arXiv subjects

Cristian F. Moukarzel

Publications and source records attributed to Cristian F. Moukarzel.

At least 19 recordsLinked to original sources

arXiv2019

Sustained rotation in a vibrated disk with asymmetric supports

A single frictional elastic disk, supported against gravity by two others, rotates steadily when the supports are vibrated and the system is tilted with respect to gravity. Rotation is here studied using Molecular Dynamics Simulations, and a detailed analysis of the dynamics of the system is made. The origin of the observed rotational ratcheting is discussed by considering simplified situations analytically. This shows that the sense of rotation is not fixed by the tilt but depends on the details of the excitation as well.

physics.class-ph↗

arXiv2015

Comment on "Penrose Tilings as Jammed Solids"

In a recent letter, Stenull and Lubensky claim that periodic approximants of Penrose tilings, which are generically isostatic, have a nonzero bulk modulus B when disordered, and, therefore, Penrose tilings are good models of jammed packings. The claim of a nonzero B, which is made on the basis of a normal mode analysis of periodic Penrose approximants for a single value of the disorder epsilon, is the central point of their letter: other properties of Penrose tilings, such as the vanishing of the shear modulus, and a flat density of vibrational states, are already shared by most geometrically disordered isostatic networks studied so far. In this comment, Conjugate Gradient is used to solve the elastic equations on approximants with up to 8x10^4 sites for several values of epsilon, to show beyond reasonable doubt that Stenull and Lubensky's claim is incorrect. The bulk modulus of generic Penrose tilings is zero asymptotically. According to our results, B grows as (epsilon^2 L^3) when (epsilon^2 L^3) << 10^2, then saturates, and finally decays as (epsilon^2 L^3)^{-2/3} ~ 1/L^2 for epsilon^2 L^3 >> 10^2. Stenull and Lubensky seem to have only analyzed one value of epsilon for which saturation is reached at the largest size studied. This led them to a wrong conclusion. We support our results by also considering generic Penrose approximants with fixed boundaries, whose bulk modulus constitutes a strict upper bound for that of periodic systems, finding that these have a vanishing B as well for large L. We conclude that the main point in Stenull and Lubensky letter is unjustified. Penrose tilings are no better models of jammed packings than any of the previously studied isostatic networks with geometric disorder.

cond-mat.dis-nn↗

arXiv2013

Two rigidity percolation transitions on binary Bethe networks and the intermediate phase in glass

Rigidity Percolation is studied analytically on randomly bonded networks with two types of nodes, respectively with coordination numbers $z_1$ and $z_2$, and with $g_1$ and $g_2$ degrees of freedom each. For certain cases that model chalcogenide glass networks, two transitions, both of first order, are found, with the first transition usually rather weak. The ensuing intermediate pase, although is not isostatic in its entirety, has very low self-stress. Our results suggest a possible mechanism for the appearance of intermediate phases in glass, that does not depend on a self-organization principle.

cond-mat.dis-nn↗

arXiv2012

Yard-Sale exchange on networks: Wealth sharing and wealth appropriation

Yard-Sale (YS) is a stochastic multiplicative wealth-exchange model with two phases: a stable one where wealth is shared, and an unstable one where wealth condenses onto one agent. YS is here studied numerically on 1d rings, 2d square lattices, and random graphs with variable average coordination, comparing its properties with those in mean field (MF). Equilibrium properties in the stable phase are almost unaffected by the introduction of a network. Measurement of decorrelation times in the stable phase allow us to determine the critical interface with very good precision, and it turns out to be the same, for all networks analyzed, as the one that can be analytically derived in MF. In the unstable phase, on the other hand, dynamical as well as asymptotic properties are strongly network-dependent. Wealth no longer condenses on a single agent, as in MF, but onto an extensive set of agents, the properties of which depend on the network. Connections with previous studies of coalescence of immobile reactants are discussed, and their analytic predictions are successfully compared with our numerical results.

