Related papers: An energy-based coupling approach to nonlocal inte…
The interaction between thin structures and incompressible Newtonian fluids is ubiquitous both in nature and in industrial applications. In this paper we present an isogeometric formulation of such problems which exploits a boundary…
In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connection, we hope to promote the cross fertilization of ideas…
Cell-cell adhesion is an inherently nonlocal phenomenon. Numerous partial differential equation models with nonlocal term have been recently presented to describe this phenomenon, yet the mathematical properties of nonlocal adhesion model…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
Non-locality is being intensively studied in various PDE-contexts and in variational problems. The numerical approximation also looks challenging, as well as the application of these models to Continuum Mechanics and Image Analysis, among…
A novel approach is being developed to introduce a parallel asynchronous implementation of non-intrusive global-local coupling. This study examines scenarios involving numerous patches, including those covering the entire structure. By…
We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, discrete, and interface contributions. Our main estimate…
Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so…
Models in which dark energy interacts with dark matter have been proposed in the literature to help explain why dark energy should only come to dominate in recent times. In this paper, we present a dynamical framework to calculate…
The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…
This paper deals with the large-time analysis of a PDE system modelling contact with adhesion, in the case when thermal effects are taken into account. The phenomenon of adhesive contact is described in terms of phase transitions for a…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
Dark energy might directly interact with cold dark matter. However, in such a scenario, an early-time large-scale instability occurs occasionally, which may be due to the incorrect treatment for the pressure perturbation of dark energy as a…
Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…
In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven…
We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…
We investigate a cosmological model in which dark energy, represented by a quintessential scalar field, is directly coupled to a dark-matter perfect fluid. We are interested in solutions of cosmological relevance, namely those for which a…
Building energy modeling plays a vital role in optimizing the operation of building energy systems by providing accurate predictions of the building's real-world conditions. In this context, various techniques have been explored, ranging…