bluuebunny/crossref_metadata_2025 huggingface dataset:
Generalized affine lie algebras and the solution of a class of flows associated with the QR eigenvalue algorithm
Authors: Deift P. A. , Li L. C.
Published: April 2007

In [3] the authors show that the QR algorithm to compute the eigenvalues of a matrix is the integer time evaluation of a completely integrable Hamiltonian system. Here the authors show that all the associated commuting integrals generate flows that can be solved explicitly via a factorization procedure on a suitable finite, or infinite‐dimensional, Lie algebra.
Molecular dynamics by the Backward‐Euler method
Authors: Peskin Charles S. , Schlick Tamar
Published: April 2007

This paper introduces a new computational method for molecular dynamics. The method combines the Backward‐Euler scheme for the solution of stiff differential equations with a Langevin‐equation approach to the establishment of thermal equilibrium. The method allows the user to choose a cutoff frequency ωc. Vibrational modes with frequencies below ωc will be fully excited (receive a mean energy of kT per mode), while modes with frequencies greater than ωc will be effectively frozen by the method. By setting ωc = kT/h, one can obtain reasonable agreement with the quantum‐mechanical energy distribution among the various modes, despite the classical character of the computation.
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

In 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

We consider solutions of the Boltzmann equation, in a d‐dimensional torus, d = 2, 3,

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For 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

We 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

We 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

We 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

Let 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 condition

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there 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

The 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

In [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

The 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

We 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

We 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

We study the limiting behavior of the solution of

with 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

We show how it is possible to approximate the Mumford‐Shah (see [29]) image segmentation functional

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by 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.
Diophantine definitions for some polynomial rings
Authors: Shlapentokh Alexandra
Published: April 2007

The author gives Diophantine definitions for polynomial rings of characteristic p > 0 over the polynomial rings with constants in finite fields, and for rational integers over polynomial rings of characteristic 0. The author also investigates Diophantine relationships between other pairs of polynomial rings of characteristic p > 0.
A higher‐order Godunov method for modeling finite deformation in elastic‐plastic solids
Authors: Trangenstein John A. , Colella Phillip
Published: April 2007

In 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

We 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

A 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

In 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

For 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

Given 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

Energy 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

We 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

We 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.
The zero dispersion limit, a deterministic analogue of turbulence
Authors: Lax Peter D.
Published: April 2007

Weak limits of oscillatory sequences of dispersive compressible flows show a remarkable resemblance to the ensemble averages of classical turbulence theory. How much relevance such ideas have for incompressible flows is not clear.
Averaging regularity results for PDEs under transversality assumptions
Authors: Gérard Patrick , Golse François
Published: April 2007

Let 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

We 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

The 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

For 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

We 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

We 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

We 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 → ∞.
Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
Authors: Bardos Claude , Golse François , Levermore C. David
Published: April 2007

Using relative entropy estimates about an absolute Maxwellian, it is shown that any properly scaled sequence of DiPerna‐Lions renormalized solutions of some classical Boltzmann equations has fluctuations that converge to an infinitesimal Maxwellian with fluid variables that satisfy the incompressibility and Boussinesq relations. Moreover, if the initial fluctuations entropically converge to an infinitesimal Maxwellian then the limiting fluid variables satisfy a version of the Leray energy inequality. If the sequence satisfies a local momentum conservation assumption, the momentum densities globaly converge to a solution of the Stokes equation. A similar discrete time version of this result holds for the Navier‐Stokes limit with an additional mild weak compactness assumption. The continuous time Navier‐Stokes limit is also discussed. © 1993 John Wiley & Sons, Inc.
Truncated newton methods and the modeling of complex immersed elastic structures
Authors: Fauci Lisa J. , Fogelson Aaron L.
Published: April 2007

Truncated Newton minimization methods are combined with Peskin's immersed boundary method to facilitate investigation of the dynamic interaction between a viscous, incompressible fluid and immersed elastic objects of complex structure. Applications to aquatic animal locomotion and platelet aggregation during blood clotting are presented. © 1993 John Wiley & Sons, Inc.
Oscillations of the zero dispersion limit of the korteweg‐de vries equation
Authors: Tian Fei Ran
Published: April 2007

