Passive quasi-free states of the noninteracting Fermi gas

The passive quasi-free states of the noninteracting Fermi gas with continuous one-particle hamiltonian H are computed. They turn out to be the well-known Fermi-Dirac states, or limits thereof. This still holds true if the spectrum of H has both a continuous and a discrete part, except for the appearance of a class of “ground state-like” states showing a local random excitation of the point spectrum in a neighborhood of the Fermi energy. When H has only pure point spectrum, the requirement that a state be passive and quasi-free is no longer sufficient to charac terize the Fermi-Dirac distributions.     

Dynamical structure factors and electron transport phenomena in simple metals

Odessa Institute of Low-Temperature Technology and Power Engineering. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 86, No. 1, pp. 111–119, January, 1991.     

Nonequilibrium stationary states of noninteracting electrons in a one-dimensional lattice

Nonequilibrium stationary states of a one-dimensional quantum conductor placed between two reservoirs are investigated. Applying the theory of C^*-algebra, as t→+∞, any state including the degrees of freedom of reservoirs is shown to weakly evolve to a quasifree stationary state with nonvanishing currents. The stationary state exhibits transports which are consistent with nonequilibrium thermodynamics and, in this sense, it has broken time symmetry. Particularly, the electric and energy currents are shown to be expressed by two-probe Landauer-type formulas and they reduce to the results by Sivan–Imry and Bagwell–Orlando in appropriate regimes. As a consequence of the time reversal symmetry, there exists another stationary state with anti-thermodynamical transports, which is the t→−∞ limit of the initial state. The consistency between the dynamical reversibility and the irreversibility of the evolution of states is discussed as well.     

Trie size in a dynamic list structure

This article considers a classical binary tree implementation of a set of keys: the trie. The trie size properties in a static environment are well known: The size is asymptotically Gaussian when the number of keys is large. In this article we analyze the trie in a dynamic environment, where the trie is allowed to grow and shrink in a probabilistic way. It appears that the trie size can be described by a stochastic process which is asymptotically Gaussian non-Markovian. This also allows the complete asymptotic analysis of the trie size maximum and the trie size integrated cost. © 1994 John Wiley & Sons, Inc.     

一类变结构动态系统的非光滑最优性条件

研究了一类事件驱动的变结构动态系统的非光滑最优性条件. 通过引入一个新的时间变量, 将变结构动态系统的最优性问题转化为古典动态系统的最优性问题. 基于广义微分和古典动态系统的最优性理论, 得到了该系统的Frechet上微分形式的必要性条件, 推广了已有文献的相关结论. 结果表明, 在系统的连续运行过程中, 控制变量、协态变量和状态变量满足最小值原理和协态方程. 在系统的运行模型发生改变时, 协态变量产生一定的跳跃, 哈密尔顿函数连续. 最后通过一个算例说明了该结论的有效性.     

Optimum control laws in a non-autonomous dynamic model of a gas field

A model of gas field development described as a nonlinear optimum control problem with an infinite planning horizon is considered. The Pontryagin maximum principle is used to solve it. The theorem on sufficient optimumity conditions in terms of constructions of the Pontryagin maximum principles is used to substantiate the optimumity of the extremal solution. A procedure for constructing the optimum solution by dynamic programming is described and is of some methodological interest. The obtained optimum solution is used to construct the Bellman function. Reference is made to a work containing an economic interpretation of the problem.     

Rapid dynamic programming algorithms for RNA secondary structure

Prediction of RNA secondary structure from the linear RNA sequence is an important mathematical problem in molecular biology. Dynamic programming methods are currently the most useful computer technique but are frequently very expensive in running time. In this paper new dynamic programming algorithms are presented which reduce the required computation. The first polynomial time algorithm is given for predicting general secondary structure.     

Flow separation structure in a nonstationary viscous gas flowing over a body

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 240–247, 1993.     

Approximate analytical solutions of fractional gas dynamic equations

In this article, differential transform method (DTM) has been successfully applied to obtain the approximate analytical solutions of the nonlinear homogeneous and non-homogeneous gas dynamic equations, shock wave equation and shallow water equations with fractional order time derivatives. The true beauty of the article is manifested in its emphatic application of Caputo fractional order time derivative on the classical equations with the achievement of the highly accurate solutions by the known series solutions and even for more complicated nonlinear fractional partial differential equations (PDEs). The method is really capable of reducing the size of the computational work besides being effective and convenient for solving fractional nonlinear equations. Numerical results for different particular cases of the equations are depicted through graphs.     

A viscous approximation for a 2-D steady semiconductor or transonic gas dynamic flow: Existence theorem for potential flow

In this paper we solve a boundary value problem in a two-dimensional domain O for a system of equations of Fluid-Poisson type, that is, a viscous approximation to a potential equation for the velocity coupled with an ordinary differential equation along the streamlines for the density and a Poisson equation for the electric field. A particular case of this system is a viscous approximation of transonic flow models. The general case is a model for semiconductors. We show existence of a density ρ, velocity potential φ, and electric potential Φ in the bounded domain O that are C^1,α(O¯), C^2,α(O¯), and W^2,α(O¯) functions, respectively, such that ρ, φ, Φ, the speed |Δφ|, and the electric field E = ΔΦ are uniformly bounded in the viscous parameter. This is a necessary step in the existing programs in order to show existence of a solution for the transonic flow problem. © 1996 John Wiley & Sons, Inc.