arXiv subjects

Mikko Alava

Publications and source records attributed to Mikko Alava.

49 records · Page 3Linked to original sources

arXiv2005

Host--parasite models on graphs

The behavior of two interacting populations, ``hosts''and ``parasites'', is investigated on Cayley trees and scale-free networks. In the former case analytical and numerical arguments elucidate a phase diagram, whose most interesting feature is the absence of a tri-critical point as a function of the two independent spreading parameters. For scale-free graphs, the parasite population can be described effectively by Susceptible-Infected-Susceptible-type dynamics in a host background. This is shown both by considering the appropriate dynamical equations and by numerical simulations on Barabási-Albert networks with the major implication that in the termodynamic limit the critical parasite spreading parameter vanishes.

cond-mat.stat-mech↗

arXiv2005

Focused Local Search for Random 3-Satisfiability

A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the presently unsatisfiedclauses is known to be very effective: the time to solution has been observed to grow only linearly in the number of variables, for a given clauses-to-variables ratio $α$ sufficiently far below the critical satisfiability threshold $α_c \approx 4.27$. We present numerical results on the behaviour of three focused local search algorithms for this problem, considering in particular the characteristics of a focused variant of the simple Metropolis dynamics. We estimate the optimal value for the ``temperature'' parameter $η$ for this algorithm, such that its linear-time regime extends as close to $α_c$ as possible. Similar parameter optimisation is performed also for the well-known WalkSAT algorithm and for the less studied, but very well performing Focused Record-to-Record Travel method. We observe that with an appropriate choice of parameters, the linear time regime for each of these algorithms seems to extend well into ratios $α> 4.2$ -- much further than has so far been generally assumed. We discuss the statistics of solution times for the algorithms, relate their performance to the process of ``whitening'', and present some conjectures on the shape of their computational phase diagrams.

cond-mat.stat-mech↗

arXiv2004

Collective roughening of elastic lines with hard core interaction in a disordered environment

We investigate by exact optimization methods the roughening of two and three-dimensional systems of elastic lines with point disorder and hard-core repulsion with open boundary conditions. In 2d we find logarithmic behavior whereas in 3d simple random walk-like behavior. The line 'forests' become asymptotically completely entangled as the system height is increased at fixed line density due to increasing line wandering.

cond-mat.dis-nn↗

arXiv2004

Entanglement transition of elastic lines in a strongly disordered environment

We investigate by exact optimization the geometrical properties of three-dimensional elastic line systems with point disorder and hard-core repulsion. The line 'forests' become entangled due to increasing line wandering as the system height is increased, at fixed line density. There is a transition height at which a cluster of pairwise entangled lines spans the system, transverse to average line orientation. Numerical evidence implies that the phenomenon is in the ordinary percolation universality class.

cond-mat.supr-con↗

arXiv2004

Imbibition in Disordered Media

The physics of liquids in porous media gives rise to many interesting phenomena, including imbibition where a viscous fluid displaces a less viscous one. Here we discuss the theoretical and experimental progress made in recent years in this field. The emphasis is on an interfacial description, akin to the focus of a statistical physics approach. Coarse-grained equations of motion have been recently presented in the literature. These contain terms that take into account the pertinent features of imbibition: non-locality and the quenched noise that arises from the random environment, fluctuations of the fluid flow and capillary forces. The theoretical progress has highlighted the presence of intrinsic length-scales that invalidate scale invariance often assumed to be present in kinetic roughening processes such as that of a two-phase boundary in liquid penetration. Another important fact is that the macroscopic fluid flow, the kinetic roughening properties, and the effective noise in the problem are all coupled. Many possible deviations from simple scaling behaviour exist, and we outline the experimental evidence. Finally, prospects for further work, both theoretical and experimental, are discussed.

cond-mat.mtrl-sci↗

arXiv2003

Self-organized criticality as a phase transition

The original sandpile model of Bak, Tang and Wiesenfeld from 1987 has inspired lots of consequent work and further ideas of how to describe the birth of scale-invariant statistics in various systems and in particular models. In this article the basic ingredients of self-organized criticality (SOC) are overviewed. In line with the orginal arguments of BTW SOC is now known to be a property of systems where dissipation and external drive maintain a delicate balance. The qualitative and quantitive understanding of the SOC state and deviations from it can thus be addressed, by mapping the typical cellular automata exhibiting SOC to theories, that in fact describe critical extended systems as such. Currently two such approaches are known, based on the connections of SOC to variants of absorbing state phase transitions and the physics of elastic manifolds or interfaces in random media. These are reviewed and discussed. Finally, some open theoretical problems and experimental suggestions are outlined.

cond-mat.stat-mech↗

arXiv2002

Transport on percolation clusters with power-law distributed bond strengths: when do blobs matter?

