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1.
Phys Rev E ; 97(3-1): 032608, 2018 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-29776041

RESUMO

We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models. Using these solutions, we calculate the drift velocity and show that the out-of-plane fluctuations of magnetization, which are not accounted for in the planar rotor model, play an important role. In the general case of arbitrary fluctuations, we investigate the temperature dependence of the drift velocity by numerically simulating a set of effective stochastic differential equations for the magnetization dynamics.

2.
Artigo em Inglês | MEDLINE | ID: mdl-26565245

RESUMO

We study the deterministic and stochastic rotational dynamics of ferromagnetic nanoparticles in a precessing magnetic field. Our approach is based on the system of effective Langevin equations and on the corresponding Fokker-Planck equation. Two key characteristics of the rotational dynamics, namely the average angular frequency of precession of nanoparticles and their average magnetization, are of interest. Using the Langevin and Fokker-Planck equations, we calculate both analytically and numerically these characteristics in the deterministic and stochastic cases, determine their dependence on the model parameters, and analyze in detail the role of thermal fluctuations.


Assuntos
Campos Magnéticos , Imãs/química , Nanopartículas , Rotação , Anisotropia , Modelos Teóricos , Processos Estocásticos , Temperatura , Viscosidade
3.
Artigo em Inglês | MEDLINE | ID: mdl-25122260

RESUMO

We derive the Fokker-Planck equation for multivariable Langevin equations with cross-correlated Gaussian white noises for an arbitrary interpretation of the stochastic differential equation. We formulate the conditions when the solution of the Fokker-Planck equation does not depend on which stochastic calculus is adopted. Further, we derive an equivalent multivariable Ito stochastic differential equation for each possible interpretation of the multivariable Langevin equation. To demonstrate the usefulness and significance of these general results, we consider the motion of Brownian particles. We study in detail the stability conditions for harmonic oscillators with two white noises, one of which is additive, random forcing, and the other, which accounts for fluctuations of either the damping or the spring coefficient, is multiplicative. We analyze the role of cross correlation in terms of the different noise interpretations and confirm the theoretical predictions via numerical simulations. We stress the interest of our results for numerical simulations of stochastic differential equations with an arbitrary interpretation of the stochastic integrals.


Assuntos
Teoria Quântica , Modelos Teóricos , Distribuição Normal , Processos Estocásticos
4.
Artigo em Inglês | MEDLINE | ID: mdl-23496470

RESUMO

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walks which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed distribution of jump lengths. Both the scaling function and the corresponding limiting probability density are determined for all admissible values of tail indexes describing the jump distribution. To analytically investigate the limiting density function, we derive a number of different representations of this function and, in this way, establish its main properties. We also develop an efficient numerical method for computing the limiting probability density and compare our analytical and numerical results.


Assuntos
Algoritmos , Difusão , Modelos Químicos , Modelos Estatísticos , Simulação por Computador
5.
Phys Rev E Stat Nonlin Soft Matter Phys ; 83(4 Pt 1): 041132, 2011 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-21599140

RESUMO

We study the long-time behavior of the probability density associated with the decoupled continuous-time random walk which is characterized by a superheavy-tailed distribution of waiting times. It is shown that, if the random walk is unbiased (biased) and the jump distribution has a finite second moment, then the properly scaled probability density converges in the long-time limit to a symmetric two-sided (an asymmetric one-sided) exponential density. The convergence occurs in such a way that all the moments of the probability density grow slower than any power of time. As a consequence, the reference random walk can be viewed as a generic model of superslow diffusion. A few examples of superheavy-tailed distributions of waiting times that give rise to qualitatively different laws of superslow diffusion are considered.

6.
Phys Rev E Stat Nonlin Soft Matter Phys ; 84(6 Pt 1): 061143, 2011 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-22304076

RESUMO

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a nondegenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox H function and find its behavior for small and large distances.


