arXiv subjects

Igor M. Sokolov

Publications and source records attributed to Igor M. Sokolov.

At least 37 records · Page 2Linked to original sources

arXiv2021

Can a patchy model describe the potential spread of West Nile virus in Germany?

In 2018, West Nile Virus (WNV) was detected for the first time in Germany. Since the first detection, 36 human cases and 175 cases in horses and birds are detected. The transmission cycle of West Nile Virus includes birds and mosquitoes and -- as dead-end hosts -- people and horses. Spatial dissemination of the disease is caused by the movements of birds and mosquitoes. While the activity and movement of mosquitoes are depending mainly on temperature, in the birds there is a complex movement pattern caused by local birds and long range dispersal birds. To this end, we have developed a metapopulation network model framework to delineate the potential spatial distribution and spread of WNV across Germany as well as to evaluate the risk throughout our proposed network model. Our model facilitates the interconnection amongst the vector, local birds and long range dispersal birds contact networks. We have assumed different distance dispersal kernels models for the vector and avian populations with the intention to include short and long range dispersal. The model includes spatial variation of mosquito abundance and the movements to resemble the reality.

physics.bio-ph↗

arXiv2021

Ticks on the run: A mathematical model of Crimean-Congo Haemorrhagic Fever (CCHF)-key factors for transmission

Crimean-Congo haemorrhagic fever (CCHF) is a tick-borne zoonotic disease caused by the Crimean-Congo hemorrhagic fever virus (CCHFV). Ticks belonging to the genus \textit{Hyalomma} are the main vectors and reservoir for the virus. It is maintained in nature in an endemic vertebrate-tick-vertebrate cycle. CCHFV is prevalent in wide geographical areas including Asia, Africa, South-Eastern Europe and the Middle East. Over the last decade, several outbreaks of CCHFV have been observed in Europe, mainly in Mediterranean countries. Due to the high case/fatality ratio of CCHFV in human sometimes, it is of great importance for public health. Climate change and the invasion of CCHFV vectors in Central Europe suggest that the establishment of the transmission in Central Europe may be possible in future. We developed a compartment-based nonlinear Ordinary Differential Equation (ODE) system to model the disease transmission cycle including blood sucking ticks, livestock and human. Sensitivity analysis of the basic reproduction number $R_0$ shows that decreasing in the tick survival time is an efficient method to eradicate the disease. The model supports us in understanding the influence of different model parameters on the spread of CCHFV. Tick to tick transmission through co-feeding and the CCHFV circulation through trasstadial and transovarial stages are important factors to sustain the disease cycle. The proposed model dynamics are calibrated through an empirical multi-country analysis and multidimensional scaling reveals the disease-parameter sets of different countries burdened with CCHF are different. This necessary information may help us to select most efficient control strategies.

physics.bio-ph↗

arXiv2020

Periodic Coupling inhibits Second-order Consensus on Networks

Consensus algorithms on networks have received increasing attention in recent years for various applications ranging from animal flocking to multi-vehicle co-ordination. Building on the established model for second-order consensus of multi-agent networks, we uncover a mechanism inhibiting the formation of collective consensus states via rather small time-periodic coupling modulations. We treat the model in its spectral decomposition and find analytically that for certain intermediate coupling frequencies parametric resonance is induced on a network level -- at odds with the expected emergence of consensus for very short and long coupling time-scales. Our formalism precisely predicts those resonance frequencies and links them to the Laplacian spectrum of the static backbone network. The excitation of the system is furthermore quantified within the theory of parametric resonance, which we extend to the domain of networks with time-periodic couplings.

nlin.AO↗

arXiv2020

Brownian motion under non-instantaneous resetting in higher dimensions

We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the mean-squared displacement (MSD) in this process. We study two different resetting protocols: exponentially distributed time intervals between the resetting events (Poissonian resetting) and resetting at fixed time intervals (deterministic resetting). We moreover discuss a general problem of the invariance of the PDF with respect to the return speed, as observed in the one-dimensional system for Poissonian resetting, and show, that this one dimensional situation is the only one in which such an invariance can be found. However, the invariance of the MSD can still be observed in higher dimensions.

