Stochastic resetting [1] can either accelerate or delay a dynamical process that takes a random time to complete (i.e., a first-passage process). Tuning system parameters can invert the effect of resetting on the mean completion time of the process, leading to a resetting transition. In this talk, I shall first explore the exact conditions where stochastic resetting accelerates diffusive...
Theoretical investigation of diffusion in heterogeneous media (such as materials with impurities, defects, fractal and random heterogeneous structures and combs, crowded environments, etc.) currently receives a considerable interest. The corresponding heterogeneous diffusion process often becomes anomalous due to the geometric constraints, random potential effects or variations of the local...
While averages and typical fluctuations often play a major role in understanding the behavior of a nonequilibrium system, this nonetheless is not always true. Rare events and large fluctuations are also pivotal when a thorough analysis of the system is being done. In this context, the statistics of extreme fluctuations in contrast to the average plays an important role, as has been discussed...
We study the diffusive motion of a test particle in a two-dimensional comb structure consisting of a main backbone channel with continuously distributed side branches, in the presence of stochastic Markovian resetting to the initial position of the particle. We assume that the motion along the infinitely long branches is biased by a confining potential. The crossover to the steady state is...
Stochastic resetting is prevalent in natural and man-made systems, giving rise to a long series of nonequilibrium phenomena. Diffusion with stochastic resetting serves as a paradigmatic model to study these phenomena but lacked a well-controlled platform by which it can be studied experimentally. Here, we report the experimental realization of colloid diffusion and resetting via holographic...
Transparent electrodes are important components of modern optoelectronic devices such as touch-screens, heaters, and solar cells. One of the most widely used kinds of transparent electrode consists of a transparent, poorly conductive film containing randomly distributed highly conductive fillers such as nanowires, nanotubes, nanorods, and nanorings.
Using a mean-field approach, we evaluate the...
We investigate the dimensionless layer monomer density profiles of a dilute solution of ideal ring and star polymers confined in a slit geometry of two parallel walls. We analyzed cases with both attractive and repulsive walls as well as one attractive and one repulsive wall. We also performed molecular dynamics simulations of a dilute solution of ring and star-shaped polymers. Analytical and...
Articulation points (APs) are nodes in complex networks whose removal would break the network component on which they are located into two or more disconnected components, while bredges (bridge-edges) are edges whose removal would break the network component on which they are located into two components. APs and bredges are thus crucial for the integrity and functionality of complex...
Relaxation of packing of elongated particles (discorectangles) aligned on a line was studied numerically. The aspect ratio (length-to-width ratio) for the discorectangles was varied within the range $\varepsilon \in [1;50]$. The initial jamming (saturated) state was produced using the basic variant of the random sequential adsorption (RSA) model with random positions and orientations of...
The network analysis of the structure of social relations in one of the most popular novels in Russian of the Soviet era by M. A. Bulgakov "The Master and Margarita" was carried out. The structure of the novel is complex, i.e., there is novel in novel. In our study, only relations between explicitly present and acting characters were taken into account; the characters mentioned and expected...
Coagulation (aggregation) is a phenomenon that consists of combining clusters into larger clusters, with the probability of merging depending on the size (or mass) of these clusters. Such an abstract definition causes that we can find coagulation in a great number of real processes: starting from blood coagulation, through the processes known from food and polymer processing, to the...
For site percolation on a square lattice, exact percolation probabilities on plane, cylinder, and torus has been found. Topological dynamic programming was applied to improve performance. Topologically equivalent states of the system and their horizontal reflections were combined. In the case of a torus and a cylinder, the shifts of topological states were also taken into account. Percolation...
The study of hyperuniform states of matter is an emerging multidisciplinary field, influencing and linking developments across the physical sciences, mathematics and biology [1,2]. A hyperuniform many-particle system in $d$-dimensional Euclidean space is characterized by an anomalous suppression of large-scale density fluctuations relative to those in typical disordered systems, such as...
Liquid crystals are a state of matter with the properties of both liquids and solids. They have a long research history dating back to the 19th century and have found countless applications, with LCDs being arguably the most important one of them. As demonstrated by Onsager, the phase transition between isotropic liquid and nematic liquid crystal can be induced by excluded volume effects...
