arXiv subjects

A. P. F. Atman

Publications and source records attributed to A. P. F. Atman.

At least 19 recordsLinked to original sources

arXiv2020

On the monotonicity of the critical time in the Constrained-degree percolation model

The Constrained-degree percolation model was introduced in [B.N.B. de Lima, R. Sanchis, D.C. dos Santos, V. Sidoravicius, and R. Teodoro, Stoch. Process. Appl. (2020)], where it was proven that this model has a non-trivial phase transition on a square lattice. We study the Constrained-degree percolation model on the $d$-dimensional hypercubic lattice ($\mathbb{Z}^d$) and, via numerical simulations, found evidence that the critical time $t_{c}^{d}(k)$ is monotonous not increasing in the constrained $k$ if $d=3,4$, like it is when $d=2$. We verify that the lowest constrained value $k$ such that the system exhibits a phase transition is $k=3$ and that the correlation critical exponent $ν$ for the Constrained-degree percolation model and ordinary Bernoulli percolation are the same.

math-ph↗

arXiv2020

The Multiplex Efficiency Index: unveiling the Brazilian Air Transportation Multiplex Network -- BATMN

Modern society is increasingly massively connected, reflecting an omnipresent tendency to organize social, economic, and technological structures in complex networks. Recently, with the advent of the so-called multiplex networks, new concepts and tools were necessary to better understand the characteristics of this type of system, as well as to analyze and quantify its performance and efficiency. The concept of diversity in multiplex networks is a striking example of this intrinsically interdisciplinary efort to better understand the nature of complex networks. In this work, we introduce the Multiplex Efficiency Index, which allows quantifying the temporal evolution of connectivity diversity, particularly when the number of layers of the multiplex network varies over time. Using data related to air passenger transportation in Brazil we investigate, through the new index, how the Brazilian air transportation network has being changing over the years due to the privatization processes of airports and mergers of airlines in Brazil. Besides that, we show how the Multiplex Efficiency Index is able to quantify fluctuations in network efficiency in a non-biased way, limiting its values between 0 and 1, taking into account the number of layers in the multiplex structure. We believe that the proposed index is of great value for the evaluation of the performance of any multiplex network, and to analyze, in a quantitative way, its temporal evolution independently of the variation in the number of layers.

physics.soc-ph↗

arXiv2020

Multirange Ising model on the square lattice

We study the Ising model on $\mathbb{Z}^{2}$ and show, via numerical simulation, that allowing interactions between spins separated by distances $1$ and $m$ (two ranges), the critical temperature, $ T_c (m) $, converges monotonically to the critical temperature of the Ising model on $\mathbb{Z}^4$ as $ m \to \infty $. Only interactions between spins located in directions parallel to each coordinate axis are considered. We also simulated the model with interactions between spins at distances of $ 1 $, $ m $ and $ u $ (three ranges), with $ u $ a multiple of $ m $; in this case our results indicate that $ T_c(m, u) $ converges to the critical temperature of the model on $ \mathbb{Z}^6$. For percolation, analogous results were proven for the critical probability $p_c$ [B. N. B. de Lima, R. P. Sanchis and R. W. C. Silva, Stochastic Process. Appl. {\bf 121}, 2043 (2011)].

cond-mat.stat-mech↗

arXiv2019

Characterizing network topology using first-passage analysis

Understanding the topological characteristics of complex networks and how they affect navigability is one of the most important goals in science today, as it plays a central role in various economic, biological, ecological and social systems. Here, we apply First Passage analysis tools to investigate the properties and characteristics of random walkers in networks with different topology. Starting with the simplest two-dimensional square lattice, we modify its topology incrementally by randomly reconnecting links between sites. We characterize these networks by First Passage Time from a significant number of random walkers without interaction, varying the departure and arrival locations. We also apply the concept of First Passage Simultaneity, which measures the likelihood of two walkers reaching their destination together. These measures, together with the site occupancy statistics during the processes, allowed to differentiate the studied networks, especially the random networks from the scale-free networks, by their navigability. We also show that small world features can also be highlighted with the proposed technique.

physics.soc-ph↗

arXiv2017

Asymmetric return rates and wealth distribution influenced by the introduction of technical analysis into a behavioral agent based model

Behavioral Finance has become a challenge to the scientific community. Based on the assumption that behavioral aspects of investors may explain some features of the Stock Market, we propose an agent based model to study quantitatively this relationship. In order to approximate the simulated market to the complexity of real markets, we consider that the investors are connected among them through a small world network; each one has its own psychological profile (Imitation, Anti-Imitation, Random); two different strategies for decision making: one of them is based on the trust neighborhood of the investor and the other one considers a technical analysis, the momentum of the market index technique. We analyze the market index fluctuations, the wealth distribution of the investors according to their psychological profiles and the rate of return distribution. Moreover, we analyze the influence of changing the psychological profile of the hub of the network and report interesting results which show how and when anti-imitation becomes the most profitable strategy for investment. Besides this, an intriguing asymmetry of the return rate distribution is explained considering the behavioral aspect of the investors. This asymmetry is quite robust being observed even when a completely different algorithm to calculate the decision making of the investors was applied to it, a remarkable result which, up to our knowledge, has never been reported before.

