Related papers: Stress concentration for closely located inclusion…
Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…
We study asymmetric exclusion processes (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or {\em defects}. We allow weak particle nonconservation via Langmuir kinetics (LK), that are…
The rheological behaviour of dense suspensions of ideally conductive particles in the presence of both electric field and shear flow is studied using large-scale numerical simulations. Under the action of an electric field, these particles…
We consider inhomogeneous $p$-Laplace type equations of the form $-\mathrm{div}\left(a(\nabla u)\right)=f$ in a possibly anisotropic setting. Under general assumptions on the source term $f$, we obtain quantitative Sobolev regularity…
We study condensation in several particle systems related to the inclusion process. For an asymmetric one-dimensional version with closed boundary conditions and drift to the right, we show that all but a finite number of particles condense…
In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are…
We study the asymptotic behaviour of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of…
The Blackstock-Crighton equation models nonlinear acoustic wave propagation in thermo-viscous fluids. In the present work we investigate the associated inhomogeneous Dirichlet and Neumann boundary value problems in a bounded domain and…
We study how local rearrangements alter droplet stresses within flowing dense quasi-two-dimensional emulsions at area fractions $\phi \geq 0.88$. Using microscopy, we measure droplet positions while simultaneously using their deformed shape…
We extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D $\subset$ R d , d = 2 or…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
This paper unveils and investigates a novel quasi-Minnaert resonance for an elastic hard inclusion embedded in a soft homogeneous medium in the sub-wavelength regime. The quasi-Minnaert resonance consists of boundary localization and…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
Consider the standard nonparametric regression model and take as estimator the penalized least squares function. In this article, we study the trade-off between closeness to the true function and complexity penalization of the estimator,…
We propose a model for a finite-size particle detector, which allows us to derive its stress-energy tensor. This tensor is obtained from a covariant Lagrangian that describes not only the quantum field that models the detector,…
The rheological behaviors of suspension of ideally conductive particles in an electric field are studied using large-scale numerical simulations in the limit of zero-shear-rate flow. Under the action of an electric field, the particles…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
Given $n \geq 2$ and $1<p<n$, we consider the critical $p$-Laplacian equation $\Delta_p u + u^{p^*-1}=0$, which corresponds to critical points of the Sobolev inequality. Exploiting the moving planes method, it has been recently shown that…
A modified Poisson-Nernst-Planck system in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. It describes the concentrations of ions immersed in a polar solvent and the correlated electric potential due to the…
In this paper, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock waves are analyzed and identified in the flux approximation limit of Riemann solutions to the extended Chaplygin gas…