results for au:Moreira_A in:cond-mat

- May 16 2018 cond-mat.stat-mech arXiv:1805.05892v1We investigate the dynamics of overdamped $D$-dimensional systems of particles repulsively interacting through short-ranged power-law potentials, $V(r)\sim r^{-\lambda}\;(\lambda/D>1)$. We show that such systems obey a non-linear diffusion equation, and that their stationary state extremizes a $q$-generalized nonadditive entropy. Here we focus on the dynamical evolution of these systems. Our first-principle $D=1,2$ many-body numerical simulations (based on Newton's law) confirm the predictions obtained from the time-dependent solution of the non-linear diffusion equation, and show that the one-particle space-distribution $P(x,t)$ appears to follow a compact-support $q$-Gaussian form, with $q=1-\lambda/D$. We also calculate the velocity distributions $P(v_x,t)$ and, interestingly enough, they follow the same $q$-Gaussian form (apparently precisely for $D=1$, and nearly so for $D=2$). The satisfactory match between the continuum description and the molecular dynamics simulations in a more general, time-dependent, framework neatly confirms the idea that the present dissipative systems indeed represent suitable applications of the $q$-generalized thermostatistical theory.
- Mar 22 2018 cond-mat.stat-mech arXiv:1803.07876v1The elastic backbone is the set of all shortest paths. We found a new phase transition at $p_{eb}$ above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in $2d$ its fractal dimension is $1.750\pm 0.003$, and one obtains a novel set of critical exponents $\beta_{eb} = 0.50\pm 0.02$, $\gamma_{eb} = 1.97\pm 0.05$, and $\nu_{eb} = 2.00\pm 0.02$ fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. Using Binder's cumulant, we determine, with high precision, the critical probabilities $p_{eb}$ for the triangular and tilted square lattice for site and bond percolation. This transition describes a sudden rigidification as a function of density when stretching a damaged tissue.
- Mar 01 2018 cond-mat.stat-mech arXiv:1802.10373v2We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node $i$ of a square lattice, following the probability, $P_{ij}\sim{r_{ij}^{-\alpha}}$ , where $r_{ij}$ is the Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is a tunable parameter. Extensive Monte Carlo simulations and a finite-size scaling analysis for different values of $\alpha$ reveal a crossover from the mean-field to $2d$ Directed Percolation universality class with increasing $\alpha$, in the range $3<\alpha<4$.
- Nov 17 2017 physics.soc-ph cond-mat.stat-mech arXiv:1711.05894v1The increasing cost of electoral campaigns raises the need for effective campaign planning and a precise understanding of the return of such investment. Interestingly, despite the strong impact of elections on our daily lives, how this investment is translated into votes is still unknown. By performing data analysis and modeling, we show that top candidates spend more money \emphper vote than the less successful and poorer candidates, a sublinearity that discloses a diseconomy of scale. We demonstrate that such electoral diseconomy arises from the competition between candidates due to inefficient campaign expenditure. Our approach succeeds in two important tests. First, it reveals that the statistical pattern in the vote distribution of candidates can be explained in terms of the independently conceived, but similarly skewed distribution of money campaign. Second, using a heuristic argument, we are able to predict a turnout percentage for a given election of approximately 63\%. This result is in good agreement with the average turnout rate obtained from real data. Due to its generality, we expect that our approach can be applied to a wide range of problems concerning the adoption process in marketing campaigns.
- Jun 14 2017 cond-mat.stat-mech arXiv:1706.03853v1We 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. The analysis of the fractal dimension of the largest cluster frontier provides evidence that this regime is reminiscent of gradient percolation. By increasing further the confining potential, most of the particles coalesce in a giant cluster, and we observe a regime where the jump size distribution takes the form of a power law. The onset of this second regime is signaled by a maximum in the fluctuation of energy.
- Aug 30 2016 cond-mat.dis-nn arXiv:1608.08147v1We report on a novel dynamic phase in electrical networks, in which current channels perpetually change in time. This occurs when the individual elements of the network are fuse-antifuse devices, namely, become insulators within a certain finite interval of local applied voltages. As a consequence, the macroscopic current exhibits temporal fluctuations which increase with system size. We determine the conditions under which this exotic situation appears by establishing a phase diagram as a function of the applied field and the size of the insulating window. Besides its obvious application as a versatile electronic device, due to its rich variety of behaviors, this network model provides a possible description for particle-laden flow through porous media leading to dynamical clogging and reopening of the local channels in the pore space.
