bluuebunny/crossref_metadata_2025_split huggingface dataset:
Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
Authors: Conley Charles , Zehnder Eduard 
Published: April 2007

AbstractAn index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse‐type existence statement for periodic solutions of a time‐dependent (periodic in time) and asymptotically linear Hamiltonian equation.
Instability of difference models for hyperbolic initial boundary value problems
Authors: Trefethen Lloyd N. 
Published: April 2007

AbstractA th00 eory of instability is presented for finite difference models of linear hyperbolic partial differential equations in one space dimension with a boundary. According to this theory, instability is caused by spurious radiation of wave energy from the boundary at a numerical group velocity C ≥ 0. To make this point of view precise, we first develop a rigorous description of group velocity for difference schemes and of reflection of waves at boundaries. From these results we then obtain lower bounds for growth rates of unstable finite difference solution operators in l2 norms, which extend earlier results due to Osher and to Gustafsson, Kreiss, and Sundström. In particular we investigate l2‐instability with respect to both initial and boundary data and show how they are affected by (a) finite versus infinite reflection coefficients and (b) wave radiation with C = 0 versus C > 0.
Nonlinear elliptic systems with certain unbounded coefficients
Authors: Smith P. D. , Stredulinsky E. W. 
Published: April 2007

AbstractWe consider nonlinear systems of the form magnified image Under suitable assumptions, Hölder continuity of weak solutions is proven in a neighborhood of the origin using weighted inequalities and a partial regularity method of M. Giaquinta and E. Giusti. These equations relate to an exterior flow problem in physics.
Asymptotic behavior of the solutions of certain parabolic equations
Authors: Lortz Dietrich , Meyer‐Spasche Rita , Stredulinsky Edward W. 
Published: April 2007

AbstractSome laws in physics describe the change of a flux and are represented by parabolic equations of the form (*) \documentclass{article}\pagestyle{empty}\begin{document}$$\frac{{\partial u}}{{\partial t}}=\frac{\partial}{{\partial x_j }}(\eta \frac{{\partial u}}{{ax_j}}-vju),$$\end{document} j≤m, where η and vj are functions of both space and time. We show under quite general assumptions that the solutions of equation (*) with homogeneous Dirichlet boundary conditions and initial condition u(x, 0) = uo(x) satisfy

The decay rate d > 0 only depends on bounds for η, v and G § Rm the spatial domain, while the constant c depends additionally on which norm is considered. For the solutions of equation (*) with homogeneous Neumann boundary conditions and initial condition u0(x) ≥ 0 we derive boundsd1u1 ≤ u(x, t) ≤ d2u2,Where di, i = 1, 2, depend on bounds for η, v and G, and the ui are bounds on the initial condition u0.
Numerical simulation of singular solutions to the two‐dimensional cubic schrödinger equation
Authors: Sulem P. L. , Sulem C. , Patera A. 
Published: April 2007

AbstractNumerical simulations of the cubic nonlinear Schrödinger equation are presented in dimension N = 2. The emphasis is on a detailed mechanism of blow up. The numerical results indicate that the blow up is not restricted to the case where the problem is posed in the entire R2‐space but also occurs with periodic boundary conditions. The structure of the solution as the singular time t* is approached has been investigated using examples with and without radial symmetry and/or periodicity. In most cases we observe that the amplitude develops something like the peaked self‐similar profile predicted by Zakharov and Synakh [38] which has a (t*‐t)‐2/3 maximum amplitude and a (t*‐t)2/3 width.
The zero dispersion limit of the korteweg‐de vries equation for initial potentials with non‐trivial reflection coefficient
Authors: Venakides Stephanos 
Published: April 2007

AbstractThe inverse scattering method is used to determine the distribution limit as ϵ → 0 of the solution u(x, t, ϵ) of the initial value problem.Ut − 6uux + ϵ2uxxx = 0, u(x, 0) = v(x), where v(x) is a positive bump which decays sufficiently fast as x x→±α. The case v(x) ≪ 0 has been solved by Peter D. Lax and C. David Levermore [8], [9], [10].The computation of the distribution limit of u(x, t, ϵ) as ϵ → 0 is reduced to a quadratic maximization problem, which is then solved.
Global existence for a nonlinear theory of bubbly liquids
Authors: Caflisch Russel E. 
Published: April 2007

