arXiv subjects

Gleb Oshanin

Publications and source records attributed to Gleb Oshanin.

At least 37 records · Page 2Linked to original sources

arXiv2022

Cooperative dynamics in two-component out-of-equilibrium systems: Molecular "spinning tops"

We study the two-dimensional Langevin dynamics of a two-component system, whose components are in contact with heat baths kept at different temperatures. Dynamics is constrained by an optical trap and the \text{dissimilar} species interact via a quadratic potential. We realize that the system evolves towards a peculiar non-equilibrium steady-state with a non-zero probability current possessing a non-zero curl, such that the randomly moving particles are spinning around themselves, like "spinning top" toys. Our analysis shows that the spinning motion is correlated and also reveals an emerging cooperative behavior of the spatial components of the probability currents of dissimilar species.

cond-mat.stat-mech↗

arXiv2022

Search efficiency in the Adam-Delbrück reduction-of-dimensionality scenario versus direct diffusive search

The time instant -- the first-passage time (FPT) -- when a diffusive particle (e.g., a ligand such as oxygen or a signalling protein) for the first time reaches an immobile target located on the surface of a bounded three-dimensional domain (e.g., a hemoglobin molecule or the cellular nucleus) is a decisive characteristic time-scale in diverse biophysical and biochemical processes, as well as in intermediate stages of various inter- and intra-cellular signal transduction pathways. Adam and Delbrück put forth the reduction-of-dimensionality concept, according to which a ligand first binds non-specifically to any point of the surface on which the target is placed and then diffuses along this surface until it locates the target. In this work, we analyse the efficiency of such a scenario and confront it with the efficiency of a direct search process, in which the target is approached directly from the bulk and not aided by surface diffusion. We consider two situations: (i) a single ligand is launched from a fixed or a random position and searches for the target, and (ii) the case of "amplified" signals when $N$ ligands start either from the same point or from random positions, and the search terminates when the fastest of them arrives to the target. For such settings, we go beyond the conventional analyses, which compare only the mean values of the corresponding FPTs. Instead, we calculate the full probability density function of FPTs for both scenarios and study its integral characteristic -- the "survival" probability of a target up to time $t$. On this basis, we examine how the efficiencies of both scenarios are controlled by a variety of parameters and single out realistic conditions in which the reduction-of-dimensionality scenario outperforms the direct search.

cond-mat.stat-mech↗

arXiv2022

Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes

We investigate the stochastic behavior of the single-trajectory spectral density $S(ω,\mathcal{T})$ of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein-Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency $ω$ and the observation time $\mathcal{T}$. We evaluate in particular the variance and the frequency-frequency correlation of $S(ω,\mathcal{T})$ for different values of $ω$. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental data.

cond-mat.stat-mech↗

arXiv2022

Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes

We discuss the statistical properties of a single-trajectory power spectral density $S(ω,\mathcal{T})$ of an arbitrary real-valued centered Gaussian process $X(t)$, where $ω$ is the angular frequency and $\mathcal{T}$ the observation time. We derive a double-sided inequality for its noise-to-signal ratio and obtain the full probability density function of $S(ω,\mathcal{T})$. Our findings imply that the fluctuations of $S(ω,\mathcal{T})$ exceed its average value $μ(ω,\mathcal{T})$. This implies that using $μ(ω,\mathcal{T})$ to describe the behavior of these processes can be problematic. We finally evaluate the typical behavior of $S(ω,\mathcal{T})$ and find that it deviates markedly from the average $μ(ω,\mathcal{T})$ in most cases.

cond-mat.stat-mech↗

arXiv2022

Fractional Brownian Gyrator

When a physical system evolves in a thermal bath at a constant temperature, it arrives eventually to an equilibrium state whose properties are independent of the kinetic parameters and of the precise evolution scenario. This is generically not the case for a system driven out of equilibrium which, on the contrary, reaches a steady-state with properties that depend on the full details of the dynamics such as the driving noise and the energy dissipation. How the steady state depends on such parameters is in general a non-trivial question. Here, we approach this broad problem using a minimal model of a two-dimensional nano-machine, the Brownian gyrator, that consists of a trapped particle driven by fractional Gaussian noises -- a family of noises with long-ranged correlations in time and characterized by an anomalous diffusion exponent $α$. When the noise is different in the different spatial directions, our fractional Brownian gyrator persistently rotates. Even if the noise is non-trivial, with long-ranged time correlations, thanks to its Gaussian nature we are able to characterize analytically the resulting nonequilibrium steady state by computing the probability density function, the probability current, its curl and the angular velocity and complement our study by numerical results.