We attack the multiphase averaged systems for the zero dispersion limit of the KdV equation. Attention is paid to the most important case—the single phase oscillations. A scheme is developed to solve the Whitham averaged system (single phase averaged system). This system, under our scheme, is transformed to a linear over‐determined system of Euler‐Poisson‐Darboux type whose solution can be written down explicitly. We show that, for any smooth initial data which has only one hump or is a nontrivial monotone function, the weak limit has single‐phase oscillations within a cusp in the x‐t plane for a short time after the breaking time for the corresponding Burgers equation. Outside the cusp, the limit satisfies the Burgers equation. More surprisingly, we also show that the weak limit has global single‐phase oscillations within a cusp for any smooth nontrivial monotone initial data with only one inflection point. © 1993 John Wiley & Sons, Inc.
Numerical methods for oscillatory solutions to hyperbolic problems
Authors: Engquist Bjorn , Liu Jian‐Guo
Published: April 2007

Difference approximations of hyperbolic partial differential equations with highly oscillatory coefficients and initial values are studied. Analysis of strong and weak convergence is carried out in the practically interesting case when the discretization step sizes are essentially independent of the oscillatory wave lengths. © 1993 John Wiley & Sons, Inc.
On the maslov index
Authors: Cappell Sylvain E. , Lee Ronnie , Miller Edward Y.
Published: April 2007

In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta invariants, spectral flow and signatures of quadratic forms) to the Maslov index are developed and formulae relating them are given. The broad presentation is designed with a view to applications both in geometry and in analysis. © 1994 John Wiley & Sons, Inc.
The collisionless shock region for the long‐time behavior of solutions of the KdV equation
Authors: Deift P. , Venakides S. , Zhou X.
Published: April 2007

The authors further develop the nonlinear steepest descent method of [5] and [6] to give a full description of the collisionless shock region for solutions of the KdV equation with decaying initial data. © 1994 John Wiley & Sons, Inc.
Potential theory for regular and mach reflection of a shock at a wedge
Authors: Morawetz Cathleen S.
Published: April 2007

If a plane shock hits a wedge, a self‐similar pattern of reflected shocks travels outward as the shock moves forward in time. The nature of the pattern is explored for weak incident shocks (strength b) and small wedge angles 2θw through potential theory, a number of different scalings, some study of mixed equations and matching asymptotics for the different scalings. The self‐similar equations are of mixed type. A linearization gives a linear mixed flow valid away from a sonic curve. Near the sonic curve a shock solution is constructed in another scaling except near the zone of interaction between the incident shock and the wall where a special scaling is used. The parameter β = c1θ2w(γ + 1)b ranges from 0 to ∞. Here γ is the polytropic constant and C1 is the sound speed behind the incident shock.

For β > 2 regular reflection (weak or strong) can occur and the whole pattern is reconstructed to lowest order in shock strength. For β < 1/2 Mach reflection occurs and the flow behind the reflection is subsonic and can be constructed in principle (with an open elliptic problem) and matched. The case β = 0 can be solved. For 1/2 < β < 2 or even larger β the flow behind a Mach reflection may be transonic and further investigation must be made to determine what happens.

The basic pattern of reflection is an almost semi‐circular shock issuing, for regular reflection, from the reflection point on the wedge and for Mach reflection, matched with a local interaction flow. Assuming their nature, choosing the least entropy generation, the weak regular reflection will occur for β sufficiently large (von Neumann paradox). An accumulation point of vorticity occurs on the wedge above the leading point. © 1994 John Wiley & Sons, Inc.
Renormalization group and asymptotics of solutions of nonlinear parabolic equations
Authors: Bricmont J. , Kupiainen A. , Lin G.
Published: April 2007

We present a general method for studying long‐time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations, to boundary conditions at infinity creating a front, and to higher (possibly fractional) differential linear terms. We present in detail the analysis for nonlinear diffusion‐type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity. In an accompanying paper, [5], the method is applied to systems of equations where some variables are “slaved,” such as the complex Ginzburg‐Landau equation. © 1994 John Wiley & Sons, Inc.
A link between sets of tensors stable under lamination and quasiconvexity
Authors: Milton Graeme W.
Published: April 2007

