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We derive a closed-form, analytical expression for the spectrum of long-wavelength density perturbations in inflationary models with two (or more) inflaton degrees of freedom that is valid in the slow-roll approximation. We illustrate…
The electrical {\em dc}-conductivity of disordered, non-interacting electrons is calculated in the asymptotic limit of high lattice dimensions $d\to \infty$. To go beyond the lowest-order contribution in the expansion parameter $1/d$ of the…
This paper studies minimax optimization problems $\min_x \max_y f(x,y)$, where $f(x,y)$ is $m_x$-strongly convex with respect to $x$, $m_y$-strongly concave with respect to $y$ and $(L_x,L_{xy},L_y)$-smooth. Zhang et al. provided the…
This paper studies in a quantitatively precise manner the field enhancement due to presence of an emitter of the dipole type near the bow-tie structure of perfectly conducting inclusions in the two-dimensional space. We put special emphasis…
We consider the dilute Fermi gas in three dimensions interacting through a positive, radially symmetric, compactly supported and integrable potential in the thermodynamic limit. We establish a second order lower bound for the ground state…
This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a…
A solution to the ultra-relativistic strong explosion problem with a non-power law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power-law with small, spherically…
We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
In this paper, we study the interaction between two closely spaced rigid inclusions suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between…
We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the…
In this paper, we consider very high concentration of electric field in between infinitely many circular perfect conductors arranged closely in two rows. In stiff fiber-reinforced composite, shear stress concentrations occur in between…
When perfectly conducting or insulating inclusions are closely located, stress which is the gradient of the solution to the conductivity equation can be arbitrarily large as the distance between two inclusions tends to zero. It is important…
We present a simulation method to study electrolyte solutions in a dielectric slab geometry using a modified 3D Ewald summation. The method is fast and easy to implement, allowing us to rapidly resum an infinite series of image charges. In…
The present study deals with total internal reflection of a plane electromagnetic wave at an infinite plane boundary between a transparent medium and an amplifying or attenuating lower-index medium. Solutions of Maxwell's equations are…
We establish upper bounds on the blow-up rate of the gradients of solutions of the Lam\'{e} system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients…
The complex physics and numerous failure modes of structural impact creates challenges when designing for impact resistance. While simple geometries of layered material are conventional, advances in 3D printing and additive manufacturing…
The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this…
The electric double layer structure in an electrolyte close to a solid substrate near the three-phase contact line is approximated by considering the linearized Poisson-Boltzmann equation in a wedge geometry. The mathematical approach…
The idea of replacing an edgy perfectly conducting boundary by the corresponding interface filled with a dielectric material of extreme complex permittivities, is examined in the present work. A semi-analytical solution to the corresponding…