Biomedical subjects

S Redner

Publications and source records attributed to S Redner.

At least 19 recordsLinked to original sources

PubMed2001

Freezing in Ising ferromagnets.

We investigate the final state of zero-temperature Ising ferromagnets that are endowed with single-spin-flip Glauber dynamics. Surprisingly, the ground state is generally not reached for zero initial magnetization. In two dimensions, the system reaches either a frozen stripe state with probability approximately 1/3 or the ground state with probability approximately 2/3. In greater than two dimensions, the probability of reaching the ground state or a frozen state rapidly vanishes as the system size increases; instead the system wanders forever in an isoenergy set of metastable states. An external magnetic field changes the situation drastically-in two dimensions the favorable ground state is always reached, while in three dimensions the field must exceed a threshold value to reach the ground state. For small but nonzero temperature, relaxation to the final state proceeds first by formation of very long-lived metastable states, as in the zero-temperature case, before equilibrium is reached.

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PubMed2001

Dissolution in a field.

We study the dissolution of a solid by continuous injection of reactive "acid" particles at a single point, with the reactive particles undergoing biased diffusion in the dissolved region. When acid encounters the substrate material, both an acid particle and a unit of the material disappear. We find that the lengths of the dissolved cavity parallel and perpendicular to the bias grow as t(2/(d+1)) and t(1/(d+1)), respectively, in d dimensions, while the number of reactive particles within the cavity grows as t(2/(d+1)). We also obtain the exact density profile of the reactive particles and the relation between this profile and the motion of the dissolution boundary. The extension to variable acid strength is also discussed.

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PubMed2001

Steady state of an inhibitory neural network.

We investigate the dynamics of a neural network where each neuron evolves according to the combined effects of deterministic integrate-and-fire dynamics and purely inhibitory coupling with K randomly chosen "neighbors." The inhibition reduces the voltage of a given neuron by an amount Delta when one of its neighbors fires. The interplay between the integration and inhibition leads to a steady state that is determined by solving the rate equations for the neuronal voltage distribution. We also study the evolution of a single neuron and find that the mean lifetime between firing events equals 1+K delta and that the probability that a neuron has not yet fired decays exponentially with time.

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PubMed2001

Degree distributions of growing networks.

The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree). The network is built by (i) creation of new nodes which each immediately attach to a preexisting node, and (ii) creation of new links between preexisting nodes. This process naturally generates correlated in-degree and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained.

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PubMed2001

Organization of growing random networks.

The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively, and linking each to an earlier node of degree k with an attachment probability A(k). When A(k) grows more slowly than linearly with k, the number of nodes with k links, N(k)(t), decays faster than a power law in k, while for A(k) growing faster than linearly in k, a single node emerges which connects to nearly all other nodes. When A(k) is asymptotically linear, N(k)(t) approximately tk(-nu), with nu dependent on details of the attachment probability, but in the range 2<nu<infinity. The combined age and degree distribution of nodes shows that old nodes typically have a large degree. There is also a significant correlation in the degrees of neighboring nodes, so that nodes of similar degree are more likely to be connected. The size distributions of the in and out components of the network with respect to a given node--namely, its "descendants" and "ancestors"-are also determined. The in component exhibits a robust s(-2) power-law tail, where s is the component size. The out component has a typical size of order ln t, and it provides basic insights into the genealogy of the network.

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PubMed2001

Fate of zero-temperature Ising ferromagnets.

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 3/10 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales with the longer stemming from the influence of a long-lived diagonal stripe defect. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically "blinking" metastable states.

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PubMed2001

Infiltration through porous media.

We study the kinetics of infiltration in which contaminant particles, which are suspended in a flowing carrier fluid, penetrate a porous medium. The progress of the "invader" particles is impeded by their trapping on active "defender" sites which are on the surfaces of the medium. As the defenders are used up, the invader penetrates further and ultimately breaks through. We study this process in the regime where the particles are much smaller than the pores so that the permeability change due to trapping is negligible. We develop a family of microscopic models of increasing realism to determine the propagation velocity of the invasion front, as well as the shapes of the invader and defender profiles. The predictions of our model agree qualitatively with experimental results on breakthrough times and the time dependence of the invader concentration at the output. Our results also provide practical guidelines for improving the design of deep bed filters in which infiltration is the primary separation mechanism.

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PubMed2000

Connectivity of growing random networks.

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) approximately k(gamma), different behaviors arise for gamma<1, gamma>1, and gamma = 1. For gamma<1, the number of sites with k links, N(k), varies as a stretched exponential. For gamma>1, a single site connects to nearly all other sites. In the borderline case A(k) approximately k, the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2<nu<infinity.

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PubMed2000

Clogging time of a filter.

We study the time until a filter becomes clogged due to the trapping of suspended particles as they pass through a porous medium. This trapping progressively impedes and eventually stops the flow of the carrier fluid. We develop a simple description for the pore geometry and the motion of the suspended particles which, together with extreme-value statistics, predicts that the distribution of times until a filter clogs has a power-law long-time tail, with an infinite mean clogging time. These results and its consequences are in accord with simulations on a square lattice porous network.

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PubMed1996