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At least 1,135 records · Page 63Linked to original sources
PubMed2001

Interplays between Harper and Mathieu equations.

This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation. For this purpose, one resorts to the nonlinear oscillations characterizing the Mathieu equation. This leads to the derivation of two kinds of energy formulas working in terms of cubic and quadratic algebraic equations, respectively. Combining such results yields quadratic equations to the energy description of the Harper equation, incorporating all parameters needed.

Journal Article↗
PubMed2001

Interplay of nonlinearity and geometry in a DNA-related, Klein-Gordon model with long-range dipole-dipole interaction.

Most of the studies on mathematical models of DNA are limited to next neighbor interaction. However, the coupling between base pairs is thought to be caused by dipole interaction, and, when the DNA strand is bent, the distances between base pairs become shorter, therefore the interactions with distant base pairs have to be taken into account. In this paper we analyze the existence and stability of breathers, i.e., localized oscillations in a simple model of bent DNA with long-range dipole interaction. Breathers have been suggested as precursors of the denaturation bubble.

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PubMed2003

Stochastic multiresonance due to interplay between noise and fractals.

Stochastic multiresonance is shown to occur in a general class of threshold-crossing systems, in which a derivative of the threshold-crossing probability with respect to a system parameter is a nonmonotonic function of the noise intensity. As an example, a two-dimensional chaotic map is considered, where the threshold-crossing probability follows the overlap of the fractal structures of chaotic saddles and the basins of escape in noise-induced crisis. The analytic theory is in reasonable agreement with the numerical results for spectral power amplification.

Journal Article↗
PubMed2003

Interplay of chemotaxis and chemokinesis mechanisms in bacterial dynamics.

Motivated by observations of the dynamics of Myxococcus xanthus, we present a self-interacting random walk model that describes the competition between chemokinesis and chemotaxis. Cells are constrained to move in one dimension, but release a chemical chemoattractant at a steady state. The bacteria sense the chemical that they produce. The probability of direction reversals is modeled as a function of both the absolute level of chemoattractant sensed directly under each cell as well as the gradient sensed across the length of the cell. If the chemical does not degrade or diffuse rapidly, the one-dimensional trajectory depends on the entire past history of the trajectory. We derive the corresponding Fokker-Planck equations, use an iterative mean-field approach that we solve numerically for short times, and perform extensive Monte Carlo simulations of the model. Cell positional distributions and the associated moments are computed in this feedback system. Average drift and mean squared displacements are found. Crossover behaviors among different diffusion regimes are found.

Bacterial Physiological Phenomena↗
PubMed2003

Prisoners' dilemma in real-world acquaintance networks: spikes and quasiequilibria induced by the interplay between structure and dynamics.

We study Nowak and May's spatial prisoners' dilemma game driven by mutations (random choices of suboptimal strategies) on empirical social networks. The time evolution of the cooperation level is highly complex containing spikes and steps between quasistable levels. A statistical characterization of the quasistable states and a study of the mechanisms behind the steps are given. We argue that the crucial structural ingredients causing the observed behavior is an inhomogeneous degree distribution and that the connections within vertices of highest degree are rather sparse. Based on these observations we construct model networks with a similar complex time evolution of the cooperation level.

Journal Article↗
PubMed2004

Interplay of impurities and solution flow as determinants of step pattern dynamics.

The first theory of step pattern evolution, the kinematic wave theory, employed the assumption of impurity effects on step kinetics. On the other hand, recent results have been considered within a framework linking step patterns to the mutual orientation of the solution flow and step motion directions in arbitrarily pure solutions. We explore the consequences of combining impurity and solution flow effects on the dynamics of the surface morphology of the (101) face of potassium dihydrogen phosphate (KDP) crystals. We employ phase-shifting interferometry for real time in situ monitoring of these dynamics. We find that, at solution supersaturations sigma</=0.035, step bunches form on all three vicinals of the (101) face regardless of the mutual orientation of the step motion and solution flow directions. Testing the mechanism of impurity-step pattern interactions, we show that bunching is caused by impurity molecules that adsorb on the surface and slow down and destabilize step trains without inducing growth cessation, i.e., the mechanism is inherently different from the one established for the (100) KDP face. We show that at sigma>0.040 impurities do not affect step bunching, and it is controlled by the direction of the solution flow, i.e., two distinct regimes of step bunching exist. The transition between the two regimes is governed by the exposure times of the terraces between steps tau : shorter tau's at higher growth rates lead to lower surface concentration of impurities and suppress the impurity effects on step kinetics and bunching.