q-fin.GN↗

arXiv2015

Analysis of the velocity field of granular hopper flow

We report the analysis of radial characteristics of the flow of granular material through a conical hopper. The discharge is simulated for various orifice sizes and hopper opening angles. Velocity profiles are measured along two radial lines from the hopper cone vertex: along the main axis of the cone and along its wall. An approximate power law dependence on the distance from the orifice is observed for both profiles, although differences between them can be noted. In order to quantify these differences, we propose a Local Mass Flow index that is a promising tool in the direction of a more reliable classification of the flow regimes in hoppers.

cond-mat.soft↗

arXiv2014

Mechanical properties of inclined frictional granular layers

We investigate the mechanical properties of inclined frictional granular layers prepared with different protocols by means of DEM numerical simulations. We perform an orthotropic elastic analysis of the stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle $α$ with respect to the critical angle $α_c$. We find that the shear modulus of the system decreases with $α$, but tends to a finite value as $α\to α_c$. We also study the behaviour of various microscopic quantities with $α$, and show in particular the evolution of the contact orientation with respect to the orthotropic axes and that of the distribution of the friction mobilisation at contact.

cond-mat.soft↗

arXiv2013

Mechanical response of an inclined frictional granular layer approaching unjamming

We present an orthotropic elastic analysis of frictional granular layers under gravity by studying their stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle α with respect to the critical angle α_c. We find that the shear modulus of the system decreases with α, but reaches a finite value as αtends to α_c. We also analyze the vibration modes of the system and show that the soft modes play an increasing, though not crucial, role approaching the transition.

cond-mat.soft↗

arXiv2012

Is the Percolation Probability on $\mathbb{Z}^d$ with Long Range Connections Monotone?

We present a numerical study for the threshold percolation probability, $p_c$, in the bond percolation model with multiple ranges, in the square lattice. A recent Theorem demonstrated by de Lima {\it et al.} [B. N. B. de Lima, R. P. Sanchis, R. W. C. Silva, STOCHASTIC PROC APPL {\bf 121}, 2043-2048 (2011)] states that the limit value of $p_c$ when the long ranges go to infinity converges to the bond percolation threshold in the hypercubic lattice, $\mathbb{Z}^d$, for some appropriate dimension $d$. We present the first numerical estimations for the percolation threshold considering two-range and three-range versions of the model. Applying a finite size analysis to the simulation data, we sketch the dependence of $p_c$ in function of the range of the largest bond. We shown that, for the two-range model, the percolation threshold is a non decreasing function, as conjectured in the cited work, and converges to the predicted value. However, the results to the three-range case exhibit a surprising non-monotonic behavior for specific combinations of the long range lengths, and the convergence to the predicted value is less evident, raising new questionings on this fascinating problem.

cond-mat.stat-mech↗

arXiv2006

New method to study stochastic growth equations: a cellular automata perspective

We introduce a new method based on cellular automata dynamics to study stochastic growth equations. The method defines an interface growth process which depends on height differences between neighbors. The growth rule assigns a probability $p_{i}(t)=ρ$ exp$[κΓ_{i}(t)]$ for a site $i$ to receive one particle at a time $t$ and all the sites are updated simultaneously. Here $ρ$ and $κ$ are two parameters and $Γ_{i}(t)$ is a function which depends on height of the site $i$ and its neighbors. Its functional form is specified through discretization of the deterministic part of the growth equation associated to a given deposition process. In particular, we apply this method to study two linear equations - the Edwards-Wilkinson (EW) equation and the Mullins-Herring (MH) equation - and a non-linear one - the Kardar-Parisi-Zhang (KPZ) equation. Through simulations and statistical analysis of the height distributions of the profiles, we recover the values for roughening exponents, which confirm that the processes generated by the method are indeed in the universality classes of the original growth equations. In addition, a crossover from Random Deposition to the associated correlated regime is observed when the parameter $κ$ is varied.

cond-mat.stat-mech↗

arXiv2006

Scale separation in granular packings: stress plateaus and fluctuations

It is demonstrated, by numerical simulations of a 2D assembly of polydisperse disks, that there exists a range (plateau) of coarse graining scales for which the stress tensor field in a granular solid is nearly resolution independent, thereby enabling an `objective' definition of this field. Expectedly, it is not the mere size of the the system but the (related) magnitudes of the gradients that determine the widths of the plateaus. Ensemble averaging (even over `small' ensembles) extends the widths of the plateaus to sub-particle scales. The fluctuations within the ensemble are studied as well. Both the response to homogeneous forcing and to an external compressive localized load (and gravity) are studied. Implications to small solid systems and constitutive relations are briefly discussed.

