Related papers: Wavelet Electrodynamics II: Atomic Composition of …
The classical free-space solutions of Maxwell's equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all…
Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago. More than 60 years ago it was shown that interfaces between optical media (including dielectrics, metals, negative-index materials) can support…
Relativistic electromagnetic plasma waves are described by a dynamical equation that can be solved not only in terms of plane waves, but for several different accelerating wavepacket solutions. Depending on the spatial and temporal…
Exact radiative wave solutions to the classical homogeneous Maxwell equations in the vacuum have been found that are not transverse, exhibit both torsion and spin, and for which the second Poincare invariant, E.B, is not zero. Two four…
The group $G_2$ of invertible affine transformations of $\mathbb{R}^2$ has, up to equivalence, one square--integrable representation. Two new realizations of this representation are presented and novel continuous wavelet transforms, acting…
Modes generally provide an economical description of waves, reducing complicated wave functions to finite numbers of mode amplitudes, as in propagating fiber modes and ideal laser beams. But finding a corresponding mode description for…
The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the…
Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…
This chapter introduces the main ideas and the most important methods for representing the electronic wavefunction through machine learning models. The wavefunction of a N-electron system is an incredibly complicated mathematical object,…
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…
Some recent methods, like the Empirical Mode Decomposition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is…
Maxwell equations provide a complete description of the electromagnetic (EM) phenomena, which have been one of the key fundamental-theories of modern physics, such as electromagnetism, optics, quantum theories, etc. The vacuum permittivity…
We consider the energy-critical wave maps equation from 1+2 dimensional Minkowski space into the 2-sphere, in the equivariant case. We prove that if a wave map decomposes, along a sequence of times, into a superposition of at most two…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
We choose a complete set of square integrable functions as basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent wave operator is tridiagonal and…
We apply variational-wavelet approach for constructing multiscale high-localized eigenmodes expansions in different models of nonlinear waves. We demonstrate appearance of coherent localized structures and stable pattern formation in…
Gaining insight into the interaction between flexible piezoelectric structures and ocean waves can inform the development of compact, high-efficiency wave-energy converters that harvest renewable energy from the marine environment. In this…
Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of…
The concept of "multiplicity of solutions" was developed in arXiv:1509.02603v2 which is based on the theory of energy operators in the Schwartz space S^-(R) and some subspaces called energy spaces first defined in arXiv:1208.3385 and…
Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of…