arXiv subjects

Bosiljka Tadic

Publications and source records attributed to Bosiljka Tadic.

54 records · Page 3Linked to original sources

arXiv2002

Voltage Distribution in Growing Conducting Networks

We investigate by random-walk simulations and a mean-field theory how growth by biased addition of nodes affects flow of the current through the emergent conducting graph, representing a digital circuit. In the interior of a large network the voltage varies with the addition time $s<t$ of the node as $V(s)\sim \ln (s)/s^θ$ when constant current enters the network at last added node $t$ and leaves at the root of the graph which is grounded. The topological closeness of the conduction path and shortest path through a node suggests that the charged random walk determines these global graph properties by using only {\it local} search algorithms. The results agree with mean-field theory on tree structures, while the numerical method is applicable to graphs of any complexity.

cond-mat.stat-mech↗

arXiv2002

Packet Transport on Scale Free Networks

We introduce a model of information packet transport on networks in which the packets are posted by a given rate and move in parallel according to a local search algorithm. By performing a number of simulations we investigate the major kinetic properties of the transport as a function of the network geometry, the packet input rate and the buffer size. We find long-range correlations in the power spectra of arriving packet density and the network's activity bursts. The packet transit time distribution shows a power-law dependence with average transit time increasing with network size. This implies dynamic queueing on the network, in which many interacting queues are mutually driven by temporally correlated packet streams.

cond-mat.stat-mech↗

arXiv2002

Switching current noise and relaxation of ferroelectric domains

We simulate field-induced nucleation and switching of domains in a three-dimensional model of ferroelectrics with quenched disorder and varying domain sizes. We study (1) bursts of the switching current at slow driving along the hysteresis loop (electrical Barkhausen noise) and (2) the polarization reversal when a strong electric field was applied and back-switching after the field was removed. We show how these processes are related to the underlying structure of domain walls, which in turn is controlled by the pinning at quenched local electric fields. When the depolarization fields of bound charges are properly screened we find that the fractal switching current noise may appear with two distinct universal behaviors. The critical depinning of plane domain walls determines the universality class in the case of weak random fields, whereas for large randomness the massive nucleation of domains in the bulk leads to different scaling properties. In both cases the scaling exponents decay logarithmically when the driving frequency is increased. The polarization reverses in the applied field as a power-law, while its relaxation in zero field is a stretch exponential function of time. The stretching exponent depends on the strength of pinning. The results may be applicable for uniaxial relaxor ferroelectrics, such as doped SBN:Ce.

cond-mat.stat-mech↗

arXiv2001

Temporal fractal structures: Origin of power-laws in the world-wide Web

Using numerical simulations and scaling theory we study the dynamics of the world-wide Web from the growth rules recently proposed in Ref. [1] with appropriate parameters. We demonstrate that the emergence of power-law behavior of the out- and in-degree distributions in the Web involves occurrence of temporal fractal structures, that are manifested in the scale-free growth of the local connectivity and in first-return time statistics. We also show how the scale-free behavior occurs in the statistics of random walks on the Web, where the walkers use information on the local graph connectivity.

cond-mat.stat-mech↗

arXiv2001

Adaptive Random Walks on the Class of Web Graph

We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadić, Physica A {\bf 293}, 273 (2001)], and are characterized by a pair of power-law distributions of out- and in-degree for each value of the parameter $β$, which measures the degree of rewiring in the graph. The walker adapts its move strategy according to locally available information both on out-degree of the visited node and in-degree of target node. A standard random walk, on the other hand, uses the out-degree only. We compute the distribution of connected subgraphs visited by an ensemble of walkers, the average access time and survival probability of the walks. We discuss these properties of the walk dynamics relative to the changes in the global graph structure when the control parameter $β$ is varied. For $β\geq 3$, corresponding to the world-wide Web, the access time of the walk to a given level of hierarchy on the graph is much shorter compared to the standard random walk on the same graph. By reducing the amount of rewiring towards rigidity limit $β\to β_c \lesss im 0.1$, corresponding to the range of naturally occurring biochemical networks, the survival probability of adaptive and standard random walk become increasingly similar. The adaptive random walk can be used as an efficient message-passing algorithm on this class of graphs for large degree of rewiring.

cond-mat.stat-mech↗

arXiv2001

Critical exponents at the ferromagnetic transition in tetrakis(diethylamino)ethylene-C$_{60}$ (TDAE-C$_{60}$)

Critical exponents at the ferromagnetic transition were measured for the first time in an organic ferromagnetic material tetrakis(dimethylamino)ethylene fullerene[60] (TDAE-C$_{60}$). From a complete magnetization-temperature-field data set near $T_{c}=16.1\pm 0.05,$ we determine the susceptibility and magnetization critical exponents $γ=1.22\pm 0.02$ and $β=0.75 \pm 0.03$ respectively, and the field vs. magnetization exponent at $T_{c}$ of $δ=2.28\pm 0.14$. Hyperscaling is found to be violated by $Ω\equiv d^{\prime}-d \approx -1/4$, suggesting that the onset of ferromagnetism can be related to percolation of a particular contact configuration of C$_{60}$ molecular orientations.