AbstractGlobal existence of smooth solutions is proved for an effective theory of bubbly liquids for either the initial value problem or initial boundary value problem in one dimension. This shows that the theory does not describe shock waves or bubble collapse. Since the analysis is not for the steady boundary value problem, there is no discussion of resonance. The proof uses a semilinear form of the equations to get local existence. A priori bounds resulting from energy conservation and a nonlinear Gronwall‐like inequality are then derived to prove global existence.
A theorem of real analysis and its application to free boundary problems
Authors: Athanasopoulos Ioannis , Caffarelli Luis A. 
Published: April 2007

AbstractIn this note we show how comparison theorems for solutions to equations with non‐smooth coefficients yield in a very simple fashion some free boundary regularity theorems in cases where there is a priori geometrical information, for instance, when one knows that the solution, u, is monotone in some given direction.
Sojourns above a high level for a gaussian process with a point of maximum variance
Authors: Berman Simeon M. 
Published: April 2007

AbstractLet X(t), 0≦t≦ 1, be a measurable Gaussian process with mean 0 and variance σ2(t) = EX2(t). Suppose that σ2(t) assumes a unique maximum value σ2 at a point τ [0,1]. Define Lu = mes(t: 0≦t≦1, X(t)>)Under appropriate conditions, there exists a function fσ(u) such that fσ(u) → ∞ for u ∞, and magnified image The function fσ and the constant δ > 0 are determined by the behavior of the function R(x) = mes(t: 0 ≦ t ≦ 1, σ2 ‐ σ2(t) ≦ x) for x > 0.
The half‐space problem for the boltzmann equation at zero temperature
Authors: Caflisch Russel E. 
Published: April 2007

AbstractAt zero temperature the Maxwellian distribution is a delta function of velocity. In this paper the Boltzmann equation is linearized around a delta function and then analyzed by a comparison method. Using these results and similar bounds for the nonlinear collision operator, a nonlinear boundary value problem at zero temperature is solved. The results are applied to the asymptotic description at the cold end of the shock profile at infinite Mach number. All solutions F are assumed to have the form F(x, ξ) = (1 ‐ a(x))δ(ξ) + f(x, ξ) in which a and f are regular functions.
Asymptotics of particle trajectories in infinite one‐dimensional systems with collisions
Authors: Dürr Detlef , Goldstein Sheldon , Lebowitz Joel L. 
Published: April 2007

AbstractWe investigate the asymptotic behavior of the trajectories of a tagged particle (tp) in an infinite one‐dimensional system of point particles. The particles move independently when not in contact: the only interactions are Harris type generalized elastic collisions which prevent crossings. This is achieved by relabeling the independent trajectories when they cross. When these trajectories are differentiable, as in particles with velocities undergoing Ornstein‐Uhlenbeck processes, collisions correspond to exchange of velocities.We prove very generally that the suitably scaled tp trajectory converges (weakly) to a simple Gaussian process. This extends the results of Spitzer for New tonian particles to very general non‐crossing processes. The proof is based on the consideration of the simpler process which counts the crossings of the origin by the independent trajectories.
Determining conductivity by boundary measurements II. Interior results
Authors: Kohn R. V. , Vogelius M. 
Published: April 2007

AbstractIn a recent paper [6] we showed that an unknown real‐analytic conductivity γ may be determined from static boundary measurements. Here we extend this analysis by demonstrating that a similar result holds for piecewise real‐analytic conductivities. In addition, for the special case of a layered structure we show that a three times continuously differentiable conductivity is identifiable by boundary measurements.
Polynomial realization of pseudoline arrangements
Authors: Goodman Jacob E. , Pollack Richard 
Published: April 2007

AbstractAn arrangement of pseudolines is called d‐stretchable if it is isomorphic to an arrangement of graphs of polynomial functions, each of degree at most d; in particular, it is 1‐stretchable (classically: “stretchable”) if and only if it is isomorphic to an arrangement of lines. We show that (i) if every arrangement of n pseudolines is d‐stretchable, then d ≦ cn1/2, and (ii) every arrangement of n pseudolines is d‐stretchable with d = cn2.
The limiting angle of certain riemannian brownian motions
Authors: Hsu Pei , March Peter 
Published: April 2007