Percolation on non-planar lattices, such as lattices with crossing bonds, are generally expected to be in the two-dimensional universality class of ordinary percolation, and indeed that is the case for the leading behavior. However, we have found that the corrections to scaling, as characterized by the exponent Omega, are different for the non-planar system. This might imply that the usual...
Random sequential adsorption (RSA) of various polydisks and rounded polygons is studied to determine the shape, which forms the densest packings. Covariance matrix adaptation evolution strategy (CMA-ES), an evolutionary optimization algorithm is used to search for optimal shapes. We found that independently of the number of component disks, the optimal polydisk resembles a triangle with...
Random Sequential Adsorption is a very simple protocol that generates random loose packings. It takes a virtual particle, randomly chooses its position and orientation, and then checks if it does not overlap with any object already placed in the packing. If so, the virtual particle is added, otherwise it is removed.
Typically, the shape that is to be deposited is always the same. In this...
Silver and nickel composites are peculiar for many reasons. As pure, both of these metals exhibit fcc crystal structures, but their lattice constants are much different. Because in the solid state they are almost insoluble, in the case of flat surfaces it may result in occurring of superlattice arrangement resulting from the mistmatch of lattice constants, with silver atoms well separated...
The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Through this work, we obtain analytical results for a microscopic model for a granular gas where particles with two-dimensional velocities are driven homogeneously and isotropically by reducing the velocities by a factor and adding a stochastic noise. We find two universal regimes. For...
It is known that in an equilibrium system approaching a critical point, the response to a change in an external thermodynamic force can become significantly large.
In other words, an equilibrium system at the verge of a second-order phase transition is highly susceptible to external thermodynamic forces.
Starting from this premise, in my talk I will discuss the properties of systems of...
A universal large $\mathcal{N}$ theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse grained thermodynamic uncertainty relations (TUR) -- one of them being an activity bound. Importantly, the activity serves as a tighter bound for the entropy production in 1D systems. These results are particularly...
It is investigated whether the non-Markovianity, i.e., the memory effects resulting from the coupling of the system to its environment, can be beneficial for the performance of quantum heat engines. Specifically, a version of a single-qubit Otto engine is studied in which the standard thermalization strokes are replaced with so-called extremal thermal operations, which cannot be realized...
Information processing in the physical world comes with an energetic cost: Landauer's principle states that erasing a 1-bit memory requires at least $k_BT_0 \ln 2$ of energy, with $k_BT_0$ the thermal energy of the surrounding bath. Practical erasures implementations require an overhead to the Landauer's bound, observed to scale as $k_BT_0 B/\tau$, with $\tau$ the protocol duration and $B$...
The title of this work is inspired by the Timur Kuran’s book entitled “Private Truths, Public Lies. The Social Consequences of Preference Falsification”. During my presentation I will talk about the idea and real-life examples of Preference Falsification (PF). Furthermore, I will propose a binary agent-based model, which allows to describe PF by introducing two levels of the opinion: the...
We study stochastic thermodynamics for non-equilibrium systems that can exhibit anomalous diffusion with the main focus on deriving an integral fluctuation relation (IFR) for the total entropy production. The dynamics of those systems are described by (i) Markovian processes with a time-dependent diffusivity such as scaled Brownian motion and (ii) non-Markovian fractional Brownian motion. The...
The $q$-neighbor Ising model is considered on multiplex networks with two layers in the form of identical random graphs, in which only a fraction of nodes belongs to both layers, forming the overlap. In this model the probability of the spin flip for a node belonging only to one layer is given by the Metropolis-like formula with the local field depending on the states of its $q$ randomly...
Swimming microorganisms and engineered artificial swimmers use multiple strategies to achieve propulsion in the viscosity-dominated microworld. A number of them use long, filamentous appendages called cilia or flagella. The motion of these slender objects is governed by a complex interplay between the driving forces, the elastic properties of the fibres, and the resistance forces of fluid. In...
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes. Their current description via diffusion equations with mixed boundary conditions is limited to simple surface reactions with infinite or constant reactivity. In...
We present the integral decomposition for the fundamental solution of the generalized Cattaneo equation with both time derivatives smeared through convoluting them with some memory kernels. For power-law kernels $t^{-\alpha}$, $\alpha\in (0, 1]$ this equation becomes the time fractional one governed by the Caputo derivatives in which the highest order is 2.To invert the solutions from the...
