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We derive the low-energy effective action for three-dimensional superfluid Fermi systems in the strong-coupling limit, where superfluidity originates from Bose-Einstein condensation of composite bosons. Taking into account density and…
Using the Fundamental-Measure Density Functional Theory, we have studied theoretically the phase behavior of extremely confined mixtures of parallel hard squares in slit geometry. The pore width is chosen such that configurations consisting…
Inspired by recent work on learning with distribution shift, we give a general outlier removal algorithm called iterative polynomial filtering and show a number of striking applications for supervised learning with contamination: (1) We…
Our focus is on simulating the dynamics of non-interacting particles including the effects of an external potential, which, under certain assumptions, can be formally described by the Dean-Kawasaki equation. The Dean-Kawasaki equation can…
Controlled activity of active entities interacting with a passive environment can generate emergent system-level phenomena, positioning such systems as promising platforms for potential downstream applications in targeted drug delivery,…
High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped…
We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…
We study the $\nabla \phi$ model with uniformly convex Hamiltonian $\mathcal{H} (\phi) := \sum V(\nabla \phi)$ and prove a quantitative rate of convergence for the finite-volume surface tension as well as a quantitative rate estimate for…
A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…
A new consistent, spatially adaptive, smoothed particle hydrodynamics (SPH) method for Fluid-Structure Interactions (FSI) is presented. The method combines several attributes that have not been simultaneously satisfied by other SPH methods.…
We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong…
This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally…
Buoyancy effects in unstably stratified mixing layers express themselves through gravity currents of heavy fluid which propagate in an ambient lighter fluid. These currents are encountered in numerous geophysical flows, industrial safety…
We consider exclusion processes with two types of particles which compete strongly with each other. In particular, we focus on the case where one species does not diffuse at all and killing rates of two species are given by monomials with…
The mechanical tension at the interface of motility-induced phase separating active Brownian particles (ABPs) remains an open question. Here, we determine the surface tension by analyzing the spatial distribution of forces at the molecular…
We investigate excluded-volume effects in a bidisperse colloidal suspension near a flexible interface. Inspired by a recent experiment by Dinsmore et al. (Phys. Rev, Lett. 80, 409 (1998)), we study the adsorption of a mesoscopic bead on the…
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive…
The physics of many materials is modeled by quantum many-body systems with local interactions. If the model of the system is sensitive to noise from the environment, or small perturbations to the original interactions, it will not properly…
We investigate four-fermion interactions with $N$-component fermion in Einstein universe for arbitrary space-time dimensions ($2 \leq D<4$). It is found that the effective potential for composite operator $\overline{\psi}\psi$ is calculable…
We investigate the steady-state organisation of active particles residing on an interface. Particle activity induces interface deformations, while the local shape of the interface guides particle movement. We consider multiple species of…