bluuebunny/crossref_metadata_2025_split huggingface dataset:
Can classical equations simulate quantum‐mechanical behavior? a molecular dynamics investigation of a diatomic molecule with a morse potential
Authors: Schlick Tamar , Peskin Charles S. 
Published: April 2007

AbstractIn a recent paper, we presented a new computational method for molecular dynamics which uses the Backward‐Euler scheme to solve the classical Langevin dynamics equations. Parameters for the simulation include a target temperature T, a time step Δt, and a cutoff frequency ωc. We showed for a harmonic oscillator system that the cutoff frequency can be set as ωc = kT/h in order to mimic quantum‐mechanical behavior. We now continue this investigation for a nonlinear case: a diatomic molecule governed by a Morse bond potential. Since approximate quantum‐mechanical energy levels are explicitly known for this model, a comparison of energies can be made with molecular dynamics results. By performing dynamics runs for a wide range of temperatures and calculating mean energies, we find a very good agreement between these energies and quantum mechanical predictions. Vibrational excitation begins at temperatures around 800 K, and for higher temperatures both energy curves (molecular dynamics and quantum mechanics) approach the classical prediction of 7/2kT energy per molecule. Future investigations will focus on more general nonlinear potential functions employed in force fields of nucleic acids and proteins.
Incompressible navier‐stokes and euler limits of the boltzmann equation
Authors: de Masi A. , Esposito R. , Lebowitz J. L. 
Published: April 2007

AbstractWe consider solutions of the Boltzmann equation, in a d‐dimensional torus, d = 2, 3,magnified imageFor macroscopic times τ = t/ϵN, ϵ « 1, t ≧ 0, when the space variations are on a macroscopic scale x = ϵN−1r, N ≧ 2, x in the unit torus. Let u(x, t) be, for t ≦ t0, a smooth solution of the incompressible Navier Stokes equations (INS) for N = 2 and of the Incompressible Euler equation (IE) for N > 2.We prove that (*) has solutions for t ≦ t0 which are close, to O(ϵ2) in a suitable norm, to the local Maxwellian [p/(2πT)d/2]exp{−[v − ϵu(x,t)]2/2T} with constant density p and temperature T. This is a particular case, defined by the choice of initial values of the macroscopic variables, of a class of such solutions in which the macroscopic variables satisfy more general hydrodynamical equations. For N ≧ 3 these equations correspond to variable density IE while for N = 2 they involve higher‐order derivatives of the density.
An anisotropic inverse boundary value problem
Authors: Sylvester John 
Published: April 2007

AbstractWe consider the impedance tomography problem for anisotropic conductivities. Given a bounded region Ω in space, a diffeomorphism Ψ from Ω to itself which restricts to the identity on ∂ Ω, and a conductivity γ on Ω, it is easy to construct a new conductivity Ψ*γ which will produce the same voltage and current measurements on ∂ Ω.We prove the converse in two dimensions (i.e., if γ1 and γ2 produce the same boundary measurements, then γ1, = Ψ*γ2 for an appropriate Ψ) for conductivities which are near a constant.
Models for queue length in clocked queueing networks
Authors: Percus Ora E. , Percus J. K. 
Published: April 2007

AbstractWe analyze a discrete‐time network of queues. The unit element of the network is the 2 × 2 buffered switch, which we regard as a system of two queues working in parallel. We show how to transform transition probability information from the output of one switch, or network stage, to the input of the next one. This is used to carry out a Markov time series input model to predict mean queue length at every stage of the system. Another model considered is a renewal process time series model, which we use to find the mean queue length of the second stage of the network. Numerical simulations fall within the narrow band spanned by the two models.
The classification of topologically expansive lorenz maps
Authors: Hubbard John H. , Sparrow Colin T. 
Published: April 2007

AbstractWe show that topologically expansive Lorenz maps can be described up to topological conjugacy by their kneading invariants. We also give a simple condition on pairs of symbol sequences which is satisfied if and only if that pair of sequences is the kneading invariant for some topologically expansive Lorenz map. A simple extension of the theorems to the case of expansive maps of the interval with multiple discontinuities is described.
Measure of the multiple self‐intersection set of a markov process
Authors: Berman Simeon M. 
Published: April 2007

