An analytical model for the energetics of quantum dots: beyond the small slope assumption

2006 ◽  
Vol 462 (2076) ◽  
pp. 3523-3553 ◽  
Author(s):  
S.P.A Gill ◽  
A.C.F Cocks
Keyword(s):  
Quantum Dots ◽  
Aspect Ratio ◽  
Elastic Properties ◽  
Analytical Model ◽  
Unit Volume ◽  
Three Dimensional ◽  
Elastic Interaction ◽  
Analytical Models ◽  
Relaxation Energy ◽  
Physical Principles

Analytical models for strained heteroepitaxial quantum dot systems have invariably assumed that the dots have a low-aspect ratio (small slopes) and that the elastic properties of the dot and the substrate are identical. In this paper, a three-dimensional analytical model for the energetics of an array of axisymmetric quantum dots is developed from physical principles. This is valid for high-aspect ratio dots (such as GeSi and InGaAs) and allows the dot and substrate to have different elastic properties. It is shown that these features are very important in determining the strain energy of both isolated dots and arrays of interacting dots. Both the elastic relaxation energy (per unit volume) of a single dot and the elastic interaction energy (per unit volume) between multiple dots are found to be greatest for tall, steep dots and for dots which are stiffer than the substrate. The equilibrium of two-facet dots is investigated and shape transition phase diagrams for small slope monoelastic theory, GeSi and InGaAs are compared. Different features of the bimodal dot size distributions in these systems are explained.

Three-Dimensional Analytical Model for Pressure-Driven Cross-Stream Diffusion in Microchannels With Arbitrary Aspect Ratios

2012 ◽  
Author(s):  
Hongjun Song ◽  
Yi Wang ◽  
Kapil Pant
Keyword(s):  
Aspect Ratio ◽  
Analytical Model ◽  
Scaling Law ◽  
Three Dimensional ◽  
Analytical Models ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Aspect Ratios ◽  
Pressure Driven Flow ◽  
Pressure Driven

The utilization of cross-stream diffusion under laminar flow for precise analyte handling plays a critical role in microfluidic biochemical assays such as sample preparation, concentration gradient generation, and molecular interactions. The non-uniform velocity profile along the cross-section of a rectangular microchannel with arbitrary aspect ratio under pressure-driven flow results in unique, heterogeneous species transport including Taylor dispersion and position-dependent diffusion scaling law. Although numerical methods such as finite difference method, finite element method, the method of lines and lattice Boltzmann (LB) method have been used for quantitative study of the phenomena, they inherently suffer from several limitations, such as difficulty to provide direct, physical insight into the underlying transport mechanism and prohibitive computational cost to suppress the artificial numerical diffusion (ND). To address these issues, several analytical models have been proposed, which share several common assumptions such as large aspect ratio and neglecting depth-wise diffusion due to the non-uniform axial velocity in the 3D convection-diffusion equation, markedly limiting their utility. In this paper, we present a three dimensional (3D) analytical model to investigate the diffusion of analyte between two cross streams in rectangular microchannels with arbitrary aspect ratios under pressure-driven flow. The 3D convection-diffusion equation is solved in a Fourier series form using a double integral transformation method and associated eigensystem calculation. Therefore, the model for the first time is capable of capturing the non-uniform transport rate (i.e., the ‘butterfly effect’) and the position-dependent scaling-law of diffusion (1/3-power at the channel wall and 1/2-pwer at the half-depth plane) through an analytical solution. Our analytical model was extensively validated against both experimental and numerical data in terms of the concentration distribution, diffusion scaling law and the mixing efficiency with excellent agreement (the relative error is much less than 0.5% in various benchmark test cases.) Quantitative comparison between our analytical model and other prior analytical models in extensive parameter space was also performed, which convincingly demonstrates that our model accommodates much broader transport regimes and more practical microfluidic applications.

Research and Development of Three-Dimensional Isolation System for Sodium-Cooled Fast Reactor: Part 1 — Proposal of Analytical Models Based on Loading Tests

2018 ◽  
Author(s):  
Tsuyoshi Fukasawa ◽  
Shigeki Okamura ◽  
Takahiro Somaki ◽  
Takayuki Miyagawa ◽  
Masato Uchita ◽  
...  
Keyword(s):  
Seismic Response ◽  
Analytical Model ◽  
Three Dimensional ◽  
Analytical Models ◽  
Response Analysis ◽  
Seismic Response Analysis ◽  
Natural Period ◽  
Isolation System ◽  
Loading Tests ◽  
Rubber Bearings

This paper describes that the analytical model for the three-dimensional isolation system [1], which consists of thick rubber bearings, disc springs and oil dampers, is created through loading tests. The new-type analytical models of each element are proposed to improve the prediction accuracy of the seismic response analysis. The concept of the three-dimensional isolation system has been proposed to ensure the structural integrity for large reactor vessels. The primary specifications of the three-dimensional isolation system are a horizontal natural period of 3.4 s and a vertical natural period of 0.33 s. The investigations of horizontal isolation performances have been conducted for the various types of isolation devices, beginning with rubber bearings, whereas the previous studies focused on the vertical isolation performances are only a few. Hence, isolation characteristics, such as restoring force and damping force, should be clarified by loading tests using vertical seismic isolation elements, and analytical model to assess the seismic response should be identified on the basis of the loading test results. This paper presents a new analytical model with providing of the differential equations to improve the prediction accuracy and demonstrates the seismic performance, including beyond-design-basis ground motion, for the three-dimensional isolation system by the seismic response analysis.

