Related papers: Local Solutions for Generic Multidimensional Reson…
High-contrast scattering problems are special among classical wave systems as they allow for strong wave focusing and localisation at low frequencies. We use an asymptotic framework to develop a landscape theory for high-contrast systems…
Recently, we have discovered a new concept of permanent wave resonance with potential spatial oscillations. This means the constant wave swinging frequency on the whole energy intervals of spectral forbidden zones destroying physical…
We present a general and practical procedure to solve the general relativistic hydrodynamic equations by using any of the special relativistic Riemann solvers recently developed for describing the evolution of special relativistic flows.…
In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray…
We study acoustic propagation in one dimensional water ducts containing many air-filled blocks. The acoustic band structures for the periodic arrangements of the blocks is calculated, whereas the transmission for various random…
A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…
We suggest a way to manipulate electromagnetic wave by introducing a rotation mapping of coordinates that can be realized by a specific transformation of permittivity and permeability of a shell surrounding an enclosed domain. Inside the…
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
Wave equations for some curved spacetimes may involve functions that prevent a solution in a closed form. In some cases, these functions can be eliminated by transformations and the solutions can be found analytically. In the cases where…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
Starting with a general discussion, a program is sketched for a quantization based on dilations. This resolving-power quantization is simplest for scalar field theories. The hope is to find a way to relax the requirement of locality so that…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
The linear algorithm of the the full non-linear large scale structure of Gaussian random fields is extended here to to perform non-linear CRs. The procedure consists of: (1) Using linear CR of low resolution data to construct a high…
Typical applications of gravitational lensing use the properties of electromagnetic or gravitational waves to infer the geometry through which those waves propagate. Nevertheless, the optical fields themselves - as opposed to their…
In this paper we consider the local X-ray transform for general flows. We extend the results on the local and global invertibility of the geodesic ray transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a general flow.…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
Accurate accounting of particle number and 4-momentum in radiative transfer may be facilitated by the use of transport equations that allow transparent conversion between volume and surface integrals in both spacetime and momentum space.…
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in…
We classify all transitive actions of Lie algebras of vector fields on C^3 and R^3 up to a local equivalence and discuss why this classification can not be extended in general to the solvable case. The main technical tool is the structure…
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-invariant is defined and described in terms…