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In this paper we argue that the pattern of cell movements in the morphogenetic process known as convergent extension can be understood as a energy minimization process, provided the cell-cell adhesive energy has a certain kind of…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
We investigate the obstructed motion of tracer (test) particles in crowded environments by carrying simulations of two-dimensional Gaussian random walk in model fibrinogen monolayers of different orientational ordering. The fibrinogen…
The ability of many living systems to actively self-propel underlies critical biomedical, environmental, and industrial processes. While such active transport is well-studied in uniform settings, environmental complexities such as geometric…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and…
Run-and-tumble processes successfully model several living systems. While studies have typically focused on particles with isotropic tumbles, recent examples exhibit "tumble-turns", in which particles undergo 90{\deg} tumbles and so possess…
Locally broken symmetries are used across fields to transport matter, particles and information in preferential directions. Beyond local mechanisms, spatially distributed nonlinearities in crystalline media have enabled non-reciprocal…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Important cellular processes, such as cell motility and cell division, are coordinated by cell polarity, which is determined by the non-uniform distribution of certain proteins. Such protein patterns form via an interplay of protein…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
The conventional assumption that the self-diffusion coefficient of a small tracer can be obtained by a local and instantaneous application of Einstein's relation in a temperature field with spatial and temporal heterogeneity is revisited.…
In this work we upscale a prototypical kinetic transport equation which models a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction and the magnitude of the cell velocity. The…
Intracellular components explore the cytoplasm via active motor-driven transport in conjunction with passive diffusion. We model the motion of organelles in narrow tubular cells using analytical techniques and numerical simulations to study…
Suspensions of swimming micro-organisms provide examples of coordinated active dynamics. That has stimulated the study of a phenomenological theory combining synchronization and polar order in active matter. Here, we consider another…
Cell migration is closely linked to cell shape, yet cell size is often assumed to remain constant. This assumption is challenged by recent experiments showing that cells undergo volume loss during spreading and swelling upon activation,…
The motility of eukaryotic cells is strongly influenced by their environment, with confined cells often developing qualitatively different motility patterns from those migrating on simple two-dimensional substrates. Recent experiments,…
The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in…
This paper extends a recently introduced theory describing particle transport for random statistically homogeneous systems in which the distribution function p(s) for chord lengths between scattering centers is non-exponential. Here, we…
Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic geometry. These objects support novel types of mesoscopic defects - discontinuity lines for the second derivative and branch points -…