Biomedical subjects

B Meerson

Publications and source records attributed to B Meerson.

16 recordsLinked to original sources

PubMed2002

Phase separation and coarsening in electrostatically driven granular media.

A continuum model for the phase separation and coarsening in electrostatically driven granular media is formulated in terms of a Ginzburg-Landau equation subject to conservation of the total number of grains. In the regime of well-developed clusters, the continuum model is used to derive "sharp-interface" equations that govern the dynamics of the interphase boundary. The model captures the essential physics of this system.

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PubMed2001

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters.

We find that globally conserved interface-controlled coarsening of diffusion-limited aggregates exhibits dynamic scale invariance (DSI) and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The general sharp-interface limit of this equation is introduced and reduced to volume preserving motion by mean curvature. A simple example of globally conserved interface-controlled coarsening system: the sublimation/deposition dynamics of a solid and its vapor in a small closed vessel, is presented in detail. The results of the numerical simulations show that the scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal dynamic scaling. A decrease of the cluster radius with time, predicted by DSI, is observed. The difference between global and local conservation is discussed.

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PubMed2001

Parametric autoresonance.

We investigate parametric autoresonance: a persisting phase locking that occurs when the driving frequency of a parametrically excited nonlinear oscillator slowly varies with time. In this regime, the resonant excitation is continuous and unarrested by the oscillator nonlinearity. The system has three characteristic time scales, the fastest one corresponding to the natural frequency of the oscillator. We perform averaging over the fastest time scale and analyze the reduced set of equations analytically and numerically. Analytical results are obtained by exploiting the scale separation between the two remaining time scales that enables one to use the adiabatic invariant of the perturbed nonlinear motion.

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PubMed2001

Area-preserving dynamics of a long slender finger by curvature: a test case for globally conserved phase ordering.

A long and slender finger can serve as a simple "test bed" for different phase-ordering models. In this work, the globally conserved, interface-controlled dynamics of a long finger is investigated, analytically and numerically, in two dimensions. An important limit is considered when the finger dynamics is reducible to area-preserving motion by curvature. A free boundary problem for the finger shape is formulated. An asymptotic perturbation theory is developed that uses the finger aspect ratio as a small parameter. The leading-order approximation is a modification of the Mullins finger (a well-known analytic solution) whose width is allowed to slowly vary with time. This time dependence is described, in the leading order, by an exponential law with the characteristic time proportional to the (constant) finger area. The subleading terms of the asymptotic theory are also calculated. Finally, the finger dynamics is investigated numerically, employing the Ginzburg-Landau equation with a global conservation law. The theory is in very good agreement with the numerical solution.

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PubMed2000

Logarithmically slow expansion of hot bubbles in gases

We predict a logarithmically slow expansion of hot bubbles in gases in the process of cooling. A model problem is first solved, when the temperature has compact support. Then the temperature profile decaying exponentially at large distances is considered. The periphery of the bubble is shown to remain essentially static ("glassy") in the process of cooling until it is taken over by a logarithmically slowly expanding "core." An analytical solution to the problem is obtained by matched asymptotic expansion. This problem gives an example of how logarithmic corrections enter dynamic scaling.

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PubMed2000

Dynamics of fractal dimension during phase ordering of a geometrical multifractal

A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at t=0 represents a nonuniform recursive fractal set, and that this set is a geometrical multifractal characterized by an f(alpha) curve. It is assumed that the droplets shrink according to their size and preserve their ordering. It is shown that at early times the Hausdorff dimension does not change with time, whereas at late times its dynamics follow the f(alpha) curve. This is illustrated by a special case of a two-scale Cantor dust. The results are then generalized to a wider range of coarsening mechanisms.

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PubMed1999

Fluctuations provide strong selection in Ostwald ripening.

A selection problem that appears in the Lifshitz-Slyozov (LS) theory of Ostwald ripening is reexamined. The problem concerns selection of a self-similar distribution function (DF) of the minority domains with respect to their sizes from a whole one-parameter family of solutions. A strong selection rule is found via an account of fluctuations. Fluctuations produce an infinite tail in the DF and drive the DF towards the "limiting solution" of LS or its analogs for other growth mechanisms.

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PubMed1996