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Text-to-image diffusion models have shown great potential for image editing, with techniques such as text-based and object-dragging methods emerging as key approaches. However, each of these methods has inherent limitations: text-based…
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…
Disordered metamaterials are promising for programming physical properties across diverse applications, yet their inverse design remains challenging due to the non-intuitive structure-property relationships and large design spaces. Recent…
During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the…
Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale $\ell$, where the fragments are subsequently allowed to settle under…
By means of analytical calculations and numerical simulations we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realisation is possible in…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
The interaction-site-density-fluctuation correlators, the dipole-relaxation functions, and the mean-squared displacements of a system of symmetric dumbbells of fused hard spheres are calculated for two representative elongations of the…
Molecular conformation generation, a critical aspect of computational chemistry, involves producing the three-dimensional conformer geometry for a given molecule. Generating molecular conformation via diffusion requires learning to reverse…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
We treat the problem of diffusion of solute atoms around screw dislocations. In particular, we express and solve the diffusion equation, in radial symmetry, in an elastic field of a screw dislocation subject to the flux conservation…
We consider two dimensional dispersions of droplets of isotropic phase in a liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a…
The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite…
Diffusion processes govern fundamental phenomena such as phase transformations, doping, and intercalation in van der Waals (vdW) bonded materials. Here, we quantify the diffusion dynamics of W atoms by visualizing the motion of individual…
Active particles under soft confinement such as droplets or vesicles present intriguing phenomena, as collective motion emerges alongside the deformation of the environment. A model is employed to systematically investigate droplet…
We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as…
We study the diffusion front for a natural two-dimensional model where many particles starting at the origin diffuse independently. It turns out that this model can be described using properties of near-critical percolation, and provides a…
Diffusion Transformers (DiTs) with billions of model parameters form the backbone of popular image and video generation models like DALL.E, Stable-Diffusion and SORA. Though these models are necessary in many low-latency applications like…