cond-mat.stat-mech↗

arXiv2005

Sensitivity of the stress response function to packing preparation

A granular assembly composed of a collection of identical grains may pack under different microscopic configurations with microscopic features that are sensitive to the preparation history. A given configuration may also change in response to external actions such as compression, shearing etc. We show using a mechanical response function method developed experimentally and numerically, that the macroscopic stress profiles are strongly dependent on these preparation procedures. These results were obtained for both two and three dimensions. The method reveals that, under a given preparation history, the macroscopic symmetries of the granular material is affected and in most cases significant departures from isotropy should be observed. This suggests a new path toward a non-intrusive test of granular material constitutive properties.

cond-mat.soft↗

arXiv2005

From the stress response function (back) to the sandpile `dip'

We relate the pressure `dip' observed at the bottom of a sandpile prepared by successive avalanches to the stress profile obtained on sheared granular layers in response to a localized vertical overload. We show that, within a simple anisotropic elastic analysis, the skewness and the tilt of the response profile caused by shearing provide a qualitative agreement with the sandpile dip effect. We conclude that the texture anisotropy produced by the avalanches is in essence similar to that induced by a simple shearing -- albeit tilted by the angle of repose of the pile. This work also shows that this response function technique could be very well adapted to probe the texture of static granular packing.

cond-mat.soft↗

arXiv2003

Numerical stress response functions of static granular layers

We investigate the stress response function of a layer of grains, i.e. the stress profile in response to a localized overload. The shape of the profile is very sensitive to the packing arrangement, and is thus a good signature of the preparation procedure of the layer. This study has been done by the use of molecular dynamics numerical simulations. Here, for a given rain-like preparation, we present the scaling properties of the response function, and in particular the influence of the thickness of the layer, and the importance of the location of the overload and measurement points (at the boundaries, in the bulk).

cond-mat.soft↗

arXiv2002

Phase diagram of a probabilistic cellular automaton with three-site interactions

We study a (1+1) dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel (DKCA), but in which the update of a given site depends on the state of {\it three} sites at the previous time step. Thus, compared with the DKCA, there is an additional parameter, $p_3$, representing the probability for a site to be active at time $t$, given that its nearest neighbors and itself were active at time $t-1$. We study phase transitions and critical behavior for the activity {\it and} for damage spreading, using one- and two-site mean-field approximations, and simulations, for $p_3=0$ and $p_3=1$. We find evidence for a line of tricritical points in the ($p_1, p_2, p_3$) parameter space, obtained using a mean-field approximation at pair level. To construct the phase diagram in simulations we employ the growth-exponent method in an interface representation. For $p_3 =0$, the phase diagram is similar to the DKCA, but the damage spreading transition exhibits a reentrant phase. For $p_3=1$, the growth-exponent method reproduces the two absorbing states, first and second-order phase transitions, bicritical point, and damage spreading transition recently identified by Bagnoli {\it et al.} [Phys. Rev. E{\bf 63}, 046116 (2001)].

cond-mat.stat-mech↗

arXiv2002

Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton

We construct the {\it quasi-stationary} (QS) probability distribution for the Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov process with an absorbing state. QS distributions are derived at both the one- and two-site levels. We characterize the distribuitions by their mean, and various moment ratios, and analyze the lifetime of the QS state, and the relaxation time to attain this state. Of particular interest are the scaling properties of the QS state along the critical line separating the active and absorbing phases. These exhibit a high degree of similarity to the contact process and the Malthus-Verhulst process (the closest continuous-time analogs of the DKCA), which extends to the scaling form of the QS distribution.

cond-mat.stat-mech↗

arXiv2001

Lattice Model for Approximate Self-Affine Soil Profiles

A modeling of the soil structure and surface roughness by means of the concepts of the fractal growth is presented. Two parameters are used to control the model: the fragmentation dimension, $D_f$, and the maximum mass of the deposited aggregates, $M_{max}$. The fragmentation dimension is related to the particle size distribution through the relation $N(r \ge R) \sim R^{D_f}$, where $N(r \ge R)$ is the accumulative number of particles with radius greater than $R$. The size of the deposited aggregates are chose following the power law above, and the morphology of the aggregate is random selected using a bond percolation algorithm. The deposition rules are the same used in the model of solid-on-solid deposition with surface relaxation. A comparison of the model with real data shows that the Hurst exponent, $H$, measured {\it via} semivariogram method and detrended fluctuation analysis, agrees in statistical sense with the simulated profiles.

cond-mat.stat-mech↗

arXiv2001

Growth Exponent in the Domany-Kinzel Cellular Automaton

In a roughening process, the growth exponent $β$ describes how the roughness $w$ grows with the time $t$: $w\sim t^β$. We determine the exponent $β$ of a growth process generated by the spatiotemporal patterns of the one dimensional Domany-Kinzel cellular automaton. The values obtained for $β$ shows a cusp at the frozen/active transition which permits determination of the transition line. The $β$ value at the transition depends on the scheme used: symmetric ($β\sim 0.83$) or non-symmetric ($β\sim 0.61$). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas are updated.

cond-mat.stat-mech↗