A search technique for global optimization in a chaotic environment

We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters.     

一类拟线性椭圆方程边值问题弱解的研究

本文应用上、下解方法和 Leray-Schauder不动点定理 ,证明了一类拟线性椭圆方程边值问题弱解的存在性 ,并且给出了一个应用实例     

GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION

A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators dt and its dual, creation operators t*.     

A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.     

Theory of interfacial phase transitions in surfactant systems

The spin-1 Ising model, which is equivalent to the three-component lattice gas model, is used to study wetting transitions in three-component surfactant systems consisting of an oil, water, and a nonionic surfactant. Phase equilibria, interfacial profiles, and interfacial tensions for three-phase equilibrium are determined in mean field approximation, for a wide range of temperature and interaction parameters. Surfactant interaction parameters are found to strongly influence interfacial tensions, reducing them in some cases to ultralow values. Interfacial tensions are used to determine whether the middle phase, rich in surfactant, wets or does not wet the interface between the oil-rich and water-rich phases. By varying temperature and interaction parameters, a wetting transition is located and found to be of the first order. Comparison is made with recent experimental results on wetting transitions in ternary surfactant systems.This paper is dedicated to J. K. Percus in honor of his 65th birthday.     

An applied cell mapping method for optimal control problems

From the application point of view, a series of modifications are proposed for the cell mapping method discussed in Ref. 1 for the optimal control analysis of dynamical systems. The cell order around the target set is rearranged. A set of common discriminate principles is used for the selection of the optimal one among competing control strategies of the same cost. Inequality constraints of the system are taken into account. The number of elements in the set of allowable time intervals is not prescribed, but left open. These modifications seem to make the cell mapping method more efficient for analyzing feedback systems and for obtaining their global optimal control information. The algorithms presented in this paper could broaden the application of the cell mapping approach of Ref. 1 to a wider class of engineering problems.     

A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

Commuting and stable feedback design for switched linear systems

In the paper, commuting and stable feedback design for switched linear systems is investigated. This problem is formulated as to build up suitable state feedback controller for each subsystem such that the closed-loop systems are not only asymptotically stable but also commuting each other. A new concept, common admissible eigenvector set (CAES), is introduced to establish necessary/sufficient conditions for commuting and stable feedback controllers. For second-order systems, a necessary and sufficient condition is established. Moreover, a parametrization of the CAES is also obtained. The motivation comes from stabilization of switched linear systems which consist of a family of LTI systems and a switching law specifying the switching between them, where if all the subsystems are stable and commuting each other, then the total system is stable under arbitrary switching.     

时变线性系统特征根判稳的推广

本文研究了二维时变线性系统零解的稳定性，给出了一些允许系数矩阵主对角元变号，系数矩阵特征根变号的判定稳定性的充分条件。