Applied Mathematics Research eXpress

A zero-sum finite-horizon differential game with linear dynamics and bounded controls is considered. The target set is a given hyperplane in the state space. The cost function is the distance between the terminal state and this hyperplane. The complete game solution is obtained in two classes of controls: open-loop and feedback-based controls.

V. Y. Glizer

V. Turetsky

Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls

线性动力学与有界控制微分博弈的完全解

The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. [6, 53, 54]. This formula was derived directly in the thermodynamic limit, within the framework of C*-algebras and noncommutative calculi defined over infinite spaces. As such, the numerical implementation of the formalism encountered fundamental obstacles. The present work defines a C*-algebra and an approximate noncommutative calculus over a finite real-space torus, which naturally leads to an approximate finite-volume noncommutative Kubo formula, amenable on a computer. For finite temperatures and dissipation, it is shown that this approximate formula converges exponentially fast to its thermodynamic limit, which is the exact noncommutative Kubo formula. The approximate noncommutative Kubo formula is then deconstructed to a form that is implementable on a computer and simulations of the quantum transport in a two-dimensional disordered lattice gas in a magnetic field are presented.

E. Prodan

Quantum Transport in Disordered Systems Under Magnetic Fields: A Study Based on Operator Algebras

磁场下无序系统的量子输运：基于算子代数的研究

In this paper, we study a model of Landau–Lifshitz equations of ferromagnetism that does not contain the regularizing term of exchange energy. Without the exchange energy, due to the lack of certain derivative estimates and compactness, such an equation becomes degenerate and cannot be studied by the usual Galerkin method based on the elliptic equation theory. For such a degenerate model, it is known that the weak solutions can be obtained through the quasi-stationary limits of certain coupled Landau–Lifshitz–Maxwell systems as the dielectric permittivity tends to zero. In this paper, we use a simplified Landau–Lifshitz–Maxwell system with constant permittivity to present a different but more direct proof of this quasi-stationary limit result. We also establish a finite-time local L2-stability result for weak solutions of the degenerate Landau–Lifshitz equation, which yields the new uniqueness result on weak solution with bounded initial data.

W. Deng

B. Yan

Quasi-Stationary Limit and a Degenerate Landau-Lifshitz Equation of Ferromagnetism

准稳态极限与铁磁性的退化朗道-利夫希茨方程

In this paper, we investigate a risk measure, namely, the worst-case value-at-risk with support information. We obtain its tractable and equivalent representations. Then by using properly defined uncertainty sets, we show that this risk measure is coherent. We extend the case with exactly known moments to uncertain situations and get corresponding optimization formulations. We report some numerical experiments for robust portfolio optimization to illustrate the efficiency of this method.

G.-M. Luo

Coherent Worst-Case Value-at-Risk with Applications to Robust Portfolio Optimization

相干最坏情况风险价值及其在鲁棒投资组合优化中的应用

The Armstrong–Frederick model for nonlinear kinematic hardening is regarded as a benchmark model in contemporary elastoplasticity. This work presents an existence result to an appropriately time-rescaled evolution for that model. To do so, we have to resort to a regularization of the dependence of the convex of plasticity upon the back stress. Such a regularization process seems to be the unfortunate price one has to pay for a successful mathematical analysis.

G. A. Francfort

U. Stefanelli

Quasi-Static Evolution for the Armstrong-Frederick Hardening-Plasticity Model

Armstrong-Frederick硬化-塑性模型准静态演化

We formulate a model for a point defect embedded in a homogeneous multilattice crystal with an empirical interatomic potential interaction. Under a natural phonon stability assumption, we quantify the decay of the long-range elastic fields with increasing distance from the defect. These decay estimates are an essential ingredient in quantifying approximation errors in coarse-grained models and in the construction of optimal numerical methods for approximating crystalline defects.

Derek Olson

Christoph Ortner

Regularity and Locality of Point Defects in Multilattices

多层晶格中点缺陷的规律性和局域性

We study the macroscopic limit of a chain of atoms governed by the Newton equation. It is known from the work of Blanc, Le Bris, and Lions, that this limit is the solution of a nonlinear wave equation, as long as this solution remains smooth. We show numerically and mathematically that if the distances between particles remain bounded, it is not the case any more when there are shocks at least for a convex nearest-neighbor interaction potential with convex derivative.

Xavier Blanc

Marc Josien

From the Newton Equation to the Wave Equation: The Case of Shock Waves

从牛顿方程到波动方程：冲击波的情况

We show that resonant states in scattering on asymptotically hyperbolic manifolds that are analytic near conformal infinity have analytic radiation patterns at infinity. On even asymptotically hyperbolic manifolds, we also show that smooth solutions of Vasy operators with analytic coefficients are also analytic. That answers a question of Zworski ([14] Conjecture 2). The proof is based on previous results of Baouendi–Goulaouic and Bolley–Camus–Hanouzet, and for convenience of the reader, we present an outline of the proof of the latter.

Claude Zuily

Real Analyticity of Radiation Patterns on Asymptotically Hyperbolic Manifolds

渐近双曲流形上辐射模式的实解析性

We investigate well-accepted formulations describing charge transport in composite cathodes of batteries. Our upscaling of carefully selected microscopic equations shows three main features: A novel set of six equations equipped with nine effective parameters which systematically couple the microscale to the macroscale. The coupling of transport and flow equations allows us to account for three scales: pore scale, Darcy scale, and macroscale. The upscaled equations take phase separation during Li-intercalation into account as well as specific particle configurations.

Markus Schmuck

Upscaling of Solid-electrolyte Composite Intercalation Cathodes for Energy Storage Systems

能源存储系统中固态电解质复合插层阴极的放大

We study the stability of the cnoidal, dnoidal and snoidal elliptic functions as spatially-periodic standing wave solutions of the 1D cubic nonlinear Schrödinger equations. First, we give global variational characterizations of each of these periodic waves, which in particular provide alternate proofs of their orbital stability with respect to same-period perturbations, restricted to certain subspaces. Second, we prove the spectral stability of the cnoidal waves (in a certain parameter range) and snoidal waves against same-period perturbations, thus providing an alternate proof of this (known) fact, which does not rely on complete integrability. Third, we give a rigorous version of a formal asymptotic calculation of Rowlands to establish the instability of a class of real-valued periodic waves in 1D, which includes the cnoidal waves of the 1D cubic focusing nonlinear Schrödinger equation, against perturbations with period a large multiple of their fundamental period. Finally, we develop a numerical method to compute the minimizers of the energy with fixed mass and momentum constraints. Numerical experiments support and complete our analytical results.

出版信息	出版商: Oxford University Press，出版周期: ，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 2004，原创研究文献占比: ，自引率:， Gold OA占比:

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