ELASTIC AND DRIFT–DIFFUSION LIMITS OF ELECTRON–PHONON INTERACTION IN SEMICONDUCTORS

1998 ◽  
Vol 08 (01) ◽  
pp. 37-53 ◽  
Author(s):  
CHRISTIAN SCHMEISER ◽  
ALEXANDER ZWIRCHMAYR
Keyword(s):  
Electron Transport ◽  
Characteristic Length ◽  
Mean Free Path ◽  
Macroscopic Model ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Phonon Interaction ◽  
Drift Diffusion ◽  
Electron Phonon Interaction ◽  
The Mean

This paper deals with electron transport in semiconductors when electron–phonon interaction is considered. Smallness of the mean free path compared to a characteristic length scale and of the phonon energy compared to the thermal energy of the crystal are assumed. The corresponding limits in the transport problem are carried out and shown not to commute. An intermediate limit leads to a new macroscopic model.

DSMC Simulation of Supersonic Gas Flow in Microchannel

2011 ◽  
Author(s):  
Mohamad M. Joneidipour ◽  
Reza Kamali
Keyword(s):  
Gas Flow ◽  
Characteristic Length ◽  
Flow Characteristics ◽  
Mean Free Path ◽  
Incoming Flow ◽  
Characteristic Length Scale ◽  
Flow Pressure ◽  
Supersonic Gas Flow ◽  
The Mean ◽  
Gas Molecules

The present study is concerned with the flow characteristics of a microchannel supersonic gas flow. The direct simulation Monte Carlo (DSMC) method is employed for predicting the density, velocity and temperature distributions. For gas flows in micro systems, the continuum hypothesis, which underpins the Navier-Stokes equations, may be inappropriate. This is because the mean free path of the gas molecules may be comparable to the characteristic length scale of the device. The Knudsen number, Kn, which is the ratio of the mean free path of the gas molecules to the characteristic length scale of the device, is a convenient measure of the degree of rarefaction of the flow. In this paper, the effect of Knudsen number on supersonic microchannel flow characteristics is studied by varying the incoming flow pressure or the microchannel height. In addition, the microchannel height and the incoming flow pressure are varied simultaneously to investigate their effects on the flow characteristics. Meanwhile, the results show that until the diffuse reflection model is used throughout the microchannel, the temperature and the Mach number in the microchannel entrance may not be equal to free-stream values and therefore a discontinuity appear in the flow field.

Multi-particle dispersion during entrainment in turbulent free-shear flows

2016 ◽  
Vol 805 ◽  
Author(s):  
Tomoaki Watanabe ◽  
Carlos B. da Silva ◽  
Koji Nagata
Keyword(s):  
Shear Flows ◽  
Size Dependence ◽  
Characteristic Length ◽  
Particle Dispersion ◽  
Length Scale ◽  
Thin Slab ◽  
Characteristic Length Scale ◽  
Particle Pairs ◽  
The Mean ◽  
Decaying Turbulence

Multi-particle dispersion is studied using direct numerical simulations of temporally evolving mixing layers and planar jets for tetrahedra consisting of four fluid particles which are seeded in the turbulent regions or in the non-turbulent regions near the turbulent/non-turbulent interface (TNTI). The modified Richardson law for decaying turbulence is observed for particle pairs. The size dependence of the mean and relative motions of the entrained tetrahedra indicates that the characteristic length scale of the entrained lumps of fluid is approximately 10 times the Kolmogorov microscale. When the tetrahedra move within the TNTI layer they are flattened and elongated by vortex stretching at a deformation rate that is characterized by the Kolmogorov time scale. The shape evolutions of the tetrahedra show that in free-shear flows, thin-slab structures of advected scalars are generated within the TNTI layers.

Identification of the characteristic length scale for fatigue cracking in fretting contacts

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-159-Pr8-166 ◽  
Author(s):  
S. Fouvry ◽  
Ph. Kapsa ◽  
F. Sidoroff ◽  
L. Vincent
Keyword(s):  
Characteristic Length ◽  
Fatigue Cracking ◽  
Length Scale ◽  
Characteristic Length Scale

scholarly journals Lettau’s Contribution to the Obukhov Length Scale: A Scientific Historical Study

2021 ◽  
Author(s):  
Thomas Foken ◽  
Michael Börngen
Keyword(s):  
Characteristic Length ◽  
Stability Parameter ◽  
Historical Study ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Obukhov Length ◽  
The Future

AbstractIt has been repeatedly assumed that Heinz Lettau found the Obukhov length in 1949 independently of Obukhov in 1946. However, it was not the characteristic length scale, the Obukhov length L, but the ratio of height and the Obukhov length (z/L), the Obukhov stability parameter, that he analyzed. Whether Lettau described the parameter z/L independently of Obukhov is investigated herein. Regardless of speculation about this, the significant contributions made by Lettau in the application of z/L merit this term being called the Obukhov–Lettau stability parameter in the future.

Mesoscopic Disorder

MRS Bulletin ◽  
1994 ◽  
Vol 19 (5) ◽  
pp. 11-13 ◽  
Author(s):  
D.A. Weitz
Keyword(s):  
Molecular Level ◽  
Characteristic Length ◽  
Disordered Materials ◽  
Length Scale ◽  
Interconnected Network ◽  
Characteristic Length Scale ◽  
Fiber Network ◽  
Disordered Structure ◽  
Reading Glasses ◽  
Strong Scattering

Disorder characterizes most of the materials that surround us in nature. Despite their great technological importance, materials with ordered crystalline structures are relatively rare. Examples of disordered materials, however, abound, and their forms can be as varied as their number. The paper on which these words are printed has a disordered structure composed of a highly interconnected network of fibers. It has also been coated with particulate materials to improve its properties and the visibility of the ink. The reading glasses you may require to focus on these words are composed of a glass or polymer material that is disordered on a molecular level. Even the structure of your hand holding this magazine is disordered. These and virtually all other disordered materials are typically parameterized by a characteristic length scale. Above this length scale, the material is homogeneous and the effects of the disorder are not directly manifest; below this characteristic length the disorder of the structure dominates, directly affecting the properties.The range of characteristic length scales for the disordered materials around us is immense. For the glass or polymer of your reading glasses, it is microscopic; the disorder is apparent only at the molecular level, while above this level the material is homogeneous. For the paper on which this magazine is printed, the scale is larger; the paper is white partly because the disordered fiber network has within it structures that are comparable in size to the wavelength of light, resulting in strong scattering of the light.

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