arXiv subjects

Oleg Kogan

Publications and source records attributed to Oleg Kogan.

14 recordsLinked to original sources

arXiv2025

Aging in a two-dimensional swarmalator crystal with delayed interactions

Time delay can have a significant impact on the properties of collective organization of active matter. In the previous paper [1], we discussed delay-induced breathing in a system of swarmalators - a model coupling particles' internal phases to spatial interactions. Here we build on that study to investigate the aging phenomenon in this system. It is the aging of a two-dimensional crystal with defects and inhomogeneous lattice constants, and takes place after the breathing transients subside. We show that aging proceeds through the gradual elimination of five-fold and seven-fold coordination number defects, which merge pairwise or migrate to the cluster boundary, incrementally increasing the hexatic order parameter in the bulk. Despite this process, defects usually do not fully disappear; some residual number of defects remain frozen in the interior. However, we found that it is possible to achieve a nearly total elimination of coordination number defects at sufficiently low delay - when the surface of the cluster develops a sufficeintly thick fluidized ``boiling layer''. This mechanism of boundary-mediated annealing reveals a non-equilibrium pathway to achieving high crystalline order in the bulk, and raises a tantalizing possibility for controlling defects in active matter with free boundaries.

cond-mat.stat-mech↗

arXiv2023

Tunable intracellular transport on converging microtubule morphologies

A common type of cytoskeletal morphology involves multiple converging microbutubules with their minus ends collected and stabilized by a microtubule organizing center (MTOC) in the interior of the cell. This arrangement enables the ballistic transport of cargo bound to microtubules, both dynein mediated transport towards the MTOC and kinesin mediated transport away from it, interspersed with diffusion for unbound cargo-motor complexes. Spatial and temporal positioning of the MTOC allows for bidirectional transport towards and away from specific organelles and locations within the cell and also the sequestering and subsequent dispersal of dynein transported cargo. The general principles governing dynamics, efficiency and tunability of such transport in the MTOC vicinity is not fully understood. To address this, we develop a one-dimensional model that includes advective transport towards an attractor (such as the MTOC), and diffusive transport that allows particles to reach absorbing boundaries (such as cellular membranes). We calculated the mean first passage time (MFPT) for cargo to reach the boundaries as a measure of the effectiveness of sequestering (large MFPT) and diffusive dispersal (low MFPT). The MFPT experiences a dramatic growth in magnitude, transitioning from a low to high MFPT regime (dispersal to sequestering) over a window of cargo attachment/detachment rates that is close to in vivo values. We find that increasing either the attachment or detachment rate, while fixing the other, can result in optimal dispersal when the attractor is placed asymmetrically. Finally, we describe a rare event regime, where the escape location is exponentially sensitive to the attractor positioning. Our results suggest that structures such as the MTOC allow for the sensitive control of the spatial and temporal features of transport and corresponding function under physiological conditions.

q-bio.CB↗

arXiv2022

Swarmalators with delayed interactions

We investigate the effects of delayed interactions in a population of ``swarmalators", generalizations of phase oscillators that both synchronize in time and swarm through space. We discover two steady collective states: a state in which swarmalators are essentially motionless in a disk arranged in a pseudo-crystalline order, and a boiling state in which the swarmalators again form a disk, but now the swarmalators near the boundary perform boiling-like convective motions. These states are reminiscent of the beating clusters seen in photoactivated colloids and the living crystals of starfish embryos.

nlin.AO↗

arXiv2020

Path-dependent course of epidemic: are two phases of quarantine better than one?