Development of a generalized analytical model for tubular braided-architecture composites

2017 ◽  
Vol 51 (28) ◽  
pp. 3861-3875 ◽  
Author(s):  
Garrett W Melenka ◽  
Jason P Carey
Keyword(s):  
Elastic Properties ◽  
Analytical Model ◽  
Volume Averaging ◽  
Analytical Models ◽  
Braided Composites ◽  
Element Analysis ◽  
Shear Moduli ◽  
Braided Structure ◽  
Braiding Angle ◽  
Analysis Models

Tubular braided composites are manufactured using a Maypole braiding machine which interlaces yarns in order to manufacture a braided structure. Braids can be produced in Diamond (1/1), Regular (2/2) and Hercules (3/3) patterns. In addition, axial yarns can be included in order to produce triaxial braid structures. Several analytical and finite element analysis models have been developed in order to predict the elastic properties of braided composites. Despite the fact that many models exist for braided composites, a comprehensive model has not been presented that can capture the variety of braiding patterns which can be manufactured using the braiding process. In this study, a new analytical model has been developed that can describe the elastic properties of Diamond, Regular and Hercules braids. The proposed analytical model uses a volume averaging stiffness method in order to account for yarn undulations and the orientation of braid yarns within the braid structure. The model presented here has been compared with the existing FEA and analytical models and has also been validated experimentally. Experimental validation comprised tensile and torsional tests in order to predict the longitudinal and shear moduli for both Diamond and Regular braid geometries. The experimental and proposed model results highlight the effect of braiding pattern and braiding angle on the mechanical properties.

Modeling Headlight Sight Distance on Three-Dimensional Highway Alignments

1997 ◽  
Vol 1579 (1) ◽  
pp. 79-88 ◽  
Author(s):  
Yasser Hassan ◽  
Said M. Easa ◽  
A. O. Abd El Halim
Keyword(s):  
Analytical Model ◽  
Three Dimensional ◽  
Computer Software ◽  
Major Elements ◽  
Geometric Design ◽  
Analytical Models ◽  
Horizontal Curve ◽  
Design Standards ◽  
Sight Distance ◽  
Element Technique

Sight distance is one of the major elements that must be considered in the geometric design to achieve safe and comfortable highways. Daytime sight distance has been extensively studied, and analytical models for two-dimensional (2-D) and three-dimensional (3-D) alignments have been developed. However, nighttime (headlight) sight distance has received less attention. Despite the higher accident rate during nighttime than during daytime, existing analytical models evaluating headlight sight distance are very primitive. Moreover, the interaction between the horizontal and vertical alignments has not been modeled. A four-phase analytical model for headlight sight distance on 3-D combined alignments is presented. The model is an application of the finite-element technique in highway geometric design. The model can determine the maximum distance that can be covered by the vehicle’s headlights and that is not obstructed by any sight obstructions including the road surface. On the basis of this analytical model, computer software was developed and used in a preliminary application for 3-D headlight sight distances on a sag or crest vertical curve combined with a horizontal curve. The application showed that the 3-D sight distance on sag vertical curves was generally lower than the corresponding 2-D value when the sag curve was overlapping with a horizontal curve. On the other hand, the overlapping of horizontal curves with crest vertical curves enhanced the 3-D sight distance. The difference between 2-D and 3-D sight distance values in both cases increased with a decrease in the horizontal curve radius and an increase in the pavement cross slope. The model was proved to be extremely valuable in establishing 3-D highway geometric design standards.

Effects of Laterally and Vertically Neighboring Quantum Dots on Formation of a New Quantum Dot

2003 ◽  
Vol 775 ◽  
Author(s):  
Bo Yang ◽  
Vinod K. Tewary
Keyword(s):  
Quantum Dots ◽  
Quantum Dot ◽  
Release Rate ◽  
Driving Force ◽  
Unit Volume ◽  
Elastic Substrate ◽  
Relaxation Energy ◽  
The Us ◽  
Us Government ◽  
Anisotropic Elastic

AbstractWe apply the elastic-energy-release rate (EERR) to identify the favored location of quantum dot (QD) formation in the presence of a laterally or vertically neighboring grown QD on a linear anisotropic elastic substrate. The EERR is defined as the relaxation energy per unit volume of QD growth. Numerical results for InAs QDs on a GaAs(001) substrate are reported. It is shown that the presence of a laterally neighboring QD inhibits the driving force for the formation of a new QD. In contrast, the presence of a buried (vertically) neighboring QD enhances the driving force for the formation of a new QD at its favorable location.(Publication of the National Institute of Standards and Technology, an agency of the US Government; not subject to copyright.)

