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Article Outline: Glossary Definition of the Subject Introduction Stochastic Processes Stochastic Time Series Analysis Applications: Processes in Time Applications: Processes in Scale Future Directions Further Reading Acknowledgment Bibliography  

The single and multiple scattering regimes of electromagnetic waves in a disordered system with fluctuating permittivity are studied by numerical simulations of Maxwell's equations. For an array of emitters and receivers in front of a medium with randomly varying dielectric constant, we calculate the backscattering matrix from the signal responses at all receiver points j to electromagnetic pulses generated at each emitter point i. We show that the statistical properties of the backscattering matrix are in agreement with the recent experimental results for ultrasonic waves (Aubry A. and Derode A., Phys. Rev. Lett., 102 (2009) 084301) and light (Popoff S. M. et al., Phys. Rev. Lett., 104... 

We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network features which is in agreement with recent empirical studies  

Packing of cubic particles arises in a variety of problems, ranging from biological materials to colloids and the fabrication of new types of porous materials with controlled morphology. The properties of such packings may also be relevant to problems involving suspensions of cubic zeolites, precipitation of salt crystals during CO2 sequestration in rock, and intrusion of fresh water in aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We present a detailed simulation and microstructural characterization of packings of nonoverlapping monodisperse cubic particles, following up on our preliminary results [H. Malmir, Sci.... 

Understanding the properties of random packings of solid objects is of critical importance to a wide variety of fundamental scientific and practical problems. The great majority of the previous works focused, however, on packings of spherical and sphere-like particles. We report the first detailed simulation and characterization of packings of non-overlapping cubic particles. Such packings arise in a variety of problems, ranging from biological materials, to colloids and fabrication of porous scaffolds using salt powders. In addition, packing of cubic salt crystals arise in various problems involving preservation of pavements, paintings, and historical monuments, mineral-fluid interactions,... 

Localization of electromagnetic waves in two-dimensional (2D) and three-dimensional (3D) media with random permittivities is studied by numerical simulations of the Maxwell's equations. Using the transfer-matrix method, the minimum positive Lyapunov exponent γm of the model is computed, the inverse of which is the localization length. Finite-size scaling analysis of γm is carried out in order to check the localization-delocalization transition in 2D and 3D. We show that in 3D disordered media γm exhibits two distinct types of frequency dependence over two frequency ranges, hence indicating the existence of a localization-delocalization transition at a critical frequency ωc. The critical... 

The formation of atomic nanoclusters on suspended graphene sheets has been investigated by employing a molecular dynamics simulation at finite temperature. Our systematic study is based on temperature-dependent molecular dynamics simulations of some transition and alkali atoms on suspended graphene sheets. We find that the transition atoms aggregate and make various size nanoclusters distributed randomly on graphene surfaces. We also report that most alkali atoms make one atomic layer on graphene sheets. Interestingly, the potassium atoms almost deposit regularly on the surface at low temperature. We expect from this behavior that the electrical conductivity of a suspended graphene doped by... 

When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real world, we need a top-down approach to complexity. In this approach, one may desire to understand general multipoint statistics. Here, such a general approach is presented and discussed based on examples from turbulence and sea waves. Our main idea is based on the cascade picture of turbulence, entangling fluctuations from large to small scales. Inspired by this cascade picture, we express the general multipoint statistics by the statistics of scale-dependent fluctuations of variables and relate it to a scale-dependent process, which finally is a stochastic cascade process. We... 

Localization of elastic waves in two-dimensional (2D) and three-dimensional (3D) media with random distributions of the Lamé coefficients (the shear and bulk moduli) is studied, using extensive numerical simulations. We compute the frequency dependence of the minimum positive Lyapunov exponent γ (the inverse of the localization length) using the transfer-matrix method, the density of states utilizing the force oscillator method, and the energy-level statistics of the media. The results indicate that all the states may be localized in the 2D media, up to the disorder width and the smallest frequencies considered, although the numerical results also hint at the possibility that there might be... 

Discontinuous molecular dynamics simulations, together with the protein intermediate resolution model, an intermediate-resolution model of proteins, are used to carry out several microsecond-long simulations and study folding transition and stability of α -de novo-designed proteins in slit nanopores. Both attractive and repulsive interaction potentials between the proteins and the pore walls are considered. Near the folding temperature Tf and in the presence of the attractive potential, the proteins undergo a repeating sequence of folding/partially folding/unfolding transitions, with Tf decreasing with decreasing pore sizes. The unfolded states may even be completely adsorbed on the pore's... 

