Asymptotic stabilization of some equilibria of an underactuated underwater vehicle

The stabilization problem for selected relative equilibria of an underactuated rigid body, modelling a simple underwater vehicle, moving in an ideal fluid is addressed. State feedback control laws achieving local asymptotic stability of a forward motion and of a diving/rising with forward/reverse motion are proposed. The control design exploits the Hamiltonian nature of the system to be controlled and it is based on the so-called interconnection and damping assignment (IDA) procedure. Simulation results complete the work.     

A stochastic maximum principle for systems with jumps, with applications to finance

We consider a stochastic control problem with linear dynamics with jumps, convex cost criterion, and convex state constraint, in which the control enters the drift, the diffusion, and the jump coefficients. We allow these coefficients to be random, and do not impose any L^p-bounds on the control.

We obtain a stochastic maximum principle for this model that provides both necessary and sufficient conditions of optimality. This is the first version of the stochastic maximum principle that covers the consumption–investment problem in which there are jumps in the price system.     

The analysis of solvation in ionic liquids and organic solvents using the Abraham linear free energy relationship

The contentions made in an earlier paper [J Chem Technol Biotechnol 80 : 133–137 (2005)] that the coefficients of the Abraham solvation equation do not provide meaningful information on the molecular properties of ionic liquid solvents is refuted. The objections noted in the earlier paper disappear when the solvation equation model is correctly applied to the experimental data. It is further shown that the coefficients of the Abraham solvation equations can be used to characterize ionic liquids and can be used to select solvents for the solubility of gaseous solutes. Copyright © 2006 Society of Chemical Industry     

Spectral approximations of the Stokes problem by divergence-free functions

The method of Moser, Moin, and Leonard (1983) for the approximation of the three-dimensional Navier-Stokes equations using divergence-free subspaces is revisited and analyzed. It is shown that the computed velocity field converges to the physical one with spectral accuracy. Moreover, a method for recovering the pressure field is proposed. This method is stable and provides a pressure that converges to the physical one with spectral accuracy.     

A conservative discontinuous Galerkin scheme for the 2D incompressible Navier–Stokes equations

In this paper we consider a conservative discretization of the two-dimensional incompressible Navier–Stokes equations. We propose an extension of Arakawa’s classical finite difference scheme for fluid flow in the vorticity–stream function formulation to a high order discontinuous Galerkin approximation. In addition, we show numerical simulations that demonstrate the accuracy of the scheme and verify the conservation properties, which are essential for long time integration. Furthermore, we discuss the massively parallel implementation on graphic processing units.     

利用Liapanov直接方法判定差分方程稳定性

研究差分方程稳定性的强有力的方法是Liapanov直接方法,这一方法的核心思想是针对所研究的方程,构造出其相应的Liapanov函数,利用它来判定方程的稳定性．     

A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion

In this paper, we propose a new compact fourth-order accurate method for solving the two-dimensional fourth-order elliptic boundary value problem with third-order nonlinear derivative terms. We use only 9-point single computational cell in the scheme. The proposed method is then employed to solve Navier–Stokes equations of motion in terms of streamfunction–velocity formulation, and the lid-driven square cavity problem. We describe the derivation of the method in details and also discuss how our streamfunction–velocity formulation is able to handle boundary conditions in terms of normal derivatives. Numerical results show that the proposed method enables us to obtain oscillation-free high accuracy solution.     

非圆曲线的数控处理及程序实现

引用优化设计中一维搜索和黄金分割法,针对数控加工中非圆曲线的处理,给出实用、简洁和新颖的宏程序实现方法,解决在数控系统中求解方程组的问题,是数控用户快速解决相关应用问题的有效手段。     

Stability and control of nonlinear systems described by retarded functional equations: a review of recent results

This paper reports on recent results in a series of the work of the authors on the stability and nonlinear control for general dynamical systems described by retarded functional differential and difference equations. Both internal and external stability properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization. In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly, sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of coupled systems comprised of retarded functional differential and difference equations.     

Linear complete differential resultants and the implicitization of linear DPPEs

The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of n$n$ linear differential polynomial parametric equations in n−1$n-1$ differential parameters. We give necessary conditions to ensure properness of the system of differential polynomial parametric equations.