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arXiv2008

Multiplicative Noise Induces Zero Critical Frequency

Stochastic Bloch equations which model the fluorescence of two level molecules and atoms, NMR experiments and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a dynamical system. Using exact solutions and the cumulant expansion we find two main effects: (i) even very weak noise may double or triple the number of critical frequencies, which is related to an instability of the system and (ii) strong multiplicative noise may induce a non-trivial zero critical frequency thus wiping out the over-damped phase.

cond-mat.stat-mech↗

arXiv2008

Magnetic and thermal properties of a one-dimensional spin-1 model

We study the one-dimensional S=1 Blume-Emery-Griffiths model. Upon transforming the spin model into an equivalent fermionic model, we provide the exact solution within the Green's function and equations of motion formalism. We show that the relevant response functions as well as thermodynamic quantities can be determined, in the whole parameters space, in terms of a finite set of local correlators. Furthermore, considering the case of an antiferromagnetic chain with single-ion anisotropy in the presence of an external magnetic field, we find three plateaus in the magnetization curve; in the neighborhood of the endpoints of the intermediate plateau, the specific heat shows a double peak structure.

cond-mat.str-el↗

arXiv2008

Decay of a metastable state activated by non-Gaussian noise: A critical review of the generalized Kramers problem

We review the problem of the noise activated escape from a metastable state in the presence of non-Gaussian noise, and present connections between various theoretical approaches. We also respond to criticism of our work by Tomáš Novotný [arXiv:0807.0387] concerning the weak damping limit. The discrepancy between our results is linked to uncontrolled approximations made by Novotný.

cond-mat.mes-hall↗

arXiv2009

Structural distance and evolutionary relationship of networks

Evolutionary mechanism in a self-organized system cause some functional changes that force to adapt new conformation of the interaction pattern between the components of that system. Measuring the structural differences one can retrace the evolutionary relation between two systems. We present a method to quantify the topological distance between two networks of different sizes, finding that the architectures of the networks are more similar within the same class than the outside of their class. With 43 cellular networks of different species, we show that the evolutionary relationship can be elucidated from the structural distances.

q-bio.QM↗

arXiv2008

Noise induced dynamics in adaptive networks with applications to epidemiology

Recent work in modeling the coupling between disease dynamics and dynamic social network geometry has led to the examination of how human interactions force a rewiring of connections in a population. Rewiring of the network may be considered an adaptive response to social forces due to disease spread, which in turn feeds back to the disease dynamics. Such epidemic models, called adaptive networks, have led to new dynamical instabilities along with the creation of multiple attracting states. The co-existence of several attractors is sensitive to internal and external fluctuations, and leads to enhanced stochastic oscillatory outbreaks and disease extinction. The aim of this paper is to explore the bifurcations of adaptive network models in the presence of fluctuations and to review some of the new fluctuation phenomena induced in adaptive networks.

cond-mat.stat-mech↗

arXiv2011

Thermodynamic consistency and fast dynamics in phase field crystal modeling

A general formulation is presented to derive the equation of motion and to demonstrate thermodynamic consistency for several classes of phase field models at once. It applies to models with a conserved phase field, describing either uniform or periodic stable states, and containing slow as well as fast thermodynamic variables. The approach is based on an entropy functional formalism previously developed in the context of phase field models for uniform states [P. Galenko and D. Jou, Phys. Rev. E {\bf 71}, 046125 (2005)] and thus allows to extend several properties of the latter to phase field models for periodic states (phase field crystal models). In particular, it allows to demonstrate the concept of thermodynamic consistency for phase field crystal models with fast dynamics.

cond-mat.mtrl-sci↗

arXiv2008

Non-relativistic AdS/CFT and Aging/Gravity Duality

We point out that the recent discussion of non-relativistic AdS/CFT correspondence has a direct application in non-equilibrium statistical physics, the fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent $z=2$ and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.

cond-mat.stat-mech↗

arXiv2008

Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain

Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant.