cond-mat.stat-mech↗

arXiv2001

Access time of an adaptive random walk on the world-wide Web

We introduce and simulate the random walk that adapts move strategies according to local node preferences on a directed graph. We consider graphs with double-hierarchical connectivity and variable wiring diagram in the universality class of the world-wide Web. The ensemble of walkers reveals the structure of local subgraphs with dominant promoters and attractors of links. The average access time decays with the distance in hierarchy $Δq$ as a power $ \sim (Δq)^{-θ}$. The access to highly connected nodes is orders of magnitude shorter compared to the standard random walk, suggesting the adaptive walk as an efficient message-passing algorithm on this class of graphs.

cond-mat.stat-mech↗

arXiv2001

Dynamics of directed graphs: the world-wide Web

We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in- and out-links and for the size of connected component. In a fully grown network of $N$ nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter---average fraction $β$ of updated and added links per time step---towards $β_c(N) < 10% $ the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for $β\equiv 0$, corresponding to the network of science citations.

cond-mat.stat-mech↗

arXiv2000

Scaling of avalanche queues in directed dissipative sandpiles

We simulate queues of activity in a directed sandpile automaton in 1+1 dimensions by adding grains at the top row with driving rate $0 < r \leq 1$. The duration of elementary avalanches is exactly described by the distribution $P_1(t) \sim t^{-3/2}\exp{(-1/L_c)}$, limited either by the system size or by dissipation at defects $L_c= \min (L,ξ)$. Recognizing the probability $P_1$ as a distribution of service time of jobs arriving at a server with frequency $r$, the model represents a new example of the $ $ server queue in the queue theory. We study numerically and analytically the tail behavior of the distributions of busy periods and energy dissipated in the queue and the probability of an infinite queue as a function of driving rate.

cond-mat.stat-mech↗

arXiv2000

Correlations of triggering noise in driven magnetic clusters

We show that the temporal fluctuations $ΔH(t)$ of the threshold driving field $H(t)$, which triggers an avalanche in slowly driven disordered ferromagnets with many domains, exhibit long-range correlations in space and time. The probability distribution of the distance between {\it successive} avalanches as well as the distribution of trapping times of domain wall at a given point in space have fractal properties with the universal scaling exponents. We show how these correlations are related to the scaling behavior of Barkhausen avalanches occurring by magnetization reversal. We also suggest a transport equation which takes into account the observed noise correlations.

cond-mat.stat-mech↗

arXiv2000

Barkhausen avalanches in anisotropic ferromagnets with $180^\circ$ domain walls

We show that Barkhausen noise in two-dimensional disordered ferromagnets with extended domain walls is characterized by the avalanche size exponent $τ_s =1.54$ at low disorder. With increasing disorder the characteristic domain size is reduced relative to the system size due to nucleation of new domains and a dynamic phase transition occurs to the scaling behavior with $τ_s=1.30$. The exponents decrease at finite driving rate. The results agree with recently observed behavior in amorphous Metglas and Fe-Co-B ribbons when the applied anisotropic stress is varied.

cond-mat.stat-mech↗

arXiv1999

Disorder-induced critical behavior in driven diffusive systems

Using dynamic renormalization group we study the transport in driven diffusive systems in the presence of quenched random drift velocity with long-range correlations along the transport direction. In dimensions $d\mathopen< 4$ we find fixed points representing novel universality classes of disorder-dominated self-organized criticality, and a continuous phase transition at a critical variance of disorder. Numerical values of the scaling exponents characterizing the distributions of relaxation clusters are in good agreement with the exponents measured in natural river networks.

cond-mat.stat-mech↗

arXiv1999

Time distribution and loss of scaling in granular flow

Two cellular automata models with directed mass flow and internal time scales are studied by numerical simulations. Relaxation rules are a combination of probabilistic critical height (probability of toppling $p$) and deterministic critical slope processes with internal correlation time $t_c$ equal to the avalanche lifetime, in Model A, and $t_c\equiv 1$, in Model B. In both cases nonuniversal scaling properties of avalanche distributions are found for $p\ge p^\star $, where $p^\star$ is related to directed percolation threshold in $d=3$. Distributions of avalanche durations for $p\ge p^\star $ are studied in detail, exhibiting multifractal scaling behavior in model A, and finite size scaling behavior in model B, and scaling exponents are determined as a function of $p$. At $p=p^\star$ a phase transition to noncritical steady state occurs. Due to difference in the relaxation mechanisms, avalanche statistics at $p^\star$ approaches the parity conserving universality class in Model A, and the mean-field universality class in Model B. We also estimate roughness exponent at the transition.