The importance of a strict quarantine has been widely debated during the COVID-19 epidemic even from the purely epidemiological point of view. One argument against strict lockdown measures is that once the strict quarantine is lifted, the epidemic comes back, and so the cumulative number of infected individuals during the entire epidemic will stay the same. We consider an SIR model on a network and follow the disease dynamics, modeling the phases of quarantine by changing the node degree distribution. We show that the system reaches different steady states based on the history: the outcome of the epidemic is path-dependent despite the same final node degree distribution. The results indicate that two-phase route to the final node degree distribution (a strict phase followed by a soft phase) are always better than one phase (the same soft one) unless all the individuals have the same number of connections at the end (the same degree); in the latter case, the overall number of infected is indeed history-independent. The modeling also suggests that the optimal procedure of lifting the quarantine consists of releasing nodes in the order of their degree - highest first.

physics.soc-ph↗

arXiv2020

FKPP dynamics mediated by a parent field with a delay

We examine a modification of the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) process in which the diffusing substance requires a parent density field for reproduction. A biological example would be the density of diffusing spores (propagules) and the density of a stationary fungus (parent). The parent produces propagules at a certain rate, and the propagules turn into the parent substance at another rate. We model this evolution by the FKPP process with delay, which reflects a finite time typically required for a new parent to mature before it begins to produce propagules. While the FKPP process with other types of delays have been considered in the past as a pure mathematical construct, in our work a delay in the FKPP model arises in a natural science setting. The speed of the resulting density fronts is shown to decrease with increasing delay time, and has a non-trivial dependence on the rate of conversion of propagules into the parent substance. Remarkably, the fronts in this model are always slower than Fisher waves of the classical FKPP model. The largest speed is half of the classical value, and it is achieved at zero delay and when the two rates are matched.

q-bio.PE↗

arXiv2016

Fragility of reaction-diffusion models to competing advective processes

We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that the front dynamics can be described by an FKPP-like equation only at sufficiently fast diffusion or large coupling strength. For such parameter regimes, we find a mapping to an effective FKPP equation. We also find that FKPP equation is fragile with respect to the coupling to an advection-only mechanism, discover conditions when the front width diverges, and when front speed is insensitive to the coupling. At zero diffusion in this mean-field description, the downwind front speed goes to a finite value as the coupling goes to zero.

nlin.PS↗

arXiv2014

Onset of Singularities in the Pattern of Fluctuational Paths of a Nonequilibrium System

Fluctuations in systems away from thermal equilibrium have features that have no analog in equilibrium systems. One of such features concerns large rare excursions far from the stable state in the space of dynamical variables. For equilibrium systems, the most probable fluctuational trajectory to a given state is related to the fluctuation-free trajectory back to the stable state by time reversal. This is no longer true for nonequilibrium systems, where the pattern of the most probable trajectories generally displays singularities. Here we study how the singularities emerge as the system is driven away from equilibrium, and whether a driving strength threshold is required for their onset. Using a resonantly modulated oscillator as a model, we identify two distinct scenarios, depending on the speed of the optimal path in thermal equilibrium. If the position away from the stable state along the optimal path grows exponentially in time, the singularities emerge without a threshold. We find the scaling of the location of the singularities as a function of the control parameter. If the growth away from the stable state is faster than exponential, characterized by the ability to reach infinity in finite time, there is a threshold for the onset of singularities, which we study for the model.

cond-mat.stat-mech↗

arXiv2014

Two-strain competition in quasi-neutral stochastic disease dynamics

We develop a new perturbation method for studying quasi-neutral competition in a broad class of stochastic competition models, and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic Susceptible-Infected-Susceptible (SIS) model. Here we extend previous results due to Parsons and Quince (2007), Parsons et al (2008) and Lin, Kim and Doering (2012). The second model, a two-strain generalization of the stochastic Susceptible-Infected-Recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of sub-population sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the sub-populations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.

cond-mat.stat-mech↗

arXiv2013

Stability of jammed packings II: the transverse length scale

As a function of packing fraction at zero temperature and applied stress, an amorphous packing of spheres exhibits a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the system should become insensitive to boundary conditions provided it is sufficiently large. Here we explore the linear response to a large class of boundary perturbations in 2 and 3 dimensions. We consider each finite packing with periodic-boundary conditions as the basis of an infinite square or cubic lattice and study properties of vibrational modes at arbitrary wave vector. We find that the stability of such modes be understood in terms of a competition between plane waves and the anomalous vibrational modes associated with the jamming transition; infinitesimal boundary perturbations become irrelevant for systems that are larger than a length scale that characterizes the transverse excitations. This previously identified length diverges at the jamming transition.

