Main current fields of activity:

Physics of molecular and ionic liquids

The main interest in this field relates to developing methods for the prediction of thermodynamical (including the speed of sound) and transport properties of organic liquids and their mixtures in a wide range of state parameters, especially at high pressures. The key idea is to get results that are quantitatively comparable with the realistic experimental data (within their range of uncertainty) at such conditions using only the easily accessible data measured at ambient pressure conditions. The physical background consists of the theory of thermodynamic fluctuations, microscopic intermolecular oscillations, and free-volume packing. Additionally, there are works related to developing mathematical and computational approaches supporting the processing and analysis of corresponding experimental data.

Transport processes in biophysical and related complex media

This area of research operates by developing various continual (PDE-based) models and numerical simulations of stochastic systems exhibiting non-trivial transport phenomena, e.g. non-Gaussian and anomalous diffusion, in complex disordered media. The latter include soft biological tissues (e.g. the brain’s intra- and extracellular spaces), their hydrogel-based phantoms, and model systems capturing the principal geometric features of such soft matter. In addition, issues of data and image analysis aimed at analysing experimental records in this field are of interest.

Biophysics, biochemistry and mathematical methods in mycobacterial studies.

This direction includes various topics of data analysis, novel optical, including photometric and colourimetric, approaches to the quantification of antimycobacterial drug action, biomarkers’ responses to drug resistance as well as a development of new computational procedures and software for this goal. The developed physical and model approaches can also be applied to a wider range of microbiological problems.

Former fields of activity:

Modelling of ferrofluid systems

Mathematical modelling related to various problems related to the ferrofluid systems: their capturing by a non-uniform magnetic field, oscillations of ferrofluid systems and waves propagating through such media, characterization of their magnetization, magnetoviscous effects, etc.

The Continuous Wavelet Transform its applications to biophysical problems

The principal activity comprised both the development of new mathematical and computational tools aimed to improve the effectiveness of the continuous wavelet transform (preferably with the Morlet wavelet and Morlet-like complex wavelet functions) in problems of local spectral analysis, as well as an application of the developed methods to practical problems of biophysical signal and image processing in the fields of neuroscience and vascular dynamics.

Computational methods based on decompositions over localised functions

There were developed several approaches motivated by practical problems of operating with signals non-stationary in temporal or spatial domains by their reducing to a low-dimensional set of different well-localised functions such as the Gaissians, discrete wavelets, etc. Among applications, there were Raman spectroscopy (the  Cascade Hilbert-Zero Decomposition), speckle contrast imaging, the Hankel transform, etc.

Population dynamics

The studies were devoted to developing compartmental models aimed at reproducing the observed epidemic outbreaks (e.g. COVID-19, tuberculosis) and epidemic waves in low-mobile populations.