Biomedical subjects

Michael Assaf

Publications and source records attributed to Michael Assaf.

4 recordsLinked to original sources

PubMed2006

Spectral theory of metastability and extinction in birth-death systems.

We suggest a general spectral method for calculating the statistics of multistep birth-death processes and chemical reactions of the type mA-->nA (m and n are positive integers) which possess an absorbing state. The method employs the generating function formalism in conjunction with the Sturm-Liouville theory of linear differential operators. It yields accurate results for the extinction statistics and for the quasistationary probability distribution, including large deviations, of the metastable state. The power of the method is demonstrated on the example of binary annihilation and triple branching 2A--> ø, A-->3A, representative of the rather general class of dissociation-recombination reactions.

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PubMed2006

Spectral formulation and WKB approximation for rare-event statistics in reaction systems.

We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master equation. We compare the stationary WKB approximation to a recent time-dependent semiclassical approximation developed, for the same class of problems, by Elgart and Kamenev [Phys. Rev. E 70, 41106 (2004)]. As a benchmark we use an exactly solvable problem of the binary annihilation reaction 2A-->0.

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PubMed2006

Experimental study of parametric autoresonance in Faraday waves.

The excitation of large amplitude nonlinear waves is achieved via parametric autoresonance of Faraday waves. We experimentally demonstrate that phase locking to low amplitude driving can generate persistent high-amplitude growth of nonlinear waves in a dissipative system. The experiments presented are in excellent agreement with theory.

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PubMed2005

Parametric autoresonance in Faraday waves.

We develop a theory of parametric excitation of weakly nonlinear standing gravity waves in a tank, which is under vertical vibrations with a slowly time-dependent ("chirped") vibration frequency. We show that, by using a negative chirp, one can excite a steadily growing wave via parametric autoresonance. The method of averaging is employed to derive the governing equations for the primary mode. These equations are solved analytically and numerically, for typical initial conditions, for both inviscid and weakly viscous fluids. It is shown that, when passing through resonance, capture into resonance always occurs when the chirp rate is sufficiently small. The critical chirp rate, above which breakdown of autoresonance occurs, is found for different initial conditions. The autoresonance excitation is expected to terminate at large amplitudes, when the underlying constant-frequency system ceases to exhibit a nontrivial stable fixed point.

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