The propagation of acoustic waves in strongly heterogeneous media is studied using direct numerical simulations. Two types of heterogeneous media are considered. In one type, the spatial distribution of the local elastic constants contain long-range correlations with a power law, nondecaying correlation function. The correlation length is, therefore, as large as the linear size of the system. In the second type of heterogeneous media the correlation length is decreased, up to the linear size of the blocks in the computational grid and, therefore, the distribution of the elastic constants is uncorrelated or white noise, but with the same mean and variance as that of the correlated media. We... 

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system. © 2021 by the authors. Licensee MDPI, Basel, Switzerland  

We consider the O (n) theory in the n → 0 limit. We show that the theory is described by logarithmic conformal field theory, and that the correlation functions have logarithmic singularities. The explicit forms of the two-, three- and four-point correlation functions of the scaling fields and the corresponding logarithmic partners are derived. © 2004 Elsevier B.V. All rights reserved  

Analysis of flow in fluidized beds, a common chemical reactor, is of much current interest due to its fundamental as well as industrial importance. Experimental data for the successive increments of the pressure fluctuations time series in a fluidized bed are analyzed by computing a multiscale probability density function (PDF) of the increments. The results demonstrate the evolution of the shape of the PDF from the short to long time scales. The deformation of the PDF across time scales may be modeled by the log-normal cascade model. The results are also in contrast to the previously proposed PDFs for the pressure fluctuations that include a Gaussian distribution and a PDF with a power-law... 

Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal's coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact... 

Over the last two decades there have been numerous reports from different seismically active regions of the world that thermal infrared (TIR) anomalies can be identified around the epicentral areas before major earthquakes [e.g. (Tronin et al., 2002)]. The TIR anomalies reportedly appear as early as 14 to 7 days before the seismic events and affect areas as large as 1000s to 100,000s km2 in size. Our case study for detection of TIRs using NOAA-AVHRR data(Band 4) is an Ms = 5.1 earthquake that occurred on 14th October 2004 near Ravar in Kerman province located in Loot and Tabas deserts, southeast-central Iran. The area is part of the Golbaf-Sirj seismogenic zone. It includes major faults... 

The electronic transmission and conductance of a gapped graphene superlattice were calculated by means of the transfer-matrix method. The system that we study consists of a sequence of electron-doped graphene as wells and hole-doped graphene as barriers. We show that the transmission probability approaches unity at some critical value of the gap. We also find that there is a domain around the critical gap value for which the conductance of the system attains its maximum value  

Complex systems involving a large number of degrees of freedom, generally exhibit non-stationary dynamics, which can result in either continuous or discontinuous sample paths of the corresponding time series. The latter sample paths may be caused by discontinuous events - or jumps - with some distributed amplitudes, and disentangling effects caused by such jumps from effects caused by normal diffusion processes is a main problem for a detailed understanding of stochastic dynamics of complex systems. Here we introduce a non-parametric method to address this general problem. By means of a stochastic dynamical jump-diffusion modelling, we separate deterministic drift terms from different... 

Emergent extreme events are a key characteristic of complex dynamical systems. The main tool for detailed and deep understanding of their stochastic dynamics is the statistics of time intervals of extreme events. Analyzing extensive experimental data, we demonstrate that for the velocity time series of fully-developed turbulent flows, generated by (i) a regular grid; (ii) a cylinder; (iii) a free jet of helium, and (iv) a free jet of air with the Taylor Reynolds numbers Reλ from 166 to 893, the interoccurrence time distributions P(τ) above a positive threshold Q in the inertial range is described by a universal q- exponential function, P(τ) = β(2 - q)[1 - β(1 - q)τ]1/(1-q), which may be due... 

Boron nitride quantum dots (BNQDs) functionalized with chemical ligands exhibit intriguing optoelectronic properties due to the quantum confinement effect. This paper presents peculiar insights on the effect of side defects on the electronic structure and optical properties of BNQDs functionalized with different chemical bonds including hydrogen (H), nitrogen (N), hydroxyl (OH), amine (NH2), and thiol groups (inspired by experimental reports of functionalized BN nanosheets and nanotubes) Weng, Chem. Soc. Rev. 45, 3989 (2016)0306-001210.1039/C5CS00869G. Hybrid density functional simulations and Green's function calculations indicate an intriguing coexistence of two different Peierls-like...