Related papers: Regularity results for transmission problems with …
One of the major problems in the theory of the porous medium equation is the regularity of the solutions and the free boundaries. Here we assume flatness of the solution in space time cylinder and derive smoothness of the interface after a…
In this paper, we investigate a transmission eigenvalue problem that couples the principles of acoustics and elasticity. This problem naturally arises when studying fluid-solid interactions and constructing bubbly-elastic structures to…
The conullity of a curvature tensor is the codimension of its kernel. We consider the cases of conullity two in any dimension and conullity three in dimension four. We show that these conditions are compatible with non-negative sectional…
Defects and interfaces are essential to understand the properties of matter. However, studying their dynamics in the quantum regime remains a challenge in particular concerning the regime of two spatial dimensions. Recently, it has been…
Spherical wave functions play an important role in the theoretical study of antenna. When they are used to investigate the stored energy outside the circumscribing sphere of the antenna, two different types of modal quality factors appear…
A particle beam may undergo an anomalous spatial shift when it is reflected at an interface. The shift forms a vector field defined in the two-dimensional interface momentum space. We show that, although the shift vector at individual…
Following P. M. H. Wilson's paper on sectional curvatures of Kahler moduli, we consider a natural Riemannian metric on a hypersurface f=1 in a real vector space, defined using the Hessian of a homogeneous polynomial f. We give examples to…
We consider the motion of point masses given by a natural extension of Newtonian gravitation to spaces of constant positive curvature. Our goal is to explore the spectral stability of tetrahedral orbits of the corresponding 4-body problem…
We report a three-dimensional mechanical metamaterial that simultaneously possesses negative stiffness, negative bulk modulus, and negative Poisson's ratio. This metamaterial is a periodic arrangement of binder-shell elements. Under…
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
This paper deals with the question of prescribing the Gaussian curvature on a disk and the geodesic curvature of its boundary by means of a conformal deformation of the metric. We restrict ourselves to a symmetric setting in which the…
We present a general solution for the radiation intensity in front of a purely absorbing slab moving toward an observer at constant speed and with a constant temperature. The solution is obtained by integrating the lab-frame radiation…
Negative refraction is a peculiar wave propagation phenomenon that occurs when a wave crosses a boundary between a regular medium and a medium with both constitutive parameters negative at the given frequency. The phase and group velocities…
This paper focuses on size effects in periodic mechanical metamaterials driven by reversible pattern transformations due to local elastic buckling instabilities in their microstructure. Two distinct loading cases are studied: compression…
When physics is expressed in a way that is independent of local choices of unit systems, Riemannian geometry is replaced by conformal geometry. Moreover masses become geometric, appearing as Weyl weights of tractors (conformal multiplets of…
We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This…
The propagation of classical wave in disordered media at the Anderson localization transition is studied. Our results show that the classical waves may follow a different scaling behavior from that for electrons. For electrons, the effect…
The standard formula, due to Spiegel, for the smoothing of temperature fluctuations by radiative transfer is unstable in relativity. This is due to the fact that Spiegel neglected the transit time of light, thereby allowing the transport…
Evolution of scalar perturbations in a universe containing solid matter with positive pressure is studied. Solution for pure solid is found and matched with solution for ideal fluid, including the case when the pressure to energy density…
We examine a one-dimensional nonlinear (Kerr) waveguide array which contains a single "void" waveguide where the nonlinearity is identically zero. We uncover a new family of nonlinear localized modes centered at or near the void, and their…