Symbolic stochastic dynamical systems viewed as binary N-step Markov chains

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding N symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length L are obtained analytically and numerically. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker-Planck equation governing the distribution function of the L-words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.Comment: 14 pages, 13 figure

Pattern formation and localization in the forced-damped FPU lattice

We study spatial pattern formation and energy localization in the dynamics of an anharmonic chain with quadratic and quartic intersite potential subject to an optical, sinusoidally oscillating field and a weak damping. The zone-boundary mode is stable and locked to the driving field below a critical forcing that we determine analytically using an approximate model which describes mode interactions. Above such a forcing, a standing modulated wave forms for driving frequencies below the band-edge, while a ``multibreather'' state develops at higher frequencies. Of the former, we give an explicit approximate analytical expression which compares well with numerical data. At higher forcing space-time chaotic patterns are observed.Comment: submitted to Phys.Rev.

Modeling of humps formation during deep-penetration laser welding

A 3-D transient model based on the numerical resolution of fluid-flow and the heat transfer equations is developped for deep penetration laser welding at high welding speed regime, whic results in the humping phenomenon. The physical mechanisms included in our model concern matter melting, vaporization inducing a recoil pressure and solidification. The implementation of developed procedures called User Defined Functions working interactively with the CFD Fluent code and a dynamic mesh method allowed us to treat the problem with specific and complex boundary conditions. As a result regular humps could be observed after resolidification on the weld seam

What we expect from weakly dissipating materials at the range of plasmon resonance frequencies

10.1109/IPGC.2008.47813482008 IEEE PhotonicsGlobal at Singapore, IPGC 2008

Enhanced scattering efficiencies in spherical particles with weakly dissipating anisotropic materials

10.1007/s00339-008-4572-5Applied Physics A: Materials Science and Processing924773-776APAM