cond-mat.soft↗

arXiv2009

Universality in the one-dimensional chain of phase-coupled oscillators

We apply a recently developed renormalization group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and couplings form frequency-synchronized clusters. Although the RG was originally intended for strong randomness, i.e. for distributions with long tails, we find good agreement with numerical simulations even in the regime of weak randomness. We use the RG flow to derive how the correlation length scales with the width of the coupling distribution in the limit of large coupling. This leads to the identification of a universality class of distributions with the same critical exponent $ν$. We also find universal scaling for small coupling. Finally, we show that the RG flow is characterized by a universal approach to the unsynchronized fixed point, which provides physical insight into low-frequency clusters.

cond-mat.stat-mech↗

arXiv2008

Renormalization Group Approach to Oscillator Synchronization

We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic frequencies and coupling strengths. The results are compared with numerical simulations of the chain dynamics and good agreement in several characteristics is found. We apply the renormalization group and simulations to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies, as well as the dependence of the characteristic cluster length upon parameters of these Lorentzian distributions.

nlin.PS↗

arXiv2008

Scaling crossovers in activated escape of nonequilibrium systems: a resonantly driven oscillator

The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. Recently such behavior was observed and some of the earlier predicted exponents were found in experiments on several types of systems described by a model of a modulated oscillator. Here we establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. The analysis is done for a nonlinear oscillator with two coexisting stable states of forced vibrations. Our numerical calculations, based on the the instanton method allow the mapping of the entire parameter range of bi-stability. We find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then were it would be expected to hold as a result of an over-damped soft mode. We also uncover a new scaling behavior with exponent of $\approx$ 1.3 which extends, numerically, beyond the close vicinity of the bifurcation point.

cond-mat.stat-mech↗

arXiv2008

Optimal Light Beams and Mirror Shapes for Future LIGO Interferometers

We report the results of a recent search for the lowest value of thermal noise that can be achieved in LIGO by changing the shape of mirrors, while fixing the mirror radius and maintaining a low diffractional loss. The result of this minimization is a beam with thermal noise a factor of 2.32 (in power) lower than previously considered Mesa Beams and a factor of 5.45 (in power) lower than the Gaussian beams employed in the current baseline design. Mirrors that confine these beams have been found to be roughly conical in shape, with an average slope approximately equal to the mirror radius divided by arm length, and with mild corrections varying at the Fresnel scale. Such a mirror system, if built, would impact the sensitivity of LIGO, increasing the event rate of observing gravitational waves in the frequency range of maximum sensitivity roughly by a factor of three compared to an Advanced LIGO using Mesa beams (assuming all other noises remain unchanged). We discuss the resulting beam and mirror properties and study requirements on mirror tilt, displacement and figure error, in order for this beam to be used in LIGO detectors.

gr-qc↗

arXiv2006

Controlling transitions in a Duffing oscillator by sweeping parameters in time

We consider a high-$Q$ Duffing oscillator in a weakly non-linear regime with the driving frequency $σ$ varying in time between $σ_i$ and $σ_f$ at a characteristic rate $r$. We found that the frequency sweep can cause controlled transitions between two stable states of the system. Moreover, these transitions are accomplished via a transient that lingers for a long time around the third, unstable fixed point of saddle type. We propose a simple explanation for this phenomenon and find the transient life-time to scale as $-(\ln{|r-r_c|})/λ_r$ where $r_c$ is the critical rate necessary to induce a transition and $λ_r$ is the repulsive eigenvalue of the saddle. Experimental implications are mentioned.

nlin.AO↗