The methods of the quantum theory few-body scattering based on the Faddeev-Yakubovsky equations [1] in momentum and configuration space are present [1,2]. Scattering states properties of three-body resonantly interacting particles are considered and are shown to be independent of a form of two-body forces, being determined only presence of resonances. The resonances produce an effective long...
We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge from an avalanche-like dynamics of a close-packed monodisperse emulsion entering a narrow orifice. We observe formation of remarkably stable single-file granular jets which occasionally break resulting in non-Gaussian...
Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their propulsion and tumbling. Such quantum-active motion realizes a jittery motion of Dirac electrons (as in the famous Zitterbewegung): the Dirac electron is a...
One of the characteristic features of a stochastic process under resetting is that the probability density converges to a non-equilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase transition, which can be interpreted as a traveling front separating spatial regions for which the probability density has relaxed to the NESS from those...
We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical
stochastic multiplicative process for non-stationary and non-ergodic dynamics. Resetting is a sudden
interruption of a process, which consecutively renews its dynamics. We show that, although resetting
renders GBM stationary, the resulting process remains non-ergodic. Quite surprisingly, the effect
of...
Stochastic resetting is a stochastic process that is reset randomly in time to its initial position and it is used in many applications as a search strategy.
In my talk I will introduce a model whose resetting events have a random amplitude instead of a back-step to the origin [1].
In particular, we study and discuss two classes of random-amplitude stochastic resetting: independent and...
Diffusion with stochastic resetting is very popular in the study of many phenomena in physics, biophysics, chemistry. A wide diversity of random processes and restart mechanisms are widespread in nature, science and technology. As a stochastic process under resetting, we consider a subordinated Brownian process, and the restart time is exponentially distributed with constant rate. In this case...
Our guts host one of the largest interaction network, only comparable in size and complexity with the nervous and the inmune systems. The intricacy of its organization it just started to be unveiled as novel DNA technology provides data. We will describe our most recent efforts in that direction.
First passage under restart has recently emerged as a conceptual framework to study various stochastic processes under a restart mechanism. Restart has been shown to expedite the completion of many first passage processes which otherwise would take a longer time to finish. However, most of the studies so far focused on continuous time and space, while discrete processes received less...
Lévy walk is a non-Markovian anomalous diffusion model that has been widely used to describe random walks in diverse fields such as biology, quantum physics, and ecology. One of the controversial issues in these fields is that whether the given diffusion dynamics can be successfully explained by a Lévy walk or not, which becomes a nontrivial issue if diffusion data is short and noisy. In this...
Active Brownian motion with intermittent direction reversals are common in a class of bacteria including M. xanthus and P. putida. We show that, for such a motion in two dimensions, the presence of the two time scales set by the rotational diffusion constant $D_R$ and the reversal rate $\gamma$ gives rise to four distinct dynamical regimes: (I) $t\ll \min (\gamma^{-1}, D_R^{-1}),$ (II)...
We study the collective dynamics for a viscoelastic active system where the fluctuation-dissipation theorem (FDT) is violated. We set up a minimal model, where an active Brownian particle (ABP) is cross-linked to a star polymer of functionality f in a viscous fluid. The ABP has self-propelled motion from its own energy consumption and attains a strong non-Markovian anomalous motion due to the...
Guided control of molecular processes and creation of the new molecular structure is a subject of active research in molecular and chemical physics. One of the most natural and general approaches in this area is a quantum few-body theory based on the Faddeev-Yakubovsky equations [1,2]. It is based on the idea, that the possible mechanisms of occurrence of chemical reactions based on a specific...
We study the effects of nonequilibrium correlations and interactions between constituent particles of a bunch, arising under the scattering of particle stream on a cluster or finite cloud of impurities. These induced correlations and dynamical friction forces on impurities are manifested most pronouncedly in the case of collective dynamical screening effect and are enhanced in the case of a...
For each material, it is possible to individually select the optimal parameters that most accurately describe its unique nature and that influence the features that interest the user. We investigate the morphology of cross-sections of the sodium alginate membranes filled with various amount of magnetite and crosslinked using different agents. We expect that different amount of magnetite...
