Recently a powerful example of a replicating nano-machinery entered our society. In principle it’s just a normal disease, that one attempt to model with 3 or 4 simple coupled equations with 2 important parameters: a timescale, and a replication factor (the famous $R_0$). And then one try to guess how changes in society changes $R_0$ and perhaps adopt some more or less strong lock-down...
In December 2019, a novel new strain of coronavirus (COVID-19) was identified as it spread through China and subsequently throughout the world, resulting in a pandemic. As the health systems became overwhelmed, a need arose for real-time surveillance and modelling to identify the breaking points caused by increased numbers of infections and hospitalised individuals. We combined surveillance...
Internal gravity waves play a primary role in geophysical fluids : they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. In addition to their very interesting and very unusual theoretical properties, these waves are linked to one of the important questions in the dynamics of the oceans: the cascade of mechanical energy in the...
In this presentation I will overview a recent progress in the theoretical, numerical and experimental analyses of spectral densities of individual random trajectories of a finite length. On example of a broad class of anomalous diffusions - the so-called fractional Brownian motion, I will demonstrate that one may calculate analytically the full probability density function of such random...
Brownian motion is a Gaussian process described by the central limit theorem. How- ever, exponential decays of the positional probability density function $P(X, t)$ of packets of spreading random walkers, were observed in numerous situations that include glasses, live cells, and bacteria suspensions. We show that such exponential behavior is generally valid in a large class of problems of...
Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features. The diffusion process followed by a passive tracer in prototypical active media, such as...
We derive exact expressions for the finite-time statistics of extrema (maximum and minimum) of the spatial displacement and the fluctuating entropy flow of biased random walks. Our approach captures key features of extreme events in molecular motor motion along linear filaments. For one-dimensional biased random walks, we derive exact results which tighten bounds for entropy production extrema...
In biophysics, the single-particle tracking (SPT) is broadly used to quantify the kinetics of fluorescently-labelled molecules/proteins in live cells. This powerful tool in microscopy permits ones to resolve modes of motion of individual molecules for better understanding their role in such systems. The motion is not limited to pure (Brownian motion) diffusion, but directed, confined,...
The KPZ equation is - as known - a stochastic field theory that describes the kinetic roughening of surfaces and interfaces, plus many other nonequilibrium processes that belong to its universality class. For $\lambda\neq 0$, the systems described are intrinsically unstable and "lack of stationary probability distribution". This can be readily inferred from the structure of the functional from...
We combine resetting and first-passage to define "first-passage resetting”, where a random walk is reset to a fixed position due to a first-passage event of the walk itself. On the infinite half-line, first-passage resetting of isotropic diffusion is non-stationary, in which the number of resetting events grows with time as $t^{1/2}$. We calculate the resulting spatial probability...
Stopping a process in its midst—only to start it all over again—may prolong, leave unchanged, or even shorten the time taken for its completion. Among these three possibilities, the latter is particularly interesting as it suggests that restart can be used to expedite the completion of complex processes involving strong elements of chance. This turned out to be important in computer science...
The Brownian noise in nonequilibrium systems commonly contains more outliers. In that case the noise is best described with a Levy distribution. Many systems in which there are fluctuations around a steady-state throughput can be modeled as a Levy-noise-subjected particle in a parabolic potential. We consider an overdamped Brownian particle in a parabolic potential. If the noise is Levy,...
Self-propelled motion on the water surface has fascinated scientists for almost two hundred years. There are many solid substances, such as camphor, camphene,
and phenanthroline, which can develop to the water surface as a molecular layer, evaporate to the air phase and continuously dissolve into the water phase. This surface layer decreases the water surface tension and this decrease is local...
When recording trajectories of biomolecules in crowded media, a question of fundamental interest is whether a tracked molecule interacts with other molecules or structures invisible to the observer. One also wants to know whether energy exchange occurs during such interactions since out-of-equilibrium interactions can be a sign of a specific biological function. Addressing these questions...
As the science and modern technologies are seizing the realm of nanoscale systems, characterization of composite materials with solid-fluid and fluid-fluid interfaces has become a problem of broad interdisciplinary interest. Properties of such complex systems, which vary in space over microscopic scales, shape important processes in engineering and biology. Estimation of the...