- Mar 01 2016 cond-mat.stat-mech arXiv:1602.09086v1We propose a general coarse-graining method to derive a continuity equation that describes any dissipative system of repulsive particles interacting through short-ranged potentials. In our approach, the effect of particle-particle correlations is incorporated to the overall balance of energy, and a non-linear diffusion equation is obtained to represent the overdamped dynamics. In particular, when the repulsive interaction potential is a short-ranged power-law, our approach reveals a distinctive correspondence between particle-particle energy and the generalized thermostatistics of Tsallis for any non-positive value of the entropic index q. Our methodology can also be applied to microscopic models of superconducting vortices and complex plasma, where particle-particle correlations are pronounced at low concentrations. The resulting continuum descriptions provide elucidating and useful insights on the microdynamical behavior of these physical systems. The consistency of our approach is demonstrated by comparison with molecular dynamics simulations.
- Mar 01 2016 cond-mat.stat-mech arXiv:1602.08948v1We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which long-range connections are randomly added according to the probability, $P_{ij}\sim{r^{-\alpha}}$, where $r_{ij}$ is the Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is a controlling parameter [J. M. Kleinberg, Nature 406, 845 (2000)]. Our results show that the collective behavior of this system exhibits a continuous order-disorder phase transition at a critical parameter, which is a decreasing function of the exponent $\alpha$. Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the system undergoes a crossover among distinct universality classes. For $\alpha\le3$ the critical behavior is described by mean-field exponents, while for $\alpha\ge4$ it belongs to the Ising universality class. Finally, in the region where the crossover occurs, $3<\alpha<4$, the critical exponents are dependent on $\alpha$.
- Jul 20 2015 cond-mat.stat-mech arXiv:1507.05074v1We disclose the origin of anisotropic percolation perimeters in terms of the Stochastic Loewner Evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multi-layered and directed percolation clusters at criticality are the scaling limits of the Loewner evolution of an anomalous Brownian motion, being subdiffusive and superdiffusive, respectively. The connection between anomalous diffusion and fractal anisotropy is further tested by using long-range power-law correlated time series (fractional Brownian motion) as driving functions in the evolution process. The fact that the resulting traces are distinctively anisotropic corroborates our hypothesis. Under the conceptual framework of SLE, our study therefore reveals new perspectives for mathematical and physical interpretations of non-Markovian processes in terms of anisotropic paths at criticality and vice-versa.
- Aug 06 2014 cond-mat.mes-hall arXiv:1408.1066v1We present a quaternion-inspired formalism specifically developed to evaluate the electric current that traverses a single molecule subjected to an externally applied voltage. The molecule of interest is covalently connected to two small metallic clusters, forming an extended molecule complex. The quaternion approach allows for an integrated treatment of the charge transport in single molecules where both ballistic and co-tunneling (coherent) mechanisms are taken on equal footing, although only in the latter case the presence of eventual transient charged states of the system needs to be considered. We use a Dyson series to obtain a generalized Fermi golden rule, from which we derive an expression for the net current the two electrodes: in doing this, we take into account all possible transitions between electronic states localized at the electrodes and levels in the extended molecule complex. In fact, one can apply the method to the entire range of coupling regimes, not only in the weak or strong cases, but also in intermediate situations, where ballistic and co-tunneling processes compete with each other. We also discuss initial results of the application of this formalism to the description of the electronic transport in two small organic molecules representative of two different limit situations. In the first case, a conjugated molecule (where spatially delocalized molecular orbitals favor ballistic contributions) is considered, and in the second, the current traverses a saturated hydrocarbon (whose structure should contain more localized molecular orbitals). In both cases, we fully describe the field-induced self-adjustment of the electronic levels of the extended molecule complex at an ab initio quantum chemical level, using density functional theory.
- We address and discuss recent trends in the analysis of big data sets, with the emphasis on studying multiscale phenomena. Applications of big data analysis in different scientific fields are described and two particular examples of multiscale phenomena are explored in more detail. The first one deals with wind power production at the scale of single wind turbines, the scale of entire wind farms and also at the scale of a whole country. Using open source data we show that the wind power production has an intermittent character at all those three scales, with implications for defining adequate strategies for stable energy production. The second example concerns the dynamics underlying human mobility, which presents different features at different scales. For that end, we analyze $12$-month data of the Eduroam database within Portuguese universities, and find that, at the smallest scales, typically within a set of a few adjacent buildings, the characteristic exponents of average displacements are different from the ones found at the scale of one country or one continent.