cond-mat.stat-mech↗

arXiv2020

Continuous time random walks under power-law resetting

We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are considered. Under complete resetting, the CTRW after the resetting event starts anew, with a new waiting time, independent of the prehistory. Under incomplete resetting, the resetting of the coordinate does not influence the waiting time until the next jump. We focus on the behavior of the mean squared displacement (MSD) of the walker from its initial position, on the conditions under which the probability density functions of the walker's displacement show universal behavior, and on this universal behavior itself. We show, that the behavior of the MSD is the same as in the scaled Brownian motion (SBM), being the mean field model of the CTRW. The intermediate asymptotics of the probability density functions (PDF) for CTRW under complete resetting (provided they exist) are also the same as in the corresponding case for SBM. For incomplete resetting, however, the behavior of the PDF for CTRW and SBM is vastly different.

cond-mat.stat-mech↗

arXiv2020

Unexpected crossovers in correlated random-diffusivity processes

The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the strong non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of "viscoelastic yet non-Gaussian" diffusion.

cond-mat.stat-mech↗

arXiv2020

Transmission spectra of bistable systems: from ultra-quantum to classical regime

We present an analytical and numerical study of the fluorescence spectra of a bistable driven system by means of Keldysh diagram technique in pseudo--particle representation. The spectra exhibit smooth transition between ultra-quantum and the quasiclassical limits and indicate the threshold value of the external field when changing of the most probable stable state occurs. The analysis of the fluorescence spectra also allows to determine the most probable stable state of the system. It was also shown that at integer and half-integer detuning-nonlinearity ratio multiphoton resonance leads to abrupt changes in fluorescence spectra. It was also revealed that the fluorescence spectra are symmetric in the limit of zero environment temperature. The predicted features of the spectra could be observed in experiments with ultra-high quality resonators in either microwave or optical domain.

cond-mat.mes-hall↗

arXiv2020

Inhomogeneous parametric scaling and variable-order fractional diffusion equations

We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time probability density functions, whose parameters are position-dependent. We concentrate on subdiffusive cases and discuss two situations as examples: A system consisting of two parts with different exponents of subdiffusion, and a system in which the subdiffusion exponent changes linearly from one end of the interval to another one. In both cases we compare the numerical solutions of generalized master equations describing the process on the lattice with the corresponding solutions of the continuous equations, which follow by exact solution of the corresponding equations in the Laplace domain with subsequent numerical inversion using the Gaver-Stehfest algorithm.

cond-mat.stat-mech↗

arXiv2020

Voltage distribution in a non-locally but globally electroneutral confined electrolyte medium: applications for nanophysiology

The distribution of voltage in sub-micron cellular domains remains poorly understood. In neurons, the voltage results from the difference in ionic concentrations which are continuously maintained by pumps and exchangers. However, it not clear how electro-neutrality could be maintained by an excess of fast moving positive ions that should be counter balanced by slow diffusing negatively charged proteins. Using the theory of electro-diffusion, we study here the voltage distribution in a generic domain, which consists of two concentric disks (resp. ball) in two (resp. three) dimensions, where a negative charge is fixed in the inner domain. When global but not local electro-neutrality is maintained, we solve the Poisson-Nernst-Planck equation both analytically and numerically in dimension 1 (flat) and 2 (cylindrical) and found that the voltage changes considerably on a spatial scale which is much larger than the Debye screening length, which assumes electro-neutrality. The present result suggests that long-range voltage drop changes are expected in neuronal microcompartments, probably relevant to explain the activation of far away voltage-gated channels located on the surface.