A link is found between quasiconvexity and the conditions for a set L of conductivity or elasticity tensors to be stable under lamination. These conditions, derived in the companion paper, are shown here to be equivalent to the condition that for every point B on the boundary of the set L an operator TB dependent on the tangent plane and curvature of the set at B is a quasiconvex translation operator. A separate class of quasiconvex translation operators is obtained which are candidates for proving that L is stable under homogenization. The region stable under homogenization associated with any one of these operators shares a common boundary point and tangent plane with the set L and has curvature at that point not greater than the curvature of L. The conditions under which there exists a representative subclass of these operators such that the associated regions stable under homogenization wrap around L remains unresolved. It is proved that L can be characterized by minimizations of sums and dual energies in much the same way that convex sets can be characterized by their Legendre transforms. © 1994 John Wiley & Sons, Inc.
Integral equations for the generalized stokes operator: Applications to high reynolds number flows
Authors: Achdou Yves
Published: April 2007

This paper deals with a boundary integral equation for the generalized Stokes problem and its approximation by simpler integral equations when the Reynolds number tends to infinity. The two‐dimensional case has been treated in [1]. This paper addresses the three‐dimensional case. © 1994 John Wiley & Sons, Inc.
Computing the weak limit of KdV
Authors: McLaughlin David W. , Strain John A.
Published: April 2007

The solution of the KdV equation with single‐minimum initial data has a zero‐dispersion limit characterized by Lax and Levermore as the solution of an infinite‐dimensional constrained quadratic minimization problem. An adaptive numerical method for computing the weak limit from this characterization is constructed and validated. The method is then used to study the weak limit. Initial simple experiments confirm theoretical predictions, while experiments with more complicated data display multiphase behavior considerably beyond the scope of current theoretical analyses. The method computes accurate weak limits with multiphase structures sufficiently complex to provide useful test cases for the calibration of numerical averaging algorithms. © 1994 John Wiley & Sons, Inc.
Existence of global weak solutions to one‐component vlasov‐poisson and fokker‐planck‐poisson systems in one space dimension with measures as initial data
Authors: Zheng Yuxi , Majda Andrew
Published: April 2007

We consider Cauchy problems for the 1‐D one component Vlasov‐Poisson and Fokker‐Planck‐Poisson equations with the initial electron density being in the natural space of arbitrary non‐negative finite measures. In particular, the initial density can be a Dirac measure concentrated on a curve, which we refer to as “electron sheet” initial data. These problems resemble both structurally and functional analytically Cauchy problems for the 2‐D Euler and Navier‐Stokes equations (in vorticity formulation) with vortex sheet initial data. Here, we need to define weak solutions more specifically than usual since the product of a finite measure with a function of bounded variation is involved. We give a natural definition of the product, establish its weak stability, and existence of weak solutions follows. Our concept of weak solutions through the newly defined product is justified since solutions to the Fokker‐Planck‐Poisson equation, the analogue of Navier‐Stokes equation, are shown to converge to weak solutions of the Vlasov‐Poisson equation as the Fokker‐Planck term vanishes. The main difficulty is the aforementioned weak stability which we establish through a careful analysis of the explicit structure of these equations. This is needed because the problem studied here is beyond the range of applicability of the “velocity averaging” compactness methods of DiPerna‐Lions. © 1994 John Wiley & Sons, Inc.
On global representation of lagrangian distributions and solutions of hyperbolic equations
Authors: Laptev A. , Safarov Yu. , Vassiliev D.
Published: April 2007

In this paper we develop a new approach to the theory of Fourier integral operators. It allows us to represent the Schwartz kernel of a Fourier integral operator by one oscillatory integral with a complex phase function. We consider Fourier integral operators associated with canonical transformations, having in mind applications to hyperbolic equations. As a by‐product we obtain yet another formula for the Maslov index. © 1994 John Wiley & Sons, Inc.
Shape theorem, lyapounov exponents, and large deviations for brownian motion in a poissonian potential
Authors: Sznitman Alain‐Sol
Published: April 2007

