23 research outputs found
Oscillations in p-adic diffusion processes and simulation of the conformational dynamics of protein
Logarithmic oscillations superimposed on a power-law trend appear in the
behavior of various complex hierarchical systems. In this paper, we study the
logarithmic oscillations of relaxation curves in p-adic diffusion models that
are used to describe the conformational dynamics of protein. We consider the
case of a purely p-adic diffusion, as well as the case of p-adic diffusion with
a reaction sink. We show that, relaxation curves for large times in these two
cases are described by a power law on which logarithmic oscillations are
superimposed whose period and amplitude are determined by the parameters of the
model. We also provide a physical explanation of the emergence of oscillations
in relaxation curves and discuss the relation of the results to the experiments
on relaxation dynamics of protein.Comment: 23 pages, 5 figure
Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees
We study the statistical and dynamic properties of the systems characterized
by an ultrametric space of states and translationary non-invariant symmetric
transition matrices of the Parisi type subjected to "locally constant"
randomization. Using the explicit expression for eigenvalues of such matrices,
we compute the spectral density for the Gaussian distribution of matrix
elements. We also compute the averaged "survival probability" (SP) having sense
of the probability to find a system in the initial state by time . Using the
similarity between the averaged SP for locally constant randomized Parisi
matrices and the partition function of directed polymers on disordered trees,
we show that for times (where is some critical
time) a "lacunary" structure of the ultrametric space occurs with the
probability . This means that the escape from some bounded
areas of the ultrametric space of states is locked and the kinetics is confined
in these areas for infinitely long time.Comment: 7 pages, 2 figures (the paper is essentially reworked
First Passage Time Distribution and Number of Returns for Ultrametric Random Walk
In this paper, we consider a homogeneous Markov process \xi(t;\omega) on an
ultrametric space Q_p, with distribution density f(x,t), x in Q_p, t in R_+,
satisfying the ultrametric diffusion equation df(x,t)/dt =-Df(x,t). We
construct and examine a random variable \tau (\omega) that has the meaning the
first passage times. Also, we obtain a formula for the mean number of returns
on the interval (0,t] and give its asymptotic estimates for large t.Comment: 20 page
p-Adic description of characteristic relaxation in complex systems
This work is a further development of an approach to the description of
relaxation processes in complex systems on the basis of the p-adic analysis. We
show that three types of relaxation fitted into the Kohlrausch-Williams-Watts
law, the power decay law, or the logarithmic decay law, are similar random
processes. Inherently, these processes are ultrametric and are described by the
p-adic master equation. The physical meaning of this equation is explained in
terms of a random walk constrained by a hierarchical energy landscape. We also
discuss relations between the relaxation kinetics and the energy landscapes.Comment: AMS-LaTeX (+iopart style), 9 pages, submitted to J.Phys.
Some aspects of the -adic analysis and its applications to -adic stochastic processes
In this paper we consider a generalization of analysis on -adic numbers
field to the case of -adic numbers ring. The basic statements, theorems
and formulas of -adic analysis can be used for the case of -adic analysis
without changing. We discuss basic properties of -adic numbers and consider
some properties of -adic integration and -adic Fourier analysis. The
class of infinitely divisible -adic distributions and the class of -adic
stochastic Levi processes were introduced. The special class of -adic CTRW
process and fractional-time -adic random walk as the diffusive limit of it
is considered. We found the asymptotic behavior of the probability measure of
initial distribution support for fractional-time -adic random walk.Comment: 18 page