AbstractLetMbe a Cartan‐Hadamard manifold of dimensiond≧ 3, letpϵMandx= exp {r(x)θ(x)} be geodesic polar coordinates with polepand letXbe the Brownian motion onM. Let SectM(x) denote the sectional curvature of any plane section inMx. We prove that for eachc> 2, there is a 0 < β < 1 such that if ‐L2r(x)2β≦ SectM(x) ≦ ‐cr(x)−2for allxin the complement of a compact set, then limt → ∞θ(Xt) exists a.s. and defines a nontrivial invariant random variable. The Dirichlet problem at infinity and a conjecture of Greene and Wu are also discussed.
Parallel algorithms for elliptic equations
Authors: McBryan Oliver A. , Van De Velde Eric F. 
Published: April 2007

AbstractWe describe a number of parallel algorithms for the numerical solution of elliptic equations and present some implementations on the Denelcor HEP Parallel Processor.The equations we study, typical of those encountered in a range of fluid pressure equations, are of the form magnified image where the coefficient tensor may represent a density, permeability or dielectric constant. We allow the possibility of discontinuities in , and of line and point sources in F. The equations are discretized using finite elements, with orders ranging from linear to bicubic.We use a tree of increasingly fine grids to achieve parallelism in the course of mesh refinement. We use conjugate gradient methods as well as multigrid methods to solve the resulting algebraic equations within each subgrid. We describe the implementation of these methods as parallel algorithms, and present results of actual performance on the HEP computer. In each case we demonstrate near optimal performance on the HEP, as measured by speedup over the corresponding serial algorithm.We would like to thank both Argonne National Laboratory and Ballistic Research Laboratory for allowing us access to their HEP computers. The operations staffs at both sites gave us unstintingly of their time, even when called on after hours. This research, on an, at times, quite temperamental machine, would never have been completed without their help. We would also like to thank Argonne National Laboratory for the excellent two‐day HEP introduction provided us prior to the start of this research. Finally, we wish to thank E. Lusk and R. Overbeek for providing us with copies of their HEP macros.
Optimal random coding
Authors: Peskin Charles S. 
Published: April 2007

AbstractWe consider a stochastic method for representing a real number x by a finite sequence of bits. The method is symmetrical with respect to interchange of the bits: it is characterized by a single function p(x) which gives the probability that any particular bit is on as a function of the real number x that is being encoded. We then consider the problem of reconstructing x from its representation. In the limiting case in which the number of bits is large, we determine the function p(x) that minimizes the expected k‐th power of the absolute error in this reconstruction. The optimal choice of p(x) is independent of k.
Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
Authors: Simon Barry , Wolff Tom 
Published: April 2007

AbstractWe consider a selfadjoint operator, A, and a selfadjoint rank‐one projection, P, onto a vector, φ, which is cyclic for A. In terms of the spectral measure dμAφ, we give necessary and sufficient conditions for A + λ P to have empty singular continuous spectrum or to have only point spectrum for a.e. λ. We apply these results to questions of localization in the one‐ and multi‐dimensional Anderson models.
Asymptotic behavior of solutions of certain parabolic problems with space and time dependent coefficients
Authors: Stredulinsky E. W. , Meyer‐Spasche Rita , Lortz Dietrich 
Published: April 2007

AbstractGiven a bounded domain G ⊂ Rm, m ≧ 2, we study weak formulations of parabolic problems

(Si)

L1 and L2 are uniformly elliptic differential operators with time and space dependent coefficients; γ1 = 1, γ2 a real function. Problem (S3) is the “time‐reversed” version of (S2): L3 = −L2, γ3 = γ2. Equations (S1), (S2) are supplemented with an initial condition, a decay condition for ∣x∣ → ∞ and conditions for smoothness or “matching” on the interface ∂G × ℝ+. Since (S3) is a backward equation the prescription of initial values is not appropriate and has to be replaced by a normalization condition for the initial values.We prove existence of unique weak solutions of all three problems and show that the solutions of (S1) decay exponentially, while the solutions of the other two problems stay bounded for all times. In an appendix we characterize exterior harmonic functions of given decay rates at infinity.
Explicit solutions of the viscous model vorticity equation
Authors: Schochet Steven 
Published: April 2007

AbstractExplicit solutions are found for the viscous version of the model vorticity equation recently proposed by P. Constantin, P. D. Lax, and A. Majda:

where H(w) is the Hilbert transform of w, and v is a positive constant. Various properties of these solutions, including the fact that they blow up after a finite time, are discussed.
The neumann problem for equations of monge‐ampère type
Authors: Lions P.‐L. , Trudinger N. S. , Urbas J. I. E. 
Published: April 2007