cond-mat.soft↗

arXiv2020

Modeling echo chambers and polarization dynamics in social networks

Echo chambers and opinion polarization recently quantified in several sociopolitical contexts and across different social media, raise concerns on their potential impact on the spread of misinformation and on openness of debates. Despite increasing efforts, the dynamics leading to the emergence of these phenomena stay unclear. We propose a model that introduces the dynamics of radicalization, as a reinforcing mechanism driving the evolution to extreme opinions from moderate initial conditions. Inspired by empirical findings on social interaction dynamics, we consider agents characterized by heterogeneous activities and homophily. We show that the transition between a global consensus and emerging radicalized states is mostly governed by social influence and by the controversialness of the topic discussed. Compared with empirical data of polarized debates on Twitter, the model qualitatively reproduces the observed relation between users' engagement and opinions, as well as opinion segregation in the interaction network. Our findings shed light on the mechanisms that may lie at the core of the emergence of echo chambers and polarization in social media.

physics.soc-ph↗

arXiv2020

Resetting processes with non-instanteneous return

We consider a random two-phase process which we call a reset-return one. The particle starts its motion at the origin. The first, displacement, phase corresponds to a stochastic motion of a particle and is finished at a resetting event. The second, return, phase corresponds to the particle's motion towards the origin from the position it attained at the end of the displacement phase. This motion towards the origin takes place according to a given equation of motion. The whole process is a renewal one. We provide general expressions for the stationary probability density function of the particle's position and for the mean hitting time in one dimension. We perform explicit analysis for the Brownian motion during the displacement phase and three different types of the return motion: return at a constant speed, return at a constant acceleration with zero initial speed and return under the action of a harmonic force. We assume that the waiting times for resetting events follow an exponential distribution, or that resetting takes place at a constant pace. For the first two types of return motion and the exponential resetting the stationary probability density function of the particle's position is invariant under return speed (acceleration), while no such invariance is found for deterministic resetting, and for exponential resetting with return under the action of the harmonic force. We discuss necessary conditions for such invariance of the stationary PDF of the positions with respect to the properties of the return process, and demonstrate some additional examples when this invariance does or does not take place.

cond-mat.stat-mech↗

arXiv2019

Enhanced excitation of a driven bistable system induced by spectrum degeneracy

The non-equilibrium statistics and kinetics of a simple bistable system (resonantly driven nonlinear oscillator coupled to reservoir) have been investigated by means of master equation for the density matrix and quasiclassical Fokker-Planck equation in quasienergy space. We found out that the system's statistical and kinetic properties drastically change when the quasienergy states become nearly degenerate and the occupation of the most excited state is strongly enhanced. It has been revealed that in nearly degenerate case a new critical quasienergy parameter emerges. Below the critical quasienergy value the eigenstates are superpositions of the quasiclassical states from different phase space regions, while above this value the eigenstates correspond to only one particular region of the phase space. We have also generalized Keldysh theory for ionization of atoms in the electromagnetic field for bistable systems. It has been demonstrated that Keldysh parameter in bistability region is large when pumping intensity is smaller than the critical value. It has been shown by direct calculations that multi-photon transition amplitude coincides with the tunneling amplitude. So, multi-photon transitions and tunneling between the regions of the phase space are just the same effects. We also demonstrated that for bistable systems the Keldysh parameter logarithmically depends on the external field amplitude.

cond-mat.mes-hall↗

arXiv2019

Effects of tunneling and multiphoton transitions on squeezed states generation in bistable driven systems

Bistability of nonlinear resonantly driven oscillator in the presence of external noise is analyzed by means of classical Fokker-Planck equation in quasienergy space with account for tunneling effects and by quantum master equation in quasienergy states representation. Two time scales responsible for different stages of bistable system relaxation have been obtained. We found out that the slow relaxation rate caused by fluctuation--induced transitions between different stable states can be enhanced by several orders due to tunneling effects. It was also revealed that tunneling between nearly degenerate quasienergy states and resonant multiphoton transitions between the genuine eigenstates of the nonlinear oscillator are just the similar effects. It was demonstrated that the quasienergy states in the bistability region corresponding to higher amplitude are squeezed. The degree of squeezing is determined by the ratio between nonlinearity and detuning, so the uncertainty of one quadrature can be considerably smaller than the quantum limit. It was found out that tunneling effects can enhance the generation of output oscillator squeezed states. It is shown that 1D Fokker--Planck equation is a quasiclassical limit of a quantum master equation.

