相关论文: Strictly convex corners scatter
The principle existence theorem (i.e. Theorem 1) of "Existence and Behavior of the Radial Limits of a Bounded Capillary Surface at a Corner" (Pacific J. Math. Vol. 176, No. 1 (1996), 165-194) is extended to the case of a contact angle…
We show that a Riemannian 3-manifold with nonnegative scalar curvature and mean-convex boundary is flat if it contains an absolutely area-minimizing (in the free boundary sense) half-cylinder or strip. Analogous results also hold for a…
Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…
In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $\phi$ to…
We consider the elastic scattering of two open strings living on two D-branes separated by a distance $r$. We compute the high-energy behavior of the amplitude, to leading order in string coupling, as a function of the scattering angle…
In a recent paper, Pelaez and Yndurain evaluate some of the low energy observables of pi pi scattering and obtain flat disagreement with our earlier results. The authors work with unsubtracted dispersion relations, so that their results are…
The total scattering and the extinction efficiencies of a nihility cylinder of infinite length and circular cross--section are identical and independent of the polarization state of a normally incident plane wave.
We provide an exact solution of the scattering problem for the potentials of the form $v(x,y)=\chi_a(x)[v_0(x)+ v_1(x)e^{i\alpha y}]$, where $\chi_a(x):=1$ for $x\in[0,a]$, $\chi_a(x):=0$ for $x\notin[0,a]$, $v_j(x)$ are real or…
We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to $L^{3/2}$ in space. The exponent…
For the spatial generalized $N$-centre problem $$ \ddot{x} = -\sum_{i=1}^{N} \frac{m_i (x - c_i)}{\vert x - c_i \vert^{\alpha+2}},\qquad x \in \mathbb{R}^3 \setminus \{c_1,\dots,c_N \}, $$ where $m_i > 0$ and $\alpha \in [1,2)$, we prove…
We prove existence of partitions of an open set $\Omega$ with a given number of phases, which minimize the sum of the fractional perimeters of all the phases, with Dirichlet boundary conditions. In two dimensions we show that, if the…
Consider an $(n+1)$-dimensional circular cone with opening angle $\alpha \in (0,\pi)$. Using a free-boundary adaptation of the classical calibration method, we prove that, for $n \geq 4$, there exists a threshold $\bar{\alpha}(n) \in…
This article is concerned with the time-harmonic electromagnetic (EM) scattering from a generic inhomogeneous medium. It is shown that if there is a right corner on the support of the medium, then it scatters every pair of incident EM…
We explore convex shapes $S$ in the Euclidean plane which have the following property: there is a circle $C$ such that the angle between the two tangents from any point of $C$ to $S$ is constant equal to $\alpha$. A dynamical formulation…
We consider scattering of a three-dimensional particle on a finite family of delta potentials. For some parameter values the scattering wavenctions exhibit nodal lines in the form of closed loops, which may touch but do not entangle. The…
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…
Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. In the absence of spin-orbit scattering, the conductivity shows universal weak localization correction. In the presence of…
General interest in a precise determination of the threshold pi-pi amplitudes has recently increased markedly due to a controversy regarding the size of <0|qbar q|0>, the scalar quark condensate. This paper examines the current experimental…
The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero…
It is shown that the supports of measures minimizing weakly repulsive energies on Riemannian manifolds with sectional curvature bounded below do not have concentration points. This extends the results of Bj\"orck and Carrillo, Figalli, and…