Assuntos
Modelos Teóricos , Probabilidade , Processos Estocásticos , Fatores de Tempo
7.
Phys Rev E Stat Nonlin Soft Matter Phys ; 81(2 Pt 1): 021117, 2010 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-20365540

RESUMO

We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The long-time behavior of the particle position is studied in the frame of a continuous-time random walk on a semi-infinite one-dimensional lattice. We formulate the conditions for anomalous diffusion, derive the diffusion laws, and analyze their dependence on the particle mass and the distribution of the random force.


Assuntos
Difusão , Modelos Teóricos , Processos Estocásticos , Temperatura
8.
Phys Rev E Stat Nonlin Soft Matter Phys ; 79(5 Pt 1): 051102, 2009 May.
Artigo em Inglês | MEDLINE | ID: mdl-19518411

RESUMO

We study directed transport of overdamped particles in a periodically rocked random sawtooth potential. Two transport regimes can be identified which are characterized by a nonzero value of the average velocity of particles and a zero value, respectively. The properties of directed transport in these regimes are investigated both analytically and numerically in terms of a random sawtooth potential and a periodically varying driving force. Precise conditions for the occurrence of transition between these two transport regimes are derived and analyzed in detail.

9.
Phys Rev E Stat Nonlin Soft Matter Phys ; 77(6 Pt 1): 061112, 2008 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-18643222

RESUMO

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric Lévy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for Lévy flights is derived and solved analytically in the steady state. It is shown that Lévy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.

10.
Phys Rev E Stat Nonlin Soft Matter Phys ; 76(3 Pt 1): 031101, 2007 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-17930193

RESUMO

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dichotomous disorder and use the corresponding characteristic function to derive prominent properties of the arrival time probability density. Specifically, we establish the scaling properties of the central moments, analyze the behavior of the probability density for short, long, and intermediate distances. In order to quantify the deviation of the arrival time distribution from a Gaussian shape, we evaluate the skewness and the kurtosis.

11.
Phys Rev E Stat Nonlin Soft Matter Phys ; 75(6 Pt 1): 061123, 2007 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-17677236

RESUMO

We perform a time-dependent study of the driven dynamics of overdamped particles that are placed in a one-dimensional, piecewise linear random potential. This setup of spatially quenched disorder then exerts a dichotomous varying random force on the particles. We derive the path integral representation of the resulting probability density function for the position of the particles and transform this quantity of interest into the form of a Fourier integral. In doing so, the evolution of the probability density can be investigated analytically for finite times. It is demonstrated that the probability density contains both a delta -singular contribution and a regular part. While the former part plays a dominant role at short times, the latter rules the behavior at large evolution times. The slow approach of the probability density to a limiting Gaussian form as time tends to infinity is elucidated in detail.

12.
Phys Rev Lett ; 97(22): 227202, 2006 Dec 01.
Artigo em Inglês | MEDLINE | ID: mdl-17155835

RESUMO

The investigation of a sizable thermal enhancement of magnetization is put forward for uniaxial ferromagnetic nanoparticles that are placed in a rotating magnetic field. We elucidate the nature of this phenomenon and evaluate the resonant frequency dependence of the induced magnetization. Moreover, we reveal the role of magnetic dipolar interactions, point out potential applications, and reason the feasibility of an experimental observation of this effect.

13.
Phys Rev E Stat Nonlin Soft Matter Phys ; 73(3 Pt 2): 036120, 2006 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-16605611

RESUMO

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact probability distribution function for the particle positions, calculate its moments, and find their corresponding long-time, asymptotic behaviors. The generally anomalous diffusive regimes of the particles are classified, and their dependence on the friction coefficient and the characteristics of the noises is analyzed in detail. The asymptotic predictions are confirmed by exact solutions for two examples.

14.
Phys Rev E Stat Nonlin Soft Matter Phys ; 71(4 Pt 2): 046137, 2005 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-15903756

RESUMO

We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive combinatorics we succeed in obtaining the one-variable probability functions for (i) the number of domain walls, (ii) the number of up domains, and (iii) the number of spins in an up domain. The corresponding averages and variances of these probability distributions are calculated and the limiting case of an infinite chain is considered. Analyzing the averages and the transition time between differing chain states at low temperatures, we also introduce a criterion of the ferromagnetic-like behavior of a finite Ising chain. The results can be used to characterize magnetism in monatomic metal wires and atomic-scale memory devices.

