Spectral Properties of Superlattices with Anisotropic Inhomogeneities. The Transition from 3D to 2D Disorder

2012 ◽  
Vol 190 ◽  
pp. 597-600
Author(s):  
V.A. Ignatchenko ◽  
A.V. Pozdnyakov
Keyword(s):  
Density Of States ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Dynamic Susceptibility ◽  
Two Dimensional ◽  
Continuous Transition ◽  
Wave Numbers ◽  
Correlation Properties

Waves in superlattice (SL) contained inhomogeneities with anisotropic correlation properties are considered. The anisotropy of the correlation during the transition from 3D to 2D disorder is characterized by the parameter , where and are the correlation wave numbers along the axis of the SL and in the plane of the its layers, respectively ( and are the correlation radii). Dependencies of both the dynamic susceptibility and density of states at the continuous transition from the isotropic three-dimensional inhomogeneities () to the two-dimensional ones () have been obtained.

Spectral Properties of Superlattices with Anisotropic Inhomogeneities. The Transition from 3D to 1D Disorder

2010 ◽  
Vol 168-169 ◽  
pp. 85-88 ◽  
Author(s):  
V.A. Ignatchenko ◽  
A.V. Pozdnyakov
Keyword(s):  
Density Of States ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Dynamic Susceptibility ◽  
Continuous Transition ◽  
One Dimensional ◽  
Wave Numbers ◽  
The One ◽  
Correlation Properties

Waves in the superlattice (SL) contained inhomogeneities with anisotropic correlation properties are considered. The anisotropy of the correlations is characterized by the parameter , where and are the correlation wave numbers along the axis of the SL and in the plane of its layers, respectively ( and are the correlation radii). Dependencies of both the dynamic susceptibility and density of states at the continuous transition from the isotropic three-dimensional inhomogeneities ( ) to the one-dimensional ones ( ) have been obtained.

Combined Effects of 2D and 3D Inhomogeneities on the Dynamic Susceptibility of Superlattices

2010 ◽  
Vol 168-169 ◽  
pp. 97-100
Author(s):  
V.A. Ignatchenko ◽  
D.S. Tsikalov
Keyword(s):  
Density Of States ◽  
Three Dimensional ◽  
Wave Number ◽  
Dynamic Susceptibility ◽  
Combined Effects ◽  
Two Dimensional ◽  
Simultaneous Presence ◽  
One Dimensional ◽  
The One ◽  
2D And 3D

The dynamic susceptibility and the one-dimensional density of states (DOS) of an initially sinusoidal superlattice (SL) with simultaneous presence of two-dimensional (2D) phase inhomogeneities that simulate the deformations of the interfaces between the SL’s layers and three-dimensional (3D) amplitude inhomogeneities of the layer material of the SL were investigated. An analytical expression for the averaged Green’s function of the sinusoidal SL with 2D phase inhomogeneities was obtained in the Bourret approximation. It was shown that the effect of increasing asymmetry of heights of the dynamic susceptibility peaks at the edge of the Brillouin zone of the SL, which was found in [6] at increasing the rms fluctuations of 2D inhomogeneities, also takes place at increasing the correlation wave number of such inhomogeneities. It was also shown that the increase of the rms fluctuations of 3D amplitude inhomogeneities in the superlattice with 2D phase inhomogeneities leads to the suppression of the asymmetry effect and to the decrease of the depth of the DOS gap.

scholarly journals Применение теории случайных матриц для описания бозонного пика в двумерных системах

2020 ◽  
Vol 62 (4) ◽  
pp. 603
Author(s):  
Д.А. Конюх ◽  
Я.М. Бельтюков
Keyword(s):  
Density Of States ◽  
Disordered Systems ◽  
Degrees Of Freedom ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Amorphous Solids ◽  
Boson Peak ◽  
Two Dimensional ◽  
Reduced Density ◽  
Vibrational Density

The random matrix theory is applied to describe the vibrational properties of two-dimensional disordered systems with a large number of degrees of freedom. It is shown that the most significant mechanical properties of amorphous solids can be taken into account using the correlated Wishart ensemble. In this ensemble, an excess vibrational density of states over the Debye law is observed as a peak in the reduced density of states g(ω)/ω. Such a peak is known as the boson peak, which was observed in many experiments and numerical simulations for two-dimensional and three-dimensional disordered systems. It is shown that two-dimensional systems have a number of differences in the asymptotic behavior of the boson peak.