The simplest transport problem, namely maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed bond strengths of the type $P(σ) \sim σ^{-α}$. Assuming that only cutting bonds determine the flow, the maxflow critical exponent $\ve$ is found to be $\ve(α)=(d-1) ν+ 1/(1-α)$. This prediction is confirmed with excellent accuracy using large-scale numerical simulation in two and three dimensions. However, in the region of anomalous bond capacity distributions ($0\leq α\leq 1$) we demonstrate that, due to cluster-structure fluctuations, it is not the cutting bonds but the blobs that set the transport properties of the backbone. This ``blob-dominance'' avoids a cross-over to a regime where structural details, the distribution of the number of red or cutting bonds, would set the scaling. The restored scaling exponents however still follow the simplistic red bond estimate. This is argued to be due to the existence of a hierarchy of so-called minimum cut-configurations, for which cutting bonds form the lowest level, and whose transport properties scale all in the same way. We point out the relevance of our findings to other scalar transport problems (i.e. conductivity).

cond-mat.stat-mech↗

arXiv2002

Structural transitions in scale-free networks

Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the (Barabasi-Albert) preferential attachment network growth capture all these aspects. We present a scaling theory to describe the behavior of the generalized models and the mean field rate equation for the problem. This is solved for a specific case with the result C(k) ~ 1/k for the clustering of a node of degree k. Numerical results agree with such a mean-field exponent which also reproduces the clustering of many real networks.

cond-mat.stat-mech↗

arXiv2002

Low Temperature Properties of the Random Field Potts Chain

The random field q-States Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case (q=2), which is also the expectation based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field pertubabtions ('chaos') and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,...,5. Finally for q=2 (Ising case) the domain length distribution is studied for correlated random fields.

cond-mat.dis-nn↗

arXiv2002

Shortest paths and load scaling in scale-free trees

The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabasi-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows a demonstration of why the distribution approaches a Gaussian in the limit of N large. The load (betweenness), the number of shortest distance paths passing through any node, is discussed in the tree presentation.

cond-mat.stat-mech↗

arXiv2002

Scaling in self-organized criticality from interface depinning?

The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Europhys. Lett.~53, 569) of many sandpile models to interface depinning is presented first, to understand how to reach the SOC ensemble and the differences of this ensemble with the usual depinning scenario. In order to derive the SOC avalanche exponents from those of the depinning critical point, a geometric description is discussed, of the quenched landscape in which the 'interface' measuring the integrated activity moves. It turns out that there are two main alternatives concerning the scaling properties of the SOC ensemble. These are outlined in one dimension in the light of scaling arguments and numerical simulations of a sandpile model which is in the quenched Edwards-Wilkinson universality class.

cond-mat.stat-mech↗

arXiv2001

Interface depinning versus absorbing-state phase transitions

According to recent numerical results from lattice models, the critical exponents of systems with many absorbing states and an order parameter coupled to a non-diffusive conserved field coincide with those of the linear interface depinning model within computational accuracy. In this paper the connection between absorbing state phase transitions and interface pinning in quenched disordered media is investigated. For that, we present a mapping of the interface dynamics in a disordered medium into a Langevin equation for the active-site density and show that a Reggeon-field-theory like description, coupled to an additional non-diffusive conserved field, appears rather naturally. Reciprocally, we construct a mapping from a discrete model belonging in the absorbing state with-a-conserved-field class to a discrete interface equation, and show how a quenched disorder is originated. We discuss the character of the possible noise terms in both representations, and overview the critical exponent relations. Evidence is provided that, at least for dimensions larger that one, both universality classes are just two different representations of the same underlying physics.

cond-mat↗

arXiv2001

Critical behavior of a one-dimensional fixed-energy stochastic sandpile

We study a one-dimensional fixed-energy version (that is, with no input or loss of particles), of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value $ζ_c$ of the particle density. Critical exponents are obtained from extensive simulations, which treat both stationary and transient properties. In contrast with other one-dimensional sandpiles, the model appears to exhibit finite-size scaling, though anomalies exist in the scaling of relaxation times and in the approach to the stationary state. The latter appear to depend strongly on the nature of the initial configuration. The critical exponents differ from those expected at a linear interface depinning transition in a medium with point disorder, and from those of directed percolation.

cond-mat.stat-mech↗