Finite-time Behavior Research Articles

Finite-time behaviour of solutions to nonlinear Schrödinger evolution equations

Finite-time behaviour of solutions to nonlinear Schrödinger evolution equations

On the finite-time behaviour for nonlinear Schrödinger equations

Consider the nonlinear Schrödinger equationu t −iΔu=f(u). Forf(u)=±|u|1+p , ±i|u|1+p , ±u|u| p (p>0), and the Dirichlet boundary or nonlinear boundary (including the Neumann boundary and the Robin boundary) conditions, we establish the local estimates for the timet to the solutions of the initial-boundary value problems. Being based up on these estimates, we investigate the blowing-up properties of the solutions.

Dynamical properties of 2D systems with site disorder

Abstract Dynamical properties are studied of particles which perform random walks on square lattices, where a fraction c of the sites has been replaced by impurities. The latter may be either better conducting than the host, or worse conducting or even non-conducting. The quantities studied are the velocity autocorelation function, the return probability, the density of states and Burnett functions. The results include short-time, finite-time and long-time behavior. Prefactors of the long-time behavior are calculated up to second order in c . Comparison with numerical simulations is made. Different definitions of the diffusion coefficient (via the second moment of displacement, the return probability or the density of states) are shown to give different answers.

Convergence and finite-time behavior of simulated annealing

Simulated annealing is a randomized algorithm which has been proposed for finding globally optimum least-cost configurations in large NP-complete problems with cost functions which may have many local minima. A theoretical analysis of simulated annealing based on its precise model, a time-inhomogeneous Markov chain, is presented. An annealing schedule is given for which the Markov chain is strongly ergodic and the algorithm converges to a global optimum. The finite-time behavior of simulated annealing is also analyzed and a bound obtained on the departure of the probability distribution of the state at finite time from the optimum. This bound gives an estimate of the rate of convergence and insights into the conditions on the annealing schedule which gives optimum performance.

Convergence and finite-time behavior of simulated annealing

Simulated annealing is a randomized algorithm which has been proposed for finding globally optimum least-cost configurations in large NP-complete problems with cost functions which may have many local minima. A theoretical analysis of simulated annealing based on its precise model, a time-inhomogeneous Markov chain, is presented. An annealing schedule is given for which the Markov chain is strongly ergodic and the algorithm converges to a global optimum. The finite-time behavior of simulated annealing is also analyzed and a bound obtained on the departure of the probability distribution of the state at finite time from the optimum. This bound gives an estimate of the rate of convergence and insights into the conditions on the annealing schedule which gives optimum performance.

Simple Finite-Time Settling Control and Manipulated-Variable Softening for Reverse Reaction, Overshoot, and Oscillatory Processes

An easily implemented digital control method based on a discrete-time process model has been extended to encompass many process types found in common industrial control problems. The system uses a controller and observer based on finite-time settling design; the controller and observer gains are computed directly (noniteratively) from the process model parameters. A softening filter which preserves the finite-time settling behavior of the closed loop system has been developed to minimize manipulated variable excursions.

On the evaluation of independent binary features (Corresp.)

On the evaluation of independent binary features (Corresp.)