In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define H∞ balancing. Furthermore, we investigate the monotonicity of the Hamilton-Jacobi-Bellman equation...

The distortion of structure of a simple, inverse-12, soft-disk fluid undergoing two-dimensional plane Couette flow was studied by nonequilibrium molecular dynamics (NEMD) simulation and by equilibrium Monte Carlo (MC) simulation with a nonequilibrium potential, under which the equilibrium structure of the fluid is that of the nonequilibrium fluid. Extension of the iterative predictor-corrector ...

A description of Monte Carlo methods for simulation of proteins is given. Advantages and disadvantages of the Monte Carlo approach are presented. The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented. Some of the standard and some of the more recent ways of performing Monte Carlo on proteins are presented. A discussion of the...

The departures of the populations of the excited states of hydrogen from those found under conditions of thermodynamic equilibrium are calculated using a general iterative method. Calculations of b, and d(ln b,,)/dn are carried out for conditions found in gaseous nebulae, and the sensitivity of the solution to certain assumptions is discussed.

A new algorithm is presented for computing Nash equilibria of ̄nite games. Using Kohlberg and Mertens' structure theorem we show that a homotopy method can be represented as a dynamical system and implemented by Smale's global Newton method. The algorithm is outlined and computational experience is reported. JEL Classi ̄cation C63.

The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions base...

We perform Monte Carlo computer simulations of nematic drops in equilibrium with their vapor using a Gay-Berne interaction between the rod-like molecules. To generate the drops, we initially perform NPT simulations close to the nematic-vapor coexistence region, allow the system to equilibrate and subsequently induce a sudden volume expansion, followed with NVT simulations. The resultant drops c...

A mathematical method of determining the values at equilibrium and the constant rates in inter-conversion process of conformational labile molecules is proposed. No measuring method is used. In most of the cases, at equilibrium, the concentrations of the main species are equal. Thus, we have equilibrium of concentrations too. The symmetry plays a central role.  2012 Trade Science Inc. INDIA

The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an alternative proof of a fundamental property of a...