arXiv subjects

Shlomo Havlin

Publications and source records attributed to Shlomo Havlin.

305 records · Page 17Linked to original sources

arXiv1999

Multifractality in Human Heartbeat Dynamics

Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system --- the healthy human heartbeat. Further, we show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

cond-mat.stat-mech↗

arXiv1999

Macroscopic Finite Size Effects in Relaxational Processes

We present results on dynamical processes that exhibit a stretched exponential relaxation. When the relaxation is a result of two competing exponential processes, the size of the system, although macroscopic, play a dominant role. There exist a crossover time tx that depends logarithmically on the size of the system, above which, the relaxation changes from a stretched exponential to a simple exponential decay. The decay rate also depends logarithmically on the size of the system. The results are relevant to large-scale Monte-Carlo simulations and should be amenable to experiments in low-dimensional macroscopic systems and mesoscopic systems.

cond-mat.stat-mech↗

arXiv1999

Anomalous Size Dependence of Relaxational Processes

We consider relaxation processes that exhibit a stretched exponential behavior. We find that in those systems, where the relaxation arises from two competing exponential processes, the size of the system may play a dominant role. Above a crossover time tx that depends logarithmically on the size of the system the relaxation changes from a stretched exponential to a simple exponential decay, where the decay rate also depends logarithmically on the size of the system. This result is relevant to large-scale Monte-Carlo simulations and should be amenable to experimental verification in low-dimensional and mesoscopic systems.

cond-mat.stat-mech↗

arXiv1999

Optimal Path in Two and Three Dimensions

We apply the Dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape. We study the geometrical and energetic scaling properties of the optimal path where the energies are taken from a uniform distribution. Our numerical results for both two and three dimensions suggest that the optimal path for random uniformly distributed energies is in the same universality class as the directed polymers. We present physical realizations of polymers in disordered energy landscape for which this result is relevant.

cond-mat.stat-mech↗

arXiv1999

Probability Distribution of the Shortest Path on the Percolation Cluster, its Backbone and Skeleton

We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and Phi(S)(r|l), giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path of length l are separated by an Euclidean distance r. Following a scaling argument due to de Gennes for self-avoiding walks, we derive analytical expressions for the exponents g1=df+dmin-d and g1B=g1S-3dmin-d, which determine the scaling behavior of the distribution functions in the limit x=r/l^(nu) much less than 1, i.e., Phi(r|l) proportional to l^(-(nu)d)x^(g1), Phi(B)(r|l) proportional to l^(-(nu)d)x^(g1B), and Phi(S)(r|l) proportional to l^(-(nu)d)x^(g1S), with nu=1/dmin, where df and dmin are the fractal dimensions of the percolation cluster and the shortest path, respectively. The theoretical predictions for g1, g1B, and g1S are in very good agreement with our numerical results.

cond-mat.stat-mech↗

arXiv1999

Distribution of Dangling Ends on the Incipient Percolation Cluster

We study numerically and by scaling arguments the probability P(M)dM that a given dangling end of the incipient percolation cluster has a mass between M and M + dM. We find by scaling arguments that P(M) decays with a power law, P(M)~M^(-(1+k)), with an exponent k=dBf/df, where df and dBf are the fractal dimensions of the cluster and its backbone, respectively. Our numerical results yield k=0.83 in d=2 and k=0.74 in d=3 in very good agreement with theory.

cond-mat.stat-mech↗

arXiv1999

Sliding Objects with Random Friction

We study the motion of elastic networks driven over a random substrate. Our model which includes local friction forces leads to complex dynamical behavior. We find a transition to a sliding state which belongs to a new universality class. The phase diagram comprises of a pinned state, a stick-slip motion phase, and a free motion phase.

cond-mat.stat-mech↗

arXiv1999

Directed Polymer -- Directed Percolation Transition

We study the relation between the directed polymer and the directed percolation models, for the case of a disordered energy landscape where the energies are taken from bimodal distribution. We find that at the critical concentration of the directed percolation, the directed polymer undergoes a transition from the directed polymer universality class to the directed percolation universality class. We also find that directed percolation clusters affect the characterisrics of the directed polymer below the critical concentration.

cond-mat.stat-mech↗

arXiv1998

Spontaneous Stratification in Granular Mixtures

Granular materials size segregate when exposed to external periodic perturbations such as vibrations. Moreover, mixtures of grains of different sizes spontaneously segregate in the absence of external perturbations: when a mixture is simply poured onto a pile, the large grains are more likely to be found near the base, while the small grains are more likely to be near the top. Here, we report a spontaneous phenomenon arising when we pour a mixture between two vertical plates: the mixture spontaneously stratifies into alternating layers of small and large grains whenever the large grains are rougher than the small grains. In contrast, we find only spontaneous segregation when the large grains are more rounded than the small grains. The stratification is related to the occurrence of avalanches; during each avalanche the grains comprising the avalanche spontaneously stratify into a pair of layers through a "kink" mechanism, with the small grains forming a sublayer underneath the layer of large grains.