q-fin.GN↗

arXiv2012

Elastic collapse in disordered isostatic networks

Isostatic networks are minimally rigid and therefore have, generically, nonzero elastic moduli. Regular isostatic networks have finite moduli in the limit of large sizes. However, numerical simulations show that all elastic moduli of geometrically disordered isostatic networks go to zero with system size. This holds true for positional as well as for topological disorder. In most cases, elastic moduli decrease as inverse power-laws of system size. On directed isostatic networks, however, of which the square and cubic lattices are particular cases, the decrease of the moduli is exponential with size. For these, the observed elastic weakening can be quantitatively described in terms of the multiplicative growth of stresses with system size, giving rise to bulk and shear moduli of order exp{-bL}. The case of sphere packings, which only accept compressive contact forces, is considered separately. It is argued that these have a finite bulk modulus because of specific correlations in contact disorder, introduced by the constraint of compressivity. We discuss why their shear modulus, nevertheless, is again zero for large sizes. A quantitative model is proposed that describes the numerically measured shear modulus, both as a function of the loading angle and system size. In all cases, if a density p>0 of overconstraints is present, as when a packing is deformed by compression, or when a glass is outside its isostatic composition window, all asymptotic moduli become finite. For square networks with periodic boundary conditions, these are of order sqrt{p}. For directed networks, elastic moduli are of order exp{-c/p}, indicating the existence of an "isostatic length scale" of order 1/p.

cond-mat.dis-nn↗

arXiv2011

Multiplicative Asset Exchange with Arbitrary Return Distributions

The conservative wealth-exchange process derived from trade interactions is modeled as a multiplicative stochastic transference of value, where each interaction multiplies the wealth of the poorest of the two intervening agents by a random gain eta=(1+kappa), with kappa a random return. Analyzing the kinetic equation for the wealth distribution P(w,t), general properties are derived for arbitrary return distributions pi(kappa). If the geometrical average of the gain is larger than one, i.e. if >0, in the long time limit a nontrivial equilibrium wealth distribution P(w) is attained. Whenever <0, on the other hand, Wealth Condensation occurs, meaning that a single agent gets the whole wealth in the long run. This concentration phenomenon happens even if the average return of the poor agent is positive. In the stable phase, P(w) behaves as w^{(T-1)} for w -> 0, and we find T exactly. This exponent is nonzero in the stable phase but goes to zero on approach to the condensation interface. The exact wealth distribution can be obtained analytically for the particular case of Kelly betting, and it turns out to be exponential. We show, however, that our model is never reversible, no matter what pi(kappa) is. In the condensing phase, the wealth of an agent with relative rank x is found to be w(x,t) \sim e^{x t } for finite times t. The wealth distribution is consequently P(w) \sim 1/w for finite times, while all wealth ends up in the hands of a single agent for large times. Numerical simulations are carried out, and found to satisfactorily compare with the above mentioned analytic results.

q-fin.GN↗

arXiv2007

Phase Transition in Liquid Drop Fragmentation

A liquid droplet is fragmented by a sudden pressurized-gas blow, and the resulting droplets, adhered to the window of a flatbed scanner, are counted and sized by computerized means. The use of a scanner plus image recognition software enables us to automatically count and size up to tens of thousands of tiny droplets with a smallest detectable volume of approximately 0.02 nl. Upon varying the gas pressure, a critical value is found where the size-distribution becomes a pure power-law, a fact that is indicative of a phase transition. Away from this transition, the resulting size distributions are well described by Fisher's model at coexistence. It is found that the sign of the surface correction term changes sign, and the apparent power-law exponent tau has a steep minimum, at criticality, as previously reported in Nuclear Multifragmentation studies [1,2]. We argue that the observed transition is not percolative, and introduce the concept of dominance in order to characterize it. The dominance probability is found to go to zero sharply at the transition. Simple arguments suggest that the correlation length exponent is nu=1/2. The sizes of the largest and average fragments, on the other hand, do not go to zero but behave in a way that appears to be consistent with recent predictions of Ashurst and Holian [3,4].

cond-mat.stat-mech↗

arXiv2003

Static response in disk packings

We present experimental and numerical results for displacement response functions in packings of rigid frictional disks under gravity. The central disk on the bottom layer is shifted upwards by a small amount, and the motions of disks above it define the displacement response. Disk motions are measured with the help of a still digital camera. The responses so measured provide information on the force-force response, that is, the excess force at the bottom produced by a small overload in the bulk. We find that, in experiments, the vertical-force response shows a Gaussian-like shape, broadening roughly as the square root of distance, as predicted by diffusive theories for stress propagation in granulates. However, the diffusion coefficient obtained from a fit of the response width is ten times larger than predicted by such theories. Moreover we notice that our data is compatible with a crossover to linear broadening at large scales. In numerical simulations on similar systems (but without friction), on the other hand, a double-peaked response is found, indicating wave-like propagation of stresses. We discuss the main reasons for the different behaviors of experimental and model systems, and compare our findings with previous works.

