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/.     

AN ESTIMATE ON THE DISTRIBUTION AND MOMENTS OF THE LAST EXIT TIME OF AN ELLIPTIC DIFFUSION PROCESS

Let LB be the last exit time from a compact set B of an elliptic diffusion process X. A moderate estimate for the distribution of LB is obtained, and the sufficient and necessary condition for Ex(LBk)<∞is proved.     

Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.     

Quantitative High Resolution Electron Microscopy

 With the resolution becoming sufficient to reveal individual atoms, HREM is now entering the stage where it can compete with X-ray methods to quantitatively determine atomic structures of materials without much prior knowledge, but with the advantage of being applicable to aperiodic objects such as crystal defects. In our view the future electron microscope will be characterised by a large versatility in experimental settings under computer control such as the illumination conditions (TEM-STEM), CBED, detecting conditions (diffraction, image, ptychography) and many other tunable parameters such as focus (g), voltage, spherical aberration (C _s ), beam tilt, etc. Since modern detectors can detect single electrons, also the counting statistics is known. The only limiting factor in the experiment will be the total number of electrons that interact with the object during the experiment due to the limitations in the exposure time or in the object damage. However, instrumental potentialities will never be exploited fully if not guided by an experimental strategy. Here intuitive guidelines can be very deceptive. For instance an image made with the best electron microscope (C _s  = 0) at the best focus (g = 0) from the best object (phase object) would show no contrast at all. Hence, questions such as what is the best C _s , focus, object thickness, etc. can only be answered properly if done using a method of experiment design.     

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.