The Debye Theory of Rotary Diffusion: History, Derivation, and Generalizations

2001 ◽  
Vol 158 (1) ◽  
pp. 1-27
Author(s):  
Eliot Fried ◽  
Shaun Sellers
Keyword(s):  
Debye Theory ◽  
Rotary Diffusion

The Debye theory of solid-state heat capacities

2021 ◽  
pp. 295-309
Author(s):  
Geoffrey Brooker
Keyword(s):  
High Temperature ◽  
Solid State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
Linear Chain ◽  
Heat Capacities ◽  
Debye Theory ◽  
State Heat ◽  
Equipartition Of Energy ◽  
Reasonable Step

“The Debye theory of solid-state heat capacities” gives a careful account of the Debye cut-off. We start by looking at a monatomic linear chain, leading to degrees of freedom and the equipartition of energy at the high-temperature (classical) limit. Reasonable approximations lead more naturally to the Born–von Karman model than to Debye, but Debye follows via a further reasonable step.

scholarly journals Fiber Orientation Predictions—A Review of Existing Models

2020 ◽  
Vol 4 (2) ◽  
pp. 69 ◽  
Author(s):  
Susanne Katrin Kugler ◽  
Armin Kech ◽  
Camilo Cruz ◽  
Tim Osswald
Keyword(s):  
Fiber Orientation ◽  
Mechanical Performance ◽  
Historical Review ◽  
Fiber Reinforced Polymers ◽  
Strong Impact ◽  
Fiber Reinforced ◽  
Reinforced Polymers ◽  
Virtual Engineering ◽  
Rotary Diffusion ◽  
Orientation Phenomenon

Fiber reinforced polymers are key materials across different industries. The manufacturing processes of those materials have typically strong impact on their final microstructure, which at the same time controls the mechanical performance of the part. A reliable virtual engineering design of fiber-reinforced polymers requires therefore considering the simulation of the process-induced microstructure. One relevant microstructure descriptor in fiber-reinforced polymers is the fiber orientation. This work focuses on the modeling of the fiber orientation phenomenon and presents a historical review of the different modelling approaches. In this context, the article describes different macroscopic fiber orientation models such as the Folgar-Tucker, nematic, reduced strain closure (RSC), retarding principal rate (RPR), anisotropic rotary diffusion (ARD), principal anisotropic rotary diffusion (pARD), and Moldflow rotary diffusion (MRD) model. We discuss briefly about closure approximations, which are a common mathematical element of those macroscopic fiber orientation models. In the last section, we introduce some micro-scale numerical methods for simulating the fiber orientation phenomenon, such as the discrete element method (DEM), the smoothed particle hydrodynamics (SPH) method and the moving particle semi-implicit (MPS) method.

Suboptical Dielectric Losses by Condensed Nonpolar Media

1973 ◽  
Vol 51 (12) ◽  
pp. 1266-1275 ◽  
Author(s):  
D. G. Frood ◽  
A. Morita
Keyword(s):  
Near Infrared ◽  
Cell Model ◽  
Harmonic Approximation ◽  
Far Infrared ◽  
Phenomenological Theory ◽  
Mode Frequency ◽  
Range Interaction ◽  
Debye Theory ◽  
Polar Media ◽  
Nonpolar Liquids

Debye theory applied to the observed microwave and far-infrared losses by nonpolar liquids based on the assumption either of (a)temporary, multipole-induced dipoles or (b) a number of equivalent equilibrium positions for the molecular charges separated by potential barriers is shown to be inadequate. In dense non-polar media absorption at suboptical frequencies, i.e. frequencies below visible and near-infrared will arise from nonharmonic properties of the relative motions of electrons and nuclei. To develop a phenomenological theory of the effect in condensed fluids, we introduce the cell model and assume densities sufficiently high that a nonpolar particle is bound harmonically to the cell center through short-range interaction with its immediate neighbors for times long compared to its period of oscillation. It also interacts with all others through long-range dipolar forces provided by the Lorentz field. Assuming the fluctuating forces lead to velocity damping of the cell, the dielectric constant is shown to have the same form as found in ionic crystals in the harmonic approximation with the residual ray frequency replaced by the infrared normal mode frequency—prescribed by the present model. The medium thus shows a maximum in its absorption coefficient at the infrared mode frequency and all nonpolar media at sufficiently high densities will exhibit infrared losses. As the density of an insulating nonpolar liquid is raised, the infrared mode frequency shifts to lower values and ultimately to zero (the "dielectric catastrophe") at which point the liquid becomes metallic.