The main difficulties in the research of few-body problems are bounded with the really many-channels and multidimensional nature of the these problem, impossible applied many well-known theories such as adiabatic, impulse, coupled hannels, etc. For this reason we proposed new method for the investigation of the different few-body processes used the mathematically rigorous formalism based on...
We explore dynamical properties of addition-shattering kinetic equations. For a long time researchers believed that only possible asymptotic regime in closed systems was a steady state. However, stable oscillatory solutions were recently discovered in a series of numerical experiments for a closed system of kinetic equations describing simultaneous aggregation
$$
[i] \oplus...
Foam is a dispersed system consisting of a large number of bubbles, which are divided by a thin liquid film (TLF), which is made of two interacting adsorption layers. A parameter describing the stability of TLF is its thickness h, its change over time determines the drainage kinetics. The laboratory model of the mentioned situation is an air bubble, which forms TLF with the free surface of the...
Macroions are an important class of compounds with properties characteristic both of polymers and charged molecules. Most commonly, macroions are studied using only experimental techniques such as dynamic light scattering (DLS), laser Doppler velocimetry (LDV) and viscosity measurements. This allows one to evaluate their molar mass distribution, the radius of gyration, the contour length,...
Cells often adhere and migrate on curved surfaces, such as the fibers of the extra-cellular matrix (ECM), cylindrical protrusions of other cells etc. However, most of the cell biological studies examine cell migration mechanisms using cells on flat surfaces. We study the spreading and migration of a cell-like vesicle on curved surfaces, such as cylinders, sinusoidal surface etc. The vesicle is...
Colloidal droplets are used in a variety of practical applications. Some applications require particles of different sizes. These include medical diagnostic methods, the creation of photonic crystals, the formation of supraparticles, and the production of membranes for biotechnology. Series of experiments have previously shown the possibility of particle separation by their size near the...
Computer simulations are a basic tool for modeling soft matter since only a handful of models can be solved exactly or they can be treated only with phenomenological theories. For most soft interactions a standard molecular dynamic (MD) integration is a go-to tool. However, hard interactions pose a problem because of infinite forces during collisions. While there exist collision event-driven...
Phenomena of Brownian particle transport and diffusion in tilted periodic potentials are realized in many diverse systems. Superionic conductors, magnetic ratchets, optical lattices, charge-density waves, granular gases, Josephson junctions, automatic phase-lock frequency control systems are some prominent examples. These phenomena have been studied meticulously in recent decades [1]. These...
Surface roughness is an essential factor determining many surface phenomena, including adhesion, friction, wave reflection, microfluidics, electrochemistry, and wettability. It is conveniently described in terms of power spectral density of 2D height profile of the surface. I will discuss the power spectral density of particle monolayers widely used as sensors, substrates, catalysts, and...
Brownian yet non-Gaussian diffusion, characterised by a linear scaling in time of the mean squared displacement but a non-Gaussian displacement distribution is a phenomenon that has been observed in a variety of systems. In my talk, after a brief historical introduction to Brownian motion and the theory of diffusion, I will review experimental evidence and show how non-Gaussian statistics...
For two molecules to react they first have to meet. Yet, reaction times are rarely on par with the first passage times that govern such molecular encounters. A prime reason for this discrepancy is stochastic transitions between reactive and nonreactive molecular states, which results in effective gating of product formation and altered reaction kinetics. To better understand this phenomenon we...
We consider the possibility of socioeconomic collapse of the population caused by epidemics spreading. Using a simple model of negative feedback we study the dynamics of epidemic spreading in a group of agents with its mutual influence on some formal resource (economical, financial, etc). A coupling mechanism between spreading- and resource-subsystem is supposed to be governed by over-barrier...
The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate in time. We report on two findings. First, we find that, unlike rare events in many other systems, here the histories leading to a rare extinction event are...
In embryo development, cells specialize into their future role by changing their gene expression levels in response to the concentrations of competing chemical signals, called morphogens. This paradigm is known as Wolpert’s French flag model. In the mathematical modelling of these phenomena, a profound role is played by the reaction-diffusion equations involving some form of activation term...
Spinal cord development is a complex process due to the interplay of signaling molecules over varying length and time scales. Despite the intrinsic stochasticity of signaling events, the resulting pattern of gene expression domains is remarkably precise and reproducible between individuals. How this patterning precision is achieved is still poorly understood. By investigating formation of...
