32 research outputs found
Functional characterization of generalized Langevin equations
We present an exact functional formalism to deal with linear Langevin
equations with arbitrary memory kernels and driven by any noise structure
characterized through its characteristic functional. No others hypothesis are
assumed over the noise, neither the fluctuation dissipation theorem. We found
that the characteristic functional of the linear process can be expressed in
terms of noise's functional and the Green function of the deterministic
(memory-like) dissipative dynamics. This object allow us to get a procedure to
calculate all the Kolmogorov hierarchy of the non-Markov process. As examples
we have characterized through the 1-time probability a noise-induced interplay
between the dissipative dynamics and the structure of different noises.
Conditions that lead to non-Gaussian statistics and distributions with long
tails are analyzed. The introduction of arbitrary fluctuations in fractional
Langevin equations have also been pointed out
Statistical Theory of Spin Relaxation and Diffusion in Solids
A comprehensive theoretical description is given for the spin relaxation and
diffusion in solids. The formulation is made in a general
statistical-mechanical way. The method of the nonequilibrium statistical
operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation
dynamics of a spin subsystem. Perturbation of this subsystem in solids may
produce a nonequilibrium state which is then relaxed to an equilibrium state
due to the interaction between the particles or with a thermal bath (lattice).
The generalized kinetic equations were derived previously for a system weakly
coupled to a thermal bath to elucidate the nature of transport and relaxation
processes. In this paper, these results are used to describe the relaxation and
diffusion of nuclear spins in solids. The aim is to formulate a successive and
coherent microscopic description of the nuclear magnetic relaxation and
diffusion in solids. The nuclear spin-lattice relaxation is considered and the
Gorter relation is derived. As an example, a theory of spin diffusion of the
nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown
that due to the dipolar interaction between host nuclear spins and impurity
spins, a nonuniform distribution in the host nuclear spin system will occur and
consequently the macroscopic relaxation time will be strongly determined by the
spin diffusion. The explicit expressions for the relaxation time in certain
physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference
The effects of environmental disturbances on tumor growth
In this study, the analytic expressions of the steady probability
distribution of tumor cells were established based on the steady state solution
to the corresponding Fokker-Planck equation. Then, the effects of two
uncorrelated white noises on tumor cell growth were investigated. It was found
that the predation rate plays the main role in determining whether or not the
noise is favorable for tumor growth.Comment: 14 pages, 11 figures. Note: The paper will be published on volume 42
of the Brazilian Journal of Physic
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Embryonic development of Girardia tigrina (Girard, 1850) (Platyhelminthes, Tricladida, Paludicola)
Effect of pressure in light water and benzene vapors on the total interaction cross section for slow neutrons
Correlated noises in an absorptive optical bistable model
We study the steady state properties of an absorptive optical bistable model in the presence of correlated noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution and the average value of the transmitted light have been investigated. We have found that fluctuations of the input light amplitude improve the transmitted light and an optimized value exists for the fluctuations of the population difference at which the transmitted light takes its maximum value. The correlation between the two noises reduce the transmitted light and the noises in the model can induce a phase transition. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200605.40.-a Nonlinear dynamics and chaos, 02.50.Ey Stochastic processes,
Stochastic Resonance Crossovers in Complex Networks
Here we numerically study the emergence of stochastic resonance as a mild phenomenon and how this transforms into an amazing enhancement of the signal-to-noise ratio at several levels of a disturbing ambient noise. The setting is a cooperative, interacting complex system modelled as an Ising-Hopfield network in which the intensity of mutual interactions or “synapses” varies with time in such a way that it accounts for, e.g., a kind of fatigue reported to occur in the cortex. This induces nonequilibrium phase transitions whose rising comes associated to various mechanisms producing two types of resonance. The model thus clarifies the details of the signal transmission and the causes of correlation among noise and signal. We also describe short-time persistent memory states, and conclude on the limited relevance of the network wiring topology. Our results, in qualitative agreement with the observation of excellent transmission of weak signals in the brain when competing with both intrinsic and external noise, are expected to be of wide validity and may have technological application. We also present here a first contact between the model behavior and psychotechnical data.The work was supported by the following: Andalusian Regional Government “Junta de Andalucía,” project number FQM–01505; Spanish Science and Innovation Ministry MICINN–FEDER, project number FIS2009–08451; and Spanish Science and Innovation Ministry MICINN-GREIB, project number GREIB.PT_2011_19