cond-mat.stat-mech↗

arXiv1998

Modeling Urban Growth Patterns with Correlated Percolation

We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. The resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient.

cond-mat.dis-nn↗

arXiv1998

Filling a silo with a mixture of grains: Friction-induced segregation

We study the filling process of a two-dimensional silo with inelastic particles by simulation of a granular media lattice gas (GMLG) model. We calculate the surface shape and flow profiles for a monodisperse system and we introduce a novel generalization of the GMLG model for a binary mixture of particles of different friction properties where, for the first time, we measure the segregation process on the surface. The results are in good agreement with a recent theory, and we explain the observed small deviations by the nonuniform velocity profile.

cond-mat.dis-nn↗

arXiv1996

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $ξ\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=ρ(r) t^{-1/2} ξ^{-2} f_d(ξ)$, where $ρ(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(ξ)$ in powers of $ξ$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(ξ)$. Namely, for $d=2$, $f_2(ξ)\simeq a_2ξ^2\lnξ+b_2ξ^2$; for $3\le d\le 5$, $f_d(ξ)\simeq a_dξ^2+b_dξ^d$; for $d=6$, $f_6(ξ)\simeq a_6ξ^2+b_6ξ^6\lnξ$; for $7\le d\le 9$, $f_d(ξ)\simeq a_dξ^2+b_dξ^6+c_dξ^d$; for $d=10$, $f_{10}(ξ)\simeq a_{10}ξ^2+b_{10}ξ^6+c_{10}ξ^{10}\lnξ$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/ρ(r)\simeq t^{-1/2}\ln t$.

cond-mat↗

arXiv1995

Quantitative Characterization of Permeability Fluctuations in Sandstone

Sedimentary rocks have complicated permeability fluctuations arising from the geological processes that formed them. These permeability fluctuations significantly affect the flow of fluids through the rocks. We analyze data on two sandstone samples from different geological environments, and find that the permeability fluctuations display long-range power-law correlations characterized by an exponent $H$. For both samples, we find $H \approx 0.82-0.90$.

cond-mat↗

arXiv1995

Method for Generating Long-Range Correlations for Large Systems

We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation.

cond-mat↗

arXiv1995

A fractal model for the first stages of thin film growth

In this paper we briefly review a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. This model allows to understand many experiments of thin film deposition. In the first part, we describe the model, which incorporates deposition, particle and cluster diffusion, and aggregation. In a second part, we study the dynamical evolution of the model. Finally, we analyze the effects of small cluster mobility, and we show that the introduction of cluster diffusion dramatically affects the dynamics of film growth. Some of these effects can be tested experimentally.

cond-mat↗

arXiv1995

Number of branches in diffusion-limited aggregates: The skeleton

We develop the skeleton algorithm to define the number of main branches $N_b$ of diffusion-limited aggregation (DLA) clusters. The skeleton algorithm provides a systematic way to remove dangling side branches of the DLA cluster and has successfully been applied to study the ramification properties of percolation. We study the skeleton of comparatively large ($\approx 10^6$ sites) off-lattice DLA clusters in two, three and four spatial dimensions. We find that initially with increasing distance from the cluster seed the number of branches increases in all dimensions. In two dimensions, the increase in the number of branches levels off at larger distances, indicating a fixed number of $N_b = 7.5\pm 1.5$ main branches of DLA. In contrast, in three and four dimensions, the skeleton continues to ramify strongly as one proceeds from the cluster center outward, and we find no indication of a constant number of main branches. Likewise, we find no indication for a fixed $N_b$ in a study of DLA on the Cayley tree. In two dimensions, we find strong corrections to scaling of logarithmic character, which can help to explain recently reported deviations from self-similar behavior.

cond-mat↗

arXiv1995

Modeling Morphology of Cities and Towns

Predicting urban growth is important for practical reasons, and also for the challenge it presents to theoretical frameworks for cluster dynamics. Recently, the model of diffusion limited aggregation (DLA) has been applied to describe urban growth, and results in tree-like dendritic structures which have a core or ``central business district'' (CBD). The DLA model predicts that there exists only one large fractal cluster that is almost perfectly screened from incoming ``development units'' (people, capital, resources, etc), so that almost all the cluster growth occurs in the extreme peripheral tips. Here we propose and develop an alternative model to DLA that describes the morphology and the area distribution of systems of cities, as well as the scaling of the urban perimeter of individual cities. Our results agree both qualitatively and quantitatively with actual urban data. The resulting growth morphology can be understood in terms of the effects of interactions among the constituent units forming a urban region, and can be modeled using the correlated percolation model in the presence of a gradient.

cond-mat↗