Related papers: Wave front evolution and pedal evolution

Assuming a-priori a smooth generating vector field, we introduce a generally covariant measure of the flow geometry called the referential gradient of the flow. The main result is the explicit relation between the referential gradient and…

In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…

Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as…

The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…

This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.

A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong…

In this paper, a fractional generalization of the wave equation that describes propagation of damped waves is considered. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional derivatives of…

Grammatical forms are said to evolve via two main mechanisms. These are, respectively, the `descent' mechanism, where current forms can be seen to have descended (albeit with occasional modifications) from their roots in ancient languages,…

Because wind-generated waves can propagate over large distances, wave spectra from a fixed point can record information about air-sea interactions in distant areas. In this study, the spectral wave climate is computed for a specific…

We numerically investigate the impact of scale evolution on double parton distributions, which are needed to compute multiple hard scattering processes. Assuming correlations between longitudinal and transverse variables or between the…

In arXiv:2205.02920 a variant of the classical elastic flow for closed curves in $\mathbb{R}^{n}$ was introduced, that is more suitable for numerical purposes. Here we investigate the long-time properties of such evolution demonstrating…

In this paper, we trace the development of the theory of the calculus of variations. From its roots in the work of Greek thinkers and continuing through to the Renaissance, we see that advances in physics serve as a catalyst for…

We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…

This paper is concerned with the globally exponential stability of traveling wave fronts for a class of population dynamics model with quiescent stage and delay. First, we establish the comparison principle of solutions for the population…

We consider a generalised Webster's equation for describing wave propagation in curved tubular structures such as variable diameter acoustic wave guides. Webster's equation in generalised form has been rigorously derived in a previous…

In this paper we suggest new classification of polynomials and evolution equations for the roots and the coefficients remaing the polynomials within proper class. In the basis of the developed evolution equations we built new dynamics…

Biquandles are generalizations of quandles. As well as quandles, biquandles give us many invariants for oriented classical/virtual/surface links. Some invariants derived from biquandles are known to be stronger than those from quandles for…

A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…

We show that, contrary to the statements made by many authors, the backflow is not a nonclassical effect. The backflow is a characteristic feature of solutions of the wave equations: quantum and classical. We present simple solutions of the…

Some features of extended loops are considered. In particular, the behaviour under diffeomorphism transformations of the wavefunctions with support on the extended loop space are studied. The basis of a method to obtain analytical…