- Apr 03 2014 cond-mat.stat-mech arXiv:1404.0632v1We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to derive a continuum nonlinear diffusion equation that displays singularities in both the diffusion and drift terms. The stationary-state solutions of this equation, which maximizes the Fermi-Dirac entropy, are in perfect agreement with the spatial profiles of time-averaged occupancy obtained from model numerical simulations in one as well as in two dimensions. Surprisingly, our results also show that, regardless of dimensionality, the presence of a confining potential can lead to the emergence of typical attributes of critical behavior in the two-state sandpile model, namely, a power-law tail in the distribution of avalanche sizes.
- The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the formation of a highly efficient structure for information propagation. Here we show that enhanced flow properties can also be observed in these complex topologies. Precisely, our model is a network built from an underlying regular lattice over which long-range connections are randomly added according to the probability, $P_{ij}\sim r_{ij}^{-\alpha}$, where $r_{ij}$ is the Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is a controlling parameter. The mean two-point global conductance of the system is computed by considering that each link has a local conductance given by $g_{ij}\propto r_{ij}^{-\delta}$, where $\delta$ determines the extent of the geographical limitations (costs) on the long-range connections. Our results show that the best flow conditions are obtained for $\delta=0$ with $\alpha=0$, while for $\delta \gg 1$ the overall conductance always increases with $\alpha$. For $\delta\approx 1$, $\alpha=d$ becomes the optimal exponent, where $d$ is the topological dimension of the substrate. Interestingly, this exponent is identical to the one obtained for optimal navigation in small-world networks using decentralized algorithms.
- Apr 18 2013 cond-mat.stat-mech arXiv:1304.4872v1We investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption (CSA) on square lattices with Arrhenius rates given by ki= q^(ni), where ni is the number of occupied neighbors of the site i, and q a controlling parameter. Our results show a dependence of the prefactors on q and a strong finite size effect for small values of this parameter, both impacting the size of the backbone and the global conductance of the system. These results might be pertinent to practical applications in processes involving adsorption of particles.
- Dec 24 2012 q-bio.NC cond-mat.dis-nn arXiv:1212.5550v1The movement of the eyes has been the subject of intensive research as a way to elucidate inner mechanisms of cognitive processes. A cognitive task that is rather frequent in our daily life is the visual search for hidden objects. Here we investigate through eye-tracking experiments the statistical properties associated with the search of target images embedded in a landscape of distractors. Specifically, our results show that the twofold process of eye movement, composed of sequences of fixations (small steps) intercalated by saccades (longer jumps), displays characteristic statistical signatures. While the saccadic jumps follow a log normal distribution of distances, which is typical of multiplicative processes, the lengths of the smaller steps in the fixation trajectories are consistent with a power-law distribution. Moreover, the present analysis reveals a clear transition between a directional serial search to an isotropic random movement as the difficulty level of the searching task is increased.
- We investigate the role of disorder on the fracturing process of heterogeneous materials by means of a two-dimensional fuse network model. Our results in the extreme disorder limit reveal that the backbone of the fracture at collapse, namely the subset of the largest fracture that effectively halts the global current, has a fractal dimension of $1.22 \pm 0.01$. This exponent value is compatible with the universality class of several other physical models, including optimal paths under strong disorder, disordered polymers, watersheds and optimal path cracks on uncorrelated substrates, hulls of explosive percolation clusters, and strands of invasion percolation fronts. Moreover, we find that the fractal dimension of the largest fracture under extreme disorder, $d_f=1.86 \pm 0.01$, is outside the statistical error bar of standard percolation. This discrepancy is due to the appearance of trapped regions or cavities of all sizes that remain intact till the entire collapse of the fuse network, but are always accessible in the case of standard percolation. Finally, we quantify the role of disorder on the structure of the largest cluster, as well as on the backbone of the fracture, in terms of a distinctive transition from weak to strong disorder characterized by a new crossover exponent.
- Jan 18 2012 cond-mat.mes-hall quant-ph arXiv:1201.3487v1We present a quaternion inspired formalism specifically developed to evaluate the intensity of the electrical current that traverses a single molecule connected to two semi-infinite electrodes as the applied external bias is varied. The self-adjustment of the molecular levels is fully described at a density functional ab initio quantum chemical level. Use of a quaternion approach allows for an integrated treatment of both coherent (ballistic) and non-coherent (co-tunneling) contributions to the effective charge transport, where the latter involve the existence of transient charged states of the corresponding molecular species. An expression for the net current is calculated by using second-order perturbation theory to take into account all possible transitions between states localized at the two different electrodes that involve intermediary levels in the so-called "extended molecule" complex that comprises the system of interest attached to two small metallic clusters. We show that by a judicious choice of the relevant molecular parameters, the formalism can be extended to describe the electronic transport both in conjugated as in saturated molecules, where localized orbitals are more likely to be found. In this manner, the method can be applied to the full range of coupling regimes, not only to the weak or strong cases, but also in intermediate situations, where ballistic and co-tunneling processes may coexist.
