Transport theory in anisotropic media

1978 ◽  
Vol 84 (3) ◽  
pp. 549-567 ◽  
Author(s):  
M. M. R. Williams
Keyword(s):  
Cross Sections ◽  
Transport Theory ◽  
Boltzmann Transport Equation ◽  
Anisotropic Media ◽  
Particle Scattering ◽  
Boltzmann Transport ◽  
Cross Sectional ◽  
Cross Sectional Dependence ◽  
Fixed Axis ◽  
The Mean

AbstractWe develop a theory of particle scattering in anisotropic media. That is, a medium in which the microstructure causes the mean free paths of the particles to become dependent on their direction of motion with respect to some fixed axis. The equation which results is similar to the normal, one-speed Boltzmann transport equation but has cross-sections which are functions of direction. This equation is solved for arbitrary cross-sectional dependence on direction in plane geometry.

scholarly journals Estimating Dynamic Common-Correlated Effects in Stata

2018 ◽  
Vol 18 (3) ◽  
pp. 585-617 ◽  
Author(s):  
Jan Ditzen
Keyword(s):  
Estimation Procedure ◽  
American Statistical Association ◽  
Small Sample ◽  
Cross Sectional ◽  
Pooled Mean Group ◽  
Common Correlated Effects ◽  
Cross Sectional Dependence ◽  
The Common ◽  
The Mean ◽  
Sample Time

In this article, I introduce a new command, xtdcce2, that fits a dynamic common-correlated effects model with heterogeneous coefficients in a panel with a large number of observations over cross-sectional units and time periods. The estimation procedure mainly follows Chudik and Pesaran (2015b, Journal of Econometrics 188: 393–420) but additionally supports the common correlated effects estimator (Pesaran, 2006, Econometrica 74: 967–1012), the mean group estimator (Pesaran and Smith, 1995, Journal of Econometrics 68: 79–113), and the pooled mean group estimator (Pesaran, Shin, and Smith, 1999, Journal of the American Statistical Association, 94: 621–634). xtdcce2 allows heterogeneous or homogeneous coefficients and supports instrumental-variable regressions and unbalanced panels. The cross-sectional dependence test is automatically calculated and presented in the estimation output. Small-sample time-series bias can be corrected by “half-panel” jackknife correction or recursive mean adjustment. I carry out a simulation to prove the estimator's consistency.

Wear Mechanism of Ceramics and Surface Topography

1986 ◽  
Vol 108 (1) ◽  
pp. 9-15 ◽  
Author(s):  
T. Hisakado
Keyword(s):  
Cross Sections ◽  
Friction And Wear ◽  
Cross Sectional ◽  
Wear Rates ◽  
Contact Points ◽  
The Coefficient Of Friction ◽  
The Mean ◽  
New Criterion ◽  
Theoretical Results ◽  
Wear Tests

Assuming that harder asperities sliding on a flat surface were semicylindrical with the hemispherical ends, whose surface consisted of a series of spherical micro-asperities, effects of the number of contact points n, total area Sp of the cross-sections of grooves ploughed by harder asperities and depth of plastic zone on the coefficient of friction and wear for ceramics were theoretically analyzed. To verify theory, wear tests with various ceramic pins and a Si3N4 disk were carried out at a sliding speed of 1.63 m/s and under load of 0.98 N with no lubrication. The sizes of wear scratches on the worn surfaces were measured by means of a Talysurf and SEM photographs. The wear rates of the pins and Si3N4 disks increased with an increase in the mean cross-sectional area Sp/n of the scratches. This trend agreed with the theoretical results, which also showed that the Sp values were proportional to the wear rates. Theory also indicated the existence of a new criterion applicable to estimation of the wear rate.

Strain-Induced Phononic and Structural Response in Wurtzite-Gallium Nitride Nanowires

2013 ◽  
Vol 1548 ◽  
Author(s):  
Jarvis Loh ◽  
Dominique Baillargeat
Keyword(s):  
Gallium Nitride ◽  
Transport Theory ◽  
Structural Response ◽  
Boltzmann Transport ◽  
Structural Morphology ◽  
Cross Sectional ◽  
Gan Nanowires ◽  
Boltzmann Transport Theory ◽  
Thermomechanical Behaviour ◽  
Structure Relationship

