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.

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.

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

The role of the geoid in one-, two-, and three-dimensional network adjustments

CISM journal ◽  
1990 ◽  
Vol 44 (1) ◽  
pp. 9-18 ◽  
Author(s):  
Michael G. Sideris
Keyword(s):  
Three Dimensional ◽  
One Dimensional ◽  
Control Networks ◽  
Deflections Of The Vertical ◽  
Dimensional Network ◽  
3D Network ◽  
Computational Procedures ◽  
The One ◽  
2D And 3D

The geoid and its horizontal derivatives, the deflections of the vertical, play an important role in the adjustment of geodetic networks. In the one-dimensional (1D) case, represented typically by networks of orthometric heights, the geoid provides the reference surface for the measurements. In the two-dimensional (2D) adjustment of horizontal control networks, the geoidal undulations N and deflections of the vertical ξ, η are needed for the reduction of the measured quantities onto the reference ellipsoid. In the three-dimensional (3D) adjustment, N and ξ, η are basically required to relate geodetic and astronomic quantities. The paper presents the major gravimetric methods currently used for predicting ξ, η and N, and briefly intercompares them in terms of accuracy, efficiency, and data required. The effects of N, ξ, η on various quantities used in the ID, 2D, and 3D network adjustments are described explicitly for each case and formulas are given for the errors introduced by either neglecting or using erroneous N, ξ, η in the computational procedures.

A novel one-dimensional silver cylinder stabilized by mixed 2-mercaptobenzoic acid and ethylenediamine ligands

2012 ◽  
Vol 68 (8) ◽  
pp. m229-m232
Author(s):  
Di Sun ◽  
Zhi-Hao Yan
Keyword(s):  
Three Dimensional ◽  
Van Der Waals Interactions ◽  
Two Dimensional ◽  
Binding Modes ◽  
Supramolecular Framework ◽  
One Pot ◽  
Tetrahedral Geometry ◽  
Coordination Environment ◽  
One Dimensional ◽  
The One

A novel infinite one-dimensional silver cylinder, namely poly[μ-ethylenediamine-μ5-(2-sulfanidylbenzoato)-μ4-(2-sulfanidylbenzoato)-tetrasilver(I)], [Ag4(C7H4O2S)2(C2H8N2)]n, has been synthesized by one-pot reaction of equivalent molar silver nitrate and 2-mercaptobenzoic acid (H2mba) in the presence of ethylenediamine (eda). One Ag atom is located in an AgS2NO four-coordinated tetrahedral geometry, two other Ag atoms are in an AgS2O three-coordinated T-shaped geometry and the fourth Ag atom is in an AgSNO coordination environment. The two mba ligands show two different binding modes. The μ2-N:N′-eda ligand, acting as a bridge, combines with mba ligands to extend the AgIions into a one-dimensional silver cylinder incorporating abundant Ag...Ag interactions ranging from 2.9298 (11) to 3.2165 (13) Å. Interchain N—H...O hydrogen bonds extend the one-dimensional cylinder into an undulating two-dimensional sheet, which is further packed into a three-dimensional supramolecular framework by van der Waals interactions; no π–π interactions were observed in the crystal structure.

scholarly journals Flat-band dark polaritons in two-dimensional chiral-waveguide quantum electrodynamics

2021 ◽  
Vol 2015 (1) ◽  
pp. 012088
Author(s):  
Y. Marques ◽  
I. A. Shelykh ◽  
I. V. Iorsh
Keyword(s):  
Quantum Dots ◽  
Quantum Electrodynamics ◽  
Semiconductor Quantum Dots ◽  
Flat Band ◽  
Combined Effects ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
One Dimensional ◽  
Flat Bands ◽  
The One

Abstract We consider a two-dimensional extension of the one-dimensional waveguide quantum electrodynamics and investigate the nature of linear excitations in two-dimensional arrays of qubits (particularly, semiconductor quantum dots) coupled to networks of chiral waveguides. We show that the combined effects of chirality and long-range photon mediated qubit-qubit interactions lead to the emergence of the two-dimensional flat bands in the polaritonic spectrum, corresponding to slow strongly correlated light.

Complex Order from Disorder and from Simple Order in Coarse-Graining Invariant Orbits of Certain Two-Dimensional Linear Cellular Automata

1997 ◽  
Vol 07 (07) ◽  
pp. 1451-1496 ◽  
Author(s):  
André Barbé
Keyword(s):  
Cellular Automata ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Complex Order ◽  
Simple Order ◽  
Problems And Solutions ◽  
The One

This paper considers three-dimensional coarse-graining invariant orbits for two-dimensional linear cellular automata over a finite field, as a nontrivial extension of the two-dimensional coarse-graining invariant orbits for one-dimensional CA that were studied in an earlier paper. These orbits can be found by solving a particular kind of recursive equations (renormalizing equations with rescaling term). The solution starts from some seed that has to be determined first. In contrast with the one-dimensional case, the seed has infinite support in most cases. The way for solving these equations is discussed by means of some examples. Three categories of problems (and solutions) can be distinguished (as opposed to only one in the one-dimensional case). Finally, the morphology of a few coarse-graining invariant orbits is discussed: Complex order (of quasiperiodic type) seems to emerge from random seeds as well as from seeds of simple order (for example, constant or periodic seeds).