cond-mat.soft↗

arXiv2003

Rigidity percolation in a field

Rigidity Percolation with g degrees of freedom per site is analyzed on randomly diluted Erdos-Renyi graphs with average connectivity gamma, in the presence of a field h. In the (gamma,h) plane, the rigid and flexible phases are separated by a line of first-order transitions whose location is determined exactly. This line ends at a critical point with classical critical exponents. Analytic expressions are given for the densities n_f of uncanceled degrees of freedom and gamma_r of redundant bonds. Upon crossing the coexistence line, n_f and gamma_r are continuous, although their first derivatives are discontinuous. We extend, for the case of nonzero field, a recently proposed hypothesis, namely that the density of uncanceled degrees of freedom is a ``free energy'' for Rigidity Percolation. Analytic expressions are obtained for the energy, entropy, and specific heat. Some analogies with a liquid-vapor transition are discussed. Particularizing to zero field, we find that the existence of a (g+1)-core is a necessary condition for rigidity percolation with g degrees of freedom. At the transition point gamma_c, Maxwell counting of degrees of freedom is exact on the rigid cluster and on the (g+1)-rigid-core, i.e. the average coordination of these subgraphs is exactly 2g, although gamma_r, the average coordination of the whole system, is smaller than 2g. gamma_c is found to converge to 2g for large g, i.e. in this limit Maxwell counting is exact globally as well. This paper is dedicated to Dietrich Stauffer, on the occasion of his 60th birthday.

cond-mat.stat-mech↗

arXiv2002

Shortest paths on systems with power-law distributed long-range connections

We discuss shortest-path lengths $\ell(r)$ on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to $P_l \sim l^{-\xpn}$. Using rescaling arguments and numerical simulation on systems of up to $10^7$ sites, we show that a characteristic length $ξ$ exists such that $\ell(r) \sim r$ for $r<ξ$ but $\ell(r) \sim r^{θ_s(\xpn)}$ for $r>>ξ$. For small p we find that the shortest-path length satisfies the scaling relation $\ell(r,\xpn,p)/ξ= f(\xpn,r/ξ)$. Three regions with different asymptotic behaviors are found, respectively: a) $\xpn>2$ where $θ_s=1$, b) $1<\xpn<2$ where $0<θ_s(\xpn)<1/2$ and, c) $\xpn<1$ where $\ell(r)$ behaves logarithmically, i.e. $θ_s=0$. The characteristic length $ξ$ is of the form $ξ\sim p^{-ν}$ with $ν=1/(2-\xpn)$ in region b), but depends on L as well in region c). A directed model of shortest-paths is solved and compared with numerical results.

cond-mat.stat-mech↗

arXiv1999

Sliding blocks with random friction and absorbing random walks

With the purpose of explaining recent experimental findings, we study the distribution $A(λ)$ of distances $λ$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $μ$ is a random function of position is considered. The problem of finding $A(λ)$ is equivalent to a First-Passage-Time problem for a one-dimensional random walk with nonzero drift, whose exact solution is well-known. From the exact solution of this problem we conclude that: a) for inclination angles $θ$ less than $θ_c=\tan(\avμ)$ the average traversed distance $\avλ$ is finite, and diverges when $θ\to θ_c^{-}$ as $\avλ \sim (θ_c-θ)^{-1}$; b) at the critical angle a power-law distribution of slidings is obtained: $A(λ) \sim λ^{-3/2}$. Our analytical results are confirmed by numerical simulation, and are in partial agreement with the reported experimental results. We discuss the possible reasons for the remaining discrepancies.

cond-mat.stat-mech↗

arXiv1999

Spreading and shortest paths in systems with sparse long-range connections

Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered by the spreading quantity on an infinite system is exactly calculated in all dimensions. We find that V(t) grows initially as t^d/d for t<< t^* = (2p Γ_d (d-1)!)^{-1/d} and later exponentially for $t>>t^*$, generalizing a previous result in one dimension. Using the properties of V(t), the average shortest-path distance \ell(r) can be calculated as a function of Euclidean distance r. It is found that \ell(r) = r for r r_c. The characteristic length r_c, which governs the behavior of shortest-path lengths, diverges with system size for all p>0. Therefore the mean separation s \sim p^{-1/d} between shortcut-ends is not a relevant internal length-scale for shortest-path lengths. We notice however that the globally averaged shortest-path length, divided by L, is a function of L/s only.