- Dec 22 2011 cond-mat.str-el arXiv:1112.5023v2A remarkable hardening (~ 30 cm-1) of the normal mode of vibration associated with the symmetric stretching of the oxygen octahedra for the Ba2FeReO6 and Sr2CrReO6 double perovskites is observed below the corresponding magnetic ordering temperatures. The very large magnitude of this effect and its absence for the anti-symmetric stretching mode provide evidence against a conventional spin-phonon coupling mechanism. Our observations are consistent with a collective excitation formed by the combination of the vibrational mode with oscillations of local Fe or Cr 3d and Re 5d occupations and spin magnitudes.
- Dec 05 2011 cond-mat.stat-mech arXiv:1112.0557v1Despite original claims of a first-order transition in the product rule model proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies indicate that this percolation model, in fact, displays a continuous transition. The distinctive scaling properties of the model at criticality, however, strongly suggest that it should belong to a different universality class than ordinary percolation. Here we introduce a generalization of the product rule that reveals the effect of non-locality on the critical behavior of the percolation process. Precisely, pairs of unoccupied bonds are chosen according to a probability that decays as a power-law of their Manhattan distance, and only that bond connecting clusters whose product of their sizes is the smallest, becomes occupied. Interestingly, our results for two-dimensional lattices at criticality shows that the power-law exponent of the product rule has a significant influence on the finite-size scaling exponents for the spanning cluster, the conducting backbone, and the cutting bonds of the system. In all three cases, we observe a continuous variation from ordinary to (non-local) explosive percolation exponents.
- Jun 17 2011 cond-mat.stat-mech arXiv:1106.3277v1In their Rejoinder [arXiv:1105.1316v1], Levin and Pakter repeat some of the points raised in their previous Comment [arXiv:1104.0697v1] (already refuted in our first Reply [arXiv:1104.5036v1]), and present some new ones concerning our recent publication [arXiv:1008.1421]. Their new criticisms are also refuted in the present Surrejoinder, whenever relevant for the results of our Letter. It is our understanding that, in their Comment and Rejoinder, Levin and Pakter do not provide any relevant contributions to the problem addressed in our previous work. We therefore consider the present discussion as closed.
- Apr 28 2011 cond-mat.stat-mech arXiv:1104.5036v1We show that the comment [arXiv:1104.0697] by Levin and Pakter on our work [arXiv:1008.1421] is conceptually unfounded, contains misleading interpretations, and is based on results of questionable applicability. We initially provide arguments to evince that, inexplicably, these authors simply choose to categorically dismiss our elaborated and solid conceptual approach, results and analysis, without employing any fundamental concepts or tools from Statistical Physics. We then demonstrate that the results of Levin and Pakter do not present any evidence against, but rather corroborates, our conclusions. In fact, the results shown in their comment correspond to a confining potential that is 1000 times stronger than the typical valued utilized in our study, therefore explaining the discrepancy between their results and ours. Furthermore, in this regime where higher vortex densities are involved, vortex cores might get so close to each other that can no longer be treated as point-like defects. As a consequence, Ginzburg-Landau equations should be employed instead, meaning that the physical conditions implied by the results of Levin and Pakter should be considered with caution in the context of the Physics of interacting superconducting vortexes.
- Oct 26 2010 cond-mat.stat-mech arXiv:1010.5097v1We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is randomly chosen. Each of these bonds is then associated with a weight given by the product of the cluster sizes that they would potentially connect, and only that bond among the q-set which has the smallest weight becomes occupied. Our results indicate that, at criticality, all finite-size scaling exponents for the spanning cluster, the conducting backbone, the cutting bonds, and the global conductance of the system, change continuously and significantly with q. Surprisingly, we also observe that systems with intermediate values of q display the worst conductive performance. This is explained by the strong inhibition of loops in the spanning cluster, resulting in a substantially smaller associated conducting backbone.
- Aug 10 2010 cond-mat.stat-mech arXiv:1008.1421v2We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be directly associated with Tsallis thermostatistics. For sufficiently high values of T, the distribution of particles becomes Gaussian, so that the classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures of the thermal bath, the system displays a mixed behavior that follows a novel type of thermostatistics, where the entropy is given by a linear combination of Tsallis and Boltzmann-Gibbs entropies.
