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Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…
A key process during animal morphogenesis is oriented tissue deformation, which is often driven by internally generated active stresses. Yet, such active oriented materials are prone to well-known instabilities, raising the question of how…
In this paper we develop a directional search-and-capture model of cytoneme-based morphogenesis. We consider a single cytoneme nucleating from a source cell and searching for a set of $N$ target cells $\Omega_k\subset \R^d$, $k=1,\ldots,N$,…
The diffusion of active microscopic organisms in complex environments plays an important role in a wide range of biological phenomena from cell colony growth to single organism transport. Here, we investigate theoretically and…
In this paper we develop an encounter-based model of reaction-subdiffusion in a domain $\Omega$ with a partially absorbing interior trap $\calU\subset \Omega$. We assume that the particle can freely enter and exit $\calU$, but is only…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
We consider aspects of the population dynamics, inside a bound domain, of diffusing agents carrying an attribute which is stochastically destroyed upon contact with the boundary. The normal mode analysis of the relevant Helmholtz equation…
Agglomeration processes occur in many different realms of science such as colloid and aerosol formation or formation of bacterial colonies. We study the influence of primary particle density in agglomerate structure using…
We present a theory of pattern formation in growing domains inspired by biological examples of tissue development. Gradients of signaling molecules regulate growth, while growth changes these graded chemical patterns by dilution and…
Generative models hold the promise of significantly expediting the materials design process when compared to traditional human-guided or rule-based methodologies. However, effectively generating high-quality periodic structures of materials…
Tissue deformations during morphogenesis can be active, driven by internal processes, or passive, resulting from stresses applied at their boundaries. Here, we introduce the Drosophila hindgut primordium as a model for studying…
We investigate the influence of multiscale aggregation and deposition on the colloidal dynamics in a saturated porous medium. At the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal…
Machine learning has demonstrated remarkable promise for solving the trajectory generation problem and in paving the way for online use of trajectory optimization for resource-constrained spacecraft. However, a key shortcoming in current…
Artificial intelligence research to a great degree focuses on the brain and behaviors that the brain generates. But the brain, an extremely complex structure resulting from millions of years of evolution, can be viewed as a solution to…
We present experimental results for spherical particles rising and settling in a still fluid. Imposing a well-controlled center of mass offset enables us to vary the rotational dynamics selectively by introducing an intrinsic rotational…
We study theoretically the mode conversion and the associated resonant absorption of p-polarized electromagnetic waves into longitudinal plasma oscillations in cold, unmagnetized and stratified plasmas with periodic spatial density…
Diffusion Models generate data by reversing a stochastic diffusion process, progressively transforming noise into structured samples drawn from a target distribution. Recent theoretical work has shown that this backward dynamics can undergo…
The time dependency of the diffusion coefficient of particles in porous media is an efficient probe of their geometry. The analysis of this quantity, measured e.g. by nuclear magnetic resonance (PGSE-NMR), can provide rich information…