cond-mat.stat-mech↗

arXiv2022

From steady-state TASEP model with open boundaries to 1D Ising model at negative fugacity

We demonstrate here a series of exact mappings between particular cases of four statistical physics models: equilibrium 1-dimensional lattice gas with nearest-neighbor repulsion, $(1+1)$-dimensional combinatorial heap of pieces, random walks on half-plane and totally asymmetric simple exclusion process (TASEP) in one dimension (1D). In particular, we show that generating function of a steady state of one-dimensional TASEP with open boundaries can be interpreted as a quotient of partition functions of 1D hard-core lattice gases with one adsorbing lattice site and negative fugacity. This result is based on the combination of (i) a representation of the steady-state TASEP configurations in terms of $(1+1)$-dimensional heaps of pieces and (ii) a theorem connecting the partition function of $(1+1)$-dimensional heaps of pieces with that of a single layer of pieces, which in this case is a 1D hard-core lattice gas.

cond-mat.stat-mech↗

arXiv2021

Distribution of first-reaction times with target regions on boundaries of shell-like domains

We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted "onion-shell" geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.

physics.chem-ph↗

arXiv2021

A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes

We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g., a signal transduction proceeds via a series of consecutive "messengers": the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.

physics.bio-ph↗

arXiv2021

Spectral density of individual trajectories of an active Brownian particle

We study analytically the single-trajectory spectral density (STSD) of an active Brownian motion as exhibited, for example, by the dynamics of a chemically-active Janus colloid. We evaluate the standardly-defined spectral density, i.e. the STSD averaged over a statistical ensemble of trajectories in the limit of an infinitely long observation time $T$, and also go beyond the standard analysis by considering the coefficient of variation $γ$ of the distribution of the STSD. Moreover, we analyse the finite-$T$ behaviour of the STSD and $γ$, determine the cross-correlations between spatial components of the STSD, and address the effects of translational diffusion on the functional forms of spectral densities. The exact expressions that we obtain unveil many distinctive features of active Brownian motion compared to its passive counterpart, which allow to distinguish between these two classes based solely on the spectral content of individual trajectories.

cond-mat.stat-mech↗

arXiv2021

Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices

We study equilibrium properties of binary lattice-gases comprising $A$ and $B$ particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials $μ_A = μ_B = μ$. The particles interact via on-site hard-core exclusion and also between the nearest-neighbours: there are a soft repulsion for $AB$ pairs and interactions of arbitrary strength $J$, positive or negative, for $AA$ and $BB$ pairs. For tree-like Bethe and Husimi lattices, we determine the full phase diagram of such a ternary mixture of particles and voids. We show that for $J$ being above a lattice-dependent threshold value, the critical behaviour is similar: the system undergoes a transition at $μ= μ_c$ from a phase with equal mean densities of species into a phase with a spontaneously broken symmetry, in which the mean densities are no longer equal. Depending on the value of $J$, this transition can be either continuous or of the first order. For sufficiently big negative $J$, the behaviour on the two lattices becomes markedly different: while for the Bethe lattice there exists a continuous transition into a phase with an alternating order followed by a continuous re-entrant transition into a disordered phase, an alternating order phase is absent on the Husimi lattice due to strong frustration effects.

cond-mat.stat-mech↗

arXiv2021

Recognition Capabilities of a Hopfield Model with Auxiliary Hidden Neurons

We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero-temperature outperform those of the original Hopfield model, due to a substantial increase of the storage capacity and the lack of a naturally defined basin of attraction. The modified model does not fall abruptly in a regime of complete confusion when memory load exceeds a sharp threshold.

cond-mat.dis-nn↗

arXiv2020

Time-dependence of the effective temperatures of a two-dimensional Brownian gyrator with cold and hot components

We consider a model of a two-dimensional molecular machine - called Brownian gyrator - that consists of two coordinates coupled to each other and to separate heat baths at temperatures respectively $T_x$ and $T_y$. We consider the limit in which one component is passive, because its bath is "cold", $T_x \to 0$, while the second is in contact with a "hot" bath, $T_y > 0$, hence it entrains the passive component in a stochastic motion. We derive an asymmetry relation as a function of time, from which time dependent effective temperatures can be obtained for both components. We find that the effective temperature of the passive element tends to a constant value, which is a fraction of $T_y$, while the effective temperature of the driving component grows without bounds, in fact exponentially in time, as the steady-state is approached.

