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Interlocking interfaces are commonly employed to mitigate relative sliding under shear.Indeed, Their geometry is typically selected on grounds of fabrication convenience rather than analytical optimality. There is no reason to suppose that…
We consider critical percolation on the triangular lattice in a bounded simply connected domain with boundary conditions that force an interface between two prescribed boundary points. We say the interface forms a "near-loop" when it comes…
We analyze the disturbed flow in the supersonic laminar boundary layer when local heated elements are placed on the surface. It is exhibited that these flows are described in terms of free interaction theory for specific sizes of thermal…
We study a general asymptotic behavior of critical points of a diffused interface energy with a fixed contact angle condition defined on a domain $\Omega \subset \mathbb{R}^n$. We show that the limit varifold derived from the diffused…
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random…
The turbulent/non-turbulent interface is analysed in a direct numerical simulation of a boundary layer in the range $Re_\theta=2800-6600$, with emphasis on the behaviour of the relatively large-scale fractal intermittent region. This…
We study a family of partial differential equations in the complex domain, under the action of a complex perturbation parameter $\epsilon$. We construct inner and outer solutions of the problem and relate them to asymptotic representations…
We consider the free boundary problem for a plasma--vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement, where the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not…
We study expansions near the boundary of solutions to the Dirichlet problem for the constant mean curvature equation in the hyperbolic space. With a characterization of remainders of the expansion by multiple integrals, we establish optimal…
We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…
We characterize surface-plasmon polaritons at lossy planar interfaces between one dispersive and one nondispersive linear isotropic homogeneous media, i.e., materials or metamaterials. Specifically we solve Maxwell's equations to obtain…
This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the variable magnetic field (involving a localization of the…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
We investigate on the existence of smooth complete hypersurface with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under the assumption that there exists an asymptotic subsolution. We give an…
The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic…
This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral…
The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small.
The classical Painlev\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the…
This paper concerns the asymptotic expansion of the solution of the Dirichlet-Laplace problem in a domain with small inclusions. This problem is well understood for the Neumann condition in dimension greater than two or Dirichlet condition…
We deepen the study of Dirichlet eigenvalues in bounded domains where a thin tube is attached to the boundary. As its section shrinks to a point, the problem is spectrally stable and we quantitatively investigate the rate of convergence of…