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Physiological whole-body models are valuable tools for the development of novel drugs where understanding the system aspects is important. This paper presents a generalized model that encapsulates the structure and flow of whole-body human…
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
Hypoxia-activated prodrugs offer a promising strategy for targeting oxygen-deficient regions in solid tumors, which are often resistant to conventional therapies. However, modeling their behavior is challenging because of the complex…
In this thesis, we develop multiscale models for particle simulations in population dynamics. These models are characterised by prescribing particle motion on two spatial scales: microscopic and macroscopic. At the microscopic level, each…
Experiments on carrier recombination in two-dimensional organic structures are often interpreted in the frame of the Langevin model with taking into account only the drift of the charge carriers in their mutual electric field. While this…
We present a non-diagonal phase field model for phase transformations with unequal but finite diffusivities in the two phases. This model allows to recover the desired boundary conditions at the interface, and especially the elimination of…
Mass transfer of gaseous components from rising bubbles to the ambient liquid can be described based on continuum mechanical sharp-interface balances of mass, momentum and species mass. In this context, the standard model consists of the…
We revisit the sharp-interface continuum thermodynamics of two-phase multicomponent fluid systems, accounting for partial mass and partial momentum balances both in the bulk phases and on the interface. This allows to describe the transfer…
Molecular communication (MC) is a new communication engineering paradigm where molecules are employed as information carriers. MC systems are expected to enable new revolutionary applications such as sensing of target substances in…
We study the problem of the motion of substance in a channel of a network for the case of channel having two arms. Stationary regime of the flow of the substance is considered. Analytical relationships for the distribution of the substance…
In this work, we present a phase-field model for tumour growth, where a diffuse interface separates a tumour from the surrounding host tissue. In our model, we consider transport processes by an internal, non-solenoidal velocity field. We…
Predicting segregation of granular materials composed of different-sized particles is a challenging problem. In this paper, we develop and implement a theoretical model that captures the interplay between advection, segregation, and…
Recent years have seen significant progress in human image generation, particularly with the advancements in diffusion models. However, existing diffusion methods encounter challenges when producing consistent hand anatomy and the generated…
In this contribution, we introduce a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes. It relies on the stationary action principle and interface geometric variables. The main ideas…
We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For…
A diffusion-based molecular communication system has two major components: the diffusion in the medium, and the ligand-reception. Information bits, encoded in the time variations of the concentration of molecules, are conveyed to the…
In this work, we propose a novel transport model for soluble surfactants in two-phase flows. In a two-phase flow, the soluble surfactants can adsorb/desorb from/into the bulk of any of the phases to the interface and can modify the…