The noise driven motion in a bistable potential acts as the archetypal model of various physical phenomena. In the weak noise limit, for the overdamped particle driven by a non-equilibrium, $\alpha$-stable noise the ratio of forward and backward transition rates depends only on the width of the potential barrier separating both minima. The poster presents analytical and numerical results...
Random sequential adsorption of various shapes built of disks is studied to determine the shape, which follows to densest random packing. Using the evolutionary algorithm to sample the space of shapes, we found that independently of the number of used disks, the optimal shape tends to a triangle with rounded corners. Thus, we run the same algorithm to study packings built of rounded...
The photoluminescence degradation of the thermally evaporated Alq3 thin films can be described by a four components model based on the Kohlrausch-Williams-Watt (KWW) function. This model improved the agreement between experimental data and the theoretical fit with respect to the four components model based on “pure” exponential functions. In fact, the negative bump in PL intensity decay...
We report a new class of Smoluchowski-like equations for ballistically aggregating particles in a space-uniform system. They naturally emerge when the derivation of the aggregation equations is performed starting from the Boltzmann kinetic equation for the mass-velocity distribution functions [1]. Then the system of equations for the zero-order moments of the distribution functions – the...
We investigate the nonequilibrium energetics near a critical point of a non-linear driven oscillator immersed in an active bacterial bath. At the critical point, we reveal a scaling exponent of the average power $\langle\dot{W}\rangle\sim (D_{\rm a}/\tau)^{1/4}$ where $D_{\rm a}$ is the effective diffusivity and $\tau$ the correlation time of the bacterial bath described by Gaussian colored...
Electronic relaxation in solution is an interesting phenomenon from experimental as well as theoretical point of view. This diffusion controlled process has been theoretically modeled by using Smoluchowski equation with a position dependent sink term. The problem has been solved for different potentials and sink functions. Single state problem where Smoluchowski equation for harmonic potential...
Efficiency of search for randomly distributed targets is a prominent problem in many branches
of the sciences. For the stochastic process of Lévy walks, a specific range of optimal efficiencies
was suggested under variation of search intrinsic and extrinsic environmental parameters. We study fractional Brownian motion as a search process, which under parameter variation
generates all three...
Based on studies where a linear piezoelectric energy harvester is subjected to external random mechanical excitations modeled through Gaussian noises (white and colored), it was decided to propose a more general colored noise of the Levy α−stable type. Analytical, exact and approximate results and numerical results are presented on the characteristics of such excitations and the electrical...
Some pacemaker neurons show a depression of their mean firing rate for intermediate noise amplitudes, which reminds the response enhancement known as “stochastic resonance” (SR). Even though its analogy with SR goes no further, this phenomenon has been termed “inverse stochastic resonance” (ISR). In a recent work, the ISR phenomenon -as well as its close relative “nonstandard SR” (or more...
Recent empirical studies provide evidence that so-called social hysteresis [1] is present in animal [1, 2, 3] as well as in human societies [4, 5, 6], which would suggest that (at least some) phase transitions observed in real social systems are discontinuous. It occurs that discontinuous phase transitions are not that typical in models of opinion dynamics. Within several versions of the...
In this talk, we provide a numerical study of the recently developed generalised temperature-dependent Smoluchowski equations. To solve the new complex system, we adapt and improve the low-rank approach of solving large ODE systems. This allows us to quickly find approximate solutions for generalised systems of Smoluchowski equations even when the collision kernels change during aggregation....
We study a system where a particle scatter on the periodic Dirac delta potential. The problem is canonical i.e. it is considered during typical quantum mechanics course. There are several approaches to solve the Schrodinger equation for such a systems [1] [2]. However most of solutions rely on different matrix method. We would like to introduce new, combinatorial method by writing system of...
Cyclic, one-dimensional Kuramoto models with various types of interactions are reviewed. Ruch models are less resilient to Byzantine perturbations than a classic solution would suggest.
The combination of polymer and inorganic substance in hybrid membrane results in favourable selectivity and permeability, and consequently such membrane becomes a promising alternative to conventional membrane materials. The resulting membranes show improved chemical, mechanical, and thermal stability and hydrophilic–hydrophobic balance. The objective of this research is to determine whether...
