Furtivity and Masking Problems in Time-Dependent Electromagnetic Obstacle Scattering

In this paper, we consider furtivity and masking problems in time-dependent three-dimensional electromagnetic obstacle scattering. That is, we propose a criterion based on a merit function to minimize or to mask the electromagnetic field scattered by a bounded obstacle when hit by an incoming electromagnetic field and, with respect to this criterion, we drive the optimal strategy. These problems are natural generalizations to the context of electromagnetic scattering of the furtivity problem in time-dependent acoustic obstacle scattering presented in Ref. 1. We propose mathematical models of the furtivity and masking time-dependent three-dimensional electromagnetic scattering problems that consist in optimal control problems for systems of partial differential equations derived from the Maxwell equations. These control problems are approached using the Pontryagin maximum principle. We formulate the first-order optimality conditions for the control problems considered as exterior problems defined outside the obstacle for systems of partial differential equations. Moreover, the first-order optimality conditions derived are solved numerically with a highly parallelizable numerical method based on a perturbative series of the type considered in Refs. 2–3. Finally, we assess and validate the mathematical models and the numerical method proposed analyzing the numerical results obtained with a parallel implementation of the numerical method in several experiments on test problems. Impressive speedup factors are obtained executing the algorithms on a parallel machine when the number of processors used in the computation ranges between 1 and 100. Some virtual reality applications and some animations relative to the numerical experiments can be found in the website http://www.econ.unian.it/recchioni/w10/.     

Single molecule study of DNA collision with elliptical nanoposts conveyed by hydrodynamics

Periodic arrays of micro‐ or nanopillars constitute solid‐state matrices with excellent properties for DNA size separation. Nanofabrication technologies offer many solutions to tailor the geometry of obstacle arrays, yet most studies have been conducted with cylinders arranged in hexagonal lattices. In this report, we investigate the dynamics of single DNA collision with elliptical nanoposts using hydrodynamic actuation. Our data show that the asymmetry of the obstacles has minor effect on unhooking dynamics, and thus confirm recent predictions obtained by Brownian dynamics simulations. In addition, we show that the disengagement dynamics are correctly predicted by models of electrophoresis, and propose that this consistency is associated to the confinement in slit‐like channels. We finally conclude that elliptical posts are expected to marginally improve the performances of separation devices.     

解单障碍问题的Lagrangian乘子非匹配网格区域分解法

针对二阶椭圆型单障碍问题提出了一类基于非匹配网格的Lagrang ian乘子非重叠型区域分解方法.并在适当条件下给出了该方法的收敛性分析和收敛速度估计.     

On unilateral contact of two plates aligned at an angle to each other

The contact problem for two elastic plates aligned at a prescribed angle to each other is considered. The set of contact points is assumed to be unknown in advance and to be determined only after the problem is solved. Various formulations of the problem are given, and their equivalence is proved. A complete set of boundary conditions fulfilled on the contact domain is found, and the character of satisfaction of these conditions is described. The asymptotic properties of solutions are studied for rigidity parameters of the contacting plates tending to infinity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 42–58, July–August, 2008.     

非齐次障碍问题的正则性结果

本文研究了非齐次椭圆方程的障碍问题,给出了二阶非齐次障碍问题解的定义,利用Poincar啨不等式,获得非齐次障碍问题的解及其导数的一些性质,填补了对非齐次障碍问题研究的空白.     

Optimal investment with transaction costs based on exponential utility function: a parabolic double obstacle problem

This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.     

Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

一类拟线性椭圆障碍问题极小正解的存在性

该文使用Ｌｉｏｎｓ的集中紧性原理和变分方法,证明了一类非齐次拟线性椭圆型方程对应的障碍问题中极小正解的存在性．     

椭圆方程双侧障碍问题解的局部有界性

研究非齐次椭圆方程divA(x,u,■u)=f(x)的双侧障碍问题,获得了解的局部有界性结果,这可以认为是经典结果的推广.