Biomedical subjects

Paolo De Gregorio

Publications and source records attributed to Paolo De Gregorio.

5 recordsLinked to original sources

PubMed2006

Dynamically arrested states of matter.

We outline current developments in our understanding of dynamical arrest, that phenomenon in which many particles stop moving in a collective manner. However in addition to the question of true dynamical arrest itself, we emphasize the development of new tools that can describe relatively sharp changes in the way that ergodic systems may be explored. We discuss the concept of new order parameters (dynamically available volume), and indicate how they may be applied to understand dramatic slowing phenomena present in particle systems, and other arenas of soft and complex matter.

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PubMed2005

Geometry of dynamically available 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 self-diffusion constant in terms of the connected hole density are presented, and some evidence is given for scaling in the limit of dynamical arrest.

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PubMed2005

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.

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PubMed2004

Clarification of the bootstrap percolation paradox.

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. Our results apply to two dimensions, but there is no significant barrier to extending them to higher dimensionality. 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.

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PubMed2002

Universality in lattice models of dynamic arrest: introduction of an order parameter.

We introduce an order parameter for dynamical arrest. Dynamically available volume (unoccupied space that is available to the motion of particles) is expressed as holes for the simple lattice models we study. Near the arrest transition the system is dilute in holes, so we expand dynamical quantities in a series of hole density. Unlike the situation when presented in particle density, all cases of simple models that we examine have a quadratic dependence of the diffusion constant on hole density. This observation implies that in certain regimes ideal dynamical arrest transitions may possess a hitherto unnoticed degree of universality.

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