arXiv subjects

Igor Aranson

Publications and source records attributed to Igor Aranson.

15 recordsLinked to original sources

arXiv2017

Focusing of Active Particles in a Converging Flow

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline. The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.

cond-mat.soft↗

arXiv2016

Flagella bending affects macroscopic properties of bacterial suspensions

To survive in harsh conditions, motile bacteria swim in complex environment and respond to the surrounding flow. Here we develop a PDE model describing how the flagella bending affects macroscopic properties of bacterial suspensions. First, we show how the flagella bending contributes to the decrease of the effective viscosity observed in dilute suspension. Our results do not impose tumbling (random re-orientation) as it was done previously to explain the viscosity reduction. Second, we demonstrate a possibility of bacterium escape from the wall entrapment due to the self-induced buckling of flagella. Our results shed light on the role of flexible bacterial flagella in interactions of bacteria with shear flow and walls or obstacles.

math.AP↗

arXiv2009

Emergence of superconducting textures in two dimensions

Self-organized regular patterns are ubiquitous in nature, and one of their most celebrated manifestations is the Abrikosov vortex lattice: under an applied magnetic field, the homogeneous superconductivity becomes unstable and cast itself into a regular texture of the "normal" filaments, called Abrikosov vortices, immersed into a superconducting matrix. Its prediction and the experimental discovery became a breakthrough in our understanding of superconductivity and founded a new direction in physics. Here we show that the interplay between the superconducting order parameter and elastic fields, which are intimately connected to the very existence of the superconductivity itself, can result in a novel superconducting state dual to the Abrikosov state: a regular texture of superconducting islands. The fact that both patterns emerge within the framework of the Ginzburg-Landau description of superconductivity indicates that the formation of regular structures may be a generic feature of any phase transition. Emergence of superconducting island arrays is not specific to the effect of the elastic forces, but can be caused by any inherent mechanism generating long-range non-local interactions in the Ginzburg-Landau functional, for example, by the Coulomb forces. In particular, our findings suggest the formation of a superconducting island textures as a scenario for a superconductor-to-insulator transition in thin films.

cond-mat.supr-con↗

arXiv2001

Vortex avalanches and magnetic flux fragmentation in superconductors

We report results of numerical simulations of non isothermal dendritic flux penetration in type-II superconductors. We propose a generic mechanism of dynamic branching of a propagating hotspot of a flux flow/normal state triggered by a local heat pulse. The branching occurs when the flux hotspot reflects from inhomogeneities or the boundary on which magnetization currents either vanish, or change direction. Then the hotspot undergoes a cascade of successive splittings, giving rise to a dissipative dendritic-type flux structure. This dynamic state eventually cools down, turning into a frozen multi-filamentary pattern of magnetization currents.

cond-mat.supr-con↗

arXiv2001

The World of the Complex Ginzburg-Landau Equation

The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity, superfluidity and Bose-Einstein condensation to liquid crystals and strings in field theory. Our goal is to give an overview of various phenomena described the complex Ginzburg-Landau equation in one, two and three dimensions from the point of view of condensed matter physicists. Our approach is to study the relevant solutions to get an insight into nonequilibrium phenomena in spatially extended systems.

cond-mat.stat-mech↗

arXiv2001

Ginzburg-Landau Description of Vortex Nucleation in Rotating Superfluid

Nucleation of vortices in rotating superfluid by spin-up and rapid thermal quench is discussed in the framework of the time-dependent Ginzburg--Landau equation (TDGLE). An analysis of the instability in inhomogeneous rotationally-invariant system results in the expression for the critical rotational velocity. A stability analysis of multicharged vortices is presented. It is shown that they are very long-living objects with lifetime inversely proportional to the dissipation rate. It was found by numerical and analytical solution of the TDGLE that vortex nucleation by rapid thermal quench in the presence of superflow is dominated by a transverse instability of the moving normal-superfluid interface.

cond-mat.soft↗

arXiv1998

Dynamics of axial separation in long rotating drums

We propose a continuum description for the axial separation of granular materials in a long rotating drum. The model, operating with two local variables, concentration difference and the dynamic angle of repose, describes both initial transient traveling wave dynamics and long-term segregation of the binary mixture. Segregation proceeds through ultra-slow logarithmic coarsening.

patt-sol↗

arXiv1998

Helicoidal instability of a scroll vortex in three-dimensional reaction-diffusion systems