Journal Article↗
PubMed2005

Interplay of instabilities in mounded surface growth.

We numerically study a one-dimensional conserved growth equation with competing linear (Ehrlich-Schwoebel) and nonlinear instabilities. As a control parameter is varied, this model exhibits a nonequilibrium phase transition between two mounded states, one of which exhibits slope selection and the other does not. The coarsening behavior of the mounds in these two phases is studied in detail. In the absence of noise, the steady-state configuration depends crucially on which of the two instabilities dominates the early time behavior.

Journal Article↗
PubMed2005

Interplay of collisions with quasilinear growth rates of relativistic electron-beam-driven instabilities in a superdense plasma.

We focus attention on the rapidly growing electromagnetic instabilities arising in the interaction of intense and relativistic electron beams (REB) with supercompressed thermonuclear fuel. REB-target system is considered neutralized in charge and current with a distribution function including beam and target temperatures. The electromagnetic filamentation (Weibel) instability is first considered analytically in a linear approximation. Relevant growth rates parameters then highlight density ratios between target and particle beams, as well as transverse temperatures. Significant refinements include mode-mode coupling and collisions with target electrons. The former qualify the so-called quasilinear (weakly turbulent) approach. Usually, it produces significantly lower growth rates than the linear ones. Collisions enhance them slightly for kc/omega(p) < 1, and dampen them strongly for kc/omega(p) < 1. In a low temperature target plasma, intrabeam scattering also contributes to the instability taming, while keeping it close to zero in a warm plasma. Our numerical exploration provides further support to the cone-angle configuration (Osaka experiment) with REB penetrating close to the dense core of superdense deuterium + tritium fuel.

Journal Article↗
PubMed2005

Interplay of entropic and memory effects in diffusion of methane in silicalite zeolites.

The role of entropic effects in methane distribution and transport in silicalite zeolites is studied using molecular dynamics in the limit of infinite dilution or small loading. Diffusive behavior and its anisotropy is assessed as a function of temperature where we find both an Arrhenius regime above 250 K and deviations thereof below such temperature. Using a previous probabilistic model, geometrical correlations or memory effects are evidenced and are shown to be enhanced as temperature is reduced. Deviations from Arrhenius behavior are concomitant with entropic effects. We find that, the preference of methane towards presence at intersections or channel centers changes at a threshold temperature. A discrete transition is found from a channel-center preferred phase, at low temperatures, versus an intersection preferred phase at high temperatures with evidence of hysteresis effects. Such entropic effects are also reflected, in diffusive transport, as non-Arrhenius-type behavior. A model based on accessible volume as a function of energy agrees with the simulated transition lending new insight into zeolite cavity design.

Journal Article↗
PubMed2006

Interplay between function and structure in complex networks.

We show that abrupt structural transitions can arise in functionally optimal networks, driven by small changes in the level of transport congestion. Our results offer an explanation as to why so many diverse species of network structure arise in nature (e.g., fungal systems) under essentially the same environmental conditions. Our findings are based on an exactly solvable model system which mimics a variety of biological and social networks. We then extend our analysis by introducing a renormalization scheme involving cost motifs, to describe analytically the average shortest path across multiple-ring-and-hub networks. As a consequence, we uncover a "skin effect" whereby the structure of the inner multi-ring core can cease to play any role in terms of determining the average shortest path across the network.

Journal Article↗