Presentation materials
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...
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...
