相关论文: Wave Equation for Fractal Solid String

In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on…

We show wave breaking for the Whitham equation in a range of fractional dispersion, i.e. the solution remains bounded but its slope becomes unbounded in finite time, provided that the initial datum is sufficiently steep.

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…

A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to…

This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…

Topological defects in the framework of effective quantum gravity model are investigated, based on the hypothesis of an effective fractal dimension of the universe. This is done by using Caputo fractional derivatives to determine the…

We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which…

We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and…

In this work, we present a mathematical model to describe the adsorption-diffusion process on fractal porous materials. This model is based on the fractal continuum approach and considers the scale-invariant properties of the surface and…

Fundamental rules and definitions of Fractional Differintegrals are outlined. Factorizing 1-D and 2-D Helmholtz equations four fractional eigenfunctions are determined. The functions exhibit incident and reflected plane waves as well as…

The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are…

We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…

Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…

Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…

The Lamb-Bateman integral equation was introduced to study the solitary wave diffraction and its solution was written in terms of an integral transform. We prove that it is essentially the Abel integral equation and its solution can be…

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integro-differentiation. The…

Space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analyzed. This model includes waves with finite speed, as well as…

A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and…

We report on generic relations between fractional flow and pressure in steady two-phase flow in porous media. The main result is a differential equation for fractional flow as a function of phase saturation. We infer this result from two…

In this work, we develop a fast and accurate method for the scattering of flexural-gravity waves by a thin plate of varying thickness overlying a fluid of infinite depth. This problem commonly arises in the study of sea ice and ice shelves,…