AbstractGallium nitride (GaN) nanowires exist in a myriad of cross-sectional shapes. In this study, a series of classical molecular dynamics simulations is performed to investigate the strain-phononics-structure relationship in rectangular and triangular wurtzite (Wz) - GaN nanowires. The thermal conductivity of the nanowires is linearly dependent on the uniaxial strain in both compressive and tensile regimes, and shows no significant dissimilitude for the same amount of strain exerted on the two types of nanowire. This is coherent with an analytical approach using the Boltzmann transport theory. However, the thermomechanical behaviour at the vertex regions shows palpable differences between the two subfamilies, relative to the non-vertex faceted regions, as the structural morphology is most disparate at the vertices.

scholarly journals Biomechanical Evaluation on the Bilateral Asymmetry of Complete Humeral Diaphysis in Chinese Archaeological Populations

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1843
Author(s):  
Yuhao Zhao ◽  
Mi Zhou ◽  
Haijun Li ◽  
Jianing He ◽  
Pianpian Wei ◽  
...  
Keyword(s):  
Cross Sections ◽  
Torsional Rigidity ◽  
Distribution Patterns ◽  
Group Differences ◽  
Micro Ct ◽  
Cross Sectional ◽  
Bilateral Asymmetry ◽  
Biomechanical Evaluation ◽  
The Mean ◽  
Humeral Diaphysis

Diaphyseal cross-sectional geometry (CSG) is an effective indicator of humeral bilateral asymmetry. However, previous studies primarily focused on CSG properties from limited locations to represent the overall bilateral biomechanical performance of humeral diaphysis. In this study, the complete humeral diaphyses of 40 pairs of humeri from three Chinese archaeological populations were scanned using high-resolution micro-CT, and their biomechanical asymmetries were quantified by morphometric mapping. Patterns of humeral asymmetry were compared between sub-groups defined by sex and population, and the representativeness of torsional rigidity asymmetry at the 35% and 50% cross-sections (J35 and J50 asymmetry) was testified. Inter-group differences were observed on the mean morphometric maps, but were not statistically significant. Analogous distribution patterns of highly asymmetrical regions, which correspond to major muscle attachments, were observed across nearly all the sexes and populations. The diaphyseal regions with high variability of bilateral asymmetry tended to present a low asymmetrical level. The J35 and J50 asymmetry were related to the overall humeral asymmetry, but the correlation was moderate and they could not reflect localized asymmetrical features across the diaphysis. This study suggests that the overall asymmetry pattern of humeral diaphysis is more complicated than previously revealed by individual sections.

A Theoretical Derivation of the Similarity of Dynamic Compaction Processes of Powder Media in Dies

1986 ◽  
Vol 108 (2) ◽  
pp. 147-152
Author(s):  
Yukio Sano
Keyword(s):  
Cross Sections ◽  
Dynamic Compaction ◽  
Simple Type ◽  
Theoretical Derivation ◽  
Cross Sectional ◽  
Density Distributions ◽  
Powder Medium ◽  
Compaction Energy ◽  
The Mean ◽  
Compaction Processes

Multiple shock compactions of powder media within a die with a rigid punch are theoretically investigated. First, similarity of dynamic compaction processes for a powder medium of a simple type is exhibited through nondimensionalized one-dimensional equations. The similarity is established after determination of three parameters, i.e., the ratio S* of the lateral surface to the cross-sectional area of the medium, the ratio M* of the mass of the punch to that of the powder medium filled in the die, and the compaction energy per unit powder volume e. The similarity indicates that the particle velocity, specific volume and pressure have the same variation with respect to nondimensional time at all points in the medium with various cross-sections and initial lengths so long as S* is kept fixed at a certain value, i.e., at the same proportional nondimensional point in the medium. The density distributions of the green compacts are necessarily identical, and so is the mean density in all compactions. Second, it is shown in one of the nondimensionalized equations that wall frictional influence in a compaction where S* → 0 is not present, while the wall frictional influence is extremely large when S* is very large, which implies that the mean densities of the compacts are larger in compactions with smaller S*. Two types of compactions can be obtained for any powder medium because the equation used is applicable to any medium.

scholarly journals Transport coefficients calculation using Inference the Momentum-Transfer and Inelastic-Collision Cross Sections of Electrons in Carbon Dioxide

2018 ◽  
Vol 29 (1) ◽  
pp. 174
Author(s):  
Jasim Mohammed salih Ali
Keyword(s):  
Transport Equation ◽  
Momentum Transfer ◽  
Drift Velocity ◽  
Cross Sections ◽  
Transport Coefficients ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Characteristic Energy ◽  
Rf Discharges ◽  
Experimental Values

