Related papers: Generalized Maass Wave Forms
We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute…
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as Mass-in-Mass systems. We use 3 distinct approaches to identify relevant traveling waves. The first consists of…
In this work, we investigate mathematical models for electromagnetic wave propagation in dispersive isotropic media. We emphasize the link between physical requirements and mathematical properties of the models. A particular attention is…
In this paper, we extend previous results to prove that generalized modular forms with rational Fourier expansions whose divisors are supported only at the cusps and certain other points in the upper half plane are actually classical…
Weierstrass's theory is a standard qualitative tool for single degree of freedom equations, used in classical mechanics and in many textbooks. In this Brief Report we show how a simple generalization of this tool makes it possible to…
The classical theory of electromagnetism has been revisited and the possibility of longitudinal photon wave is explored. It is shown that the emergence of longitudinal wave is a consequence of Lorenz gauge (condition) violation. Proca,…
In this paper we present a complete characterization of geometric and linear multiplier sequences for generalized Laguerre bases. In addition, we give a partial characterization of the generic multiplier sequence for such bases, and pose…
A wide class of nonuniformly totally polarized beams is introduced that preserve their transverse polarization pattern during paraxial propagation. They are obtained as suitable combinations of Gaussian modes and find applications in…
We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…
Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…
We generalize the notions of locally and polar harmonic Maass forms to general orthogonal groups of signature $(2, n)$ with singularities along real analytic and algebraic cycles. We prove a current equation for locally harmonic Maass forms…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
The basic premise of Quantum Mechanics, embodied in the doctrine of wave-particle duality, assigns both, a particle and a wave structure to the physical entities. The classical laws describing the motion of a particle and the evolution of a…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable…
This is a survey paper based on previous results of the author. In the paper, we define and discuss the generalizations of linear partial differential equations to multidimensional variational problems. We consider two examples of such…
A large number of wave modes exist in a magnetized plasma. Their properties are determined by the interaction of particles and waves. In a simulation code, the correct treatment of field quantities and particle behavior is essential to…
Waves of various types carry momentum, which is associated with their propagation direction, i.e., the phase gradient. The circulation of the wave momentum density gives rise to orbital angular momentum (AM). Additionally, for waves…
An axiomatic theory of classical nondissipative waves is proposed that is constructed based on the definition of a wave as a multidimensional oscillator. Waves are represented as abstract vectors $|\psi\rangle$ in the appropriately defined…
In terms of the derivative operator, integral operator and Saalsch\"{u}tz's theorem, two families of summation formulae involving generalized harmonic numbers are established.