cond-mat.soft↗

arXiv2010

Non-Abelian self-organized criticality model with one stochastic site in any avalanche shows multifractal scaling

I have proposed a\textit{non-Abelian}and stochastic self-organized criticality model in which each avalanche contains one stochastic site and all remaining sites in the avalanche are deterministic with a constant threshold $E_{c}^{I}$. Studies of avalanche structures, waves and autocorrelations, size moments and probability distribution functions of avalanche size, for the thresholds $4\leq E_{c}^{I}\leq256$, were performed. The shell-like avalanche structures, correlated waves within avalanches, complex size moments and probability distribution functions show multifractal scaling like the \textit{Abelian} and deterministic BTW model despite the fact that the model is \textit{non-Abelian}and stochastic with unbalanced relaxation rules at each stochastic site.

cond-mat.stat-mech↗

arXiv2008

Competing jump cycles for vacancy diffusion in binary alloys

The mean-first-passage-times (MFPTs) for a vacancy that diffuses (via one- and six-jump cycles) in a two dimensional ordered binary alloy are evaluated using the properties of random walks on networks. We investigate the effect of temperature and relative barrier height on the ratio between the MFPTs of the two cycles. We find that the six-jump cycle takes shorter time than the one-jump cycle for the range of parameters considered.

cond-mat.mtrl-sci↗

arXiv2008

On the Depletion Effect in Colloids: Correlated Brownian Motions

Our object is to formulate and analyze a physically plausible and mathematically sound model to better understand the phenomenon of clumping in colloid dispersions. Our model is stochastic but rigorously derived from a deterministic setup in a Newtonian setting. A rigorous transition from deterministic mean-field dynamics of several large particles and infinitely many small particles to the stochastic motion of the large particles is invoked. Then the stochastic motion of the large particles is described by a system of correlated Brownian motions. The scaling in the transition preserves a characteristic correlation length. From the limiting stochastic equations we compute the probability fluxes for the separation between two large particles. We show that, for short times, two particles sufficiently close together tend to be attracted to each other. This agrees with the observed depletion phenomena in colloids. To do this computation, we extend the notion of Van Kampen's one-dimensional flux rate in an appropriate way to account for higher dimensional effect.

cond-mat.mtrl-sci↗

arXiv2008

Cooper problem in a lattice

Cooper problem for interacting fermions is solved in a lattice. It is found that the binding energy of the Cooper problem can behave qualitatively differently from the gap parameter of the BCS theory and that pairs of non-zero center of mass momentum are favored in systems with unequal Fermi energies.

cond-mat.stat-mech↗

arXiv2008

A dialectical view of the variational principles of mechanics

The aim of this work is to provide a possible philosophical motivation to the variational principles of physics in general and a possible way to unify the axiomatizations of mechanics theories. The leitmotif of this work is a dialectical view of the world: any smooth motion in nature is the consequence of the interplay and dynamical balance between pairs of opposite elements of the motion. We stress that the opposite property here differs from the common sense of opposing elements (of conflicting appearance but of same nature) such action/reaction forces between two bodies. The opposite elements here are incompatible and mutual exclusive in nature, with contrasting and complementary characteristics such as active/passive, disorder/order, curvature/flatness, etc. The dynamical balance is defined by an invariant variational relationship between all the pairs of opposite elements active in the considered motion. From this idea, an axiomatization of quantum mechanics is proposed in addition to the derivation of several existing variational principles of mechanics.

