Intervalley kinetic energy terms in the effective mass equation: a one-dimensional analytical study

1989 ◽  
Vol 67 (9) ◽  
pp. 896-903 ◽  
Author(s):  
Lorenzo Resca
Keyword(s):  
Kinetic Energy ◽  
Effective Mass ◽  
Analytical Study ◽  
Three Dimensional ◽  
Real Space ◽  
The Other ◽  
Alternative Formulation ◽  
One Dimensional ◽  
Symmetry Properties ◽  
Band Case

We show that a one-dimensional analytical study allows us to test and clarify the derivation, assumptions, and symmetry properties of the intervalley effective mass equation (IVEME). In particular, we show that the IVEME is consistent with a two-band case, and is in fact exact for a model that satisfies exactly all its assumptions. On the other hand, an alternative formulation in k-space that includes intervalley kinetic energy terms is consistent with a one-band case, provided that intra-valley kinetic energy terms are also calculated consistent with one band. We also show that the standard symmetry assumptions for both real space and k-space formulations are not actually exact, but are consistent with a "total symmetric" projection, or with taking spherical averages in a three-dimensional case.

EFFECTIVE-MASS APPROXIMATION IN GRADED CRYSTALS

1990 ◽  
Vol 04 (15n16) ◽  
pp. 2357-2369 ◽  
Author(s):  
Y. FU ◽  
K. A. CHAO
Keyword(s):  
Kinetic Energy ◽  
Exact Solutions ◽  
Effective Mass ◽  
Three Dimensional ◽  
Energy Operator ◽  
Effective Mass Approximation ◽  
Kinetic Energy Operator ◽  
Energy Dispersion ◽  
One Dimensional ◽  
Mass Approximation

The effective mass approximation (EMA), when applied to graded crystals, needs a modified form [Formula: see text] for the kinetic energy operator, where 2α + β = −1 and m(z) is the position-dependent effective mass. We have analyzed the energy dispersion of the EMA Hamiltonian, and performed a one-dimensional and a three-dimensional exact calculation to determine the proper value of β. Our conclusion is that when β = −1 the EMA provides better agreement with the exact solutions.

scholarly journals Vortex states in an acoustic Weyl crystal with a topological lattice defect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qiang Wang ◽  
Yong Ge ◽  
Hong-xiang Sun ◽  
Haoran Xue ◽  
Ding Jia ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Lattice Defect ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Lattice Defects ◽  
One Dimensional ◽  
Topological Features ◽  
Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

A novel one-dimensional CoIIcoordination polymer:catena-poly[[hexaaquacobalt(II)] [[diaquabis(sulfato-κO)cobalt(II)]-μ-4,4′-bipyridine-κ2N:N′] [[triaqua(sulfato-κO)cobalt(II)]-μ-4,4′-bipyridine-κ2N:N′]]

2012 ◽  
Vol 68 (9) ◽  
pp. m265-m268 ◽  
Author(s):  
Kai-Long Zhong ◽  
Ming-Yi Qian
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
The Other ◽  
Water Molecules ◽  
Supramolecular Network ◽  
Sulfate Ion ◽  
Sulfate Ions ◽  
One Dimensional ◽  
The Third ◽  
Hydrogen Bonding Interactions

The title compound, {[Co(H2O)6][Co(SO4)(C10H8N2)(H2O)3][Co(SO4)2(C10H8N2)(H2O)2]}n, contains three crystallographically unique CoIIcentres, all of which are in six-coordinated environments. One CoIIcentre is coordinated by two bridging 4,4′-bipyridine (4,4′-bipy) ligands, one sulfate ion and three aqua ligands. The second CoIIcentre is surrounded by two N atoms of two 4,4′-bipy ligands and four O atoms,i.e.two O atoms from two monodentate sulfate ions and two from water molecules. The third CoIIcentre forms part of a hexaaquacobalt(II) ion. In the crystal structure, there are two different one-dimensional chains, one being anionic and the other neutral, and adjacent chains are arranged in a cross-like fashion around the mid-point of the 4,4′-bipy ligands. The structure features O—H...O hydrogen-bonding interactions between sulfate anions and water molecules, resulting in a three-dimensional supramolecular network.

Heat Conduction in Three Dimensional Stacked Packages

2005 ◽  
Author(s):  
Anand Desai ◽  
James Geer ◽  
Bahgat Sammakia
Keyword(s):  
Heat Conduction ◽  
Thermal Management ◽  
Heat Generation ◽  
Analytical Study ◽  
Three Dimensional ◽  
The Other ◽  
Heat Generation Rate ◽  
Potential Applications ◽  
Steady State Heat ◽  
Spatially Varying

This paper presents the results of an analytical study of steady state heat conduction in multiple rectangular domains. Any finite number of such domains may be considered in the current study. The thermal conductivity and thickness of these domains may be different. The entire geometry composed of these connected domains is considered as adiabatic on the lateral surfaces and can be subjected to uniform convective cooling at one end. The other end of the geometry may be adiabatic and a specified, spatially varying heat generation rate can be applied in each of the domains. The solutions are found to be in agreement with known solutions for simpler geometries. The analytical solution presented here is very general in that it takes into account the interface resistances between the layers. One application of this analytical study relates to the thermal management of a 3-D stack of devices and interconnect layers. Another possible application is to the study of hotspots in a chip stack with non uniform heat generation. Many other potential applications may also be simulated.

