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Milena Vesković, Milica Labudović-Borović, Ivan Zaletel, Jelena Rakočević, Dušan Mladenović, Bojan Jorgačević, Danijela Vučević, Tatjana Radosavljević
The effects of betaine on hepatocytes chromatin architecture changes were examined by using fractal and gray-level co-occurrence matrix (GLCM) analysis in methionine/choline-deficient (MCD) diet-induced, nonalcoholic fatty liver disease (NAFLD). Male C57BL/6 mice were divided into groups: (1) Control: standard diet; (2) BET: standard diet and betaine supplementation through drinking water (solution 1.5%); (3) MCD group: MCD diet for 6 weeks; (4) MCD+BET: fed with MCD diet + betaine for 6 weeks. Liver tissue was collected for histopathology, immunohistochemistry, and determination of fractal dimension and GLCM parameters...
January 19, 2018: Microscopy and Microanalysis
Frigyes Samuel Racz, Peter Mukli, Zoltan Nagy, Andras Eke
Brain function is organized as a network of functional connections between different neuronal populations with connection strengths dynamically changing in time and space. Studies investigating functional connectivity (FC) usually follow a static approach when describing FC by considering the connectivity strengths constant, however a dynamic approach seems more reasonable, as this way the spatio-temporal dynamics of the underlying system can also be captured. Objective: The scale-free, i.e. fractal nature of neural dynamics is an inherent property of the nervous system...
January 19, 2018: Physiological Measurement
Jonas Grimm, Maxim Dolgushev
We investigate the dynamics of fractals and other networks in a viscoelastic and active environment. The viscoelastic dynamics is modeled based on the generalized Langevin equation, where the activity is introduced to it by means of the exponentially correlated noise. The intramolecular interactions are taken into account by the bead-spring picture. The microscopic connectivity (studied in the form of Vicsek fractals, of dual Sierpiński gaskets, of NTD trees, and of a family of deterministic small-world networks) reveals itself in the multiscale monomeric dynamics, which shows vastly different behaviors in the active and passive baths...
January 19, 2018: Soft Matter
Hai-Chuan Xu, Gao-Feng Gu, Wei-Xing Zhou
In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent τ(q) is related to the partition function and the multifractal spectrum f(α) can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional p-model, the two-dimensional p-model, and the fractional Brownian motions...
November 2017: Physical Review. E
R S Pires, A A Moreira, H A Carmona, J S Andrade
We investigate the properties of a two-state sandpile model subjected to a confining potential in two dimensions. From the microdynamical description, we derive a diffusion equation, and find a stationary solution for the case of a parabolic confining potential. By studying the systems at different confining conditions, we observe two scale-invariant regimes. At a given confining potential strength, the cluster size distribution takes the form of a power law. This regime corresponds to the situation in which the density at the center of the system approaches the critical percolation threshold...
November 2017: Physical Review. E
Pietro Rotondo, Alessandro Luigi Sellerio, Pietro Glorioso, Sergio Caracciolo, Marco Cosentino Lagomarsino, Marco Gherardi
Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the nonequilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory...
November 2017: Physical Review. E
Konark Bisht, Stefan Klumpp, Varsha Banerjee, Rahul Marathe
A human pathogen, Neisseria gonorrhoeae (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The tug-of-war between the pili results in a two-dimensional stochastic motion called twitching motility. In this paper, with the help of real-time NG trajectories, we develop coarse-grained models for their description. The fractal properties of these trajectories are determined and their influence on first passage time and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) there exists a characteristic persistent length l_{p}^{*}, which yields the fastest growth of bacterial aggregates or biofilms...
November 2017: Physical Review. E
J Cheraghalizadeh, M N Najafi, H Dashti-Naserabadi, H Mohammadzadeh
The self-organized criticality on the random fractal networks has many motivations, like the movement pattern of fluid in the porous media. In addition to the randomness, introducing correlation between the neighboring portions of the porous media has some nontrivial effects. In this paper, we consider the Ising-like interactions between the active sites as the simplest method to bring correlations in the porous media, and we investigate the statistics of the BTW model in it. These correlations are controlled by the artificial "temperature" T and the sign of the Ising coupling...
November 2017: Physical Review. E
Pierre Gaspard
The kinetic equations of DNA replication are shown to be exactly solved in terms of iterated function systems, running along the template sequence and giving the statistical properties of the copy sequences, as well as the kinetic and thermodynamic properties of the replication process. With this method, different effects due to sequence heterogeneity can be studied, in particular, a transition between linear and sublinear growths in time of the copies, and a transition between continuous and fractal distributions of the local velocities of the DNA polymerase along the template...