15.
Phys Rev E Stat Nonlin Soft Matter Phys ; 71(1 Pt 2): 016104, 2005 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-15697655

RESUMO

We study analytically and numerically the overdamped, deterministic dynamics of a chain of charged, interacting particles driven by a longitudinal alternating electric field and additionally interacting with a smooth ratchet potential. We derive the equations of motion, analyze the general properties of their solutions and find the drift criterion for chain motion. For ratchet potentials of the form of a double-sine and a phase-modulated sine it is demonstrated that both, a so-called integer and fractional transport of the chain, can occur. Explicit results for the directed chain transport for these two classes of ratchet potentials are presented.

16.
Phys Rev E Stat Nonlin Soft Matter Phys ; 68(4 Pt 2): 046132, 2003 Oct.
Artigo em Inglês | MEDLINE | ID: mdl-14683027

RESUMO

We study the role that the cross-correlation of noises plays in the statistical behavior of systems driven by two multiplicative Gaussian white noises. The temporal evolution of the system is described by a Langevin equation, for which we adopt a general interpretation that includes the Ito as well as the Stratonovich interpretation. We derive the stochastically equivalent Fokker-Planck equation by means of the two-stage averaging of a state-dependent function. Analyzing the stationary solution of the Fokker-Planck equation for specific examples, we show explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.

17.
Phys Rev E Stat Nonlin Soft Matter Phys ; 65(6 Pt 1): 061109, 2002 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-12188705

RESUMO

We study the temporal evolution of a system that has an absorbing state and that is driven by colored Gaussian noise, whose amplitude depends on the system state x as [x](alpha). Exact, analytical expressions for the probability density functions of the system and of the absorption time are derived. We also calculate numerical characteristics of the probability density functions, namely, the fractional moments of the system and the mean absorption time, and analyze the role of the functional form of the noise correlation function.

18.
Phys Rev E Stat Nonlin Soft Matter Phys ; 65(3 Pt 1): 031105, 2002 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-11909027

RESUMO

We derive the time-dependent univariate and bivariate probability distribution function for an overdamped system with a quadratic potential driven by colored Gaussian noise, whose amplitude depends on the system state x as [x](alpha). Particular attention is paid to the effect of the correlation function of the noise on the statistical properties of the system. We obtain exact expressions for the fractional moments as well as the correlation function of the system and calculate the fractal dimension. We also consider the special case of a constant potential and determine the criteria for anomalous diffusion and stochastic localization of free particles.

19.
Mol Biol (Mosk) ; 35(6): 1032-8, 2001.
Artigo em Russo | MEDLINE | ID: mdl-11771127

RESUMO

Analysis of DNA sequences of the human chromosomes 21 and 22 performed using a specially designed MegaGene software allowed us to obtain the following results. Purine and pyrimidine nucleotide residues are unevenly distributed along both chromosomes, displaying maxima and minima (Y waves phi) with a period of about 3 Mbp. Distribution of G + C along both chromosomes has no distinct maxima and minima, however, chromosome 21 contains considerably less G + C than chromosome 22. Both exons and Alu repeats are unevenly distributed along chromosome 21: they are scarce in its left part and abundant in the right part, while MIR elements are quite monotonously spread along this chromosome. The Alu repeats show a wave-like distribution pattern similar for both repeat orientations. The number of the Alu repeats of opposite orientations was equal for both studied chromosomes, and this may be considered a new property of the human genome. The positive correlation between the exon and Alu distribution patterns along the chromosome, the concurrent distribution of Alu repeats in both orientations along the chromosome, and the equal copy numbers for Alu in direct and inverted orientations within an individual chromosome point to their important role in the human genome, and do not fit the notion that Alu repeats belong to parasitic (junk) DNA.


Assuntos
Cromossomos Humanos Par 21 , Cromossomos Humanos Par 22 , Éxons , Genoma Humano , Sequências Repetitivas de Ácido Nucleico , Ilhas de CpG , DNA/genética , Humanos
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