- Nov 02 2009 cond-mat.stat-mech cond-mat.dis-nn arXiv:0910.5918v1We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We show that the following two ingredients are essential for obtaining an abrupt (first-order) transition in the fraction of the system occupied by the largest cluster: (i) the size of all growing clusters should be kept approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds connecting vertices in different clusters) should dominate with respect to the redundant bonds (i.e., bonds connecting vertices in the same cluster). Moreover, in the extreme limit where only merging bonds are present, a complete enumeration scheme based on tree-like graphs can be used to obtain an exact solution of our model that displays a first-order transition. Finally, the proposed mechanism can be viewed as a generalization of standard percolation that discloses an entirely new family of models with potential application in growth and fragmentation processes of real network systems.
- Sep 02 2009 cond-mat.dis-nn arXiv:0909.0253v1Optimal paths play a fundamental role in numerous physical applications ranging from random polymers to brittle fracture, from the flow through porous media to information propagation. Here for the first time we explore the path that is activated once this optimal path fails and what happens when this new path also fails and so on, until the system is completely disconnected. In fact numerous applications can be found for this novel fracture problem. In the limit of strong disorder, our results show that all the cracks are located on a single self-similar connected line of fractal dimension $D_{b} \approx 1.22$. For weak disorder, the number of cracks spreads all over the entire network before global connectivity is lost. Strikingly, the disconnecting path (backbone) is, however, completely independent on the disorder.
- Aug 27 2009 cond-mat.stat-mech cond-mat.dis-nn arXiv:0908.3786v1Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes $i$ and $j$ to be retained is proportional to $(k_ik_j)^{-\alpha}$ with $k_i$ and $k_j$ the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating functions method. The theory is found to agree quite well with simulations. By introducing an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well described by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous couplings.
- Dec 19 2008 cond-mat.dis-nn cond-mat.stat-mech arXiv:0812.3591v1We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$. The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$ through $p_{ij}\propto(k_{i}k_{j})^{-\alpha}$. By varying the exponent $\alpha$, we interpolate between random ($\alpha=0$) and systematic failure. For $\alpha >0 $ ($<0$) the most (least) connected nodes are depreciated first. This topological bias introduces a characteristic scale in $P(k)$ of the depreciated network, marking a crossover between two distinct power laws. The critical percolation threshold, at which global connectivity is lost, depends both on $\gamma$ and on $\alpha$. As a consequence, network robustness or fragility can be controlled through fine tuning of the topological bias in the failure process.
- Mar 11 2006 cond-mat.dis-nn arXiv:cond-mat/0603272v1Understanding the process by which the individuals of a society make up their minds and reach opinions about different issues can be of fundamental importance. In this work we propose an idealized model for competitive cluster growth in complex networks. Each cluster can be thought as a fraction of a community that shares some common opinion. Our results show that the cluster size distribution depends on the particular choice for the topology of the network of contacts among the agents. As an application, we show that the cluster size distributions obtained when the growth process is performed on hierarchical networks, e.g., the Apollonian network, have a scaling form similar to what has been observed for the distribution of number of votes in an electoral process. We suggest that this similarity is due to the fact that social networks involved in the electoral process may also posses an underlining hierarchical structure.
- Feb 07 2006 cond-mat.mtrl-sci arXiv:cond-mat/0602092v1We report high resolution transmission electron microscopy and classical molecular dynamics simulation results of mechanically stretching copper nanowires conducting to linear atomic suspended chains (LACs) formation. In contrast with some previous experimental and theoretical work in literature that stated that the formation of LACs for copper should not exist our results showed the existence of LAC for the [111], [110], and [100] crystallographic directions, being thus the sequence of most probable occurence.
- Sep 01 2005 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/0508767v1Charged soft-matter systems--such as colloidal dispersions and charged polymers--are dominated by attractive forces between constituent like-charged particles when neutralizing counterions of high charge valency are introduced. Such counter-intuitive effects indicate strong electrostatic coupling between like-charged particles, which essentially results from electrostatic correlations among counterions residing near particle surfaces. In this paper, the attraction mechanism and the structure of counterionic correlations are discussed in the limit of strong coupling based on recent numerical and analytical investigations and for various geometries (planar, spherical and cylindrical) of charged objects.