AbstractWe prove the existence of a classical solution to a Neumann type problem for nonlinear elliptic equations of Monge‐Ampère type. The methods depend upon the establishment of a priori derivative estimates up to order two and yield a sharp result for the equation of prescribed Gauss curvature. We also present applications to asymptotic problems which approach the non‐unique case and maximum principles for linear equations of Aleksandrov‐Bakelman type.
Shock waves for compressible navier‐stokes equations are stable
Authors: Liu Tai‐Ping 
Published: April 2007

AbstractIt is shown that shock waves for the compressible Navier‐Stokes equations are nonlinearly stable. A perturbation of a shock wave tends to the shock wave, properly translated in phase, as time tends to infinity. Through the consideration of conservation of mass, momentum and energy we obtain an a priori estimate of the amount of translation of the shock wave and the strength of the linear and nonlinear diffusion waves that arise due to the perturbation. Our techniques include the energy method for parabolic‐hyperbolic systems, the decomposition of waves, and the energy‐characteristic method for viscous conservation laws introduced earlier by the author.
Symmetry and phaselocking in chains of weakly coupled oscillators
Authors: Kopell N. , Ermentrout G. B. 
Published: April 2007

AbstractWeakly coupled chains of oscillators with nearest‐neighbor interactions are analyzed for phaselocked solutions. It is shown that the symmetry properties of the coupling affect the qualitative form of the phaselocked solutions and the scaling behavior of the system as the number of oscillators grows without bound. It is also shown that qualitative behavior of these solutions depends on whether the coupling is “diffusive” or “I synaptic”. terms defined in the paper. The methods include the demonstration that the equations for phaselocked solutions can be approximated by a singularly perturbed two‐point (continuum) boundary value problem that is easier to analyze; the issue of convergence of the phaselocked solutions to solutions of the continuum equation is closely related to questions involving numerical entropy in computation schemes for a conservation law. An application to the neurophysiology of motor behavior is discussed briefly.
The mass of an asymptotically flat manifold
Authors: Bartnik Robert 
Published: April 2007

AbstractWe show that the mass of an asymptotically flat n‐manifold is a geometric invariant. The proof is based on harmonic coordinates and, to develop a suitable existence theory, results about elliptic operators with rough coefficients on weighted Sobolev spaces are summarised. Some relations between the mass, scalar curvature and harmonic maps are described and the positive mass theorem for n‐dimensional spin manifolds is proved.
Homogenization of elliptic equations with principal part not in divergence form and hamiltonian with quadratic growth
Authors: Bensoussan A. , Boccardo L. , Murat F. 
Published: April 2007

AbstractIn this paper, we consider the following problem:

equation image

Here the coefficients aij and bi are smooth, periodic with respect to the second variable, and the matrix (aij)ij is uniformly elliptic. The Hamiltonian H is locally Lipschitz continuous with respect to uϵ and Duϵ, and has quadratic growth with respect to Duϵ. The Hamilton‐Jacobi‐Beliman equations of some stochastic control problems are of this type.Our aim is to pass to the limit in (0ϵ) as ϵ tends to zero. We assume the coefficients bi to be centered with respect to the invariant measure of the problem (see the main assumption (3.13)). Then we derive L∞, H and W, p0 > 2, estimates for the solutions of (0ϵ). We also prove the following corrector's result:

equation image

This allows us to pass to the limit in (0ϵ) and to obtain

equation image

This problem is of the same type as the initial one. When (0ϵ) is the Hamilton‐Jacobi‐Bellman equation of a stochastic control problem, then (00) is also a Hamilton‐Jacobi‐Bellman equation but one corresponding to a modified set of controls.
On the riemann problem for a prototype of a mixed type conservation law
Authors: Holden Helge 
Published: April 2007

AbstractWe study the system of conservation laws given by magnified image With initial value magnified image The system is elliptic when u2 + v2 < ρ2 and hyperbolic when u2 + v2 ≧ ρ2. Following Liu's construction it is found that the system always has a weak solution which however is not necessarily unique.
Unraveling the o‐Methoxy Effect in the CO/Ethene Copolymerization Reaction by Diphosphanepalladium(II) Catalysis
Authors: Bianchini Claudio , Meli Andrea , Oberhauser Werner , Claver Carmen , Garcia Suarez Eduardo J. 
Published: April 2007