Self-Organization in Three-Dimensional Hydrodynamic Turbulence Self-Organization in Three-Dimensional Hydrodynamic Turbulence

1990 ◽  
Vol 45 (9-10) ◽  
pp. 1059-1073 ◽  
Author(s):  
G. Knorr ◽  
J. P. Lynov ◽  
H. L. Pécseli
Keyword(s):  
Euler Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Self Organization ◽  
Two Dimensional ◽  
Hydrodynamic Turbulence ◽  
Available Energy ◽  
Wave Numbers ◽  
Negative Helicity ◽  
Incompressible Euler

Abstract The three-dimensional incompressible Euler equations are expanded in eigenflows of the curl operator, which represent positive and negative helicity flows in a particularly simple and convenient way. Four different basic types of interactions between eigenflows are found. Two represent an "inverse cascade", the interaction familiar from the two-dimensional Euler equations, in which only modes of the same sign of the helicity interact. The other two interactions mix positive and negative helicity modes. Only these interactions can transport all of the available energy to higher wave numbers. Initial conditions, which lead to the appearance of structures and self-organization, are discussed.

Two Dimensional Photonic Crystal Modes and Resonances in Three-dimensional Structures

2001 ◽  
Vol 694 ◽  
Author(s):  
Shanhui Fan ◽  
J. D. Joannopoulos
Keyword(s):  
Spectral Properties ◽  
Three Dimensional ◽  
Reflection Spectra ◽  
Two Dimensional ◽  
Quality Factors ◽  
Transmission And Reflection Spectra ◽  
General Physical ◽  
Two Dimensional Photonic Crystal ◽  
Index Modulation ◽  
Transmission And Reflection

AbstractWe present three-dimensional analysis of two-dimensional guided resonances in photonic crystalslab structures. This analysis leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and eflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes, and the strength ofthe index modulation.

Two Dimensional Photonic Crystal Modes and Resonances in Three-dimensional Structures

2001 ◽  
Vol 692 ◽  
Author(s):  
Shanhui Fan ◽  
J. D. Joannopoulos
Keyword(s):  
Photonic Crystal ◽  
Spectral Properties ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Quality Factors ◽  
Photonic Crystal Slab ◽  
Transmission And Reflection Spectra ◽  
General Physical ◽  
Two Dimensional Photonic Crystal ◽  
Transmission And Reflection

AbstractWe present three-dimensional analysis of two-dimensional guided resonances in photonic crystal slab structures. This analysis leads to a new understanding of the complex spectral properties of such systems. Specifically, we calculate the dispersion diagrams, the modal patterns, and transmission and reflection spectra of these resonances. From these calculations, a key observation emerges involving the presence of two temporal pathways for transmission and reflection processes. Using this insight, we introduce a general physical model that explains the essential features of complex spectral properties. Finally, we show that the quality factors of these resonances are strongly influenced by the symmetry of the modes, and the strength of the index modulation.

Extensional Vibrations of Elastic Plates

1959 ◽  
Vol 26 (4) ◽  
pp. 561-569
Author(s):  
R. D. Mindlin ◽  
M. A. Medick
Keyword(s):  
Three Dimensional ◽  
Infinite Plate ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Wave Numbers ◽  
Complex Wave ◽  
Shear Modes ◽  
Thickness Shear

Abstract A system of approximate, two-dimensional equations of extensional motion of isotropic, elastic plates is derived. The equations take into account the coupling between extensional, symmetric thickness-stretch and symmetric thickness-shear modes and also include two face-shear modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite plate is explored in detail and compared with the corresponding solution of the three-dimensional equations.

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