We study the dynamics of scroll vortices in excitable reaction-diffusion systems analytically and numerically. We demonstrate that intrinsic three-dimensional instability of a straight scroll leads to the formation of helicoidal structures. This behavior originates from the competition between the scroll curvature and unstable core dynamics. We show that the obtained instability persists even beyond the meander core instability of two-dimensional spiral wave.

patt-sol↗

arXiv1997

Spiral Motion in a Noisy Complex Ginzburg-Landau Equation

The response of spiral waves to external perturbations in a stable regime of the two-dimensional complex Ginzburg-Landau equation (CGLE) is investigated. It is shown that the spiral core has a finite mobility and performs Brownian motion when driven by white noise. Combined with simulation results, this suggests that defect-free and quasi-frozen states in the noiseless CGLE are unstable against free vortex excitation at any non-zero noise strength.

patt-sol↗

arXiv1997

Stretching of vortex lines and generation of vorticity in the three-dimensional complex Ginzburg-Landau Equation

The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is proved that a straight vortex line is unstable with respect to spontaneous stretching and bending in a certain range of parameters of the CGLE, resulting in formation of persistent entangled vortex configurations. The analysis shows that the standard approach relating the velocity of the filament with the local curvature, is insufficient to describe the instability and self-generation of vorticity.

patt-sol↗

arXiv1997

Localized and Cellular Patterns in a Vibrated Granular Layer

We propose a phenomenological model for pattern formation in a vertically vibrated layer of granular material. This model exhibits a variety of stable cellular patterns including standing rolls and squares as well as localized objects (oscillons and worms), similar to recent experimental observations(Umbanhowar et al., 1996). The model is an amplitude equation for the parametrical instability coupled to the mass conservation law. The structure and dynamics of the solutions resemble closely the properties of localized and cellular patterns observed in the experiments.

patt-sol↗

arXiv1997

Evolution on a Rugged Landscape:Pinning and Aging

Population dynamics on a rugged landscape is studied analytically and numerically within a simple discrete model for evolution of N individuals in one-dimensional fitness space. We reduce the set of master equations to a single Fokker-Plank equation which allows us to describe the dynamics of the population in terms of thermo-activated Langevin diffusion of a single particle in a specific random potential. We found that the randomness in the mutation rate leads to pinning of the population and on average to a logarithmic slowdown of the evolution, resembling aging phenomenon in spin glass systems. In contrast, the randomness in the replication rate turns out to be irrelevant for evolution in the long-time limit as it is smoothed out by increasing ``evolution temperature''. The analytic results are in a good agreement with numerical simulations.

adap-org↗

arXiv1996

Large-Scale Flow and Spiral Core Instability in Rayleigh-Benard Convection

The spiral core instability, observed in large aspect ratio Rayleigh-Benard convection, is studied numerically in the framework of the Swift-Hohenberg equation coupled to a large-scale flow. It is shown that the instability leads to non-trivial core dynamics and is driven by the self-generated vorticity. Moreover, the recently reported transition from spirals to hexagons near the core is shown to occur only in the presence of a non-variational nonlinearity, and is triggered by the spiral core instability. Qualitative agreement between the simulations and the experiments is demonstrated.

patt-sol↗

arXiv1995

Aggregation Patterns in Stressed Bacteria

We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a chemoattractant concentration as well as to nutrient and waste fields. The latter serves as a triggering field for emission of chemoattractant. Important elements in the proposed model include the propagation of a front of motile bacteria radially outward form an initial site, a Turing instability of the uniformly dense state and a reduction of motility for cells sufficiently far behind the front. The wide variety of patterns seen in the experiments is explained as being due the variation of the details of the initiation of the chemoattractant emission as well as the transition to a non-motile phase.

patt-sol↗

arXiv1994

Hole Solutions in the 1d Complex Ginzburg-Landau Equation

The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family of traveling localized source solutions. These so called 'Nozaki-Bekki holes' are (dynamically) stable in some parameter range, but always structually unstable: A perturbation of the equation in general leads to a (positive or negative) monotonic acceleration or an oscillation of the holes. This confirms that the cubic CGLE has an inner symmetry. As a consequence small perturbations change some of the qualitative dynamics of the cubic CGLE and enhance or suppress spatio-temporal intermittency in some parameter range. An analytic stability analysis of holes in the cubic CGLE and a semianalytical treatment of the acceleration instability in the perturbed equation is performed by using matching and perturbation methods. Furthermore we treat the asymptotic hole-shock interaction. The results, which can be obtained fully analytically in the nonlinear Schroedinger limit, are also used for the quantitative description of modulated solutions made up of periodic arrangements of traveling holes and shocks.

patt-sol↗