cond-mat.mes-hall↗

arXiv2019

Comparison of three approaches to light scattering by dilute cold atomic ensembles

Collective effects in atom-light interaction is of great importance for cold-atom-based quantum devices or fundamental studies on light transport in complex media. Here we discuss and compare three different approaches to light scattering by dilute cold atomic ensembles. The first approach is a coupled-dipole model, valid at low intensity, which includes cooperative effects, like superradiance, and other coherent properties. The second one is a random-walk model, which includes classical multiple scattering and neglects coherence effects. The third approach is a crude approximation only based on the attenuation of the excitation beam inside the medium, the so-called "shadow effect". We show that in the case of a low-density sample, the random walk approach is an excellent approximation for steady-state light scattering, and that the shadow effect surprisingly gives rather accurate results at least up to optical depths on the order of 15.

physics.atom-ph↗

arXiv2019

Non-renewal resetting of scaled Brownian motion

We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{α-1}$, $α>0$ (scaled Brownian motion), is stochastically reset to its initial position and starts anew. The resetting follows a renewal process with either exponential or power-law distribution of the waiting times between successive renewals. The resetting events, however, do not affect the time dependence of the diffusion coefficient, so that the whole process appears to be a non-renewal one. We discuss the mean squared displacement of a particle and probability density function of its positions in such a process. We show that scaled Brownian motion with resetting demonstrates a rich behavior whose properties essentially depend on the interplay of the parameters of the resetting process and the particle's displacement in a free motion. The motion of particles can remain either almost unaffected by resetting, but can also get slowed down or even be completely suppressed. Especially interesting are the nonstationary situations in which the mean squared displacement stagnates but the distribution of positions does not tend to any steady state. \color{black} This behavior is compared to the situation (discussed in the other paper of this series) in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. \color{black}

cond-mat.stat-mech↗

arXiv2019

Scaled Brownian motion with renewal resetting

We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t) \sim t^{α-1}$ with $α> 0$ (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. \color{black} In the present work we discuss the situation, in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when the resetting of coordinate does not affect the diffusion coefficient's time dependence is considered in the other work of this series. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. \color{black} In addition we discuss the first passage properties of the scaled Brownian motion with renewal resetting and consider the dependence of the efficiency of search on the parameters of the process.

cond-mat.stat-mech↗

arXiv2018

Influencers identification in complex networks through reaction-diffusion dynamics

A pivotal idea in network science, marketing research and innovation diffusion theories is that a small group of nodes -- called influencers -- have the largest impact on social contagion and epidemic processes in networks. Despite the long-standing interest in the influencers identification problem in socio-economic and biological networks, there is not yet agreement on which is the best identification strategy. State-of-the-art strategies are typically based either on heuristic centrality metrics or on analytic arguments that only hold for specific network topologies or peculiar dynamical regimes. Here, we leverage the recently introduced random-walk effective distance -- a topological metric that estimates almost perfectly the arrival time of diffusive spreading processes on networks -- to introduce a new centrality metric which quantifies how close a node is to the other nodes. We show that the new centrality metric significantly outperforms state-of-the-art metrics in detecting the influencers for global contagion processes. Our findings reveal the essential role of the network effective distance for the influencers identification and lead us closer to the optimal solution of the problem.

physics.soc-ph↗

arXiv2018

Reaction-diffusion on random spatial networks with scale-free jumping rates via effective medium theory

We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium approximation (EMA) that is capable of dealing with these long-range connections. Using a Feynman-Kac argument in the effective medium, we derive an estimate on the size of the infected domain, and reproduce the known result of its exponential growth in time. We hereby demonstrate the applicability of long-range EMA to dynamical processes on networks more intricate than simple diffusion.

physics.soc-ph↗