AbstractLet X(t), t ≧ 0, be a Markov process in Rm with homogeneous transition density p(t; x, y). For a closed bounded set B ⊂ Rm, X is said to have a self‐intersection of order r ≧ 2 in B if there are distinct points t1 < … < tr such that X(t1) ∈ B and X(tj) = X(t1), for j = 2,…, r. The focus of this work is the Hausdorff measure, suitably defined, of the set of such r‐tuples. The main result is that under general conditions on p(t; x, y) as well as the specific conditionmagnified imagethere is a measure function M(t), defined in terms of the integral above, such that the corresponding Hausdorff measure of self‐intersection set is positive, with positive probability. The results are applied to Lévy and diffusion processes, and are shown to extend recent results in this area.
Representations for the conductivity functions of multicomponent composites
Authors: Milton G. W. , Golden K. 
Published: April 2007

AbstractThe effective conductivity σ* of a multicomponent composite material is considered. Integral representations for σ* treated as a holomorphic function on a polydisk with values in a half‐plane are analyzed. A representation for σ* is introduced which is symmetric in the component conductivities and for which the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. This second feature, which is important for obtaining bounds on σ*, was previously available only in the two‐component case. In addition, a bound valid for any holomorphic function of the above type is proven.
Queue length distributions in a markov model of a multistage clocked queueing network
Authors: Percus Ora E. , Percus J. K. 
Published: April 2007

AbstractIn [4], we treated the problem of passage through a discrete‐time clock‐regulated multistage queueing network by modeling the input time series {an} to each queue as a Markov chain. We showed how to transform probability transition information from the input of one queue to the input of the next in order to predict mean queue length at each stage. The Markov approximation is very good for p = E(an) ≦ ½, which is in fact the range of practical utility. Here we carry out a Markov time series input analysis to predict the stage to stage change in the probability distribution of queue length. The main reason for estimating the queue length distribution at each stage is to locate “hot spots”, loci where unrestricted queue length would exceed queue capacity, and a quite simple expression is obtained for this purpose.
Deterministic diffusion of particles
Authors: Russo Giovanni 
Published: April 2007

AbstractThe diffusion of the particles is described in terms of a mean motion with a speed equal to the osmotic velocity associated with the diffusion process. Three numerical schemes are presented. The first two are based on the approximation of the gradient on an irregular mesh. The third is derived from a finite‐element approach. Voronoi diagrams are used to handle the irregular grid of the particles. The convergence of the schemes is studied numerically, by comparing the results with the exact solution. Applications to the Fokker‐Planck equation and to the problem of disposing particles according to a given probability distribution are presented.
On rotating black holes in equilibrium in general relativity
Authors: Weinstein Gilbert 
Published: April 2007

AbstractWe study asymptotically flat axially symmetric stationary solutions of the Einstein vacuum equations. These represent rotating black holes in equilibrium. The equations reduce outside the axis of symmetry to a harmonic map problem into the hyperbolic plane, with prescribed rates of blow‐up for the map on the axis and at infinity as boundary conditions. We prove existence and uniqueness of solutions in the case of zero total angular momentum.
Convergence of the point vortex method for the 3‐D euler equations
Authors: Hou Thomas Y. , Lowengrub John 
Published: April 2007

AbstractWe prove consistency, stability, and convergence of a point vortex approximation to the 3‐D incompressible Euler equations with smooth solutions. The 3‐D algorithm we consider here is similar to the corresponding 3‐D vortex blob algorithm introduced by Beale and Majda; see [3]. We first show that the discretization error is second‐order accurate. Then we show that the method is stable in lp norm for the particle trajectories and in w−1.p norm for discrete vorticity. Consequently, the method converges up to any time for which the Euler equations have a smooth solution. One immediate application of our convergence result is that the vortex filament method without smoothing also converges.
On the slowness of phase boundary motion in one space dimension
Authors: Bronsard Lia , Kohn Robert V. 
Published: April 2007