cond-mat.dis-nn↗

arXiv1999

Infinite characteristic length on small-world systems

It was recently claimed that on d-dimensional small-world networks with a density p of shortcuts, the typical separation s(p) ~ p^{-1/d} between shortcut-ends is a characteristic length for shortest-paths{cond-mat/9904419}. This contradicts an earlier argument suggesting that no finite characteristic length can be defined for bilocal observables on these systems {cont-mat/9903426}. We show analytically, and confirm by numerical simulation, that shortest-path lengths \ell(r) behave as \ell(r) ~ r for r < r_c, and as \ell(r) ~ r_c for r > r_c, where r is the Euclidean separation between two points and r_c(p,L) = p^{-1/d} log(L^dp) is a characteristic length. This shows that the mean separation s between shortcut-ends is not a relevant length-scale for shortest-paths. The true characteristic length r_c(p,L) diverges with system size L no matter the value of p. Therefore no finite characteristic length can be defined for small-world networks in the thermodynamic limit.

cond-mat.dis-nn↗

arXiv1999

Directed rigidity and bootstrap percolation in (1+1) dimensions

We study directed rigidity percolation (equivalent to directed bootstrap percolation) on three different lattices: square, triangular, and augmented triangular. The first two of these display a first-order transition at p=1, while the augmented triangular lattice shows a continuous transition at a non-trivial p_c. On the augmented triangular lattice we find, by extensive numerical simulation, that the directed rigidity percolation transition belongs to the same universality class as directed percolation. The same conclusion is reached by studying its surface critical behavior, i.e. the spreading of rigidity from finite clusters close to a non-rigid wall. Near the discontinuous transition at p=1 on the triangular lattice, we are able to calculate the finite-size behavior of the density of rigid sites analytically. Our results are confirmed by numerical simulation.

cond-mat.stat-mech↗

arXiv1998

Comparison of rigidity and connectivity percolation in two dimensions

Using a recently developed algorithm for generic rigidity of two-dimensional graphs, we analyze rigidity and connectivity percolation transitions in two dimensions on lattices of linear size up to L=4096. We compare three different universality classes: The generic rigidity class; the connectivity class and; the generic ``braced square net''(GBSN). We analyze the spanning cluster density P_\infty, the backbone density P_B and the density of dangling ends P_D. In the generic rigidity and connectivity cases, the load-carrying component of the spanning cluster, the backbone, is fractal at p_c, so that the backbone density behaves as B ~ (p-p_c)^{β'} for p>p_c. We estimate β'_{gr} = 0.25 +/- 0.02 for generic rigidity and β'_c = 0.467 +/- 0.007 for the connectivity case. We find the correlation length exponents, ν_{gr} = 1.16 +/- 0.03 for generic rigidity compared to the exact value for connectivity ν_c = 4/3. In contrast the GBSN undergoes a first-order rigidity transition, with the backbone density being extensive at p_c, and undergoing a jump discontinuity on reducing p across the transition. We define a model which tunes continuously between the GBSN and GR classes and show that the GR class is typical.

cond-mat.stat-mech↗

arXiv1998

Isostatic phase transition and instability in stiff granular materials

In this letter, structural rigidity concepts are used to understand the origin of instabilities in granular aggregates. It is shown that: a) The contact network of a noncohesive granular aggregate becomes exactly isostatic in the limit of large stiffness-to-load ratio. b) Isostaticity is responsible for the anomalously large susceptibility to perturbation of these systems, and c) The load-stress response function of granular materials is critical (power-law distributed) in the isostatic limit. Thus there is a phase transition in the limit of intinitely large stiffness, and the resulting isostatic phase is characterized by huge instability to perturbation.

cond-mat.stat-mech↗

arXiv1998

Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices

We show that negative of the number of floppy modes behaves as a free energy for both connectivity and rigidity percolation, and we illustrate this result using Bethe lattices. The rigidity transition on Bethe lattices is found to be first order at a bond concentration close to that predicted by Maxwell constraint counting. We calculate the probability of a bond being on the infinite cluster and also on the overconstrained part of the infinite cluster, and show how a specific heat can be defined as the second derivative of the free energy. We demonstrate that the Bethe lattice solution is equivalent to that of the random bond model, where points are joined randomly (with equal probability at all length scales) to have a given coordination, and then subsequently bonds are randomly removed.

cond-mat.stat-mech↗

arXiv1998

Comparison of connectivity and rigidity percolation

We summarize ideas and methods that apply to rigidity and connectivity percolation. These include: constraint counting concepts, exact calculations on diluted trees and numerical results on diluted lattices using matching algorithms. The similarities and differences between connectivity and rigidity percolation are discussed.

cond-mat.stat-mech↗