Abstract: In this work, we were calculate the electron diffusion coefficients, such as, the drift velocity, characteristic energy, and collision frequencies using the cross sections of the momentum transfer and inelastic for electrons in CO2 from figure(1) after solving the Boltzmann transport equation numerically using the Finite-Difference Method in gas medium through applied electric field at 300 oK. The theoretical predictions were obtained in agreement with the experimental values was publishered. Keyword: CO2 lasers, Boltzmann Transport Equation, RF Discharges, Transport coefficients, Plasma discharge, Drift velocity. الخلاصة: في هذا العمل ، تم حساب معاملات انتشار الالكترونات مثل سرعة الانجراف، الطاقة الميزة و ترددات التصادم باستعمال المقاطع العرضية المرنة وغير مرنة للالكترونات في غاز ثاني أوكسيد الكاربون CO2 من شكل (1) خلال حل معادلة الانتقال لبولتزمان عددياً باستخدام طريقة التفريق المحدد في وسط غازي بعد تسليط مجال كهربائي عليه عند درجة حرارة 300 كلفن . النتائج التي تم الحصول عليها تنبأ بأنها متوافقة مع النتائج العملية المنشورة. الكلمات المفتاحية : ليزرات CO2 ، معادلة الانتقال لبولتزمان ، نموذج التفريغ ، معاملات الانتقال ، تفريغ البلازما ، سرعة الانجراف.

Classical Transport Theory and the Imaging of Thick Specimens

1975 ◽  
Vol 33 ◽  
pp. 190-191
Author(s):  
T. Groves
Keyword(s):  
Transport Theory ◽  
Image Formation ◽  
Mean Free Path ◽  
Boltzmann Transport ◽  
Amorphous Films ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
The Mean ◽  
Electron Microscopes ◽  
Classical Transport

It is common in transmission electron microscopy to use specimens which are of the order of a micron in thickness. For such thicknesses it becomes likely that an incident electron will scatter more than once, and one would expect some drastic effects on image formation. A theory of image formation has been derived for thick specimens in the conventional (CEM) and scanning transmission (STEM) electron microscopes. This theory is based on a solution of the Boltzmann transport equation for plural scattering, and is expected to apply to the imaging of small objects embedded in thick amorphous films.We imagine an idealized specimen shown in Fig. 1. A point-like object is embedded in a thick film at a depth n1, measured in units of the mean free path λ for elastic scattering.

scholarly journals An Efficient Solution Scheme for the Spherical-Harmonics Expansion of the Boltzmann Transport Equation Applied to Two-Dimensional Devices

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 239-242
Author(s):  
Maria Cristina Vecchi ◽  
Jan Mohring ◽  
Massimo Rudan
Keyword(s):  
Transport Equation ◽  
Spherical Harmonics ◽  
Numerical Scheme ◽  
Boltzmann Transport Equation ◽  
Boltzmann Transport ◽  
Cpu Time ◽  
Low Energies ◽  
Energy Domain ◽  
The Mean ◽  
Spherical Harmonics Expansion

This paper presents a novel numerical scheme applicable to the solution of the Boltzmann transport equation by means of a spherical-harmonics expansion. This scheme improves the solution at low energies, keeping the desired accuracy in the calculation of the mean quantities while saving a significant amount of CPU time. This is important in view of the applications of the method, since the typical number of nodes to be used in the combined space-energy domain is in the range of 104–105.

On approximative linear Boltzmann transport equation for charged particles

2018 ◽  
Vol 28 (14) ◽  
pp. 2905-2939
Author(s):  
J. Tervo ◽  
P. Kokkonen ◽  
M. Frank ◽  
M. Herty
Keyword(s):  
Transport Equation ◽  
Cross Sections ◽  
Differential Operators ◽  
Boltzmann Transport Equation ◽  
Partial Differential Operator ◽  
Collision Integral ◽  
Boltzmann Transport ◽  
Slowing Down ◽  
Pseudo Differential Operators ◽  
Positivity Of Solutions

We present results on existence and positivity of solutions for a linear Boltzmann transport equation used for example in radiotherapy applications and more generally in charged particle transports. Therein, some differential cross-sections, that is, kernels of collision integral operators, may become hyper-singular. These collision operators need to be approximated for analytical and numerical treatments. Here, we present an approximation leading to pseudo-differential operators. The final approximation, for which the existence and positivity of solutions is shown, is an integro-partial differential operator which is known as Continuous Slowing Down Approximation (CSDA).

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