- Aug 16 2005 cond-mat.stat-mech arXiv:cond-mat/0508359v1We study in this work the properties of the $Q_{mf}$ network which is constructed from an anisotropic partition of the square, the multifractal tiling. This tiling is build using a single parameter $\rho$, in the limit of $\rho \to 1$ the tiling degenerates into the square lattice that is associated with a regular network. The $Q_{mf}$ network is a space-filling network with the following characteristics: it shows a power-law distribution of connectivity for $k>7$ and it has an high clustering coefficient when compared with a random network associated. In addition the $Q_{mf}$ network satisfy the relation $N \propto \ell^{d_f}$ where $\ell$ is a typical length of the network (the average minimal distance) and $N$ the network size. We call $d_f$ the fractal dimension of the network. In tne limit case $\rho \to 1$ we have $d_{f} \to 2$.
- Aug 03 2005 cond-mat.dis-nn cond-mat.stat-mech arXiv:cond-mat/0508074v1We investigate the process of invasion percolation between two sites (injection and extraction sites) separated by a distance r in two-dimensional lattices of size L. Our results for the non-trapping invasion percolation model indicate that the statistics of the mass of invaded clusters is significantly dependent on the local occupation probability (pressure) Pe at the extraction site. For Pe=0, we show that the mass distribution of invaded clusters P(M) follows a power-law P(M) ~ M^-\alpha for intermediate values of the mass M, with an exponent \alpha=1.39. When the local pressure is set to Pe=Pc, where Pc corresponds to the site percolation threshold of the lattice topology, the distribution P(M) still displays a scaling region, but with an exponent \alpha=1.02. This last behavior is consistent with previous results for the cluster statistics in standard percolation. In spite of these discrepancies, the results of our simulations indicate that the fractal dimension of the invaded cluster does not depends significantly on the local pressure Pe and it is consistent with the fractal dimension values reported for standard invasion percolation. Finally, we perform extensive numerical simulations to determine the effect of the lattice borders on the statistics of the invaded clusters and also to characterize the self-organized critical behavior of the invasion percolation process.
- Jun 14 2005 cond-mat.dis-nn arXiv:cond-mat/0506290v1We show that flowsheets of oil refineries can be associated to complex network topologies that are scale-free, display small-world effect and possess hierarchical organization. The emergence of these properties from such man-made networks is explained as a consequence of the currently used principles for process design, which include heuristics as well as algorithmic techniques. We expect these results to be valid for chemical plants of different types and capacities.
- Apr 28 2005 cond-mat.dis-nn arXiv:cond-mat/0504722v1Boolean Networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean systems built from arbitrary ensembles of Boolean functions. In particular, we solve the critical condition for systems of units operating according to canalizing functions and present strong numerical evidence that our approach correctly predicts the phase transition from order to chaos in such systems.
- A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. Here, we show that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by $1/f$-scaling of their power spectra, can emerge in networks of simple signaling units. We find that under general conditions, complex dynamics can be generated by systems fulfilling two requirements: i) a ``small-world'' topology and ii) the presence of noise. Our findings support two notable conclusions: first, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions (i) and (ii) are robust to some degree of degradation, i.e., they will still be able to generate $1/f$-dynamics.
- Nov 04 2003 cond-mat.supr-con cond-mat.stat-mech arXiv:cond-mat/0311034v1We study flux penetration in a disordered type II superconductor by simulations of interacting vortices, using a Monte Carlo method for vortex nucleation. Our results show that a detailed description of the nucleation process yields a correction to the scaling laws usually associated with flux front invasion. We propose a simple model to account for these corrections.
- Oct 28 2002 cond-mat.stat-mech arXiv:cond-mat/0210585v1We study the statistics of the backbone cluster between two sites separated by distance $r$ in two-dimensional percolation networks subjected to spatial long-range correlations. We find that the distribution of backbone mass follows the scaling \it ansatz, $P(M_B)\sim M_B^{-(\alpha+1)}f(M_B/M_0)$, where $f(x)=(\alpha+ \eta x^{\eta}) \exp(-x^{\eta})$ is a cutoff function, and $M_0$ and $\eta$ are cutoff parameters. Our results from extensive computational simulations indicate that this scaling form is applicable to both correlated and uncorrelated cases. We show that the exponent $\alpha$ can be directly related to the fractal dimension of the backbone $d_B$, and should therefore depend on the imposed degree of long-range correlations.
- Oct 15 2002 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/0210282v1Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (``virial'') expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters $d_+$ and $d_-$ and charge valences $q_+$ and $q_-$ of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically $d_+ \sim d_-$ and $q_+ \sim q_-$, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient.
- Oct 15 2002 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/0210281v1We consider counterions in the presence of a single planar surface with a spatially inhomogeneous charge distribution using Monte-Carlo simulations and strong-coupling theory. For high surface charges, multivalent counterions, or pronounced substrate charge modulation the counterions are laterally correlated with the surface charges and their density profile deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.