Processes involving Brownian motion of small reactants toward much larger static particles (sinks) and subsequent trapping of these reactants by the sinks are very commonly encountered in both nature and in artificial media. Theoretically these processes are described by so-called trapping model of the irreversible bulk diffusion-controlled reactions. To avoid difficulties of classical...
We present a model of atomic force microscope indentation measurements using the finite element method. The focus is set on a thorough representation of the complex structure of an animal cell. Crucial constituent is the cell cortex — a stiff layer of cytoplasmic proteins present on the inner side of the cell membrane. It plays a vital role in the mechanical interactions between cells. In our...
In this work, we study a kinetic model of aggregation process with collisional fragmentation with use of two efficient implementations of numerical methods: direct simulation Monte Carlo and finite-difference scheme exploiting the low-rank matrix representations of the utilized kinetic coefficients. We concentrate our efforts on the analysis of the solutions for a particular class of non-local...
We address the question of energy transport in out-of-equilibrium systems. The experiment consists in two coupled granular gas Non-Equilibrium Steady State (NESS) heat baths, in which $2$ cm-scale rotors are imbedded. These Brownian-like mobiles are electro-mechanically coupled with a resistor R, allowing energy to flow between them. The mean flux is non-zero if the temperatures of the baths...
Schizophrenia is the most common form of psychotic behaviour where patients experiences hallucination, dillusion or chaotic speech. Schizophrenia is difficult to detect and easily go undetected for years. Here we propose the idea of detecting schizophrenia by a network of interacting chemical oscillators. We optimized a classifier based on six interacting oscillator using genetic algorithm and...
The endometrium is the tissue lining the uterus cavity. The most important role of this tissue is enabling the embryo to implant and providing it with good conditions for growth and development.
According to many literature reports, cell and tissue mechanical properties have a significant role in many disease states. Changes in cell properties such as elasticity are observed in the case of...
Studying the dynamics of a system at the atomic level provides important information about the behaviour of the system. For example, studying the dynamics of enzymes allows us to understand their biological function. Among the available techniques, studying the dynamics of a system by means of neutron scattering is of exceptional meaning, as neutrons scatter at the nuclei themselves.
Van...
The ‘Arcsine’ laws of Brownian particles in one dimension describe
distributions of three quantities: the time $t_m$ to reach maximum position, the
time $t_r$ spent on the positive side and the time $t_l$ of the last visit to the
origin. Interestingly, the cumulative distribution of all three quantities are the
same and given by Arcsine function. In this paper, we study distribution of
these...
The growing popularity of bibliometric indexes goes hand in hand with their critique by those who claim that scientist’s impact cannot be reduced to a single number. Some even believe that such a complex reality fails to submit to any quantitative description. We argue that neither of the two controversial extremes is true. With our new agent-based model (doi.org/10.1073/pnas.2001064117) we...
A concept of a biopolimer network immersed within an aqueous solution as addressed in terms of flexibility vs. mechanical stability criterion has been proposed. It is based on a transmission of correlated wave of (hydrogen) ions emerging from breaking in a massive way the hydrogen bonds between the biopolymers, such as hyaluronan, and their non-ideal aqueous solution’s surroundings.
Based on...
Adsorption on smooth and atomistically flat surface is well understood, while still very few works concern adsorption on rough and heterogeneous surfaces. In this study, we investigate the properties of packings of balls obtained via random sequential adsorption (RSA) on a sinusoidal substrate. Our main goal is to observe surface inhomogeneities on a scale smaller than particles' size. We...
Galilean invariance is a cornerstone of classical mechanics. It states that the equations of motion are the same in different inertial frames meaning they do not change under a Galilean transformation. Inertial frames, in turn, are reference frames describing closed systems where the frame-internal physics is not affected by frame-external forces. The description of real world systems,...
The generalized Cattaneo equation (GTE) involving memory effect is introduced by smearing the time derivatives. Consistency conditions which the smearing functions obey restrict freedom in their choice. The proposed scheme goes beyond the approach based on using fractional derivatives. I present the conditions under which solutions of the GTE can be recognized as probability distribution, i.e....
