaulieu Christopher H. , Pelc Norbert J. 
Published: August 2005

AbstractChemical shift based methods are often used to achieve uniform water–fat separation that is insensitive to Bo inhomogeneities. Many spin‐echo (SE) or fast SE (FSE) approaches acquire three echoes shifted symmetrically about the SE, creating time‐dependent phase shifts caused by water–fat chemical shift. This work demonstrates that symmetrically acquired echoes cause artifacts that degrade image quality. According to theory, the noise performance of any water–fat separation method is dependent on the proportion of water and fat within a voxel, and the position of echoes relative to the SE. To address this problem, we propose a method termed “iterative decomposition of water and fat with echo asymmetric and least‐squares estimation” (IDEAL). This technique combines asymmetrically acquired echoes with an iterative least‐squares decomposition algorithm to maximize noise performance. Theoretical calculations predict that the optimal echo combination occurs when the relative phase of the echoes is separated by 2π/3, with the middle echo centered at π/2+πk (k = any integer), i.e., (–π/6+πk, π/2+πk, 7π/6+πk). Only with these echo combinations can noise performance reach the maximum possible and be independent of the proportion of water and fat. Close agreement between theoretical and experimental results obtained from an oil–water phantom was observed, demonstrating that the iterative least‐squares decomposition method is an efficient estimator. Magn Reson Med, 2005. © 2005 Wiley‐Liss, Inc.
Incremental plasticity analysis of frictional soils
Authors: Christian J. T. , Hagmann A. J. , Marr W. A. 
Published: August 2005

AbstractThree constitutive models of soil are used in finite element analyses of lateral earth pressure and bearing capacity. The three models are an elasto‐plastic formulation derived from the Mohr‐Coulomb law, a similar model with the plastic dilatancy removed, and a strain hardening model with a capped yield criterion. Stiffness formulations are described; the non‐dilatant model has a non‐symmetric stiffness. The results for the retaining walls are in close agreement with classical soil mechanics, but the bearing capacity analyses greatly overestimate the bearing capacity. The patterns of motion are, however, reasonable. Reasons for the discripancies in the bearing capacity case include: (a) the elements are too stiff and do not permit sliding on discrete failure planes; (b) the bearing capacity problem is itself not well settled theoretically; (c) very fine element divisions are necessary in areas of strong stress gradients and (d) rotation of principal stresses is significant.