- Aug 07 2002 cond-mat.soft arXiv:cond-mat/0208102v1We theoretically study the polarizability and the interactions of neutral complexes consisting of a semi-flexible polyelectrolyte adsorbed onto an oppositely charged spherical colloid. In the systems we studied, the bending energy of the chain is small compared to the Coulomb energy and the chains are always adsorbed on the colloid. We observe that the polarizability is large for short chains and small electrical fields and shows a non-monotonic behavior with the chain length at fixed charge density. The polarizability has a maximum for a chain length equal to half of the circumference of the colloid. For long chains we recover the polarizability of a classical conducting sphere. For short chains, the existence of a permanent dipole moment of the complexes leads to a van der Waal's-type long-range attraction between them. This attractive interaction vanishes for long chains (i.e., larger than the colloidal size), where the permanent dipole moment is negligible. For short distances the complexes interact with a deep short-ranged attraction which is due to energetic bridging for short chains and entropic bridging for long chains. Exceeding a critical chain length eventually leads to a pure repulsion. This shows that the stabilization of colloidal suspensions by polyelectrolyte adsorption is strongly dependent on the chain size relative to the colloidal size: for long chains the suspensions are always stable (only repulsive forces between the particles), while for mid-sized and short chains there is attraction between the complexes and a salting-out can occur.
- May 21 2002 cond-mat.dis-nn arXiv:cond-mat/0205411v1We investigate the statistics of the most connected nodes in scale-free networks. For a scale-free network model with homogeneous nodes, we show by means of extensive simulations that the exponential truncation--due to the finite size of the network--of the degree distribution governs the scaling of the extreme values. We also find that the distribution of maxima obeys scaling and follows the Gumbel statistics. For a scale-free network model with heterogeneous nodes, we show that scaling no longer holds and that the truncation of the degree distribution no longer controls the maximum distribution. Moreover, we find that neither the Gumbel nor the Frechet statistics describe the data.
- May 21 2002 cond-mat.supr-con arXiv:cond-mat/0205414v1We investigate flux penetration in a disordered type II superconductor by molecular dynamics simulations of interacting vortices. We focus on the effect of different boundary conditions on the scaling laws for flux front propagation. The numerical results can be interpreted using a coarse grained description of the system in terms of a non-linear diffusion equation. We propose a phenomenological equation for the front position that captures the essential behavior of the system and recovers the scaling exponents.
- May 21 2002 cond-mat.dis-nn arXiv:cond-mat/0205420v1We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective movement of tracer particles driven by a pressure difference between two fixed sites (''wells'') separated by Euclidean distance r. For strongly correlated pore networks at criticality, we find that the probability distribution functions P(l) and P(t) follow the same scaling Ansatz originally proposed for the uncorrelated case, but with quite different scaling exponents. We relate these changes in dynamical behavior to the main morphological difference between correlated and uncorrelated clusters, namely, the compactness of their backbones. Our simulations reveal that the dynamical scaling exponents for correlated geometries take values intermediate between the uncorrelated and homogeneous limiting cases.
- Apr 02 2002 cond-mat.stat-mech arXiv:cond-mat/0204034v2We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs statistics is always recovered, regardless of the type of potential among interacting particles. This approach provides, moreover, a one-to-one correspondence between the generalized entropy and the Hamiltonian structure of a wide class of systems, revealing a possible origin for the intrinsic nonlinear features present in the Tsallis formalism that lead naturally to power-law behavior. Finally, we confirm these exact results through extensive numerical simulations of the Fermi-Pasta-Ulam chain of anharmonic oscillators.
- Jul 13 2001 cond-mat.stat-mech cond-mat.dis-nn arXiv:cond-mat/0107231v1We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a deterministic connection between the generalized nonextensive entropy and power law behavior. For the case of a simple one-dimensional harmonic oscillator, we confirm by numerical simulation of the dynamics that the distribution of energy H follows precisely the canonical q-statistics for different values of the parameter q. The approach is further tested for classical many-particle systems by means of molecular dynamics simulations. The results indicate that the intrinsic nonlinear features of the nonextensive formalism are capable to generate energy fluctuations that obey anomalous probability laws. For q<1 a broad distribution of energy is observed, while for q>1 the resulting distribution is confined to a compact support.
- Feb 27 2001 cond-mat.supr-con arXiv:cond-mat/0102461v1We investigate flux front penetration in a disordered type II superconductor by molecular dynamics (MD) simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood performing a coarse graining of the system and writing a disordered non-linear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.
