Showing papers by "Alexander M. Samsonov published in 2009"

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures

Abstract: We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Nonlinear long-wave models for imperfectly bonded layered waveguides

Abstract: We propose a composite lattice model for describing nonlinear waves in a two-layer waveguide with adhesive bonding. We first consider waves in an anharmonic chain of oscillating dipoles and show that the corresponding asymptotic long-wave model for longitudinal waves coincides with the Boussinesq-type equation previously derived for a macroscopic waveguide using the nonlinear elasticity approach. We also show that in this model, there is no simple analogy between long longitudinal and long flexural waves. Then, for a composite lattice, we derive two new model systems of coupled Boussinesq-type equations for long nonlinear longitudinal waves and conjecture that a similar description exists in the framework of dynamic nonlinear elasticity.

DEEP - Differential Evolution Entirely Parallel Method for Gene Regulatory Networks

Abstract: DEEP - Differential Evolution Entirely Parallel method is applied to the biological data fitting problem. We introduce a new migration scheme, in which the best member of the branch substitutes the oldest member of the next branch, that provides a high speed of the algorithm convergence. We analyze the performance and efficiency of the developed algorithm on a test problem of finding the regulatory interactions within the network of gap genes that control the development of early Drosophila embryo. The parameters of a set of nonlinear differential equations are determined by minimizing the total error between the model behavior and experimental observations. The age of the individuum is defined by the number of iterations this individuum survived without changes. We used a ring topology for the network of computational nodes. The computer codes are available upon request.