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At least 451 records · Page 25Linked to original sources
PubMed2005

Logarithmic coarsening and glassy behavior in a polymer model with mass-dependent diffusion.

We present a model of polymer growth and diffusion with frustration mechanisms for density increase and with diffusion rates of Arrhenius form with mass-dependent energy barriers Gamma(m) approximately (m-1)gamma. It shows nonuniversal logarithmic coarsening involving the exponent gamma. Strong-glass behavior is found in the typical times for disappearance of all polymers up to a given length, without reference to the equilibrium states of the macroscopic system. These features are predicted by numerical simulations, scaling theories, and an analytic solution of the master equation within an independent interval approximation, which also provides the cluster size distribution.

Journal Article↗
PubMed2005

Nonequilibrium statistical mechanical models for cytoskeletal assembly: towards understanding tensegrity in cells.

The cytoskeleton is not an equilibrium structure. To develop theoretical tools to investigate such nonequilibrium assemblies, we study a statistical physical model of motorized spherical particles. Though simple, it captures some of the key nonequilibrium features of the cytoskeletal networks. Variational solutions of the many-body master equation for a set of motorized particles accounts for their thermally induced Brownian motion as well as for the motorized kicking of the structural elements. These approximations yield stability limits for crystalline phases and for frozen amorphous structures. The methods allow one to compute the effects of nonequilibrium behavior and adhesion (effective cross-linking) on the mechanical stability of localized phases as a function of density, adhesion strength, and temperature. We find that nonequilibrium noise does not necessarily destabilize mechanically organized structures. The nonequilibrium forces strongly modulate the phase behavior and have comparable effect as the adhesion due to cross-linking. Modeling transitions such as these allows the mechanical properties of cytoskeleton to rapidly and adaptively change. The present model provides a statistical mechanical underpinning for a tensegrity picture of the cytoskeleton.

Animals↗
PubMed2005

Signatures of chaoticlike and nonchaoticlike behavior in a nonlinear quantum oscillator through photon detection.

The driven nonlinear Duffing oscillator is a very good, and standard, example of a quantum mechanical system from which classical-like orbits can be recovered from unravelings of the master equation. In order to generate such trajectories in the phase space of this oscillator, in this paper we use the quantum jump unraveling together with a suitable application of the correspondence principle. We analyze the measured readout by considering the power spectra of photon counts produced by the quantum jumps. Here we show that localization of the wave packet from the measurement of the oscillator by the photon detector produces a concomitant structure in the power spectra of the measured output. Furthermore, we demonstrate that this spectral analysis can be used to distinguish between different modes of the underlying dynamics of the oscillator.

Journal Article↗
PubMed2006

Generalized model and optimum performance of an irreversible quantum Brayton engine with spin systems.

The purpose of this paper is to establish a model of an irreversible quantum Brayton engine using many noninteracting spin systems as the working substance and consisting of two irreversible adiabatic and two isomagnetic field processes. The time evolution of the total magnetic moment M is determined by solving the generalized quantum master equation of an open system in the Heisenberg picture. The time of two irreversible adiabatic processes is considered based on finite-rate evolution. The relationship between the power output P and the efficiency eta for the irreversible quantum Brayton engine with spin systems is derived. The optimally operating region (or criteria) for the engine is determined. The influences of these important parameters on the performances (P and eta) of the engine are discussed. The results obtained herein will be useful for the further understanding and the selection of the optimal operating conditions for an irreversible quantum Brayton engine with spin systems.

Journal Article↗
PubMed2006

Drift of particles in self-similar systems and its Liouvillian interpretation.

We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems, the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities. For systems (i) and (ii), we explain the drift from the properties of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors.

Journal Article↗
PubMed2006

Frequency of elemental events of intracellular Ca(2+) dynamics.

The dynamics of intracellular Ca(2+) is driven by random events called Ca(2+) puffs, in which Ca(2+) is liberated from intracellular stores. We show that the emergence of Ca(2+) puffs can be mapped to an escape process. The mean first passage times that correspond to the stochastic fraction of puff periods are computed from a novel master equation and two Fokker-Planck equations. Our results demonstrate that the mathematical modeling of Ca(2+) puffs has to account for the discrete character of the Ca(2+) release sites and does not permit a continuous description of the number of open channels.

Calcium↗
PubMed2006

Glauber model in a quantum representation.

The Glauber model is reconsidered based on a quantum formulation of the master equation. Unlike the conventional approach the temperature and the Ising energy are included from the beginning by introducing a Heisenberg-like picture of the second quantized operators. This method enables us to get an exact expression for the transition rate of a single flip process w(i)(sigma(i)) which is in accordance with the principle of detailed balance. The transition rate differs significantly from the conventional one due to Glauber in the low-temperature regime. Here the behavior is controlled by the Ising energy and not by the microscopic time scale.

Journal Article↗
PubMed2006

Velocity and diffusion coefficient of A + A <--> A reaction fronts in one dimension.

We study front propagation in the reversible reaction-diffusion system A + A <--> A on a one-dimensional lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame attached to this particle. This approach provides a systematic way to improve on estimates of front speed obtained earlier. We also find that the leading particle performs a correlated random walk and this correlation needs to be taken into account to get the correct the value of the front diffusion coefficient.

Journal Article↗
PubMed2006

Fluctuation theorems and the nonequilibrium thermodynamics of molecular motors.