physics.hist-ph↗

arXiv2008

Diffusion in confined geometries

Diffusive transport of particles or, more generally, small objects is a ubiquitous feature of physical and chemical reaction systems. In configurations containing confining walls or constrictions transport is controlled both by the fluctuation statistics of the jittering objects and the phase space available to their dynamics. Consequently, the study of transport at the macro- and nanoscales must address both Brownian motion and entropic effects. With this survey we report on recent advances in the theoretical and numerical investigation of stochastic transport occurring either in micro-sized geometries of varying cross section or in narrow channels wherein the diffusing particles are hindered from passing each other (single file diffusion). For particles undergoing biased diffusion in static suspension media enclosed by confining geometries, transport exhibits intriguing features such as (i) a decrease of nonlinear mobility with increasing temperature or, also, (ii) a broad excess peak of the effective diffusion above the free diffusion limit. These paradoxical aspects can be understood in terms of entropic contributions resulting from the restricted dynamics in phase space. If, in addition, the suspension medium is subjected to external, time-dependent forcing, rectification or segregation of the diffusing Brownian particles becomes possible. Likewise, the diffusion in very narrow, spatially modulated channels gets modified via contact particle-particle interactions, which induce anomalous sub-diffusion. The effective sub-diffusion constant for a driven single file also develops a resonance-like structure as a function of the confining coupling constant.

cond-mat.stat-mech↗

arXiv2009

Scaling and Universality in Models of Step Bunching: The "C+-C-" Model

We study further the recently introduced [Ranguelov et al., Comptes Rendus de l'Acad. Bulg. des Sci. 60, 4 (2007) 389] "C+-C-" model of step flow crystal growth over wide range of model parameters. The basic assumption of the model is that the reference ("equilibrium") densities used to compute the supersaturation might be different on either side of a step. We obtain the condition for linear stability of the whole step train in the form CL/CR>1 (L/R stands for left/right in a descending from left to right step train). Further we integrate numerically the equations of step motion to monitor the bunching process in the long times limit. Thus we obtain the exact size- and time- scaling of the step bunches including the numerical prefactors. We show that in a broad range of parameters the morphology is characterized with appearance of the minimal interstep distance in the bunch in the beginning of the bunches (at the trailing edge of the bunch) and may be described by a single universality class, different from those already generated by continuum theories [Krug et al., PRB 71, 045412].

cond-mat.stat-mech↗

arXiv2008

Free Solution Electrophoresis of Homopolyelectrolytes

We investigate the behavior of single polyelectrolytes in multivalent salt solutions under the action of electric fields through computer simulations. The chain is unfolded in a strong electric field and aligned parallel to the field direction, and the chain size shows a sigmoidal transition. The unfolding electric field $E^*$ depends on the salt concentration and scales as $V^{-1/2}$ with $V$ being the ellipsoidal volume occupied by the chain. The magnitude of the electrophoretic mobility of chain drastically increases during the unfolding. The fact that $E^*$ depends on the chain length provides a plausible mechanism to separate long charged homopolymers by size in free solution electrophoresis via the unfolding transition of globule polyelectrolytes condensed by multivalent salt.

cond-mat.soft↗

arXiv2009

Effects of an oscillating field on magnetic domain patterns: Numerical and theoretical studies on the concentric-ring patterns surrounding a strong defect

Oscillating fields can make domain patterns change into various types of structures. Numerical simulations show that concentric-ring domain patterns centered at a strong defect are observed under a rapidly oscillating field in some cases. The concentric-ring pattern appears near the threshold of spatially-uniform patterns in high-frequency cases. The threshold is theoretically estimated and the theoretical threshold is in good agreement with numerical one in a high-frequency region. The theoretical analysis gives also good estimations of several characteristics of domain patterns for high-frequencies.

cond-mat.stat-mech↗

arXiv2008

Coarse-graining stochastic biochemical networks: quasi-stationary approximation and fast simulations using a stochastic path integral technique

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenheimer approximation in quantum mechanics, follows from the stochastic path integral representation of the full counting statistics of reaction events (also known as the cumulant generating function). In applications with a small number of chemical reactions, this approach produces analytical expressions for moments of chemical fluxes between slow variables. This allows for a low-dimensional, interpretable representation of the biochemical system, that can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we consider a chain of biochemical reactions, derive its coarse-grained description, and show that the Gillespie simulations of the original stiff system, the coarse-grained simulations, and the full analytical treatment are in an agreement, but the coarse-grained simulations are three orders of magnitude faster than the Gillespie analogue.

q-bio.MN↗