Application of a one-dimensional classical model of atom-oscillator scattering to atom-surface accommodation coefficient theory

1976 ◽  
Vol 60 (1) ◽  
pp. 45-64 ◽  
Author(s):  
Frank O Goodman
Keyword(s):  
Classical Model ◽  
Accommodation Coefficient ◽  
One Dimensional

Velocity Distribution of Electrons Escaping from a Potential Well

2000 ◽  
Vol 651 ◽  
Author(s):  
James P. Lavine
Keyword(s):  
Velocity Distribution ◽  
Classical Model ◽  
Thermionic Emission ◽  
Electron Velocity ◽  
Phonon Interaction ◽  
Electron Velocity Distribution ◽  
One Dimensional ◽  
Electron Phonon Interaction ◽  
Electron Escape ◽  
Effective Temperatures

AbstractElectron escape over a one-dimensional potential barrier is treated with a Monte Carlo method that incorporates simple models for the electron-phonon interaction. The consequences of these models are considered here through the calculation of the escaping electron velocity distribution and the electron energy distribution before escape. Effective temperatures are derived from both distributions. The numerical results are compared with those from the classical model of thermionic emission.

scholarly journals УЗАГАЛЬНЕННЯ МОДЕЛІ ФОЛЬКЕРСЕНА НА ВИПАДОК ОСЬОВОЇ СИМЕТРІЇ

2021 ◽  
pp. 78-89
Author(s):  
К. П. Барахов
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Stress State ◽  
Boundary Conditions ◽  
Classical Model ◽  
The Finite Element Method ◽  
Premature Failure ◽  
One Dimensional ◽  
Element Method

Thin-walled structures may contain defects as cracks and holes that are leftovers of the material the construction, is made of or they occur during the operation as a result of, for example, mechanical damage. The presence of holes in the plate causes a concentration of stresses at the boundary of the holes and ultimately leads to premature failure of the structural element. Repair of local damage of modern aircraft structures can be made by creating overlays that are glued to the main structure. The overlay takes on part of the load, unloading the damaged area. This method of repair provides tightness and aerodynamic efficiency to the structure. The calculation of the stress state of such glued structures is usually performed by using the finite element method. The classic models of the stress state of overlapped joints are one-dimensional. That is, the change of the stress state along only one coordinate is considered. At the same time, the connections of a rectangular form are also considered. The purpose of this work is to create a mathematical model of the stress state of circular axisymmetric adhesive joints and to build an appropriate analytical solution to the problem. It is assumed that the bending of the plates is absent; the deformation of the plates is even by thickness. The adhesive layer works only on the shift. The main plate and the overlay are considered isotropic. The solution is built on polar coordinates. The stress state of the connection depends only on the radial coordinate, i.e. one-dimensional. The solution is obtained in analytical form. This mathematical model is a generalization of the classical model of the adhesive connection of Volkersen to a circular or annular region and is considered for the first time. Boundary conditions are met exactly. The satisfaction of marginal conditions, as well as boundary conditions, leads to a system of linear equations with respect to the unknown coefficients of the obtained solutions. The model problem is solved and the numerical results are compared with the results of calculations performed by using the finite element method. It is shown that the proposed model has sufficient accuracy for engineering problems and can be used to solve problems of the design of aerospace structures.

scholarly journals Variational wave function for generalized Wigner lattices in one dimension

2002 ◽  
Vol 12 (9) ◽  
pp. 69-72
Author(s):  
S. Fratini ◽  
B. Valenzuela ◽  
D. Baeriswyl
Keyword(s):  
Long Range ◽  
Degrees Of Freedom ◽  
Classical Model ◽  
Charge Order ◽  
Energy Scale ◽  
Coulomb Interactions ◽  
Magnetic Exchange ◽  
One Dimensional ◽  
Quantum Version ◽  
Variational Wave

We study a system of electrons on a one-dimensional lattice, interacting through the long range Coulomb forces, by means of a variational technique which is the strong coupling analog of the Gutzwiller approach. The problem is thus the quantum version of Hubbard's classical model of the generalized Wigner crystal [J. Hubbard, Phys. Rev. B 17, 494 (1978)]. The magnetic exchange energy arising from quantum fluctuations is calculated, and turns out to be smaller than the energy scale governing charge degrees of freedom. This approach could be relevant in insulating quasi-one-dimensional compounds where the long range Coulomb interactions are not screened. In these compounds charge order often appears at high temperatures and coexists with magnetic order at low temperatures.

Simulating Area Conservation and the Gas-Wall Interface for One-Dimensional Based Diesel Particulate Filter Models

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Christopher Depcik ◽  
Dennis Assanis
Keyword(s):  
Classical Model ◽  
Particulate Filter ◽  
Gas Temperature ◽  
Flow Area ◽  
Diesel Particulate ◽  
One Dimensional ◽  
Flow Equations ◽  
Particulate Filters ◽  
Soot Loading ◽  
Physical Phenomena

Researchers have been using one-dimensional based models of diesel particulate filters (DPFs) for over two decades with good success in comparison to measured experimental data. Recent efforts in literature have expanded the classical model to account for the effects of varying soot layer thickness on the flow area of the gases. However, some discrepancies exist with respect to this formulation and the physical phenomena modeled in the channel equations. In addition, there is still some discussion regarding the calculation of the gas temperature within the soot and wall layers. As a result, this paper presents a model to discuss these different phenomena to remove or validate previous assumptions. In specific, formulation of the flow equations in area-conserved format (or quasi-one-dimensional) allows the model to account for the changes in the gaseous area as a function of soot loading. In addition, imposing thermodynamic equilibrium at the interface of the channels and wall layers allows the model to capture the thermal entrance lengths. These tasks were undertaken to illustrate whether or not the results justify the effort is worthwhile and this additional complexity needs to be incorporated within the model. By utilizing linear density interpolation in the wall to increase the computational efficiency of the code, it was determined that the classical model assumptions of neglecting soot thickness and gas temperature in the wall are valid within the range of typical DPF applications.

scholarly journals Immiscible capillary flows in non-uniform channels

2021 ◽  
Vol 925 ◽  
Author(s):  
Patrick K. Mortimer ◽  
Andrew W. Woods
Keyword(s):  
Pore Space ◽  
Classical Model ◽  
Early Time ◽  
Bond Number ◽  
Late Time ◽  
Exchange Flow ◽  
One Dimensional ◽  
Capillary Flows ◽  
Intermediate Time ◽  
Wetting Fluid

We consider the release of preferentially wetting fluid in a laterally extensive V-shaped channel initially filled with a second fluid, presenting solutions for the initial exchange flow and the late time spreading of the wetting fluid along the narrow part of the channel. We also show that, if there is a buoyancy force acting in the cross-channel direction, the early time exchange flow depends on the Bond number, and the intermediate time slumping flow may initially be dominated by buoyancy, but at long times becomes controlled by capillarity. Where there is an along-channel component of gravity we show that the flow spreads out downslope, with capillarity controlling the structure of the nose. We then consider the case where the channel is connected to a reservoir of wetting fluid at constant pressure. We show that, depending on this pressure, either a zero flux exchange flow develops, or a net inflow through the whole width of the channel develops, as in the classical Washburn, Lucas, Bell and Cameron capillary imbibition flow. We show these flows are analogous to the classical model for one-dimensional capillary driven flows in porous media, with the current width in the channel corresponding to the saturation in the pore space.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

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