We derive a large deviation principle governing the position of a d‐dimensional Brownian motion moving in a Poissonian potential. The derivation of this large deviation principle, and the form of the rate function rely on a result similar to the “shape theorem” of first passage percolation. This result produces certain constants which play in this multidimensional situation a similar role as the Lyapounov exponents in the one‐dimensional case. The large deviation principle enables us to investigate the transition of regime, which occurs between the small ∣h∣ and the large ∣h∣ case, for Brownian motion with a constant drift h moving in the same potential. © 1994 John Wiley & Sons, Inc.
On the exponentially slow motion of a viscous shock
Authors: Reyna Luis G. , Ward Michael J.
Published: April 2007

Using formal asymptotic methods, we study the internal layer behavior associated with the following viscous shock problem in the limit ε → 0: magnified image The convex nonlinearity f(u) satisfies f(α) = f(–α). For the steady problem, we show that the method of matched asymptotic expansions fails to uniquely determine the location of the equilibrium shock layer solution. This indeterminacy, resulting from neglecting certain exponentially small effects, is eliminated by using the projection method, which exploits certain properties of the spectrum associated with the linearized operator. For the time dependent problem, we show that the viscous shock, which is formed from initial data, drifts towards the equilibrium solution on an exponentially long time interval of the order O(eC/ε), for some C > 0. This exponentially slow behavior is analyzed by deriving an equation of motion for the location of the viscous shock. For Burgers equation (f(u) = u2/2), the results give an analytical characterization of the slow shock layer motion observed numerically in Kreiss and Kreiss; see [11]. We also show that the shock layer behavior is very sensitive to small changes in the boundary operator. In addition, using a WKB‐type method, the slow viscous shock motion is studied numerically for small ε, the results comparing favorably with corresponding analytical results. Finally, we relate the slow viscous shock motion to similar slow internal layer motion for the Allen‐Cahn equation.
Schwarz methods of neumann‐neumann type for three‐dimensional elliptic finite element problems
Authors: Dryja Maksymilian , Widlund Olof B.
Published: April 2007

Several domain decomposition methods of Neumann‐Neumann type are considered for solving the large linear systems of algebraic equations that arise from discretizations of elliptic problems by finite elements. We will only consider problems in three dimensions. Several new variants of the basic algorithm are introduced in a Schwarz method framework that provides tools which have already proven very useful in the design and analysis of other domain decomposition and multi‐level methods.

The Neumann‐Neumann algorithms have several advantages over other domain decomposition methods. The subregions, which define the subproblems, only share the boundary degrees of freedom with their neighbors. The subregions can also be of quite arbitrary shape and many of the major components of the preconditioner can be constructed from subprograms available in standard finite element program libraries. In its original form, however, the algorithm lacks a mechanism for global transportation of information and its performance therefore suffers when the number of subregions increases. In the new variants of the algorithms, considered in this paper, the preconditioners include global components, of low rank, to overcome this difficulty. Bounds are established for the condition number of the iteration operator, which are independent of the number of subregions, and depend only polylogarithmically on the number of degrees of freedom of individual local subproblems. Results are also given for problems with arbitrarily large jumps in the coefficients across the interfaces separating the subregions. ©1995 John Wiley & Sons, Inc.
Convergence of vortex methods for weak solutions to the 2‐D euler equations with vortex sheet data
Authors: Liu Jian‐Guo , Xin Zhouping
Published: April 2007

We prove the convergence of vortex blob methods to classical weak solutions for the two‐dimensional incompressible Euler equations with initial data satisfying the conditions that the vorticity is a finite Radon measure of distinguished sign and the kinetic energy is locally bounded. This includes the important example of vortex sheets. The result is valid as long as the computational grid size h does not exceed the smoothing blob size ε, i.e., h/ε ≦ C.. ©1995 John Wiley & Sons, Inc.
Activity in field‐coupled nanomagnet arrays
Authors: Csaba György , Porod Wolfgang , Lugli Paolo , Csurgay Árpád I.
Published: April 2007