The shape of many biomolecules is similar to the Coxeter-Boerdijk (CB) helix, made of tetrahedra placed next to each other in such a way that the tetrahedrons are adjacent to each other with their faces. The helix CB is the solution to the maximum packing task. In the collagen helix, every third amino acid is glycine (Gly), and the entire chain contains primarily proline (Pro). Half of the Pro...
Brownian escape is key to a wealth of physico-chemical processes, including polymer folding and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show theoretically and experiment tally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates,...
I will report on a novel class of Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, the probability density for the particle spreading is Gaussian like, but the probability distribution for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behavior is not a...
In this talk I will consider persistent random walkers, also known as run and tumble particles, which are emerging as a fundamental microscopic model of active matter. I will review the properties of a single persistent walker then consider the case of two persistent random walkers that interact through an exclusion interaction. An exact expression for the stationary state of two such walkers...
Motivated by the fact that, in the literature dedicated to random walks for anomalous diffusion, it is disregarded if the walker does not move in the majority of the iterations because the most frequent jump-size is zero (i.e., the jump-size distribution is unimodal with mode located in zero) or, in opposition, if the walker always moves because the jumps with zero-size never occur (i.e., the...
The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. In this talk we will explore properties of the escape of an inertial particle driven by Lévy noise from a bounded domain, restricted by two absorbing boundaries. The properties of the mean first passage time for the integrated Ornstein--Uhlenbeck process driven by...
The dynamic critical behaviour of active matter systems is of theoretical interest in itself but also because of its relevance to swarming in biological groups, where the dynamic critical exponent can be an element to discriminate between alternative models. Here we study the crossover between the equilibrium and off-equilibrium dynamic universality classes in the Vicsek model near...
Experimental possibility of single particle tracking on molecular scales lead to a splash of interest to the precise forms of the probability density functions (PDFs) of displacements of classical particles diffusing in complex environments. This lead to the discovery of an intriguing phenomenon of Brownian yet non-Gaussian diffusion in which these PDFs are strongly non-Gaussian (at least at...
In this talk, we will go through the whole single-particle tracking procedure, from the extraction of trajectories from a microscopy video to the statistical analysis of particles dynamics. We will consider typical problems arising on the experimental as well as image processing level which lead to inaccurate, fragmented trajectories of short length, and propose several strategies for dealing...
We introduce a new method to detect transient trapping events within a single
particle trajectory, thus allowing the explicit accounting of changes in the particle’s dynamics over
time. Our method is based on new measures of a smoothed recurrence matrix. The newly introduced set of measures takes into account both the spatial and temporal structure of the trajectory. Therefore,
it is adapted...
Human body conducts electricity. It is obvious, but many important details are not. It is argued why the most popular theory of conductance in living tissue is not precise and requires a lot more of physics. The foundations of molecular theory of biopotentials are sketched out and the role of various molecular mechanisms of conductance and polarization is explained. It is shown, that there are...
Single-particle tracking routinely measures the motion of different particles in biological and soft-matter systems and often unveils characteristic deviations of the observed stochastic dynamics from standard Brownian motion. To identify the correct underlying physical mechanism often tools such as machine-learning and Bayesian inference are employed. These methods are technically involved...
Continuous-time random walk (CTRW) has found many applications in modelling complex systems dynamics, especially physical or socio-economic phenomena [1]. It is also successfully used to describe the behaviour of prices in the stock markets [2]. Spatial jumps represent price increments and inter-trade times are considered as waiting times. One of the most well-known stylized fact about...
Starting from the time behavior of the functional (NEP) arising in the variational approach to the KPZ equation, we have studied fluctuation theorems in such a system, adapting a path-integral scheme that adequately fits to this kind of study dealing with unstable systems. We show how to proceed in order to obtain detailed as well as integral fluctuation theorems, and obtain particular...
The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, and biomedical engineering. The mathematical challenge in these type of model systems is to match the solutions of the time-dependent diffusion equation in each layer, such that the boundary conditions at the interfaces between them are...
A brief survey of known analytical methods to obtain a generalization of classical Smoluchowski’s formula for the trapping reaction rate coefficient [1] including effects of diffusive interaction in domains of complex geometry [2] is given.
Then we present an analytical approach in order to investigate the time-dependent diffusive interaction between stationary uncharged sinks of different...