AbstractWe study the limiting behavior of the solution ofwith a Neumann boundary condition or an appropriate Dirichlet condition. The analysis is based on “energy methods”. We assume that the initial data has a “transition layer structure”, i.e.,uϵ≈ ±+M 1 except near finitely many transition points. We show that, in the limit as ϵ → 0, the solution maintains its transition layer structure, and the transition points move slower than any power of ϵ.
Approximation of functional depending on jumps by elliptic functional via t‐convergence
Authors: Ambrosio Luigi , Tortorelli Vincenzo Maria 
Published: April 2007

AbstractWe show how it is possible to approximate the Mumford‐Shah (see [29]) image segmentation functionalmagnified imageby elliptic functionals defined on Sobolev spaces. The heuristic idea is to consider functionals 𝒢h(u, z) with z ranging between 0 and 1 and related to the set K. The minimizing zh are near to 1 in a neighborhood of the set K, and far from the neighborhood they are very small. The neighborhood shrinks as h → + ∞. For a similar approach to the problem compare Kulkarni; see [25]. The approximation of 𝒢h to 𝒢 takes place in a variational sense, the De Giorgi F‐convergence.
A higher‐order Godunov method for modeling finite deformation in elastic‐plastic solids
Authors: Trangenstein John A. , Colella Phillip 
Published: April 2007

AbstractIn this paper we develop a first‐order system of conservation laws for finite deformation in solids, describe its characteristic structure, and use this analysis to develop a second‐order numerical method for problems involving finite deformation and plasticity. The equations of mass, momentum, and energy conservation in Lagrangian and Eulerian frames of reference are combined with kinetic equations of state for the stress and with caloric equations of state for the internal energy, as well as with auxiliary equations representing equality of mixed partial derivatives of the deformation gradient. Particular attention is paid to the influence of a curl constraint on the deformation gradient, so that the characteristic speeds transform properly between the two frames of reference. Next, we consider models in rate‐form for isotropic elastic‐plastic materials with work‐hardening, and examine the circumstances under which these models lead to hyperbolic systems for the equations of motion. In spite of the fact that these models violate thermodynamic principles in such a way that the acoustic tensor becomes nonsymmetric, we still find that the characteristic speeds are always real for elastic behavior, and essentially always real for plastic response. These results allow us to construct a second‐order Godunov method for the computation of three‐dimensional displacement in a one‐dimensional material viewed in the Lagrangian frame of reference. We also describe a technique for the approximate solution of Riemann problems in order to determine numerical fluxes in this algorithm. Finally, we present numerical examples of the results of the algorithm.
A vortex method for fluid‐particle systems
Authors: Papanicolaou George , Zhu Jingyi 
Published: April 2007

AbstractWe consider a two‐dimensional, dilute fluid‐particle system with low Reynolds number for the flow around the particles and high Reynolds number for the bulk flow. We use a vortex method to calculate numerically the incompressible fluid phase. For the compressible particle phase we use a particle method and Voronoi diagrams to calculate the particle density. We use the Stokes‐Oseen formula to represent approximately the force of the fluid on the particles. We give the results of a numerical experiment that show the effect of fluid particle interaction on the bulk flow.
Fast wavelet transforms and numerical algorithms I
Authors: Beylkin G. , Coifman R. , Rokhlin V. 
Published: April 2007

AbstractA class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors. Previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices. In contrast, the methods presented here are based on the recently developed theory of wavelets and are applicable to all Calderon‐Zygmund and pseudo‐differential operators. The algorithms of this paper require order O(N) or O(N log N) operations to apply an N × N matrix to a vector (depending on the particular operator and the version of the algorithm being used), and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here.
Nonsymmetric ground states of symmetric variational problems
Authors: Esteban Maria J. 
Published: April 2007

AbstractIn this paper we study a minimization problem which is invariant by rotation. The corresponding Euler‐Lagrange equations are semilinear elliptic equations in an exterior domain with Neumann boundary conditions. We prove that this minimization problem has at least one solution. Yet all its solutions are shown not to be rotationally invariant. Furthermore we describe how the radial symmetry is broken.
Smooth tame Fréchet algebras and lie groups of pseudodifferential operators
Authors: Payne Kevin R. 
Published: April 2007

