S. S. Vergeles

Dynamics of Nearly Spherical Vesicles in an External Flow

Tank-treading, tumbling, and trembling are different types of the vesicle behavior in an external flow. We derive a dynamical equation enabling us to establish a state of nearly spherical vesicles. For a 2D external flow, the character of the vesicle dynamics is determined by two dimensionless parameters, depending on the vesicle excess area, fluid viscosities, membrane viscosity and bending modulus, strength of the flow, and ratio of the elongational and rotational components of the flow. The tank-treading to tumbling transition occurs via a saddle-node bifurcation, whereas the tank-treading to trembling transition occurs via a Hopf bifurcation. A slowdown of vesicle dynamics should be observed in a vicinity of a point separating the transition lines. We show that the slowdown can be described by a power law with two different critical exponents 1/4 and 1/2 corresponding to the slowdown of tumbling and trembling cycles.

Wave kinetics of random fibre lasers

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. Kinetic theory is a mathematical framework that is used to describe non-linear systems with a large number of degrees of freedom. Here, the authors develop a concept of active wave kinetics of cyclic systems and describe the function of random fibre laser.

Nearly spherical vesicles in an external flow

We theoretically analyze a vesicle with small excess area, which is immersed in an external flow. A dynamical equation for the vesicle evolution is obtained by solving the Stokes equation with suitable boundary conditions imposed on the membrane. The equation has solutions corresponding to different types of motion, such as tank-treading, tumbling and trembling. A phase diagram reflecting the regimes is constructed in terms of two dimensionless parameters that depend on the vesicle excess area, the fluid viscosities, the membrane viscosity and bending modulus, the strength of the flow, and the ratio of the elongational and rotational components of the flow. We investigate the peculiarities of the vesicle dynamics near the tank-treading to tumbling and the tank-treading to trembling transitions, which occur via a saddle-node bifurcation and a Hopf bifurcation, respectively. We examine the slowdown of the vesicle dynamics near the merging point and also predict the existence of a novel dynamic regime, which we call spinning.

Wrinkling of vesicles during transient dynamics in elongational flow.

Recent experiments by Kantsler et. al. (2007) have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. Formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasi-spherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established and confirmed numerically.

Nonlinear Generation of Vorticity by Surface Waves.

We demonstrate that waves excited on a fluid surface produce local surface rotation owing to hydrodynamic nonlinearity. We examine theoretically the effect and obtain an explicit formula for the vertical vorticity in terms of the surface elevation. Our theoretical predictions are confirmed by measurements of surface motion in a cell with water where surface waves are excited by vertical and harmonic shaking the cell. The experimental data are in good agreement with the theoretical predictions. We discuss physical consequences of the effect.

Giant enhancement of electric field between two close metallic grains due to plasmonic resonance

We theoretically examine plasmonic resonance between two close metallic grains separated by a gap of width much less than the length of the incident electromagnetic wave. Resonance conditions are established and the electric field enhancement is found. Our general arguments are confirmed by analytic solution of the problem for simplest geometries. We discuss an extension of our results to more complex cases.

Quantum theory of a spaser-based nanolaser

We present a quantum theory of a spaser-based nanolaser, under the bad-cavity approximation. We find first- and second-order correlation functions g(1)(τ) and g(2)(τ) below and above the generation threshold, and obtain the average number of plasmons in the cavity. The latter is shown to be of the order of unity near the generation threshold, where the spectral line narrows considerably. In this case the coherence is preserved in a state of active atoms in contradiction to the good-cavity lasers, where the coherence is preserved in a state of photons. The damped oscillations in g(2)(τ) above the generation threshold indicate the unusual character of amplitude fluctuations of polarization and population, which become interconnected in this case. Obtained results allow to understand the fundamental principles of operation of nanolasers.

Localized surface plasmon modes in a system of two interacting metallic cylinders

We study an optical response of a system of two parallel close metallic cylinders having nanoscale dimensions. Surface plasmon excitation in the gap between the cylinders is specifically analyzed. In particular, resonance frequencies and field enhancement were investigated as functions of geometrical characteristics of the system and ohmic losses in the metal. The results of numerical simulations were systematically compared with the analytical theory, obtained in the quasi-static limit. The analytical method was generalized in order to take into account the retardation effects. We also present the physical qualitative picture of the plasmon modes, which is validated by numerical simulations and analytical theory.

Rheological properties of a vesicle suspension

The rheological properties of a vesicle suspension have been investigated in the limit of strong flows destroying the stationary form of vesicles. The dependence of the effective viscosity of the suspension on the velocity gradient and the properties of vesicles has been obtained for the case of the plane flow. In particular, it has been shown that the effective viscosity of the suspension can strongly depend on its initial state. The effect of thermal fluctuations on the rheological properties of the suspension has been analyzed.

Interaction of solitons through radiation in optical fibers with randomly varying birefringence

Propagation of solitons in optical fibers is studied taking into account the polarization mode dispersion (PMD) effect. We show that the soliton interaction caused by the radiation emitted by solitons due to the PMD disorder leads to soliton jitter, and we find its statistical properties. The theoretical predictions are justified by direct numerical simulations.