Magnetic‐field coupling emerges as a new possibility for nanoscale device integration. This paper investigates power flow between field‐coupled single‐domain nanomagnets. Using an equivalent‐circuit formulation, we demonstrate that nanomagnet circuits can perform power gain in an entirely magnetic way, i.e. they can direct power from an external magnetic pumping field into a magnetic signal path. It was recently shown that networks of coupled nanomagnets can realize Boolean logic operations. This, combined with our finding that they also are active devices, promises the possibility of building complex all‐magnetic digital and analog circuits. We also outline an analogy between the operating principles of field‐coupled nanomagnet circuits and previous work on magnetic amplifiers. Copyright © 2007 John Wiley & Sons, Ltd.
Alternating and Non‐Alternating Pd‐Catalysed Co‐ and Terpolymerisation of Carbon Monoxide and Alkenes
Authors: García Suárez Eduardo J. , Godard Cyril , Ruiz Aurora , Claver Carmen
Published: April 2007

The co‐ and terpolymerisation of carbon monoxide and alkenes are usually catalysed by palladium complexes, and the properties of the produced polyketones can be finely tuned by an appropriate choice of catalyst and olefinic monomer. After a general overview of the topic, selected recent advances in this field are described. The use of palladium systems containing modified diphosphane and/or new phosphorus‐based ligands, and the results obtained using a series of modular N and S ligands, including chiral ligands, in CO/styrene co‐ and terpolymerisations are reported. The use of new P‐O ligands in non‐alternating CO/ethene copolymerisation is also described. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)
CRTC1/MAML2 fusion transcript in high grade mucoepidermoid carcinomas of salivary and thyroid glands and Warthin's tumors: Implications for histogenesis and biologic behavior
Authors: Tirado Yamilet , Williams Michelle D. , Hanna Ehab Y. , Kaye Frederic J. , Batsakis John G. , El‐Naggar Adel K.
Published: April 2007

We analyzed 55 primary salivary gland tumors including 22 mucoepidermoid carcinomas (MECs) to determine the association of MECT1/TORC1/CRTC1‐MAML2 fusion transcript to tumor types, level of MEC differentiation and clinicopathologic parameters. Our primary salivary gland tumors were composed of 22 MECs, 11 Warthin's tumors, 10 adenoid cystic carcinomas, two basaloid carcinomas, five salivary duct carcinomas, and five adenocarcinomas, not otherwise specified. We also included, for the first time, three primary MECs of the thyroid gland. We used nested RT‐PCR and subsequent sequencing techniques for detection and verification of the fusion transcript in fresh and archival specimens. Eighteen (81%) of the 22 primary salivary and one of the three thyroid glands with MEC were positive for the fusion transcript. The transcript was detected equally in low, intermediate and high grade as well as low and high stage MECs. Significant correlation between fusion negative tumors and distant metastasis was noted (P = 0.005). Four (36%) of the 11 Warthin's tumors were also positive for the transcript. None of the 22 primary non‐MEC gland salivary carcinomas were positive for the transcript. We conclude that the CRTC1/MAML2 transcript may be detected in both low and high grade MEC, that fusion negative tumors may define a subset of biologically aggressive MEC's tumors, that the fusion is present in primary MECs of the thyroid gland and is also detectable in Warthin's tumor, and that a subset of MECs can be targeted for therapeutic intervention. © 2007 Wiley‐Liss, Inc.
Chinese demented inpatients admitted following a suicide attempt: a case series
Authors: Tsai Chia‐Fen , Tsai Shih‐Jen , Yang Cheng‐Hung , Hwang Jen‐Ping
Published: April 2007

Objective

Suicide attempt is rarely reported in dementia. This study explores the clinical and phenomenological aspects as well as the treatment of Chinese demented patients who have attempted suicide.

Methods

During a 1‐year period, demented patients admitted to a geropsychiatric unit as a result of suicide attempt were investigated for factors related to suicide attempt, such as motives and method.

Results

In this 1‐year survey, seven demented patients (11.7% of all demented patients) were admitted immediately following a suicide attempt. All seven patients had mild or moderate dementia. Three had significant clinical depression symptoms on admission. In all patients, delusions were the primary cause of suicide attempt. Their suicidal ideations were improved with antipsychotic and antidepressant treatment.

Conclusion

These cases, taken together, suggest that suicide attempt can occur in patients with dementia. It is important for clinicians to be aware of the risk of suicide in patients with dementia, especially those associated with delusions, even if they have no major depression or suicide attempt history. Antidepressants and antipsychotics may play a critical role in the treatment of suicide attempt in dementia. Copyright © 2007 John Wiley & Sons, Ltd.