Biomedical subjects

Uri Keshet

Publications and source records attributed to Uri Keshet.

4 recordsLinked to original sources

PubMed2006

Analytical study of diffusive relativistic shock acceleration.

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. The particle spectral index s is found to be sensitive to D, particularly downstream and at certain angles. The analysis, confirmed numerically, justifies and generalizes previous results for isotropic diffusion. It can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by gamma-ray burst afterglow observations.

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PubMed2005

Survival probabilities of history-dependent random walks.

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase transition occurs when the correlation strength parameter mu reaches a critical value mu(c). For strong positive correlations, mu > mu(c), the survival probability is asymptotically finite, whereas for mu < mu(c) it decays as a power law in time (chain length).

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PubMed2005

Energy spectrum of particles accelerated in relativistic collisionless shocks.

We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this relation, we obtain s=(3beta(u)-2beta(u)beta(2)(d)+beta(3)(d))/(beta(u)-beta(d)) for isotropic diffusion, where beta(u) (beta(d)) is the upstream (downstream) fluid velocity normalized to the speed of light. This result is in agreement with previous numerical determinations of s for all (beta(u),beta(d)), and yields s=38/9 in the ultrarelativistic limit. The spectrum-anisotropy connection is useful for testing numerical studies and constraining anisotropic diffusion results. It suggests that the spectrum is highly sensitive to the form of the diffusion function for particles traveling along the shock front.

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PubMed2004

Phase transition in random walks with long-range correlations.

Motivated by recent results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase transition from normal diffusion, in which the variance D(L) scales as the string's length L, into a superdiffusion phase ( D(L) approximately Lalpha,alpha>1), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.

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