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Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address…
In the paper, we discuss the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. In the previous works it is shown that in these models of classical…
This work assesses Lagrangian droplet evaporation models frequently used in spray combustion simulations, with the purpose of identifying the influence of modeling decisions on the single droplet behavior. Besides more simplistic models,…
Three-dimensional, time-dependent direct simulations of step emulsification micro-devices highlight two essential mechanisms for droplet formation: first, the onset of an adverse pressure gradient driving a back-flow of the continuous phase…
The fundamental processes of biological development are governed by multiple signaling molecules that create non-uniform concentration profiles known as morphogen gradients. It is widely believed that the establishment of morphogen…
We extract electron transport properties from atomistic simulations of a two-component plasma, by mapping the long-wavelength behaviour to a two-fluid model. The mapping procedure is performed via Markov Chain Monte Carlo sampling over…
We study a pattern forming instability in a laser driven optically thick cloud of cold two-level atoms with a planar feedback mirror. A theoretical model is developed, enabling a full analysis of transverse patterns in a medium with…
Precipitation patterns generated by A^{+}+B^{-} --> C type reaction-diffusion processes are studied. It is shown both theoretically and experimentally that the patterns can be controlled by an appropriately designed, time-dependent electric…
We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is…
This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of…
We present herein the derivation of a lubrication-mediated (LM) quasi-potential model for droplet rebounds off deep liquid baths, assuming the presence of a persistent dynamic air layer which acts as a lubricating pressure transfer. We then…
We present results of direct numerical simulation of incompressible fluid flow over a thick bed of mobile, spherically-shaped particles. The algorithm is based upon the immersed boundary technique for fluid-solid coupling and uses a…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…
We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
Modeling is a very important tool for scientific processes, requiring long-term dedication, desire, and continuous reflection. In this work, we discuss several aspects of modeling, and the reasons for doing it. We discuss two major modeling…
From infiltration of water into the soil during rainstorms to seasonal plant growth and death, the ecohydrological processes that are thought to be relevant to the formation of banded vegetation patterns in drylands occur across multiple…