arXiv subjects

Muhammad Sahimi

Publications and source records attributed to Muhammad Sahimi.

31 records · Page 2Linked to original sources

arXiv2007

Uncertainty in the Fluctuations of the Price of Stocks

We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stocks' prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty.

q-fin.ST↗

arXiv2006

Stochastic $ϕ^4-$Theory in the Strong Coupling Limit

The stochastic $ϕ^4$-theory in $d-$dimensions dynamically develops domain wall structures within which the order parameter is not continuous. We develop a statistical theory for the $ϕ^4$-theory driven with a random forcing which is white in time and Gaussian-correlated in space. A master equation is derived for the probability density function (PDF) of the order parameter, when the forcing correlation length is much smaller than the system size, but much larger than the typical width of the domain walls. Moreover, exact expressions for the one-point PDF and all the moments $<ϕ^n>$ are given. We then investigate the intermittency issue in the strong coupling limit, and derive the tail of the PDF of the increments $ϕ(x_2) - ϕ(x_1)$. The scaling laws for the structure functions of the increments are obtained through numerical simulations. It is shown that the moments of field increments defined by, $C_b=< |ϕ(x_2)-ϕ(x_1)|^b>$, behave as $|x_1-x_2|^{ξ_b}$, where $ξ_b=b$ for $b\leq 1$, and $ξ_b=1$ for $b\geq1$

cond-mat.other↗

arXiv2006

Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency $ν_{αx_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $α$ such that, $h({\bf x},t)-\bar{h}=α$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ is the surface height at time $t$, and $\bar{h}$ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number $N^+$ of such level-crossings with positive slope in all the directions is then shown to scale with time as $t^{d/2}$ for both the KPZ equation and the RD model.

cond-mat.stat-mech↗

arXiv2006

Can a few fanatics influence the opinion of a large segment of a society?

Models that provide insight into how extreme positions regarding any social phenomenon may spread in a society or at the global scale are of great current interest. A realistic model must account for the fact that globalization and internet have given rise to scale-free networks of interactions between people. We propose a novel model which takes into account the nature of the interactions network, and provides some key insights into this phenomenon, including: (1) There is a fundamental difference between a hierarchical network whereby people are influenced by those that are higher on the hierarchy but not by those below them, and a symmetrical network where person-on-person influence works mutually. (2) A few "fanatics" can influence a large fraction of the population either temporarily (in the hierarchical networks) or permanently (in symmetrical networks). Even if the "fanatics" disappear, the population may still remain susceptible to the positions advocated by them. The model is, however, general and applicable to any phenomenon for which there is a degree of enthusiasm or susceptibility to in the population.

physics.soc-ph↗

arXiv2006

Analysis of Non-stationary Data for Heart-Rate Fluctuations in Terms of Drift and Diffusion Coefficients

We describe a method for analyzing the stochasticity in the non-stationary data for the beat-to-beat fluctuations in the heart rates of healthy subjects, as well as those with congestive heart failure. The method analyzes the returns time series of the data as a Markov process, and computes the Markov time scale, i.e., the time scale over which the data are a Markov process. We also construct an effective stochastic continuum equation for the return series. We show that the drift and diffusion coefficients, as well as the amplitude of the returns time series for healthy subjects are distinct from those with CHF. Thus, the method may potentially provide a diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, as it can distinguish small differences between the data for the two classes of subjects in terms of well-defined and physically-motivated quantities.

physics.bio-ph↗

arXiv2006

New Computational Approaches to Analysis of Interbeat Intervals in Human Subjects

We investigate the Markov nature, Cascade of information from large time scale to small scale and extended self similarity properties of the beat to beat fluctuations of healthy subjects as well as those with congestive heart failure. To check the Markov nature, we use a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects.To investigate the cascade of information from large to small time scales we also analyze the statistical properties of interbeat intervals cascade by considering the joint probability distribution for two interbeat increments. As a result, the joint probability distributions of the increments in the interbeat intervals obey a Fokker-Planck equation. Finally we analyze the extended self-similarity (ESS) in the beat-to-beat fluctuations in the heart rates of healthy and congestive heart failure subjects.The proposed methods provide the novel techniques for distinguishing the two classes of subjects in terms of the drift and diffusion coefficients, intermittency exponents which behave differently for two classes of the subjects, namely, healthy subjects and those with congestive heart failure.

