arXiv subjects

Aonghus Lawlor

Publications and source records attributed to Aonghus Lawlor.

28 records · Page 2Linked to original sources

arXiv2013

Critical phenomena in heterogeneous k-core percolation

$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous $k$-core percolation and it is characterized by several interesting critical phenomena. Here we analytically investigate binary mixtures in a wide class of configuration model networks and categorize the different critical phenomena which may occur. We observe the presence of critical and tricritical points and give a general criterion for the occurrence of a tricritical point. The calculated critical exponents show cases in which the model belongs to the same universality class of facilitated spin models studied in the context of the glass transition.

cond-mat.dis-nn↗

arXiv2011

Tricritical point in heterogeneous k-core percolation

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understand the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k_i. In this paper we identify a binary mixture of heterogeneous k-core which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erdos-Renyi networks and 2d square lattices.

cond-mat.dis-nn↗

arXiv2011

Lattice Model of Glasses

Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple model that (possessing both liquid-crystal and glass transition) unifies different approaches, producing most of the phenomena associated with real glasses, without loss of the simplicity that theorists require. Within the model we calculate energy relaxation, non-exponential slowing phenomena, the Kauzmann temperature and other classical signatures. Moreover, the model reproduces a sub-diffusive exponent observed in experiments of dense systems. The simplicity of the model allows us to identify the microscopic origin of glassification, leaving open the possibility for theorists to make further progress.

cond-mat.dis-nn↗

arXiv2011

Crystallization in the vicinity of dynamical arrest

Dating from experiments more than 20 years ago, it has been realized that the crystallization of hard colloidal particles in the vicinity of dynamical arrest has several anomalies, that render the conventional nucleation and growth model inappropriate. Subsequently, key researchers have shown the influence of gravity. Here we show that a simple lattice model can capture most of the phenomena associated with such systems. In particular, the model reproduces not only characteristic signatures of glass-forming systems, but also the interplay between quasi arrested dynamics and crystal nucleation.

cond-mat.dis-nn↗

arXiv2005

Geometry of Empty Space is the Key to Near-Arrest Dynamics

We study several examples of kinetically constrained lattice models using dynamically accessible volume as an order parameter. Thereby we identify two distinct regimes exhibiting dynamical slowing, with a sharp threshold between them. These regimes are identified both by a new response function in dynamically available volume, as well as directly in the dynamics. Results for the selfdiffusion constant in terms of the connected hole density are presented, and some evidence is given for scaling in the limit of dynamical arrest.

cond-mat.stat-mech↗

arXiv2005

Exact Solution of a Jamming Transition: Closed Equations for a Bootstrap Percolation Problem

Jamming, or dynamical arrest, is a transition at which many particles stop moving in a collective manner. In nature it is brought about by, for example, increasing the packing density, changing the interactions between particles, or otherwise restricting the local motion of the elements of the system. The onset of collectivity occurs because, when one particle is blocked, it may lead to the blocking of a neighbor. That particle may then block one of its neighbors, these effects propagating across some typical domain of size named the dynamical correlation length. When this length diverges, the system becomes immobile. Even where it is finite but large the dynamics is dramatically slowed. Such phenomena lead to glasses, gels, and other very long-lived nonequilibrium solids. The bootstrap percolation models are the simplest examples describing these spatio-temporal correlations. We have been able to solve one such model in two dimensions exactly, exhibiting the precise evolution of the jamming correlations on approach to arrest. We believe that the nature of these correlations and the method we devise to solve the problem are quite general. Both should be of considerable help in further developing this field.

cond-mat.stat-mech↗

arXiv2005

Finite Energy Extension of a Lattice Glass Model

We extend a previously studied lattice model of particles with infinite repulsions to the case of finite energy interactions. The phase diagram is studied using grand canonical Monte Carlo simulation. Simulations of dynamical phenomena are made using the canonical ensemble. We find interesting order-disorder transitions in the equilibrium phase diagram and identify several anomalous regimes of diffusivity. These phenomena may be relevant to the case of strong orientational bonding near freezing.

cond-mat.stat-mech↗

arXiv2004

Competition between Short-Ranged Attraction and Short-Ranged Repulsion in Crowded Configurational Space; A Lattice Model Description

We describe a simple nearest-neighbor Ising model that is capable of supporting a gas, liquid, crystal, in characteristic relationship to each other. As the parameters of the model are varied one obtains characteristic patterns of phase behavior reminiscent of continuum systems where the range of the interaction is varied. The model also possesses dynamical arrest, and although we have not studied it in detail, these 'transitions' appear to have a reasonable relationship to the phases and their transitions.

cond-mat.stat-mech↗

arXiv2004

Clarification of the Bootstrap Percolation Paradox

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory, and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.

cond-mat.stat-mech↗

arXiv2001

Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions. Application to protein crystallization

We have studied a model of a complex fluid consisting of particles interacting through a hard core and a short range attractive potential of both Yukawa and square-well form. Using a hybrid method, including a self-consistent and quite accurate approximation for the liquid integral equation in the case of the Yukawa fluid, perturbation theory to evaluate the crystal free energies, and mode-coupling theory of the glass transition, we determine both the equilibrium phase diagram of the system and the lines of equilibrium between the supercooled fluid and the glass phases. For these potentials, we study the phase diagrams for different values of the potential range, the ratio of the range of the interaction to the diameter of the repulsive core being the main control parameter. Our arguments are relevant to a variety of systems, from dense colloidal systems with depletion forces, through particle gels, nano-particle aggregation, and globular protein crystallization.

cond-mat.soft↗