October 2017: Physical Review. E
Alexandre Morin, David Lopes Cardozo, Vijayakumar Chikkadi, Denis Bartolo
Combining experiments and theory, we address the dynamics of self-propelled particles in crowded environments. We first demonstrate that motile colloids cruising at constant speed through random lattices undergo a smooth transition from diffusive to subdiffusive to localized dynamics upon increasing the obstacle density. We then elucidate the nature of these transitions by performing extensive simulations constructed from a detailed analysis of the colloid-obstacle interactions. We evidence that repulsion at a distance and hard-core interactions both contribute to slowing down the long-time diffusion of the colloids...
October 2017: Physical Review. E
H Dashti-Naserabadi, M N Najafi
We present extensive numerical simulations of Bak-Tang-Wiesenfeld (BTW) sandpile model on the hypercubic lattice in the upper critical dimension D_{u}=4. After re-extracting the critical exponents of avalanches, we concentrate on the three- and two-dimensional (2D) cross sections seeking for the induced criticality which are reflected in the geometrical and local exponents. Various features of finite-size scaling (FSS) theory have been tested and confirmed for all dimensions. The hyperscaling relations between the exponents of the distribution functions and the fractal dimensions are shown to be valid for all dimensions...
October 2017: Physical Review. E
K Choi, Deokjae Lee, Y S Cho, J C Thiele, H J Herrmann, B Kahng
Recently, a hybrid percolation transition (HPT) that exhibits both a discontinuous transition and critical behavior at the same transition point has been observed in diverse complex systems. While the HPT induced by avalanche dynamics has been studied extensively, the HPT induced by cluster merging dynamics (HPT-CMD) has received little attention. Here, we aim to develop a theoretical framework for the HPT-CMD. We find that two correlation-length exponents are necessary for characterizing the giant cluster and finite clusters separately...
October 2017: Physical Review. E
Denis S Grebenkov, Dmitry Beliaev
We study the fractal structure of diffusion-limited aggregation (DLA) clusters on a square lattice by extensive numerical simulations (with clusters having up to 10^{8} particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and one-dimensional. At the same time, on all scales from the particle size to the size of the entire cluster it has a nontrivial box-counting fractal dimension which corresponds to the overall growth rate, which, in turn, is smaller than the growth rate along the axes...
October 2017: Physical Review. E
Guiomar Ruiz, Ugur Tirnakli, Ernesto P Borges, Constantino Tsallis
We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional S_{BG}[p(x)]=-k∫dxp(x)lnp(x). In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional S_{q}[p(x)]=k1-∫dx[p(x)]^{q}/q-1 (q∈R;S_{1}=S_{BG}). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map...
October 2017: Physical Review. E
Hangmo Yi
Quantum phase transitions of a q-state Potts model in fractal lattices are studied using a continuous-time quantum Monte Carlo simulation technique. For small values of q, the transition is found to be second order and critical exponents of the quantum critical point are calculated. The dynamic critical exponent z is found to be greater than one for all fractals studied, which is in contrast to integer-dimensional regular lattices. When q is greater than a certain value q_{c}, the phase transition becomes first order, where q_{c} depends on the lattice...
December 2017: Physical Review. E
Johannes Zierenberg, Niklas Fricke, Martin Marenz, F P Spitzner, Viktoria Blavatska, Wolfhard Janke
We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details...
December 2017: Physical Review. E
E G Iashina, E V Velichko, M V Filatov, W G Bouwman, C P Duif, A Brulet, S V Grigoriev
Small-angle neutron scattering (SANS) on nuclei of chicken erythrocytes demonstrates the cubic dependence of the scattering intensity Q^{-3} in the range of momentum transfer Q∈10^{-3}-10^{-2}nm^{-1}. Independent spin-echo SANS measurements give the spin-echo function, which is well described by the exponential law in a range of sizes (3×10^{2})-(3×10^{4}) nm. Both experimental dependences reflect the nature of the structural organization of chromatin in the nucleus of a living cell, which corresponds to the correlation function γ(r)=ln(ξ/r) for r<ξ, where ξ=(3...
July 2017: Physical Review. E
Maxim Dolgushev, Adrian L Hauber, Philipp Pelagejcev, Joachim P Wittmer
We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures...
July 2017: Physical Review. E
James Corson, George W Mulholland, Michael R Zachariah
We apply our extended Kirkwood-Riseman theory to compute the translation, rotation, and coupling friction tensors and the scalar rotational friction coefficient for an aerosol fractal aggregate in the transition flow regime. The method can be used for particles consisting of spheres in contact. Our approach considers only the linear velocity of the primary spheres in a rotating aggregate and ignores rotational and coupling interactions between spheres. We show that this simplified approach is within approximately 40% of the true value for any particle for Knudsen numbers between 0...
July 2017: Physical Review. E
Domenico Lippolis, Li Wang, Yun-Feng Xiao
A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling...
July 2017: Physical Review. E
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