Electron–phonon interaction in three-, two- and one-dimensional ternary mixed crystals

2016 ◽  
Vol 30 (15) ◽  
pp. 1650182
Author(s):  
Junhua Hou ◽  
Yunpeng Fan
Keyword(s):  
Cell Volume ◽  
Effective Mass ◽  
Unit Cell Volume ◽  
Three Dimensional ◽  
Unit Cell ◽  
Mixed Crystals ◽  
Phonon Interaction ◽  
One Dimensional ◽  
Electron Phonon Interaction ◽  
Self Trapping

The electron–phonon (e–p) interaction in three-dimensional (3D), two-dimensional (2D) and one-dimensional (1D) ternary mixed crystals is studied. The e–p interaction Hamiltonians including the unit cell volume variation in ternary mixed crystals are obtained by using the modified random-element-isodisplacement model and Born–Huang method. The polaronic self-trapping energy and renormalized effective mass of GaAs[Formula: see text]Sb[Formula: see text], GaP[Formula: see text]As[Formula: see text] and GaP[Formula: see text]Sb[Formula: see text] compounds are numerically calculated. It is confirmed theoretically that the nonlinear variation of the self-trapping energy and effective mass with the composition is essential and the unit cell volume effects cannot be neglected except the weak e–p coupling. The dimensional effect cannot also be ignored.

On the Spectra of Turbulent Velocity Field in a Stably Stratified Flow

1991 ◽  
Vol 46 (5) ◽  
pp. 462-468
Author(s):  
A. K. Chakraborty ◽  
B. E. Vembe ◽  
H. P. Mazumdar
Keyword(s):  
Heat Flux ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
Inertial Subrange ◽  
Coefficient Function ◽  
One Dimensional ◽  
Kinetic Energy Spectrum

Abstract This paper describes a method to solve the spectral equation for the balance of turbulent kinetic energy in a stably stratified turbulent shear flow. The cospectra of vertical momentum and heat flux arc modelled with the aid of a basic eddy-viscosity (or turbulent exchange coefficient) function. For the term representing the inertial transfer of turbulent kinetic energy, Pao's [Phys. Fluids 8 (1965)] form is assumed. Analytical expressions for the three-dimensional kinetic energy spectrum as well as the cospectra of momentum and heat flux are obtained over the range of wave numbers k≥kb, which includes the inertial subrange kb≪k≪ks and the viscous subrange k>ks (kb and ks are the buoyancy and Kolmogorov wavenumbers, respectively). The two one-dimensional spectra, e.g., the kinetic energy spectra of the horizontal and vertical components of turbulence are derived from the three-dimensional kinetic energy spectrum. These one-dimensional spectra are compared with the measured data of Gargett et al. [J. Fluid Mech. 144 (1984)] for the case I ( = ks/kb) = 630. Finally, we compute the basic eddy-viscosity function and discuss its behavio

A sulfur coordination polymer with wide bandgap semiconductivity formed from zinc(II) and 5-methylsulfanyl-1,3,4-thiadiazole-2-thione

2019 ◽  
Vol 75 (9) ◽  
pp. 1243-1249
Author(s):  
Jun Zhang ◽  
Xiaofan Ma ◽  
Weili Kong ◽  
Fazhi Xie ◽  
Shizhen Yuan ◽  
...  
Keyword(s):  
Coordination Polymer ◽  
Hydrogen Bonds ◽  
Three Dimensional ◽  
Chain Structure ◽  
The Other ◽  
Linear Temperature Dependence ◽  
Linear Temperature ◽  
One Dimensional ◽  
Hydrogen Bond Interactions ◽  
The One

