We study a system which consists of two media divided by a thin partially permeable membrane. One of these media is diffusive. The second one is subdiffusive. Moreover, transported particles can be absorbed in the subdiffusive medium. In order to find methematical description of a transport process we use a new, universal model that is presented in details in \textit{T. Koszto\l{}owicz, Phys....
We investigate an adaptive network model describing human smoking behavior incorporating the social processes homophily and induction introduced by Schleussner et al. (Sci Rep 2016). Upon social transition, the smoking prevalence in the model decreases, leaving remaining smokers clustered and marginalized in the network. Intriguingly, the model qualitatively resembles empirical findings....
Continuoustime random walk (CTRW) is a stochastic process with continuous and fluctuating waiting (interevent) time. It was first introduced to physics by Montroll and Weiss. Since then it has been used in many areas of science [1]. CTRW is also successfully applied in econophysics [2], for example, it is used to describe stock price dynamics. We can consider the stock price as the price of...
Using a new method, time evolution of the probability distribution of the number of particle passes through a thin membrane will be derived. As far as we know, a distribution of the number of particle's passes between selected points of the system (membrane surfaces) have not been determined yet.
We assume that a passage of a particle through the membrane may cause a change in particle's state...
Hard objects can behave differently from the objects/particles that are interacting through soft potential. The main difference is that soft interacting particles can store potential energy accomodating at the same time their positions. Hard interacting particles possess no potential energy and their arrangement is fully according to the entropic and geometry conditions. The excluded volume...
The structural relaxation of dense liquids displays a drastic slowing down upon compression or cooling, a phenomenon which is commonly identified with the glass transition. Many dynamical properties of the glass transition in bulk liquids have been successfully described by modecoupling theory (MCT [1]). Even more involved is the description of confined liquids since they already exhibit...
Technological applications of liquid crystals (LC) have been for many decades a continous driving force for investigating properties of this fascinating state of matter by theorists as well as by experimentalists. Still many questions about LC properties need to be answered. Special attention is paid to the optical characteristics of liquid crystalline thin films. In the current...
This work aims to create prototype structures of hybrid polymeric membranes with the desired quantity, size and distribution of obstacles, which corresponds to the given amount of magnetite in the hybrid alginate membrane. The membrane is represented by a black and white image where the black regions corresponds to polymer matrix and are available for diffusive particles and the white ones are...
Bentshaped particles gain more and more interest nowadays
due to the formation of novel liquid crystalline structures. Here, we investigate impact of molecular shape and conformational degrees of freedom on stabilization of nematic phases in two dimensional systems. Analyzed particles are composed of two and three arms built of either hard disks or hard needles. Additionally, they have...
Biological molecular machines are enzymes that simultaneously catalyze
two processes, one donating free energy and second accepting it. Recent
studies show that most native protein enzymes have a rich stochastic dynamics
that often manifests in fluctuating rates of the calatyzed processes and
the presence of shortterm memory resulting from transient nonergodicity.
For such dynamics, we prove...
We report on a new kinetic equation for an auxiliary twoparticle distribution function
$f({\bf k_1}, {\bf v_1}, {\bf k_2}, {\bf v_2}, t)$.
Its general form reads
\begin{equation}
\begin{array}{l}
\displaystyle
\left(\frac{\partial}{\partial t} \, + \, {\rm i} \, {\bf k_1} {v_1} \, + \, {\rm i} \ {\bf k_2} {v_2} \right)
f({\bf k_1}, {\bf v_1}, {\bf k_2}, {\bf v_2}, t) \, = ...
Selective imaging is a challenge in Biology. OutofPhase Imaging after Optical Modulation (OPIOM) [1] exploits reversibly photoswitchable fluorophores to selectively detect a target species in the presence of spectrally interfering fluorescent species. The method combines optimized periodic illumination and phasesensitive detection, which matches the dynamics of the targeted photoreactive...
Binary mixtures, i.e. the systems composed of two different species of particles, exhibit a huge variety of dynamical modes and phase transitions. This includes demixing effects and several combinations of mobility and arrest, e.g. the collective critical slowdown of the bigger particles mediated by the presence of the smaller molecules. It was recently realized that the interactions in such...
We develop an extended multifractal analysis based on the LegendreFenchel transform (some times referred to as Legendre multibranched one) rather than the routinely used canonical Legendre transform. In our variant of coarsegraining preprocessing, the local detrending of time series has been replaced by an appropriate averaging over days combined with properlysuited detrending on a daily...