AbstractFor pseudodifferential operator algebras with globally defined 0‐order symbols belonging to either the Hörmander class S(ℝ) or certain prescribed subspaces, it is shown that these algebras possess important smooth tame structures that make them amenable to nonlinear functional analysis of Nash‐Moser type.
Polar factorization and monotone rearrangement of vector‐valued functions
Authors: Brenier Yann 
Published: April 2007

AbstractGiven a probability space (X, μ) and a bounded domain Ω in ℝd equipped with the Lebesgue measure |·| (normalized so that |Ω| = 1), it is shown (under additional technical assumptions on X and Ω) that for every vector‐valued function u ∈ Lp (X, μ; ℝd) there is a unique “polar factorization” u = ∇Ψs, where Ψ is a convex function defined on Ω and s is a measure‐preserving mapping from (X, μ) into (Ω, |·|), provided that u is nondegenerate, in the sense that μ(u−1(E)) = 0 for each Lebesgue negligible subset E of ℝd.Through this result, the concepts of polar factorization of real matrices, Helmholtz decomposition of vector fields, and nondecreasing rearrangements of real‐valued functions are unified.The Monge‐Ampère equation is involved in the polar factorization and the proof relies on the study of an appropriate “Monge‐Kantorovich” problem.
On nematic liquid crystals with variable degree of orientation
Authors: Lin Fang Hua 
Published: April 2007

AbstractEnergy minimizing static configurations of nematic liquid crystals with variable degree of orientation can be described by a map which minimizes certain degenerate variational integrals. This mathematical model was recently posed by J. L. Erickson. In this paper, we shall prove the existence, local uniqueness, and global regularity of minimizers. We shall also estimate the size of possible defects.
Microscopic shock structure in model particle systems: The Boghosian‐Levermore cellular automation revisited
Authors: Cheng Z. , Lebowitz J. L. , Speer E. R. 
Published: April 2007

AbstractWe carried out new computer simulations of the Boghosian‐Levermore stochastic cellular automaton for the Burgers equation. The existence of an extra “conservation law” in the dynamics—even and odd lattice sites exchange their contents at every time step—implies that the automaton decomposes into two independent subsystems; the simulations show that the density from each subsystem exhibits a “shock front” which does not broaden with time. The location of the shock in a particular microscopic realization differs from that predicted by the Burgers equation by an amount which depends only on the initial microscopic density of the particle system, that is, fluctuations in the stochastic dynamics do not affect the shock profile on the time scale considered. This is in complete accord with theoretical expectations. The apparent broadening of the shock in the original Boghosian‐Levermore simulations is shown to result from averaging the two subsystem densities.
The initial‐value problem for measure‐valued solutions of a canonical 2 × 2 system with linearly degenerate fields
Authors: Weinan E. , Kohn Robert V. 
Published: April 2007

AbstractWe discuss Serre's restricted formulation of the notion of a measure‐valued solution, for a 2 × 2 system whose characteristic fields are both linearly degenerate. We prove existence, uniqueness, and regularity results for this formulation. As an application, we prove the convergence of a particle method when the high‐frequency component of the exact solution is not resolved by the computational grid.
Averaging regularity results for PDEs under transversality assumptions
Authors: Gérard Patrick , Golse François 
Published: April 2007

AbstractLet u = u(x,y) and f = f(x,y) be two functions related by a PDE P(x,y,Dx,Dy)u = f; the regularity of the y‐average ∫ u(x,·)dy as a function of x is investigated knowing that of u and f. Our method consists in reducing P to a microlocal normal form under a natural transversality assumption. The 2‐microlocal regularity of u is also determined knowing that of f. These results are then applied to a homogenization problem. This article generalizes the results of [16] and [12] on velocity averaging and homogenization for kinetic equations.
Stationary points of the Yang‐Mills action
Authors: Sadun Lorenzo , Segert Jan 
Published: April 2007