The sulfur coordination polymer catena-poly[zinc(II)-μ2-bis[5-(methylsulfanyl)-2-sulfanylidene-2,3-dihydro-1,3,4-thiadiazol-3-ido-κ2 N 3:S]], [Zn(C3H3N2S3)2] n or [Zn2MTT4] n , constructed from Zn2+ ions and 5-methylsulfanyl-1,3,4-thiadiazole-2-thione (HMTT), was synthesized successfully and structurally characterized. [Zn2MTT4] n crystallizes in the tetragonal space group I\overline{4} (No. 82). Each MTT− ligand (systematic name: 5-methylsulfanyl-2-sulfanylidene-2,3-dihydro-1,3,4-thiadiazol-3-ide) coordinates to two different ZnII ions, one via the thione group and the other via a ring N atom, with one ZnII atom being in a tetrahedral ZnS4 and the other in a tetrahedral ZnN4 coordination environment. These tetrahedral ZnS4 and ZnN4 units are alternately linked by the organic ligands, forming a one-dimensional chain structure along the c axis. The one-dimensional chains are further linked via C—H...N and C—H...S hydrogen bonds to form a three-dimensional network adopting an ABAB-style arrangement that lies along both the a and b axes. The three-dimensional Hirshfeld surface analysis and two-dimensional (2D) fingerprint plots confirm the major interactions as C—H...S hydrogen bonds with a total of 35.1%, while 7.4% are C—H...N hydrogen-bond interactions. [Zn2MTT4] n possesses high thermal and chemical stability and a linear temperature dependence of the bandgap from room temperature to 270 °C. Further investigation revealed that the bandgap changes sharply in ammonia, but only fluctuates slightly in other solvents, indicating its promising application as a selective sensor.

scholarly journals A Survey of Supramolecular Aggregation Based on Main Group Element⋯Selenium Secondary Bonding Interactions—A Survey of the Crystallographic Literature

Crystals ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 503 ◽  
Author(s):  
Edward R. T. Tiekink
Keyword(s):  
Crystal Structures ◽  
Three Dimensional ◽  
Main Group ◽  
Group Element ◽  
The Other ◽  
One Dimensional ◽  
Supramolecular Architectures ◽  
Main Group Element ◽  
Supramolecular Aggregation ◽  
Secondary Bonding

The results of a survey of the crystal structures of main group element compounds (M = tin, lead, arsenic, antimony, bismuth, and tellurium) for intermolecular M⋯Se secondary bonding interactions is presented. The identified M⋯Se interactions in 58 crystals can operate independent of conventional supramolecular synthons and can sustain zero-, one-, two, and, rarely, three-dimensional supramolecular architectures, which are shown to adopt a wide variety of topologies. The most popular architecture found in the crystals stabilized by M⋯Se interactions are one-dimensional chains, found in 50% of the structures, followed by zero-dimensional (38%). In the majority of structures, the metal center forms a single M⋯Se contact; however, examples having up to three M⋯Se contacts are evident. Up to about 25% of lead(II)-/selenium-containing crystals exhibit Pb⋯Se tetrel bonding, a percentage falling off to about 15% in bismuth analogs (that is, pnictogen bonding) and 10% or lower for the other cited elements.

scholarly journals Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias

2011 ◽  
Vol 467 (2134) ◽  
pp. 3022-3032 ◽  
Author(s):  
Luciano Telesca ◽  
Michele Lovallo
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Three Dimensional ◽  
The Other ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
One Dimensional ◽  
Single Voice ◽  
Analysis Application ◽  
The One ◽  
Detrended Fluctuation

The one-, two- and three-dimensional multifractal detrended fluctuation analysis (MF-DFA) was applied to Bach's Sinfonias, which are characterized by the superposition of three different voices. Each voice, represented as a time series, can be considered as a component of a one-, two- or three-dimensional vector. The one-dimensional MF-DFA was applied to any single voice, while the two- and three-dimensional MF-DFA was applied to the couples of voices and to the triple, respectively. Each voice is characterized by a multifractal degree (MD), indicated by the range of the generalized Hurst exponents; the higher the MD, the larger the amount of heterogeneity and irregularity. Competitive scaling multifractal behaviours in Bach's Sinfonias were revealed; although one (or two) voices showed a relatively high MD, the other two voices, or voice, are characterized by a low MD. Nevertheless, the overall effect of the Sinfonia, measured by the MD of the triple, tends towards homogeneity, or at least to an average between the different competitive scaling behaviour shown by the different voices.

scholarly journals Analytical Study of Cavitation Surge in a Hydraulic System

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Donghyuk Kang ◽  
Kazuhiko Yokota
Keyword(s):  
Hydraulic System ◽  
Analytical Study ◽  
The Other ◽  
Stable Region ◽  
Performance Curve ◽  
Hydraulic Systems ◽  
Inlet Pipe ◽  
One Dimensional ◽  
Suction Performance ◽  
Negative Gradient

In order to clarify effects of an accumulator, pipe lengths and gradients of pressure and suction performances on cavitation surge, one-dimensional stability analyses of cavitation surge were performed in hydraulic systems consisting of an upstream tank, an inlet pipe, a cavitating pump, a downstream pipe, and a downstream tank. An accumulator located upstream or downstream of the cavitating pump was included in the analysis. Increasing the distance between the upstream accumulator and the cavitating pump enlarged the stable region. On the other hand, decreasing the distance between the downstream accumulator and the cavitating pump enlarged the stable region. Furthermore, the negative gradient of a suction performance curve and the positive gradient of a pressure performance curve cause cavitation surge.

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