Stationary states for a particle moving in a singlewell, steeper than parabolic, potential driven by Lévy noise can be bimodal. We explore in details conditions required to induce multimodal stationary states with a modality higher than two and provide phenomenological arguments determining necessary conditions for emergence of stationary states with an anticipated multimodality. The poster...
Reaction currents in chemical networks can decrease when increasing their driving affinities. Such negative differential response (NDR), a hallmark of nonequilibrium physics, is found in reaction schemes of major biological relevance, namely, substrate inhibition and autocatalysis. We display it by deriving the full counting statistics of two minimal representative models by large deviation...
The FokkerPlanck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the FokkerPlanck equation picks up a tensorial coefficient, which reflects the anisotropy of the particle motion. This tensor, however, can not be interpreted as a diffusion tensor; there are antisymmetric...
Polymers are a group of molecules that presents various physicochemical properties. Some of these properties result from specific chemical groups in the polymer. Another properties are universal, they result from the fact of the chain structure of the molecule. To describe these universal properties of polymers, there are coarsegrained models, which represents this molecule as a chain. Such...
Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for the dynamics of an asset due to the fattailed properties found in empirical distributions of the asset returns. To capture this phenomenon three approaches have been...
Anderson localization (AL), the absence of diffusion, is one of the most famous phenomena occurring in disordered systems. Since the original Anderson’s paper [1], AL was thoroughly investigated theoretically and observed in numerous experimental setups including light, classical waves and quantum systems. Presence of localization leads to many surprising phenomena. One of them is the *quantum...
Random sequential adsorption (RSA) is a protocol to generate random packing in the following way:

a virtual particle position and orientation in case of anisotropic shapes is selected randomly inside the packing;

if the virtual particle does not intersect with any object on the plane, it is added to the packing. Otherwise, it is removed from the system and abandoned.
One of is's key...
The role of thermal fluctuations is crucial in certain important biological processes, such as, transcription, translation, replication mechanisms, as they take place in very small scale systems.
We propose paradigmatic models for the transcription, i.e., DNA to mRNA formation and DNA replication to see the effect of the environment on these important biological processes. We consider these...
The problem of packing objects into limited space has an ancient history and is still of great importance from both utilitarian and fundamental point of view. Threedimensional random packings are especially important due to their potential application in a granular matter and life sciences, while twodimensional packings can, for example, model adsorption monolayers. These packings are...
In this presentation, we discuss the possible generalizations of the social influence with recurrent mobility (SIRM) model [Phys. Rev. Lett. 112, 158701 (2014)]. Although the SIRM model worked approximately satisfying when U.S. election was modeled, it has its limits: it has been developed only for twoparty systems and can lead to unphysical behavior when one of the parties has extreme vote...
When studying packings of objects one observes the depencence of packing density on various factors, the symmetry of particles included. For example, the packings of ellipsoids can be denser than the packings of spheres, which represents the general trend in a transition between two continuous symmetries. Here, our main goal was to check, whether a similar effect can be observed for shapes of...
I will address the problem of computing dynamic correlation functions in Integrable QFT’s at finite temperature and out of equilibrium. The approach is based on the formfactor expansion of the correlation functions. Thanks to the integrability, the formfactors at finite temperature can be effectively bootstrapped, through a procedure generalizing the Smirnov’s bootstrap program for vacuum...
Dispersive transport of photoinjected carriers in arrays of vertically aligned fractal nanowires is considered. The conditions of the timeofflight experiment are assumed. Photocurrent response after injection of nonequilibrium carriers by the short light pulse is studied. Carriers are injected instantaneously from the left side of the array, then, move along wires under the action of a...
We are investigating a conformational entropy of mucin protein to discern its correlation with the viscoelastic properties of the biopolymer system in various thermodynamic conditions. The mucin is believed to be responsible for gel formation inside synovial fluid of joints system which is very sensitive on both temperature and concentration changes[1]. The conformational entropy is computed...
Twistbend nematic $\left(N_\text{TB}\right)$ [1, 2] is a fifth member of the nematic family, beyond uniaxial $\left(N_\text{U}\right)$ and biaxial $\left(N_\text{B}\right)$ nematics, cholesteric $\left(N^{\ast}\right)$ and blue phases $\left(\text{BP}\right)$. Its uniqueness arises from a double degenerate groundstate (ambidextrous chirality) with a periodically modulated heliconical...