- Sep 26 2000 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/0009377v1Similarly and highly charged plates in the presence of multivalent counter ions attract each other, leading to electrostatically bound states. Using Monte-Carlo simulations we obtain the inter-plate pressure in the global parameter space. The equilibrium plate separation, where the pressure changes from attractive to repulsive, exhibits a novel unbinding transition. A systematic and asymptotically exact strong-coupling field-theory yields the bound state from a competition between counter-ion entropy and electrostatic attraction, in agreement with simple scaling arguments.
- Sep 26 2000 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/0009376v1The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature. In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling. Formally, it corresponds to a standard virial expansion. Long-range divergences, which render the virial expansion intractable for homogeneous bulk systems, are shown to be renormalizable for the case of inhomogeneous distribution functions by a systematic expansion in inverse powers of the coupling parameter. For a planar charged wall, our analytical results compare quantitatively with extensive Monte-Carlo simulations.
- Sep 12 2000 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/0009150v1We study the phase behavior of solutions consisting of positive and negative ions of valence z to which a third ionic species of valence Z>z is added. Using a discretized Debye-Hueckel theory, we analyze the phase behavior of such systems for different values of the ratio Z/z. We find, for Z/z>1.934, a three-phase coexistence region and, for Z/z>2, a closed (reentrant) coexistence loop at high temperatures. We characterize the behavior of these ternary ionic mixtures as function of charge asymmetry and temperature, and show the complete phase diagrams for the experimentally relevant cases of Z/z=2 and Z/z=3, corresponding to addition of divalent and trivalent ions to monovalent ionic fluids, respectively.
- Aug 10 1999 cond-mat.stat-mech arXiv:cond-mat/9908131v1Using field-theoretic methods, we calculate the internal energy for the One-Component Plasma (OCP). We go beyond the recent calculation by Brilliantov [N. Brilliantov, Contrib. Plasma Phys. 38, pg. 489 (1998) / cond-mat/9805358] by including non-Gaussian terms. We show that, for the whole range of the plasma parameter Gamma, the effect of the higher-order terms is small and that the final result is not improved relative to the Gaussian theory when compared to simulations.
- Mar 01 1999 cond-mat.soft cond-mat.stat-mech arXiv:cond-mat/9902356v1Criticality in a fluid of dielectric constant D that exhibits Ising-type behavior is studied as additional electrostatic (i.e., ionic) interactions are turned on. An exploratory perturbative calculation is performed for small ionicity as measured by the ratio of the electrostatic energy to the strength of the short-range nonionic (i.e., van der Waals) interactions in the uncharged fluid. With the aid of distinct transformations for the short-range and for the Coulombic interactions, an effective Hamiltonian with coefficients depending on the ionicity is derived at the Debye-Hueckel limiting-law level for a fully symmetric model. The crossover between classical (mean-field) and Ising behavior is then estimated using a Ginzburg criterion. This indicates that the reduced crossover temperature depends only weakly on the ionicity (and on the range of the nonionic potentials); however, the trends do correlate with the, much stronger, dependence observed experimentally.
- Sep 08 1997 cond-mat.stat-mech arXiv:cond-mat/9709082v1We study the two-dimensional contact process (CP) with quenched disorder (DCP), and determine the static critical exponents beta and nu_perp. The dynamic behavior is incompatible with scaling, as applied to models (such as the pure CP) that have a continuous phase transition to an absorbing state. We find that the survival probability (starting with all sites occupied), for a finite-size system at critical, decays according to a power law, as does the off-critical density autocorrelation function. Thus the critical exponent nu_parallle, which governs the relaxation time, is undefined, since the characteristic relaxation time is itself undefined. The logarithmic time-dependence found in recent simulations of the critical DCP [Moreira and Dickman, Phys. Rev. E54, R3090 (1996)] is further evidence of violation of scaling. A simple argument based on percolation cluster statistics yields a similar logarithmic evolution.
- Apr 25 1996 cond-mat arXiv:cond-mat/9604148v1We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point $\lambda_c$ is characterized by the critical exponents of directed percolation: in $2+1$ dimensions, $\delta = 0.46$, $\eta = 0.214$, and $z = 1.13$. Disorder causes a dramatic change in the critical exponents, to $\delta \simeq 0.60$, $\eta \simeq -0.42$, and $z \simeq 0.24$. These exponents govern spreading following a long crossover period. The usual hyperscaling relation, $4 \delta + 2 \eta = d z$, is violated. Our results support the conjecture by Bramson, Durrett, and Schonmann [Ann. Prob. \bf 19, 960 (1991)], that in two or more dimensions the disordered CP has only a single phase transition.