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The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is…
We investigate the dynamics of a colony of crawling, proliferating cells with a minimal, mechanical cell model. The cells consist of two disks, modelling the cell body and a pseudopod, connected by a finite extensible spring. The cells…
Cellular life requires the presence of a set of biochemical mechanisms in order to maintain a predictable process of growth and division. Several attempts have been made towards the building of minimal protocells from a top-down approach,…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
We define a continuum percolation model that provides a collection of random ellipses on the plane and study the behavior of the covered set and the vacant set, the one obtained by removing all ellipses. Our model generalizes a construction…
In a uniform radio-frequency (RF) plasma between a large electrode pair, the addition of an axial magnetic field induces diverse longitudinal filaments. To reveal its pattern dynamics, we conduct two-dimensional (2D) Particle-In-Cell (PIC)…
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…
Understanding the spatial organisation of the genome in the cell nucleus is one of the current grand challenges in biophysics. Certain biochemical -- or epigenetic -- marks that are deposited along the genome are thought to play an…
In photosynthetic organisms, the energy of light during illumination is absorbed by the antenna complexes, which is transmitted by excitons and is either absorbed by the reaction centers (RCs), which have been closed in this way, or emitted…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems raging from the brain to high-order social networks.…
Diffraction of elastic waves is considered for a system consisting of two parallel arrays of thin (subwavelength) cylinders that are arranged periodically. The embedding media supports waves with all polarizations, one longitudinal and two…
Radiative corrections to electronic structure are characterized by perturbative expansions in $\alpha$ and $Z\alpha$, where $\alpha$ is the fine-structure constant and $Z$ is the nuclear charge. A formulation of the leading-order…
Quantifying the outcomes of cells collisions is a crucial step in building the foundations of a kinetic theory of living matter. Here, we develop a mechanical theory of such collisions by first representing individual cells as extended…
The dielectric behavior of a linear cluster of two or more living cells connected by tight junctions is analyzed using a spectral method. The polarizability of this system is obtained as an expansion over the eigenmodes of the linear…
This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation…
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
Despite substantial research into the biological basis of memory, the precise mechanisms by which experiences are encoded, stored, and retrieved in the brain remain incompletely understood. A growing body of evidence supports the engram…
During developmental processes such as embryogenesis, how a group of cells fold into specific structures, is a central question in biology that defines how living organisms form. Establishing tissue-level morphology critically relies on how…