The optimal fluctuation method — essentially geometrical optics — gives a valuable insight into large deviations of constrained Brownian motion, and it achieves this purpose by simple means. I will illustrate these points by revisiting the Airy distribution - the probability distribution of the
area under a Brownian excursion - and considering some additional statistics of Brownian...
We study fluctuating dynamics of a freely movable piston that separates an infinite cylinder into two regions filled with ideal gas particles at the same pressure but different temperatures. To investigate statistical properties of the time-averaged velocity of the piston in the long-time limit, we perturbatively calculate the large deviation function of the time-averaged velocity. Then, we...
We study simple random-walk models with asymmetric time delays. Probability of a walker to move to the right or to the left depends on a difference between two state-dependent functions evaluated at states of the walker at two different times in the past. This might be seen as a model of a discrete replicator dynamics with strategy-dependent time delays. We assume hyperbolic-tangent fitness...
A feedback loop between the network topology and dynamical processes that occur between nodes is common in real-world networks. The topology impacts the evolution of node states, which in turn influence the way the structure itself is modified. This feedback is a signature of networks that are called adaptive or coevolutionary. Adaptive networks are especially relevant for social systems,...
The $q$-voter model with both attractive (roughly speaking, ferromagnetic-like) and repulsive (antiferromagnetic-like) interactions on random graphs is investigated. In this model the agent, represented by a two-state spin located in a node of a graph, with probability $1-p$ changes his/her opinion under the influence of a clique of $q$ randomly chosen neighbors and with probability $p$ acts...
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 the openness of debates. Despite increasing efforts, the dynamics leading to the emergence of these phenomena remain unclear. We propose a model that introduces the dynamics of...
Measurements of durations of nonequilibrium stochastic processes provide valuable information on underlying microscopic kinetics and energetics. Theories for corresponding experiments to date are well-developed for single-particle systems only. Little is known for interacting systems in nonequilibrium environments. We introduce and discuss a basic model for cycle processes interacting with an...
We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous time-reversal allows us to derive a tighter version of the thermodynamic uncertainty relation (TUR) involving observables evaluated in different physical...
Ergotropy is a state function of a density matrix which physical interpretation is the optimal work that can be extracted through the arbitrary unitary channel. The concept naturally appears in frameworks with implicit work reservoirs (e.g. external fields modeled by time-dependent Hamiltonians), where, in particular, the process of charging and discharging of so-called quantum batteries is...
I will describe recent progress in nonequilibrium thermodynamics based on stochastic thermodynamics and chemical reaction network theory. I will discuss the relevance of these results for biology and the many open challenges to be addressed.
A network of timed automata (NTA), inspired by Greenberg-Hastings cellular automata, can efficiently and faithfully reflects the work of the real pacemaker [1]. In this system, each automaton cyclically switches between three states of a certain length of time: from $F$ firing state of length $f$, to $R$ refractory state of length $r$ and then to $A$ activity state of length $a$, what...
Gene expression in cells is a stochastic process. Experiments have shown that noise in protein levels does not decrease to zero as mean gene expression increases. The origins of the noise floor are still debated. The goal of our study was to check how several basic mechanisms affect the noise floor level. These mechanisms are: Cell-cycle dependent gene expression, translational bursting,...
Characterization of the differences between biological and random networks can reveal the design principles that enable the robust realization of crucial biological functions including the establishment of different cell types. Previous studies, focusing on identifying topological features that are present in biological networks but not in random networks, have, however, provided few...
Ionic transport in nano- to sub-nano-scale pores is highly dependent on translocation barriers and potential wells. These features in the free-energy landscape are primarily the result of ion dehydration and electrostatic interactions. For pores in atomically thin membranes, such as graphene, other factors come into play. Ion dynamics both inside and outside the geometric volume of the pore...
Confinement occurs naturally in many physical, chemical and biological systems such as nanotubes, porous rocks or crowded living cells. The effect of confinement on the properties of simple liquids has therefore been carefully studied with experiments [1] and simulations [2,3] showing a large variety of interesting phenomena. Even for the simplest case of hard spheres confined between...