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.

GENERALIZATIONS OF THE CHUA EQUATIONS

1992 ◽  
Vol 02 (04) ◽  
pp. 889-909 ◽  
Author(s):  
RAY BROWN
Keyword(s):  
Piecewise Linear ◽  
Three Dimensional ◽  
Type Ii ◽  
Two Dimensional ◽  
Chua’S Circuit ◽  
Unimodal Maps ◽  
One Dimensional ◽  
Chua's Circuit ◽  
The One ◽  
Block Approach

In this paper we present two generalizations of the equations governing Chua’s circuit. In order to obtain the first generalization we simplify Chua’s equations by replacing the piecewise-linear term with a signum function. The resulting simplified system produces a double scroll similar to the one observed experimentally in Chua’s circuit. What is significant about this simplified system is that it can be reduced to what we shall call a two-dimensional single scroll, and from the two-dimensional single scroll we are able to derive a one-dimensional map. This entire derivation is carried out analytically, in contrast to the one-dimensional map analysis that has been carried out for the Lorenz equations which is based on axioms. After we have carried out our analysis for this simplified version of Chua’s equations, we use these equations as a guide to the construction of the first generalization to be presented in this paper. We call this a type-I generalization of Chua’s equations. The generalization consists in using a two-dimensional autonomous flow as a component in a three-dimensional autonomous flow in such a way that the resulting equations will have double scroll attractors similar to those observed experimentally in Chua’s circuit. The value of this generalization is that: (1) it provides a building block approach to the construction of chaotic circuits from simpler two-dimensional components which are not chaotic by themselves. In so doing it provides an insight into how chaotic systems can be built up from simple nonchaotic parts; (2) it illustrates a precise relationship between three-dimensional flows and one-dimensional maps. Of particular significance in this regard is a recent paper of Misiurewicz [1993], which analytically connects the two-dimensional single scroll to the class of unimodal maps, thus providing a framework within which a theory linking unimodal maps to three-dimensional flows may be possible. The second generalization is suggested by considering three-dimensional flows whose only nonlinearities are sigmoid, sgn, or piecewise-linear functions. Clearly, such flows are a generalization of the Chua equations. We call these equations type-II generalization Chua equations. The significance of this direction of investigation is that attractors similar to the Lorenz and Rössler attractors can be produced from type-II generalized Chua equations in a building block approach using only piecewise-linear vector fields. As a result we have a method of producing the Lorenz and Rössler dynamics in a circuit without the use of multipliers. This suggests that the type-II generalized Chua equations are in some sense fundamental in that the dynamics of the three most important autonomous three-dimensional differential equations producing chaos are seen as variations of a single class of equations whose nonlinearities are generalizations of the Chua diode.

One- and two-dimensional CdIIcoordination polymers incorporating organophosphinate ligands

2014 ◽  
Vol 70 (11) ◽  
pp. 1069-1074 ◽  
Author(s):  
Jeffrey A. Rood ◽  
Steven Boyer ◽  
Allen G. Oliver
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Cadmium Nitrate ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
One Dimensional ◽  
Phenyl Rings ◽  
Ft Ir ◽  
Ir Analysis ◽  
The One

Reaction of cadmium nitrate with diphenylphosphinic acid in dimethylformamide solvent yielded the one-dimensional coordination polymercatena-poly[[bis(dimethylformamide-κO)cadmium(II)]-bis(μ-diphenylphosphinato-κ2O:O′)], [Cd(C12H10O2P)2(C3H7NO)2]n, (I). Addition of 4,4′-bipyridine to the synthesis afforded a two-dimensional extended structure, poly[[(μ-4,4′-bipyridine-κ2N:N′)bis(μ-diphenylphosphinato-κ2O:O′)cadmium(II)] dimethylformamide monosolvate], {[Cd(C12H10O2P)2(C10H8N2)]·C3H7NO}n, (II). In (II), the 4,4′-bipyridine molecules link the CdIIcenters in the crystallographicadirection, while the phosphinate ligands link the CdIIcenters in the crystallographicbdirection to complete a two-dimensional sheet structure. Consideration of additional π–π interactions of the phenyl rings in (II) produces a three-dimensional structure with channels that encapsulate dimethylformamide molecules as solvent of crystallization. Both compounds were characterized by single-crystal X-ray diffraction and FT–IR analysis.

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