Related papers: Filament structure of random waves
A one-dimensional wave propagation through elastically asymmetric media is investigated. A class of metamaterials possessing an arbitrary elastic asymmetry is proposed. This asymmetry results in different wave speeds of tensile and…
In this paper we investigate the properties of nodal structures in random wave fields, and in particular we scrutinize their recently proposed connection with short-range percolation models. We propose a measure which shows the difference…
The statistical theory of certain complex wave interference phenomena, like the statistical fluctuations of transmission and reflection of waves, is of considerable interest in many fields of physics. In this article we shall be mainly…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
It is shown that spatially periodic one-dimensional surface waves in shallow water behave almost linearly, provided large part of the energy is contained in sufficiently high frequencies. The amplitude is not required to be small (apart…
This paper brings a comparative analysis between dynamic models of couple-stress elastic materials and structured Rayleigh beams on a Winkler foundation. Although physical phenomena have different physical origins, the underlying equations…
We consider the spreading of the wave packet in the generalized Rosenzweig-Porter random matrix ensemble in the region of non-ergodic extended states $1<\gamma<2$. We show that despite non-trivial fractal dimensions $0 < D_{q}=2-\gamma<1$…
The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and nature of asphericity as well as their respective averages we find two distinct shape regimes…
The exploration of the rich dynamics of electrons is a frontier in fundamental nano-physics. The dynamical behavior of electrons is dominated by random and chaotic thermal motion with ultrafast ($\approx$ ps) and nanoscale scatterings. This…
It has recently become popular to analyze the behavior of excess dislocations in plastic deformation under the assumption that such dislocations are arranged into walls with periodic dislocation spacing along the wall direction. This…
A random field composed by Poisson distributed Brownian vortex filaments is constructed. The filament have a random thickness, length and intensity, governed by a measure $\gamma$. Under appropriate assumptions on $\gamma$ we compute the…
Many natural patterns and shapes, such as meandering coastlines, clouds, or turbulent flows, exhibit a characteristic complexity mathematically described by fractal geometry. In recent years, the engineering of self-similar structures in…
We present a theory for describing the inner structure of the electron bunch in the bubble regime starting from a random distribution of electrons inside the bubble and subsequently minimizing the system's energy. Consequently, we find a…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Space-time light structuring has emerged as a very powerful tool for controlling the propagation dynamics of pulsed beam. The ability to manipulate and generate space-time distributions of light has been remarkably enhanced in past few…
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…
The optical properties of PT-symmetric periodic stack of the layers with balanced loss and gain are examined. We demonstrate that tunnelling phenomenon in periodic structures is connected with excitation of surface waves at the boundaries…
We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices $n=2$ and 3, exhibit strong localization of simple geometric shape, and we…
We consider two aspects of scattering in strong plane wave backgrounds. First, we show that the infra-red divergences in elastic scattering depend on the structure of the background, but can be removed using the usual Bloch-Nordsieck…
This chapter is a pedagogical review of methods and results for studying wave propagation in one-dimensional complex structures. We describe and compare the tight-binding, scattering matrix, transfer matrix and Riccati formalisms. We…