AbstractRelevant steps in the CO/ethene copolymerization reaction, namely the migratory insertion of [Pd(Me)(CO)(P‐P)]BAr′4 and the carbonylation of the β‐keto chelates [Pd(CH2CH2C(O)Me)(P‐P)]BAr′4 have been studied by in situ high‐pressure NMR spectroscopy in CH2Cl2; P‐P = 1,2‐bis[bis(2‐methoxyphenyl)phosphanyl]ethane or 1,3‐bis[bis(2‐methoxyphenyl)phosphanyl]propane. This study, backed by batch catalytic reactions in the same solvent, has contributed to rationalizing the higher catalytic activity of PdII catalysts modified with o‐methoxy‐substituted diphosphane ligands as compared to analogous PdII catalysts with 1,2‐bis(diphenylphosphanyl)ethane (dppe) and 1,3‐bis(diphenylphosphanyl)propane (dppp) ligands. It was found that o‐MeO substituents on the phosphorus aryl rings ease the opening of the β‐chelate ring by CO and affect the kinetics of the overall CO/ethene copolymerization. Indeed, unlike the catalysts with the dppe and dppp ligands, the rate of carbonylation of the o‐MeO‐modified β‐keto chelates is limited by the Pd(alkyl)(CO) migratory insertion, which makes the overall copolymerization process independent of the CO pressure. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)
Organocatalysis with Chiral Formamides: Asymmetric Allylation and Reduction of Imines
Authors: Baudequin Christine , Chaturvedi Devdutt , Tsogoeva Svetlana B. 
Published: April 2007

AbstractSimple aldimine, derived from p‐nitrobenzaldehyde and 2‐aminophenol, reacts with allyltrichlorosilane in the presence of chiral N‐formylproline activator 5 and an L‐proline additive to afford the corresponding homoallylic amine in good yield (84 %) and with moderate enantioselectivity (43 % ee). The role of the second formamide moiety in the activator is crucial to bring about the enhancement in the reaction rate and enantioselectivity, as C2‐chiral bisformamide 1 promotes for the same allylation reaction in higher yield (94 %) and enantioselectivity (83 % ee). Chiral monoformamide 5 (10 mol‐%), with the assistance of HMPA as an additive, also catalyses the asymmetric reduction of ketimine 13 in the presence of trichlorosilane in good yield and enantioselectivity (75 %, 81 % ee). (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)
Pt‐Nanoparticle Incorporated Carbon Paste Electrode for the Determination of Cu(II) Ion by Anodic Stripping Voltammetry
Authors: Yoon Jang‐Hee , Muthuraman G. , Yang JeeEun , Shim Yoon‐Bo , Won Mi‐Sook 
Published: April 2007

AbstractPt‐nanoparticles were synthesized and introduced into a carbon paste electrode (CPE), and the resulting modified electrode was applied to the anodic stripping voltammetry of copper(II) ions. The synthesized Pt‐nanoparticles were characterized by cyclic voltammetry, scanning electron microscopy and X‐ray photoelectron spectroscopy techniques to confirm the purity and the size of the prepared Pt‐nanoparticles (ca. 20 nm). This incorporated material seems to act as catalysts with preconcentration sites for copper(II) species that enhances the sensitivity of Cu(II) ions to Cu(I) species at a deposition potential of −0.6 V in an aqueous solution. The experimental conditions, such as, the electrode composition, pH of the solution, pre‐concentration time, were optimized for the determination of Cu(II) ion using as‐prepared electrode. The sensitivity changes on the different binder materials and the presence of surfactants in the test solution. The interference effect of the coexisted metals were also investigated. In the presence of surfactants, especially TritonX‐100, the Cu(II) detection limit was lowered to 3.9×10−9 M. However, the Pt‐nanoparticle modified CPE begins to degrade when the period of deposition exceeds to 10 min. Linear response for copper(II) was found in the concentration range between 3.9×10−8 M and 1.6×10−6 M, with an estimated detection limit of 1.6×10−8 M (1.0 ppb) and relative standard deviation was 4.2% (n=5).
Automatic generation control of multi‐area power system using fuzzy logic controller
Authors: Subbaraj P. , Manickavasagam K. 
Published: April 2007

AbstractThis paper presents an application of Fuzzy Logic Controller (FLC) with triangular and gauss membership functions to study Automatic Generation Control (AGC) of a four‐area interconnected power system. Out of the four areas three have steam turbines and one has hydro turbine. All steam turbines in the system contain the reheat effect of non‐linearity and hydro turbine contains upper and lower constraints for generation rate. The result proves that the performance of FLC with Gaussian membership function is better than that of conventional controller. Copyright © 2007 John Wiley & Sons, Ltd.