q-bio.QM↗

arXiv2006

Statistical Properties of the Interbeat Interval Cascade in Human Subjects

Statistical properties of interbeat intervals cascade are evaluated by considering the joint probability distribution $P(Δx_2,τ_2;Δx_1,τ_1)$ for two interbeat increments $Δx_1$ and $Δx_2$ of different time scales $τ_1$ and $τ_2$. We present evidence that the conditional probability distribution $P(Δx_2,τ_2|Δx_1,τ_1)$ may obey a Chapman-Kolmogorov equation. The corresponding Kramers-Moyal (KM) coefficients are evaluated. It is shown that while the first and second KM coefficients, i.e., the drift and diffusion coefficients, take on well-defined and significant values, the higher-order coefficients in the KM expansion are very small. As a result, the joint probability distributions of the increments in the interbeat intervals obey a Fokker-Planck equation. The method provides a novel technique for distinguishing the two classes of subjects in terms of the drift and diffusion coefficients, which behave differently for two classes of the subjects, namely, healthy subjects and those with congestive heart failure.

q-bio.QM↗

arXiv2005

Regeneration of Stochastic Processes: An Inverse Method

We propose a novel inverse method that utilizes a set of data to construct a simple equation that governs the stochastic process for which the data have been measured, hence enabling us to reconstruct the stochastic process. As an example, we analyze the stochasticity in the beat-to-beat fluctuations in the heart rates of healthy subjects as well as those with congestive heart failure. The inverse method provides a novel technique for distinguishing the two classes of subjects in terms of a drift and a diffusion coefficients which behave completely differently for the two classes of subjects, hence potentially providing a novel diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, even at the early stages of the disease development.

cond-mat.stat-mech↗

arXiv2005

Dynamics of the Markov Time Scale of Seismic Activity May Provide a Short-Term Alert for Earthquakes

We propose a novel method for analyzing precursory seismic data before an earthquake that treats them as a Markov process and distinguishes the background noise from real fluctuations due to an earthquake. A short time (on the order of several hours) before an earthquake the Markov time scale $t_M$ increases sharply, hence providing an alarm for an impending earthquake. To distinguish a false alarm from a reliable one, we compute a second quantity, $T_1$, based on the concept of extended self-similarity of the data. $T_1$ also changes strongly before an earthquake occurs. An alarm is accepted if {\it both} $t_M$ and $T_1$ indicate it {\it simultaneously}. Calibrating the method with the data for one region provides a tool for predicting an impending earthquake within that region. Our analysis of the data for a large number of earthquakes indicate an essentially zero rate of failure for the method.

physics.geo-ph↗

arXiv2005

Diffusion in scale-free networks with annealed disorder

The scale-free (SF) networks that have been studied so far contained quenched disorder generated by random dilution which does not vary with the time. In practice, if a SF network is to represent, for example, the worldwide web, then the links between its various nodes may temporarily be lost, and re-established again later on. This gives rise to SF networks with annealed disorder. Even if the disorder is quenched, it may be more realistic to generate it by a dynamical process that is happening in the network. In this paper, we study diffusion in SF networks with annealed disorder generated by various scenarios, as well as in SF networks with quenched disorder which, however, is generated by the diffusion process itself. Several quantities of the diffusion process are computed, including the mean number of distinct sites visited, the mean number of returns to the origin, and the mean number of connected nodes that are accessible to the random walkers at any given time. The results including, (1) greatly reduced growth with the time of the mean number of distinct sites visited; (2) blocking of the random walkers; (3) the existence of a phase diagram that separates the region in which diffusion is possible from one in which diffusion is impossible, and (4) a transition in the structure of the networks at which the mean number of distinct sites visited vanishes, indicate completely different behavior for the computed quantities than those in SF networks with quenched disorder generated by simple random dilution.

cond-mat.dis-nn↗

arXiv2005

Discrete Simulation of the Dynamics of Opinions about Extremism

We propose a discrete model for how opinion about a given phenomenon, about which various groups of a population have different degrees of enthusiasm, such as fanaticism and extreme social and political positions, including terrorism, may spread. The model, in a certain limit, is the discrete analogue of a deterministic continuum model suggested by others. We carry out extensive computer simulation of the model by utilizing it on lattices with infinite- or short-range interactions, and on (directed) Barabasi-Albert scale-free networks. Several interesting features of the model are demonstrated, and comparison is made with the continuum model.

physics.soc-ph↗

arXiv2005

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in {\it any} dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.

cond-mat.stat-mech↗

arXiv1992

Fractal Properties of the Distribution of Earthquake Hypocenters

We investigate a recent suggestion that the spatial distribution of earthquake hypocenters makes a fractal set with a structure and fractal dimensionality close to those of the backbone of critical percolation clusters, by analyzing four different sets of data for the hypocenter distributions and calculating the dynamical properties of the geometrical distribution such as the spectral dimension $d_s$. We find that the value of $d_s$ is consistent with that of the backbone, thus supporting further the identification of the hypocenter distribution as having the structure of the percolation backbone.

cond-mat↗