arXiv subjects

H. Eugene Stanley

Publications and source records attributed to H. Eugene Stanley.

321 records · Page 18Linked to original sources

arXiv1997

Effect of Size Dispersity On the Melting Transition

We present a molecular dynamics simulation study of the liquid-solid transition in a two dimensional system consisting of particles of two different sizes interacting via a truncated Lennard-Jones potential. We work with equal number of particles of each kind and the dispersity $Δ$ in the sizes of the particles is varied by changing the ratio of the particle sizes only. For the monodisperse case ($Δ= 0$) and for small values of $Δ$, we find a first order liquid-solid transition on increasing the volume fraction $ρ$ of the particles . As we increase $Δ$, the first-order transition coexistence region weakens gradually and completely disappears at high dispersities around $Δ= 0.10$ . At these values of dispersity the high density phase lacks long range translational order but possesses orientational order with a large but finite correlation length. The consequences of this effect of dispersity on the glass transition and on the melting transition in general are discussed.

cond-mat.mtrl-sci↗

arXiv1996

Scaling for the Coalescence of Microfractures before Breakdown

We study the behavior of fracture in disordered systems close to the breakdown point. We simulate numerically both scalar (resistor network) and vectorial (spring network) models with threshold disorder, driven at constant current and stress rate respectively. We analyze the scaling of the susceptibility and the cluster size close to the breakdown. We observe avalanche behavior and clustering of the cracks. We find that the scaling exponents are consistent with those found close to a mean-field spinodal and present analogies between the coalescence of microfractures and the coalescence of droplets in a metastable magnetic system. Finally, we discuss different experimental conditions and some possible theoretical interpretations of the results.

cond-mat.mtrl-sci↗

arXiv1996

Modeling Acoustic Emission in Microfracturing Phenomena

It has been recently observed that synthetic materials subjected to an external elastic stress give rise to scaling phenomena in the acoustic emission signal. Motivated by this experimental finding we develop a mesoscopic model in order to clarify the nature of this phenomenon. We model the synthetic material by an array of resistors with random failure thresholds. The failure of a resistor produces an decrease in the conductivity and a redistribution of the disorder. By increasing the applied voltage the system organizes itself in a stationary state. The acoustic emission signal is associated with the failure events. We find scaling behavior in the amplitude of these events and in the times between different events. The model allows us to study the geometrical and topological properties of the micro-fracturing process that drives the system to the self-organized stationary state.

cond-mat.mtrl-sci↗

arXiv1996

First-Order Transition in the Breakdown of Disordered Media

We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the predictions of the mean-field theory using numerical simulations of discrete models. Widely distributed avalanches and the corresponding mean-field scaling are explained by the long-range nature of elastic interactions. We discuss the analogy of our results to driven disordered first-order transitions and spinodal nucleation in magnetic systems.

cond-mat.stat-mech↗

arXiv1996

Turbulence and finance?

Analogies between the price dynamics in the foreign exchange market and 3-dimensional fully developed turbulence were recently presented in Nature vol. 381, 767-769 (1996). Independently, we have carried out a study comparing the parallel of the dynamical properties of the S&P 500 index and of the time evolution of a 3-dimensional fully turbulent fluid, but our study arrives at rather different conclusions. Specifically, we find while intermittency -- i.e. abrupt changes of activity in the time evolution of the variance of price changes and of the mean energy dissipation -- and non-Gaussian behavior (for short times) in the probability distribution of price and velocity changes characterize both systems, the stochastic nature of the two processes is quantitatively quite different.

cond-mat↗

arXiv1996

Interface Roughening in a Hydrodynamic Lattice-Gas Model with Surfactant

Using a hydrodynamic lattice-gas model, we study interface growth in a binary fluid with various concentrations of surfactant. We find that the interface is smoothed by small concentrations of surfactant, while microemulsion droplets form for large surfactant concentrations. To assist in determining the stability limits of the interface, we calculate the change in the roughness and growth exponents $α$ and $β$ as a function of surfactant concentration along the interface.

cond-mat↗

arXiv1996

The Pinning Paths of an Elastic Interface

We introduce a model describing the paths that pin an elastic interface moving in a disordered medium. We find that the scaling properties of these ``elastic pinning paths'' (EPP) are different from paths embedded on a directed percolation cluster, which are known to pin the interface of the ``directed percolation depinning'' class of surface growth models. The EPP are characterized by a roughness exponent $α=1.25$, intermediate between that of the free inertial process ($α=3/2$) and the diode-resistor problem on a Cayley tree ($α=1$). We also calculate numerically the mean cluster size and the cluster size distribution for the EPP.

cond-mat↗

arXiv1996

Temporal Scaling of Interfaces Propagating in Porous Media

To better understand the temporal behavior of a roughening meniscus driven by capillary forces during the imbibition of a viscous fluid in porous media, we measure the height-height autocorrelation function $C(t)$ using a constant driving force. We find $C(t)\sim t^β$, with $β= 0.56\pm 0.03$, and provide the first experimental evidence for driving force independent temporal scaling behavior of a propagating wetting front in the presence of quenched noise. We interpret the value of $β$ in terms of the possibility that the dynamics may be governed by nonvanishing non-linearity due to anisotropic depinning.

cond-mat↗

arXiv1996

Sandpile Model on Sierpinski Gasket Fractal

We investigate the sandpile model on the two--dimensional Sierpinski gasket fractal. We find that the model displays novel critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes and topplings and calculate the associated critical exponents $τ= 1.51 \pm 0.04$, $α= 1.63 \pm 0.04$ and $μ= 1.36 \pm 0.04$. The avalanche size distribution shows power law behavior modulated by logarithmic oscillations which can be related to the discrete scale invariance of the underlying lattice. Such a distribution can be formally described by introducing a complex scaling exponent $τ^{*} \equiv τ+ i δ$, where the real part $τ$ corresponds to the power law and the imaginary part $δ$ is related to the period of the logarithmic oscillations.

cond-mat↗

arXiv1996

Self-organized branching processes: Avalanche models with dissipation

We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the model self-organizes not into a critical state but rather into a subcritical state: when dissipation is present, the dynamical fixed point does not coincide with the critical point. Thus the level of dissipation acts as a relevant parameter in the renormalization-group sense. We study the model numerically and compute analytically the critical exponents for the avalanche size and lifetime distributions and the scaling exponents for the corresponding cutoffs.

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

Elastic String in a Random Medium

We consider a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We present evidence that the consideration of longitudinal fluctuations leads to nonlinear behavior in the equation of motion which is {\it kinematically} generated by the motion of the string. The strength of the nonlinear effects depends on the anisotropy of the medium and the distance from the depinning transition. On the other hand the consideration of restricted solid on solid conditions imposed to the growth of the string leads to a nonlinear term in the equation of motion with a {\it diverging} coefficient at the depinning transition.

cond-mat↗

arXiv1995

Self-Organized Branching Processes: A Mean-Field Theory for Avalanches

We discuss mean-field theories for self-organized criticality and the connection with the general theory of branching processes. We point out that the nature of the self-organization is not addressed properly by the previously proposed mean-field theories. We introduce a new mean-field model that explicitly takes the boundary conditions into account; in this way, the local dynamical rules are coupled to a global equation that drives the control parameter to its critical value. We study the model numerically, and analytically we compute the avalanche distributions.

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↗