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L. A. Braunstein

Publications and source records attributed to L. A. Braunstein.

46 records · Page 3Linked to original sources
arXiv2006

Optimal Path and Minimal Spanning Trees in Random Weighted Networks

We review results on the scaling of the optimal path length in random networks with weighted links or nodes. In strong disorder we find that the length of the optimal path increases dramatically compared to the known small world result for the minimum distance. For Erdős-Rényi (ER) and scale free networks (SF), with parameter $λ$ ($λ>3$), we find that the small-world nature is destroyed. We also find numerically that for weak disorder the length of the optimal path scales logaritmically with the size of the networks studied. We also review the transition between the strong and weak disorder regimes in the scaling properties of the length of the optimal path for ER and SF networks and for a general distribution of weights, and suggest that for any distribution of weigths, the distribution of optimal path lengths has a universal form which is controlled by the scaling parameter $Z=\ell_{\infty}/A$ where $A$ plays the role of the disorder strength, and $\ell_{\infty}$ is the length of the optimal path in strong disorder. The relation for $A$ is derived analytically and supported by numerical simulations. We then study the minimum spanning tree (MST) and show that it is composed of percolation clusters, which we regard as "super-nodes", connected by a scale-free tree. We furthermore show that the MST can be partitioned into two distinct components. One component the {\it superhighways}, for which the nodes with high centrality dominate, corresponds to the largest cluster at the percolation threshold which is a subset of the MST. In the other component, {\it roads}, low centrality nodes dominate. We demonstrate the significance identifying the superhighways by showing that one can improve significantly the global transport by improving a very small fraction of the network.

cond-mat.dis-nn↗
arXiv2005

Exact scalings in competitive growth models

A competitive growth model (CGM) describes aggregation of a single type of particle under two distinct growth rules with occurrence probabilities $p$ and $1-p$. We explain the origin of scaling behaviors of the resulting surface roughness with respect to $p$ for two CGMs which describe random deposition (RD) competing with ballistic deposition (BD) and RD competing with the Edward Wilkinson (EW) growth rule. Exact scaling exponents are derived and are in agreement with previously conjectured values. Using this analytical result we are able to derive theoretically the scaling behaviors of the coefficients of the continuous equations that describe their universality classes. We also suggest that, in some CGM, the $p-$dependence on the coefficients of the continuous equation that represents the universality class can be non trivial. In some cases the process cannot be represented by a unique universality class. In order to show this we introduce a CGM describing RD competing with a constrained EW (CEW) model. This CGM show a transition in the scaling exponents from RD to a Kardar-Parisi-Zhang behavior when $p \to 0$ and to a Edward Wilkinson one when $p \to 1$. Our simulation results are in excellent agreement with the analytic predictions.

cond-mat.stat-mech↗
arXiv2004

Universal Behavior of the Coefficients of the Continuous Equation in Competitive Growth Models

The competitive growth models involving only one kind of particles (CGM), are a mixture of two processes one with probability $p$ and the other with probability $1-p$. The $p-$dependance produce crossovers between two different regimes. We demonstrate that the coefficients of the continuous equation, describing their universality classes, are quadratic in $p$ (or $1-p$). We show that the origin of such dependance is the existence of two different average time rates. Thus, the quadratic $p-$dependance is an universal behavior of all the CGM. We derive analytically the continuous equations for two CGM, in 1+1 dimensions, from the microscopic rules using a regularization procedure. We propose generalized scalings that reproduce the scaling behavior in each regime. In order to verify the analytic results and the scalings, we perform numerical integrations of the derived analytical equations. The results are in excellent agreement with those of the microscopic CGM presented here and with the proposed scalings.

cond-mat.dis-nn↗
arXiv1999

Theoretical Continuous Equation Derived from the Microscopic Dynamics for Growing Interfaces in Quenched Media

We present an analytical continuous equation for the Tang and Leschhorn model [Phys. Rev A {\bf 45}, R8309 (1992)] derived from his microscopic rules using a regularization procedure. As well in this approach the nonlinear term $(\nabla h)^2$ arises naturally from the microscopic dynamics even if the continuous equation is not the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. {\bf 56}, 889 (1986)] with quenched noise (QKPZ). Our equation looks like a QKPZ but with multiplicative quenched and thermal noise. The numerical integration of our equation reproduce the scaling exponents of the roughness of this directed percolation depinning model.

