Sergey Belan

Particle Dispersion in the Neutral Atmospheric Surface Layer

We address theoretically the longstanding problem of particle dispersion in the lower atmosphere. The evolution of particle concentration under an absorbing boundary condition at the ground is described. We derive a close-form solution for the downwind surface density of deposited particles and find how the number of airborne particles decreases with time. The problem of the plume formation above the extended surface source is also solved analytically. At the end, we show how turbophoresis modifies the mean settling velocity of particles.

Plasmon mode propagation in array of closely spaced metallic cylinders

Chain plasmonic waveguides are formed by linear arrays of metallic grains embedded in a dielectric matrix. Plasmonic structures of this kind have potential applications to subwavelength guiding, subwavelength imaging and SERS technology. We present qualitative analysis and numerical results for bound plasmonic modes propagating along the chain of closely spaced silver cylinders of subwavelength diameter. The dispersion relation and electromagnetic field structure of the modes are calculated by the cylindrical harmonic expansion method. We demonstrate that it is possible to match simultaneously both the frequency and wave number of the fundamental transverse mode and the first longitudinal mode in optical range. The application of dense chain of cylinders for optical switching between guided modes is discussed.

Phase transitions in the distribution of inelastically colliding inertial particles

It was recently suggested that the sign of particle drift in inhomogeneous temperature or turbulence depends on the particle inertia: weakly inertial particles localize near minima of temperature or turbulence intensity (effects known as thermophoresis and turbophoresis), while strongly inertial particles fly away from minima in an unbounded space. The problem of a particle near minima of turbulence intensity is related to that of two particles in a random flow, so that the localization-delocalization transition in the former corresponds to the path-coalescence transition in the latter. The transition is signaled by the sign change of the Lyapunov exponent that characterizes the mean rate of particle approach to the minimum (which could be wall or another particle). Here we solve analytically this problem for inelastic collisions and derive the phase diagram for the transition in the inertia-inelasticity plane. An important feature of the phase diagram is the region of inelastic collapse: if the restitution coefficient of particle velocity is smaller than some critical value, then the particle is localized for any inertia. We present direct numerical simulations which support the theory and in addition reveal the dependence of the transition of the flow correlation time, characterized by the Stokes number.

Confinement of inertial particles in the viscous boundary layer of a turbulent flow

We examine space and momentum probability distribution of inertial particles when they are placed in the viscous boundary sublayer of a turbulent flow. We demonstrate that at varying elasticity of the particle collisions with the wall the confinement-deconfinement transition occurs: at β < βc the particles are blocked near the wall whereas at β > βc they gradually pass into bulk. Here, β is the elasticity coefficient and βc = exp(−π/√3).

Negative-angle refraction and reflection of visible light with a planar array of silver dimers

We study the plane wave scattering on a planar periodic array of silver dimers. It is found that an appropriately designed array provides the sharp turn of TE-polarized incident beam in orthogonal (opposite) directions through the effects of negative-angle refraction (reflection).

Boundary layer of elastic turbulence

We investigate theoretically the near-wall region in elastic turbulence of a dilute polymer solution in the limit of large Weissenberg number. As it was established experimentally, the elastic turbulence possesses a boundary layer where the fluid velocity field can be approximated by a steady shear flow with relatively small fluctuations on the top of it. Assuming that at the bottom of the boundary layer the dissolved polymers can be considered as passive objects, we examine analytically and numerically statistics of the polymer conformation, which is highly nonuniform in the wall-normal direction. Next, imposing the condition that the passive regime terminates at the border of the boundary layer, we obtain an estimate for the ratio of mean flow to the magnitude of flow fluctuations. The ratio is determined by polymer concentration, radius of gyration of the polymers and their length in fully extended state. The results of our asymptotic analysis reproduce the qualitative features of the elastic turbulence at a finite Weissenberg number.

Synchronization dynamics in diverse ensemble of noisy phase oscillators with asynchronous phase updates.

We study a synchronization phenomenon in the self-correcting population of noisy phase oscillators with randomly distributed natural frequencies. In our model each oscillator stochastically switches its phase to the ensemble-averaged value ψ at a typical rate which is linearly proportional to the degree of coherence r. The system exhibits a continuous phase transition to collective synchronization similar to classical Kuramoto model. Based on the self-consistent arguments and linear stability analysis of the incoherent state we derive analytically the threshold value kc of coupling constant corresponding to the onset of partially synchronized state. Just above the transition point the linear scaling law r ∝ k−kc is found. We also show that nonlinear relation between rate of phase correction and order parameter leads to non-trivial transition between incoherence and synchrony. To illustrate our results, numerical simulations have been performed for large population of phase oscillators with proposed type of coupling. The present model could become useful for explaining cooperative phenomena in communities of oscillatory units and in designing self-correcting systems with well-controlled rhythmical behaviour.Decentralized control of autonomous phase oscillators integrated into networked systems is of great interest for many technological applications, from clock synchronization in sensor nets to coordinated motion in swarm robotics. In the simplest distributed synchronization scheme, each oscillator updates its phase from time to time to a new value equal to the average of its present phase and the phases of its neighbors. Here we describe the resulting synchronization dynamics within a mean-field model where the update actions of different oscillators are completely asynchronous. In particular, it is shown how the steady-state level of synchrony depends on noise intensity and frequency diversity for any given rate of updates. The central part of the analysis is devoted to the case when the correction rate positively correlates with the degree of macroscopic coherence. We demonstrate that depending on relation between correction rate and phase coherence the oscillators may exhibit both continuous and discontinuous transition from incoherence to synchrony upon the change of interaction constant. To illustrate our analytical results, numerical simulations have been performed for a large population of phase oscillators with the proposed type of coupling.