Prediction of Elastic Properties of 3D4d Braided Composite Based on Hybrid Model

2017 ◽  
Vol 754 ◽  
pp. 222-225
Author(s):  
Di Zhang ◽  
Xi Tao Zheng ◽  
Tian Chi Wu
Keyword(s):  
Elastic Properties ◽  
Hybrid Model ◽  
Structural Model ◽  
Three Dimensional ◽  
Analytical Models ◽  
Braided Composites ◽  
Braided Composite ◽  
Relative Errors ◽  
Braiding Angle ◽  
Stress Models

This paper presents a meso-scale hybrid model which is used to predict the elastic properties of three-dimensional (3D) four-directional (4d) braided composites. At first, based on meso-structural model of 3D4d braided composite and the assumptions of iso-strain and iso-stress, two analytical models are established. Secondly, a hybrid model used to predict the elastic modulus of the 3D4d braided composite is established which introduces a new factor called hybrid-coefficient Ψ, which incorporates the iso-strain and iso-stress models at the same time, the value of Ψ is dependant on the braiding angle. Comparison between theoretical and experimental results shows that the hybrid model is more accurate than the iso-strain and iso-stress models, and can be used to predict the elastic properties of 3D4d braided composites, with the relative errors around 10%.

Electron Microscopy and image reconstruction reveal the structural basis for spectrin's elastic properties

1992 ◽  
Vol 50 (1) ◽  
pp. 510-511
Author(s):  
Amy M. McGough ◽  
Robert Josephs
Keyword(s):  
Electron Microscopy ◽  
Elastic Properties ◽  
Conformational Changes ◽  
Quaternary Structure ◽  
Three Dimensional ◽  
Membrane Skeleton ◽  
Projection Algorithm ◽  
Structural Basis ◽  
Iterative Approximation ◽  
Membrane Skeletons

The remarkable deformability of the erythrocyte derives in large part from the elastic properties of spectrin, the major component of the membrane skeleton. It is generally accepted that spectrin's elasticity arises from marked conformational changes which include variations in its overall length (1). In this work the structure of spectrin in partially expanded membrane skeletons was studied by electron microscopy to determine the molecular basis for spectrin's elastic properties. Spectrin molecules were analysed with respect to three features: length, conformation, and quaternary structure. The results of these studies lead to a model of how spectrin mediates the elastic deformation of the erythrocyte.Membrane skeletons were isolated from erythrocyte membrane ghosts, negatively stained, and examined by transmission electron microscopy (2). Particle lengths and end-to-end distances were measured from enlarged prints using the computer program MACMEASURE. Spectrin conformation (straightness) was assessed by calculating the particles’ correlation length by iterative approximation (3). Digitised spectrin images were correlation averaged or Fourier filtered to improve their signal-to-noise ratios. Three-dimensional reconstructions were performed using a suite of programs which were based on the filtered back-projection algorithm and executed on a cluster of Microvax 3200 workstations (4).

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

scholarly journals Novel Structure and Thermal Design and Analysis for CubeSats in Formation Flying

Aerospace ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 150
Author(s):  
Yeon-Kyu Park ◽  
Geuk-Nam Kim ◽  
Sang-Young Park
Keyword(s):  
Analytical Model ◽  
Formation Flying ◽  
Thermal Environment ◽  
Thermal Analyses ◽  
Thermal Design ◽  
Analytical Models ◽  
Test Results ◽  
Solar Panels ◽  
Novel Structure ◽  
Micro Propulsion

The CANYVAL-C (CubeSat Astronomy by NASA and Yonsei using a virtual telescope alignment for coronagraph) is a space science demonstration mission that involves taking several images of the solar corona with two CubeSats—1U CubeSat (Timon) and 2U CubeSat (Pumbaa)—in formation flying. In this study, we developed and evaluated structural and thermal designs of the CubeSats Timon and Pumbaa through finite element analyses, considering the nonlinearity effects of the nylon wire of the deployable solar panels installed in Pumbaa. On-orbit thermal analyses were performed with an accurate analytical model for a visible camera on Timon and a micro propulsion system on Pumbaa, which has a narrow operating temperature range. Finally, the analytical models were correlated for enhancing the reliability of the numerical analysis. The test results indicated that the CubeSats are structurally safe with respect to the launch environment and can activate each component under the space thermal environment. The natural frequency of the nylon wire for the deployable solar panels was found to increase significantly as the wire was tightened strongly. The conditions of the thermal vacuum and cycling testing were implemented in the thermal analytical model, which reduced the differences between the analysis and testing.

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