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A simple model of an active colloid consisting of dumbbell-shaped particles that cyclically change their length without propelling themselves is proposed and analyzed. At nanoscales, it represents an idealization for bacterial cytoplasm or…
Some new unusual physical phenomena and effects associated with dielectric mesoscale particles with Mie size parameter near 10 were studied and have been discovered during the last decade. In this paper, we propose nanoholes structured…
We consider reaction-diffusion equations on the planar square lattice that admit spectrally stable planar travelling wave solutions. We show that these solutions can be continued into a branch of travelling corners. As an example, we…
We analyze scattering in a system of two (distinguishable) particles moving on the half-line $\overline{\rz}_+$ under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions…
Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While…
Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…
In this paper we provide a mathematical framework for localized plasmon resonance of nanoparticles. Using layer potential techniques associated with the full Maxwell equations, we derive small-volume expansions for the electromagnetic…
We develop a theoretical framework to describe the dielectric response of live cells in suspensions when placed in low external electric fields. The treatment takes into account the presence of the cell's membrane and of the charge movement…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
A continuum model for a population of self-propelled particles interacting through nematic alignment is derived from an individual-based model. The methodology consists of introducing a hydrodynamic scaling of the corresponding mean-field…
We present a dynamic model to study ordering of particles on arbitrary curved surfaces. Thereby the particles are represented as maxima in a density field and a surface partial differential equation for the density field is solved to the…
The behavior of colloidal particles with a hard core and a soft shell has attracted the attention for researchers in the physical-chemistry interface not only due the large number of applications, but due the unique properties of these…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
This letter introduces an analytical model that gives the asymptotic cumulative number of molecules absorbed by spherical receivers in a diffusive multiple-input multiple-output (MIMO) molecular communication (MC) system with pointwise…
The theory for the electric and magnetic fields energy absorption by small metallic particles subjected to the irradiation by ultrashort laser pulses of different duration in the region of surface plasmon excitation is developed. For the…
Recent years have seen a surge of interest in nanopores because such structures show a strong potential for characterizing nanoparticles, proteins, DNA, and even single molecules. These systems have been extensively studied in experiment as…
The increasing scientific and technological interest in nanoparticles has raised the need for fast, efficient and precise characterization techniques. Powder diffraction is a very efficient experimental method, as it is straightforward and…
We propose a model for cell polarization as a response to an external signal which results in a system of PDEs for different variants of a protein on the cell surface and interior respectively. We study stationary states of this model in…
Localized surface plasmons are charge density oscillations confined to metallic nanoparticles. Excitation of localized surface plasmons by an electromagnetic field at an incident wavelength where resonance occurs results in a strong light…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…