The goal of this paper is two-fold. First, based on the interpretation of a quantum tight-binding model in terms of a classical Hamiltonian map, we consider the Anderson localization (AL) problem as the Fermi-Pasta-Ulam (FPU) effect in a modified dynamical system containing both stable and unstable (inverted) modes. Delocalized states in the AL are analogous to the stable quasi-periodic motion ...

We consider the FPU model with nonlinearity starting with terms of order n ≥ 3. We compute the resonant normal form in the region where only one low-frequency mode is excited and deduce rigorous results on the correspondence between the dynamics of the normal form and that of the complete system. As n varies, we give a criterion in order to deduce whether the FPU phenomenon (formation of a meta...

This paper focuses on the solution to a system of linear equations by iterative methods. A short survey is presented on direct and iterative methods. Three practical iterative methods are discussed. Two preconditioning techniques are employed to speed up the iterations. Two testbeds are used to carry out a comparison of these iterative methods. For the Dell8200 PC testbed, we show the pros and ...

We study, both numerically and analytically, the time needed to observe the breaking of an FPU α-chain in two or more pieces, starting from an unbroken configuration at a given temperature. It is found that such a “chopping” time is given by a formula that, at low temperatures, is of the Arrhenius-Kramers form, so that the chain does not break up on an observable time-scale. The result explains...

In this paper, we develop dispersive PDE techniques for the Fermi–Pasta–Ulam (FPU) system with infinitely many oscillators, and show that general solutions to infinite FPU can be approximated by counter-propagating waves governed Korteweg–de Vries (KdV) equation as lattice spacing approaches zero. Our result not only simplifies hypotheses but also reduces regularity requirement in previous stud...

Abstract The double revolving fiber positioning unit (FPU) is one of the key technologies Large Sky Area Multi-Object Fiber Spectroscope Telescope (LAMOST). accuracy computer controlled FPU depends on robot as well initial parameters FPU. These may deteriorate with time when running in non-supervision mode, which would lead to bad position and further efficiency degradation subsequent surveys. ...

Bushes of normal modes represent the exact excitations in the nonlinear physical systems with discrete symmetries [Physica D 117 (1998) 43]. The present paper is the continuation of our previous paper [Physica D 166 (2002) 208], where these dynamical objects of new type were discussed for the monoatomic nonlinear chains. Here, we develop a simple crystallographic method for finding bushes in no...

We present a nonlinear model that allows exploration of the relationship between energy relaxation, thermal conductivity and the excess of low-frequency vibrational modes (LFVMs) that are present in glasses. The model is a chain of the Fermi-Pasta-Ulam (FPU) type, with nonlinear second neighbour springs added at random. We show that the time for relaxation is increased as LFVMs are removed, whi...