bluuebunny/crossref_metadata_2025_split huggingface dataset:
Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
Authors: Bardos Claude , Golse François , Levermore C. David 
Published: April 2007

AbstractUsing 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

AbstractTruncated 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

AbstractWe 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

AbstractDifference 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

AbstractIn 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

AbstractThe 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

AbstractIf 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

AbstractWe 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

AbstractA 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

AbstractThis 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

AbstractThe 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

AbstractWe 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

AbstractIn 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

AbstractWe 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

AbstractUsing 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

AbstractSeveral 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

AbstractWe 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

AbstractMagnetic‐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

AbstractThe 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

AbstractWe 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

AbstractObjectiveSuicide 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.MethodsDuring 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.ResultsIn 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.ConclusionThese 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.
Magnetic resonance imaging as a tool for in vivo and ex vivo anatomical phenotyping in experimental genetic models
Authors: Pitiot Alain , Pausova Zdenka , Prior Malcolm , Perrin Jennifer , Loyse Naomi , Paus Tomáš 
Published: April 2007

AbstractThis article describes a suite of computational approaches suitable for deriving various quantitative phenotypes from structural magnetic resonance (MR) images obtained in rodents and used subsequently in genetic studies of complex traits. We begin by introducing the basic principles of genetic studies of complex traits in experimental models. We then illustrate the use of MR‐based computational anatomy in vivo and ex vivo, and in combination with histology. This work was carried out in two inbred strains of rats, namely spontaneously hypertensive rats and Brown Norway rats; these are parental strains of the only existing panel of recombinant inbred strains of rats. The rats were scanned in vivo at two time points (at 8 and 12 weeks of age) and ex vivo (at 12 weeks of age). We describe between‐strain differences and across‐time changes in brain and kidney volumes, as well as regional variations in brain structure using surface‐ and deformation‐based approaches. We conclude by discussing the power of the population‐based computational analysis of MR images, and their fusion with histology, in studies of complex traits. Hum Brain Mapp, 2007. © 2007 Wiley‐Liss, Inc.