Biomedical subjects

Pavel V Sasorov

Publications and source records attributed to Pavel V Sasorov.

7 recordsLinked to original sources

PubMed2006

Scaling and self-similarity in an unforced flow of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell.

We investigate quasi-two-dimensional relaxation, by surface tension, of a long straight stripe of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. Combining analytical and numerical solutions, we describe the emergence of a self-similar dumbbell shape and find nontrivial dynamic exponents that characterize scaling behavior of the dumbbell dimensions.

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PubMed2004

Phase diagram of van der Waals-like phase separation in a driven granular gas.

Equations of granular hydrostatics are used to compute the phase diagram of the recently discovered van der Waals-like phase separation in a driven granular gas. The model two-dimensional system consists of smooth hard disks in a rectangular box, colliding inelastically with each other and driven by a "thermal" wall at zero gravity. The spinodal line and the critical point of the phase separation are determined. Close to the critical point, the spinodal and binodal (coexistence) lines are determined analytically. Effects of the finite size of the confining box in the direction parallel to the thermal wall are investigated. These include suppression of the phase separation by heat conduction in the lateral direction and a change from supercritical to subcritical bifurcation.

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PubMed2004

Giant fluctuations at a granular phase separation threshold.

We investigate a phase separation instability that occurs in a system of nearly elastically colliding hard spheres driven by a thermal wall. If the aspect ratio of the confining box exceeds a threshold value, granular hydrostatics predict phase separation: the formation of a high-density region coexisting with a low-density region along the wall that is opposite to the thermal wall. Event-driven molecular dynamics simulations confirm this prediction. The theoretical bifurcation curve agrees with the simulations quantitatively well below and well above the threshold. However, in a wide region of aspect ratios around the threshold, the system is dominated by fluctuations, and the hydrostatic theory breaks down. Two possible scenarios of the origin of the giant fluctuations are discussed.

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PubMed2002

Symmetry breaking and coarsening of clusters in a prototypical driven granular gas.

Granular hydrodynamics predicts symmetry-breaking instability in a two-dimensional ensemble of nearly elastically colliding smooth hard disks driven, at zero gravity, by a rapidly vibrating sidewall. Supercritical and subcritical symmetry-breaking bifurcations of the stripe state are identified, and the supercritical bifurcation curve is computed. The cluster dynamics proceed as a coarsening process mediated by the gas phase. Well above the bifurcation point the final steady state, selected by coarsening, represents a single strongly localized densely packed "droplet."

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PubMed2002

Anomalous dynamic scaling in locally conserved coarsening of fractal clusters.

We report two-dimensional phase-field simulations of locally conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter, and solute mass are measured as functions of time. Analyzing the correlation function dynamics, we identify two different time-dependent length scales that exhibit power laws in time. The exponents of these power laws do not show any dependence on D; one of them is apparently the "classical" exponent 1/3. The solute mass versus time exhibits dynamic scaling with a D-dependent exponent, in agreement with a simple scaling theory.

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PubMed2002

Phase ordering with a global conservation law: Ostwald ripening and coalescence.

Globally conserved phase ordering dynamics is investigated in systems with short range correlations at t=0. A Ginzburg-Landau equation with a global conservation law is employed as the phase field model. The conditions are found under which the sharp-interface limit of this equation is reducible to the area-preserving motion by curvature. Numerical simulations show that, for both critical and off-critical quench, the equal-time pair correlation function exhibits dynamic scaling, and the characteristic coarsening length obeys l(t) approximately t(1/2). For the critical quench, our results are in excellent agreement with earlier results. For off-critical quench (Ostwald ripening) we investigate the dynamics of the size distribution function of the minority phase domains. The simulations show that, at large times, this distribution function has a self-similar form with growth exponent 1/2. The scaled distribution, however, strongly differs from the classical Wagner distribution. We attribute this difference to coalescence of domains. A theory of Ostwald ripening is developed that takes into account binary coalescence events. The theoretical scaled distribution function agrees well with that obtained in the simulations.

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PubMed2002

Symmetry-breaking instability and strongly peaked periodic clustering states in a driven granular gas.

An ensemble of inelastically colliding grains driven by a horizontally vibrating wall in two dimensions exhibits clustering. Working in the limit of nearly elastic collisions and employing granular hydrodynamics, we predict, by a marginal stability analysis, a spontaneous symmetry breaking of the laterally uniform clustering state. Two-dimensional steady-state solutions found numerically describe laterally periodic clustering states. Well within the instability region the density of these states is strongly peaked, with most of the granulate located in "density islands." Time-dependent granular hydrodynamic simulations show that strongly peaked states can develop from small-amplitude single-mode density perturbations.

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