cond-mat.stat-mech↗
arXiv1999

A review of growing interfaces in quenched disordered media

We make a review of the two principal models that allows to explain the imbibition of fluid in porous media. These models, that belong to the directed percolation depinning (DPD) universality class, where introduced simultaneously by the Tang and Leschhorn [Phys. Rev A 45, R8309 (1992)] and Buldyrev et al. [Phys. Rev. A 45, R8313 (1992)] and reviewed by Braunstein et al. [J. Phys. A 32, 1801 (1999); Phys. Rev. E 59, 4243 (1999)]. Even these models have been classified in the same universality class than the Kardar-Parisi-Zhang equation [Phys. Rev. Lett. 56, 889, (1986)] with quenched noise (QKPZ), the contributions to the growing mechanisms are quite different. The lateral contribution in the DPD models, leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution always flattens the roughness. These results suggest that the QKPZ equation does not describe properly the DPD models even when the exponents derived from this equation are similar to the one obtained from the simulations of these models. This fact is confirmed trough the deduced analytical equation for the Tang and Leschhorn model. This equation has the same symmetries than the QKPZ one but its coefficients depend on the balance between the driving force and the quenched noise.

cond-mat.stat-mech↗
arXiv1999

Does the Quenched Kardar-Parisi-Zhang Equation Describe the Directed Percolation Depinning Models?

The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889, (1986)] with quenched noise (QKPZ). We express the evolution equations for the mean height and the roughness into two contributions: the local and the lateral one. We compare this two contributions with the ones obtained for two directed percolation deppining models (DPD): the Tang and Leschhorn model [Phys. Rev A 45, R8309 (1992)] and the Buldyrev et al. model [Phys. Rev. A 45, R8313 (1992)] by Braunstein al. [J. Phys. A 32, 1801 (1999); Phys. Rev. E 59, 4243 (1999)]. Even these models have being classified in the same universality class that the QKPZ the contributions to the growing mechanisms are quite different. The lateral contribution in the DPD models, leads to an increasing of the roughness near the criticality while in the QKPZ equation this contribution always flattens the roughness. These results suggest that the QKPZ equation does not describe properly the DPD models even when the exponents derived from this equation are similar to the one obtained from simulations of these models.

cond-mat.stat-mech↗
arXiv1999

Directed percolation depinning models: Evolution equations

We present the microscopic equation for the growing interface with quenched noise for the model first presented by Buldyrev et al. [Phys. Rev. A 45, R8313 (1992)]. The evolution equation for the height, the mean height, and the roughness are reached in a simple way. The microscopic equation allows us to express these equations in two contributions: the contact and the local one. We compare this two contributions with the ones obtained for the Tang and Leschhorn model [Phys. Rev A 45, R8309 (1992)] by Braunstein et al. [Physica A 266, 308 (1999)]. Even when the microscopic mechanisms are quiet different in both model, the two contribution are qualitatively similar. An interesting result is that the diffusion contribution, in the Tang and Leschhorn model, and the contact one, in the Buldyrev model, leads to an increase of the roughness near the criticality.

cond-mat.stat-mech↗
arXiv1999

Growing interfaces in quenched disordered media

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [{\em Phys. Rev.} {\bf A 45}, R8309 (1992)]. The evolution equations for the mean heigth and the roughness are reached in a simple way. Also, an equation for the interface activity density (i.e. interface density of free sites) as function of time is obtained. The microscopic equation allows us to express these equations in two contributions: the diffusion and the substratum one. All the equation shows the strong interplay between both contributions in the dynamics. A macroscopic evolution equation for the roughness is presented for this model for the critical pressure $p=0.461$. The dynamical exponent $β=0.629$ is analitically obtained in a simple way. Theoretical results are in excellent agreement with the Monte Carlo simulation.

cond-mat.stat-mech↗
arXiv1999

Microscopic equation for growing interfaces in quenched disordered media

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [L. H. Tang and H. Leschhorn, Phys. Rev. A {\bf 45}, R8309 (1992)]. The evolution equation for the height, the mean height, and the roughness are reached in a simple way. An equation for the interface activity density (or free sites density) as function of time is obtained. The microscopic equation allows us to express these equations into two contributions: the diffusion and the substratum contributions. All these equations shows the strong interplay between the diffusion and the substratum contribution in the dynamics.

cond-mat.stat-mech↗