Related papers: Surveying Diffusion in Complex Geometries. An Essa…
Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of…
When the motion of a motile cell is observed closely, it appears erratic, and yet the combination of nonequilibrium forces and surfaces can produce striking examples of organization in microbial systems. While most of our current…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…
Molecular dynamics (MD) has long been the de facto choice for simulating complex atomistic systems from first principles. Recently deep learning models become a popular way to accelerate MD. Notwithstanding, existing models depend on…
Routing choices of walking pedestrians in geometrically complex environments are regulated by the interplay of a multitude of factors such as local crowding, (estimated) time to destination, (perceived) comfort. As individual choices…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview…
In both nature and engineering, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We…
We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at…
Experiments have shown that self-propelled particles can slide along the surface of a circular obstacle without becoming trapped over long times. Using simulations and theory, we study the impact of boundary conditions on the diffusive…
Controllable spherical panoramic image generation holds substantial applicative potential across a variety of domains.However, it remains a challenging task due to the inherent spherical distortion and geometry characteristics, resulting in…
We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is…
Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientation and speed fluctuations. This interplay of…
A fundamental challenge in text-to-3D face generation is achieving high-quality geometry. The core difficulty lies in the arbitrary and intricate distribution of vertices in 3D space, making it challenging for existing models to establish…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…