AbstractWe examine the structure of a recently discovered set of non‐self‐dual solutions of the Yang‐Mills equations. These solutions have a symmetry that reduces the YM equations to a set of ODE's. The distinct solutions are indexed by two postive odd integers. We develop a scheme to approximate on a computer the solutions for small values of the indexing integers and present some numerical results. We then analyze the asymptotic behavior of the solutions as the indexing integers become large.
Generalizations of the neumann system—a curve theoretical approach part III: Order n systems
Authors: Schilling Randolph James 
Published: April 2007

AbstractThe Neumann system is a well‐known algebraically completely integrable Hamiltonian system. Its geometry has roots in hyperelliptic curve theory and the isospectral deformation theory of Hill's operator. In this paper generalizations of the Neumann system are found for n‐sheeted Riemann surfaces and the isospectral deformation theory of operators of order n. Trace formulas, Lax pairs, and constants of motion are found. The new systems are shown to be algebraically completely integrable.
Asymptotic symmetry of solutions of nonlinear partial differential equations
Authors: Badiale Marino , Bardi Martino 
Published: April 2007

AbstractFor a large class of partial differential equations on exterior domains or on ℝN we show that any solution tending to a limit from one side as x goes to infinity satisfies the property of “asymptotic spherical symmetry”. The main examples are semilinear elliptic equations, quasilinear degenerate elliptic equations, and first‐order Hamilton‐Jacobi equations.
The stationary axisymmetric two‐body problem in general relativity
Authors: Weinstein Gilbert 
Published: April 2007

AbstractWe continue our study, begun in [7], into the stationary axisymmetric solutions of the Einstein vacuum equations containing two (or more) black holes. This problem reduces to an elliptic system of nonlinear partial differential equations with prescribed blow‐up as boundary conditions. We show the existence of solutions to the reduced system for any value of the five parameters of the problem. We show some regularity at the poles of the horizons. Using this result, we simplify the formula for the angle of deficiency of the conical singularity on the component of the axis of symmetry between the two horizons. This is to be interpreted as the gravitational force between rotating black holes. We also prove that the metrics constructed from solutions of the reduced system are indeed asymptotically flat.
N‐waves in elasticity
Authors: Zumbrun Kevin 
Published: April 2007

AbstractWe study the large time behavior of solutions of the one‐dimensional equations of elasticity, typically a nonconvex system of conservation laws. We show that solutions with compact initial support converge in L1 to a superposition of N‐waves, at algebraic rate. Likewise, we show that the perturbation expansion of weakly nonlinear geometric optics is uniformly valid to second order. Our analysis uses approximate scalar laws, together with L1 stability of scalar solutions and decay in total variation of the wave speed.
Evolution of nonparametric surfaces with speed depending on curvature II. The mean curvature case
Authors: Oliker Vladimir I. , Uraltseva Nina N. 
Published: April 2007

AbstractWe consider an evolution which starts as a flow of smooth surfaces in nonparametric form propagating in space with normal speed equal to the mean curvature of the current surface. The boundaries of the surfaces are assumed to remain fixed. G. Huisken has shown that if the boundary of the domain over which this flow is considered satisfies the “mean curvature” condition of H. Jenkins and J. Serrin (that is, the boundary of the domain is convex “in the mean”) then the corresponding initial boundary value problem with Dirichlet boundary data and smooth initial data admits a smooth solution for all time. In this paper we consider the case of arbitrary domains with smooth boundaries not necessarily satisfying the condition of Jenkins‐Serrin. In this case, even if the flow starts with smooth initial data and homogeneous Dirichlet boundary data, singularities may develop in finite time at the boundary of the domain and the solution will not satisfy the boundary condition. We prove, however, existence of solutions that are smooth inside the domain for all time and become smooth up to the boundary after elapsing of a sufficiently long period of time. From that moment on such solutions assume the boundary values in the classical sense. We also give sufficient conditions that guarantee the existence of classical solutions for all time t ≧ 0. In addition, we establish estimates of the rate at which solutions tend to zero as t → ∞.