cond-mat.stat-mech↗

arXiv1999

Temporally disordered granular flow: A model of landslides

We propose and study numerically a stochastic cellular automaton model for the dynamics of granular materials with temporal disorder representing random variation of the diffusion probability $1-μ(t)$ around threshold value $1-μ_0$ during the course of an avalanche. Combined with the slope threshold dynamics, the temporal disorder yields a series of secondary instabilities, resembling those in realistic granular slides. When the parameter $μ_0$ is lower than the critical value $μ_{0}^\star \approx 0.4$, the dynamics is dominated by occasional huge sandslides. For the range of values $μ_{0}^\star \le μ_0 < 1$ the critical steady states occur, which are characterized by multifractal scaling properties of the slide distributions and continuously varying critical exponents $τ_X(μ_0)$. The mass distribution exponent for $μ_0\approx 0.45$ is in agreement with the reported value that characterizes Himalayan sandslides. At $μ_{0}= μ_{0}^\star$ the exponents governing distributions of large relaxation events reach numerical values which are close to those of parity-conserving universality class, whereas for small avalanches they are close to the mean-field exponents.

cond-mat.stat-mech↗

arXiv1999

Scale-free energy dissipation and dynamic phase transition in stochastic sandpiles

We study numerically scaling properties of the distribution of cumulative energy dissipated in an avalanche and the dynamic phase transition in a stochastic directed cellular automaton [B. Tadić and D. Dhar, Phys. Rev. Lett. {\bf 79}, 1519 (1997)] in d=1+1 dimensions. In the critical steady state occurring for the probability of toppling $p\ge p^\star$= 0.70548, the dissipated energy distribution exhibits scaling behavior with new scaling exponents $τ_E $ and D_E for slope and cut-off energy, respectively, indicating that the sandpile surface is a fractal. In contrast to avalanche exponents, the energy exponents appear to be p- dependent in the region $p^\star \le p <1$, however the product $(τ_E-1)D_E$ remains universal. We estimate the roughness exponent of the transverse section of the pile as $χ=0.44\pm 0.04$. Critical exponents characterizing the dynamic phase transition at $p^\star $ are obtained by direct simulation and scaling analysis of the survival probability distribution and the average outflow current. The transition belongs to a new universality class with the critical exponents $ν_\| =γ=1.22 \pm 0.02$, $β=0.56\pm 0.02$ and $ν_\bot = 0.761 \pm 0.029$, with apparent violation of hyperscaling. Generalized hyperscaling relation leads to $β+ β^\prime = (d-1)ν_\bot $, where $β^\prime = 0.195 \pm 0.012$ is the exponent governed by the ultimate survival probability.

cond-mat.stat-mech↗

arXiv1996

Nonuniversal scaling behavior of Barkhausen noise

We simulate Barkhausen avalanches on fractal clusters in a two-dimensional diluted Ising ferromagnet with an effective Gaussian random field. We vary the concentration of defect sites $c$ and find a scaling region for moderate disorder, where the distribution of avalanche sizes has the form $D(s,c,L) = s^{-(1+τ(c))}{\cal{D}}(sL^{-D_s(c)})$. The exponents $τ(c)$ for size and $α(c)$ for length distribution, and the fractal dimension of avalanches $D_s(c)$ satisfy the scaling relation $D_s(c)τ(c) =α(c)$. For fixed disorder the exponents vary with driving rate in agreement with experiments on amorphous Si-Fe alloys.

cond-mat↗

arXiv1996

Role of Defects in Self-Organized Criticality: A Directed Coupled Map Lattice Model

We study a directed coupled map lattice model in two dimensions, with two degrees of freedom associated with each lattice site. The two freedoms are coupled at a fraction $c$ of lattice bonds acting as quenched random defects. In the case of conservative dynamics, at any concentration of defects the system reaches a self-organized critical state with universal critical exponents close to the mean-field values. The probability distributions follow the general scaling form $P(X,L)= L^{-α}{\cal{P}}(XL^{-D_X})$, where $α\approx 1$ is the scaling exponent for the distribution of avalanche lengths, $X$ stands for duration, size or released energy, and $D_X$ is the fractal dimension with respect to $X$. The distribution of current is nonuniversal, and does not show any apparent scaling form. In the case of nonconservative dynamics---obtained by incomplete energy transfer at the defect bonds--- the system is driven out of the critical state. In the scaling region close to $c=0$ the probability distributions exhibit the general scaling form $P(X,c,L)=X^{-τ_X }{\cal{P}}(X/ξ_X (c), XL^{-D_X})$, where $τ_X =α/D_X$ and the coherence length $ξ_X (c)$ depends on the concentration of defect bonds $c$ as $ξ_X (c)\sim c^{-D_X}$.

cond-mat↗

arXiv1995

Criticality in driven cellular automata with defects

We study three models of driven sandpile-type automata in the presence of quenched random defects. When the dynamics is conservative, all these models, termed the random sites (A), random bonds (B), and random slopes (C), self-organize into a critical state. For Model C the concentration-dependent exponents are nonuniversal. In the case of nonconservative defects, the asymptotic state is subcritical. Possible defect-mediated nonequilibrium phase transitions are also discussed.

cond-mat↗