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We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on…
The problem of constructing an exact solution of singular integro-differential equations related to problems of adhesive interaction between elastic thin semi-infinite homogeneous patch and elastic plate is investigated. For the patch…
Two model problems of an elastic wedge with an internal and edge crack are analyzed. The problem of an internal crack reduces to an order-4 vector Riemann-Hilbert problem whose matrix kernel entries are meromorphic functions and have…
The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…
This work focuses on an efficient stress recovery procedure for laminated composite curved structures, which relies on Isogeometric Analysis (IGA) and equilibrium. Using a single element through the thickness in combination with a…
We present a closed description of the charge carrier injection process from a conductor into an insulator. Common injection models are based on single electron descriptions, being problematic especially once the amount of charge-carriers…
The design of the performance index, also referred to as cost or reward shaping, is central to both optimal control and reinforcement learning, as it directly determines the behaviors, trade-offs, and objectives that the resulting control…
Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier-Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the…
We consider, in any dimension, the constrained lattice gas introduced by Rossi et al., which is an exclusion process on a d-dimensional lattice following the additional constraint that only particles with at least one occupied neighbour can…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
At low temperature, T -> 0, the yield stress of a perfect crystal is equal to its so called theoretical strength. The yield stress of non-perfect crystals is controlled by the stress threshold of dislocation mobility. A non-crystalline…
This paper develops divergence-free mixed finite element methods for the Stokes equation. Using H(div)-conforming velocities and discontinuous pressures ensures the inf-sup condition for the velocity--pressure pair and yields pointwise…
Thermal fluctuations, geometric exclusion, and external driving all govern the mechanical response of dense particulate suspensions. Here, we measure the stress-strain response of quasi-two-dimensional flow-stabilized microsphere heaps in a…
We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion…
In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. In the present work, we consider a very…
We investigate the electronic structure induced by wedge-disclinations (conical singularities) in a honeycomb lattice model realizing Chern numbers $\gamma=\pm 1$. We establish a correspondence between the bound state of (i) an isolated…
We consider the isentropic compressible Euler equations in the half-line which govern the motion of gaseous fluids in contact with stationary vacuum boundary. We construct a large class of solutions that are initially smooth and…
This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…
This paper extends our earlier work [arXiv:2309.13595] on the $L^p$ approximation of the shape tensor by Laurain and Sturm. In particular, it is shown that the weighted $L^p$ distance to an affine space of admissible symmetric shape tensors…
Consider the diffusive Hamilton-Jacobi equation $$u_t-\Delta u=|\nabla u|^p+h(x)\ \ \text{ in } \Omega\times(0,T)$$ with Dirichlet conditions, which arises in stochastic control problems as well as in KPZ type models. We study the question…