The fluctuation theorems for the currents and the dissipated work are considered for molecular motors which are driven out of equilibrium by chemical reactions. Because of the molecular fluctuations, these nonequilibrium processes are described by stochastic models based on a master equation. Analytical expressions are derived for the fluctuation theorems, allowing us to obtain predictions on the work dissipated in the motor as well as on its rotation near and far from thermodynamic equilibrium. We show that the fluctuation theorems provide a method to determine the affinity or thermodynamic force driving the motor. This affinity is given in terms of the free enthalpy of the chemical reactions. The theorems are applied to the F1 rotary motor which turns out to be a stiff system typically functioning in the nonlinear regime of nonequilibrium thermodynamics. We show that this nonlinearity confers a robustness to the functioning of the molecular motor.

Computer Simulation↗
PubMed2006

Transport on adaptive random lattices.

In this paper, we present a method for the solution of those linear transport processes that may be described by a master equation, such as electron, neutron, and photon transport, and more exotic variants thereof. We base our algorithm on a Markov process on a Voronoi-Delaunay grid, a nonperiodic lattice which is derived from a random point process that is chosen to optimally represent certain properties of the medium through which the transport occurs. Our grid is locally translation and rotation invariant in the mean. We illustrate our approach by means of a particular example, in which the expectation value of the length of a grid line corresponds to the local mean free path. In this example, the lattice is a direct representation of the "free path space" of the medium. Subsequently, transport is defined as simply moving particles from one node to the next, interactions taking place at each point. We derive the statistical properties of such lattices, describe the limiting behavior, and show how interactions are incorporated as global coefficients. Two elementary linear transport problems are discussed: that of free ballistic transport, and the transport of particles through a scattering medium. We also mention a combination of these two. We discuss the efficiency of our method, showing that it is much faster than most other methods because the operation count does not scale with the number of sources. We test our method by focusing on the transport of ionizing radiation through a static medium, and show that the computed results for the classical test case of an ionization front expanding in a homogeneous medium agree perfectly with the analytic solution. We finish by illustrating the efficiency and flexibility of our method with the results of a simulation of the reionization of the large scale structure of the Universe.

Journal Article↗
PubMed2006

Spectral formulation and WKB approximation for rare-event statistics in reaction systems.

We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master equation. We compare the stationary WKB approximation to a recent time-dependent semiclassical approximation developed, for the same class of problems, by Elgart and Kamenev [Phys. Rev. E 70, 41106 (2004)]. As a benchmark we use an exactly solvable problem of the binary annihilation reaction 2A-->0.

Journal Article↗
PubMed2000

Completely positive quantum dissipation

A completely positive master equation describing quantum dissipation for a Brownian particle is derived starting from microphysical collisions, exploiting a recently introduced approach to subdynamics of a macrosystem. The obtained equation can be cast into Lindblad form with a single generator for each Cartesian direction. Temperature dependent friction and diffusion coefficients for both position and momentum are expressed in terms of the collision cross section.

Journal Article↗
PubMed2000

From microscopic interactions to macroscopic laws of cluster evolution

We derive macroscopic governing laws of growth velocity, surface tension, mobility, critical nucleus size, and morphological evolution of clusters, from microscopic scale master equations for a prototype surface reaction system with long range adsorbate-adsorbate interactions.

Journal Article↗
PubMed2000

Pumped biochemical reactions, nonequilibrium circulation, and stochastic resonance.

Based on a master equation formalism for mesoscopic, unimolecular biochemical reactions, we show the periodic oscillation arising from severe nonequilibrium pumping is intimately related to the periodic motion in recently studied stochastic resonance (SR). The white noise in SR is naturally identified with the temperature in the biochemical reactions; the drift in the SR is associated with the circular flux in nonequilibrium steady state (NESS). As in SR, an optimal temperature for biochemical oscillation is shown to exist. A unifying framework for Hill's theory of NESS and the SR without periodic forcing is presented. The new formalism provides an analytically solvable model for SR.

Biological Clocks↗
PubMed2000

Random signal fluctuations can reduce random fluctuations in regulated components of chemical regulatory networks.

Many intracellular components are present in low copy numbers per cell and subject to feedback control. We use chemical master equations to analyze a negative feedback system where species X and S regulate each other's synthesis with standard intracellular kinetics. For a given number of X-molecules, S-variation can be significant. We show that this signal noise does not necessarily increase X-variation as previously thought but, surprisingly, can be necessary to reduce it below a Poissonian limit. The principle resembles Stochastic Resonance in that signal noise improves signal detection.

DNA Replication↗
PubMed2000

Decoherence via the dynamical casimir effect

We derive a master equation for a mirror interacting with the vacuum field via radiation pressure. The dynamical Casimir effect leads to decoherence of a superposition state in a time scale that depends on the degree of "macroscopicity" of the state components, and which may be much shorter than the relaxation time scale. Coherent states are selected by the interaction as pointer states.

Journal Article↗
PubMed2000

Robustness and diffusion of pointer states

Classical properties of an open quantum system emerge through its interaction with other degrees of freedom (decoherence). We treat the case where this interaction produces a Markovian master equation for the system. We derive the corresponding distinguished local basis (pointer basis) by three methods. The first demands that the pointer states mimic as closely as possible the local nonunitary evolution. The second demands that the local entropy production be minimal. The third imposes robustness on the inherent quantum and emerging classical uncertainties. All three methods lead to localized Gaussian pointer states, their formation and diffusion being governed by well-defined quantum Langevin equations.

Journal Article↗
PubMed2000

Strong coupling theory for driven tunneling and vibrational relaxation

We investigate on a unified basis tunneling and vibrational relaxation in driven dissipative multistable systems described by their N lowest lying unperturbed levels. By use of the discrete variable representation we derive a set of coupled non-Markovian master equations. We present analytical treatments that describe the dynamics in the regime of strong system-bath coupling. Our findings are corroborated by "ab initio" real-time path integral calculations.

Journal Article↗