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Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…

In this paper, we study large-time asymptotics for heat and fractional heat equations in two discrete settings: the full lattice \(\mathbb Z^d\) and finite connected subgraphs with Dirichlet boundary condition. These results provide a…

This paper deals with the time differential dual-phase-lag heat transfer models aiming, at first, to identify the eventually restrictions that make them thermodynamically consistent. At a first glance it can be observed that the capability…

The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…

One of the key objectives in investigating small stochastic systems is the development of micrometer-sized engines and the understanding of their thermodynamics. However, the primary mathematical tool used for this purpose, the overdamped…

Preparing thermal (Gibbs) states is a common task in physics and computer science. Recent algorithms mimic cooling via system-bath coupling, where the cost is determined by mixing time, akin to classical Metropolis-like algorithms. However,…

We apply the dual fermion approach with a second-order approximation to the self-energy to the Mott transition in the two-dimensional Hubbard model. The approximation captures nonlocal dynamical short-range correlations as well as several…

In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…

The Lieb-Robinson bound implies that the unitary time evolution of an operator can be restricted to an effective light cone for any Hamiltonian with short-range interactions. Here we present a very efficient renormalization group algorithm…

The low-temperature properties of the two-dimensional attractive Hubbard model are strongly influenced by the fermion density. Away from half-filling, there is a finite-temperature transition to a phase with s-wave pairing order. However,…

In this study, we present a simulation-based numerical method for solving a class of singularly perturbed second-order differential equations that come from a simplified biologically motivated model of human gait. Important physical factors…

Employing universal relations for the Onsager coefficients in the linear regime at the symmetric point of the single impurity Anderson model, we calculate the conditions under which the quantum scattering phase shift should satisfy to…

The current study aims to develop a non-intrusive Reduced Order Model (ROM) to reconstruct the full temperature field for a large-scale industrial application based on both numerical and experimental datasets. The proposed approach is…

We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary $S$ enclosing the scatterer,…

We consider the spreading of a thin two-dimensional droplet on a solid substrate. We use a model for viscous fluids where the evolution is governed by Darcy's Law. At the triple point where air and liquid meet the solid substrate, the…

In the work we consider a boundary value problem for a second order equation with variable coefficients in a multi-dimensional domain perforated by small cavities closely spaced along a given manifold. We assume that the linear sizes of all…

The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…

This paper investigates shape optimization problems in the context of heat transfer, with a focus on the stability and non-optimality of round domains under Robin boundary conditions. Using the flow approach and Steklov eigenvalue…

We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $\Lambda$-system based on electromagnetically induced transparency (EIT). In the ideal…

We present a numerical analysis of a higher order unfitted space-time Finite Element method applied to a convection-diffusion model problem posed on a moving bulk domain. The method uses isoparametric space-time mappings for the geometry…