cond-mat.stat-mech↗

arXiv2020

Equilibrium properties of two-species reactive lattice gases on random catalytic chains

We focus here on the thermodynamic properties of adsorbates formed by two-species $A+B \to \oslash$ reactions on a one-dimensional infinite lattice with heterogeneous "catalytic" properties. In our model hard-core $A$ and $B$ particles undergo continuous exchanges with their reservoirs and react when dissimilar species appear at neighboring lattice sites in presence of a "catalyst." The latter is modeled by supposing either that randomly chosen bonds in the lattice promote reactions (Model I) or that reactions are activated by randomly chosen lattice sites (Model II). In the case of annealed disorder in spatial distribution of a catalyst we calculate the pressure of the adsorbate by solving three-site (Model I) or four-site (Model II) recursions obeyed by the corresponding averaged grand-canonical partition functions. In the case of quenched disorder, we use two complementary approaches to find $\textit{exact}$ expressions for the pressure. The first approach is based on direct combinatorial arguments. In the second approach, we frame the model in terms of random matrices; the pressure is then represented as an averaged logarithm of the trace of a product of random $3 \times 3$ matrices -- either uncorrelated (Model I) or sequentially correlated (Model II).

cond-mat.stat-mech↗

arXiv2020

From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers

We consider the first-passage problem for $N$ identical independent particles that are initially released uniformly in a finite domain $Ω$ and then diffuse toward a reactive area $Γ$, which can be part of the outer boundary of $Ω$ or a reaction centre in the interior of $Ω$. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the $N$ particles reacts with $Γ$. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fastest first-passage time with the particle number $N$, namely, a much stronger dependence ($1/N$ and $1/N^2$ for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.

cond-mat.stat-mech↗

arXiv2019

Tracer Diffusion on a Crowded Random Manhattan Lattice

We study by extensive numerical simulations the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder - frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour $\sim t^{4/3}$, $t$ being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position $X$ along the $x$-axis. Our analysis evidences that in absence of the lattice gas particles the latter has a Gaussian central part $\sim \exp(- u^2)$, where $u = X/t^{2/3}$, and exhibits slower-than-Gaussian tails $\sim \exp(-|u|^{4/3})$ for sufficiently large $t$ and $u$. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.

cond-mat.dis-nn↗

arXiv2019

Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control

Text-book concepts of diffusion- versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants -- the inverse of the mean-first-passage-time to the reaction-event. In contradistinction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly-solvable model we study the conspiratory effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delimited by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.

physics.chem-ph↗

arXiv2019

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior

We develop a theory of charge storage in ultra-narrow slit-like pores of nano\-structured electrodes. Our analysis is based on the Blume-Capel model in external field, which we solve analytically on a Bethe lattice. The obtained solutions allow us to explore the complete phase diagram of confined ionic liquids in terms of the key parameters characterising the system, such as pore ionophilicity, interionic interaction energy and voltage. The phase diagram includes the lines of first and second-order, direct and re-entrant, phase transitions, which are manifested by singularities in the corresponding capacitance-voltage plots. To test our predictions experimentally requires mono-disperse, conducting, ultra-narrow slit pores, permitting only one layer of ions, and thick pore walls, preventing interionic interactions across the pore walls. However, some qualitative features, which distinguish the behavior of ionophilic and ionophobic pores, and its underlying physics, may emerge in future experimental studies of more complex electrode structures.

cond-mat.soft↗

arXiv2019

Passive advection of fractional Brownian motion by random layered flows

We study statistical properties of the process $Y(t)$ of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion $X(t)$ with the Hurst index $H \in (0,1)$. We show that the disorder-averaged mean-squared displacement of the passive advection grows in the large time $t$ limit in proportion to $t^{2 - H}$, which defines a family of anomalous super-diffusions. We evaluate the disorder-averaged Wigner-Ville spectrum of the advection process $Y(t)$ and demonstrate that it has a rather unusual power-law form $1/f^{3 - H}$ with a characteristic exponent which exceed the value $2$. Our results also suggest that sample-to-sample fluctuations of the spectrum can be very important.

cond-mat.stat-mech↗