scholarly journals Partially Coherent, Radially Polarized Beam with Annular Apodization

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
C. Mariyal ◽  
P. Suresh ◽  
K. B. Rajesh ◽  
T. V. S. Pillai
Keyword(s):  
Focal Depth ◽  
Focal Region ◽  
Debye Theory ◽  
Partially Coherent ◽  
Tight Focusing ◽  
Polarized Beam ◽  
Microscopy Techniques ◽  
Radially Polarized ◽  
High Na Lens ◽  
Focusing Properties

Based on the vectorial Debye theory, the tight focusing properties of partially coherent, radially polarized vortex beams are investigated in detail. In this paper, we propose to use an amplitude modulated filter in combination with a high NA lens to generate long focal depth in the focal region. Numerical results show that the generation of long focal depth of FWHM (22.08λ) is achieved, which finds useful application in microscopy techniques such as particle acceleration, laser processing, optical micromanipulation, and beam shaping.

Gravitational and Coulomb Potentials Interference in Heliosphere

2020 ◽  
pp. 93-121
Author(s):  
P.I. Vysikaylo ◽  
N.S. Ryabukha
Keyword(s):  
Solar Wind ◽  
Solar Wind Plasma ◽  
The Sun ◽  
Number Density ◽  
Heavy Particles ◽  
Debye Theory ◽  
Experimental Values ◽  
First Time ◽  
Small Charge ◽  
Coulomb Potentials

Interference of gravitational and Coulomb potentials in the entire heliosphere is considered, it is being manifested in generation of two opposite flows of charged particles: 1) that are neutral or with a small charge to the Sun, and 2) in the form of a solar wind from the Sun. According to the Einstein --- Smoluchowski relation Te(R) = eDe / µe ~ (E/N)0.75 based on the N experimental values (heavy particles number density --- the ne electron concentration), the Te electron temperature in the entire heliosphere was for the first time analytically calculated depending on the charge of the Sun and distance to it R. Calculated values of the registered ion parameters in the solar wind were compared with experimental observations. Reasons for generating the ring current in inhomogeneous heliosphere and inapplicability of the Debye theory in describing processes in the solar wind (plasma with current) are considered

Non-Destructive Tracking of Structural Changes of Concrete Mixtures during Thermal Stress

2014 ◽  
Vol 617 ◽  
pp. 152-155 ◽  
Author(s):  
Ivo Kusák ◽  
Miroslav Lunak ◽  
Zdeněk Chobola
Keyword(s):  
Thermal Stress ◽  
Structural Reliability ◽  
Structural Changes ◽  
Dielectric Material ◽  
Temperature Treatment ◽  
High Temperature Treatment ◽  
Model Parameters ◽  
Debye Theory ◽  
Concrete Mixtures ◽  
Non Destructive

This paper deals with the application of the method of impedance spectroscopy to testing of cement-based composites prepared from a mix of cement mortar and quartz sand, which were intentionally degraded by high-temperature treatment (in the temperatures range from 25 °C to 400 °C). The monitoring of structural changes in the thermal stress is very important, for example for determining the reliability of the whole structure. Based on the Debye theory of dielectric the models were created, their applications and received parameters measured dielectric material is characterized and discussed the uniqueness of determining the values of model parameters. Development of electrical parameters and permittivity at each temperature areas reliably show these structural changes and thus the structural reliability.

THE INFLUENCE OF CATION RADIUS AND SALT CONCENTRATION IN THE SALTING OUT OF ETHYL ETHER FROM AQUEOUS NITRATE SOLUTIONS AT 25°C.

1951 ◽  
Vol 29 (7) ◽  
pp. 563-574
Author(s):  
H. G. Heal
Keyword(s):  
Aqueous Solutions ◽  
Ethyl Ether ◽  
Salt Concentration ◽  
Alkali Metals ◽  
Infinite Dilution ◽  
Salting Out ◽  
Debye Theory ◽  
Cation Radius ◽  
Alkaline Earths ◽  
Nitrate Solutions

The solubility of ethyl ether in aqueous solutions of the nitrates of the alkali metals, the alkaline earths and magnesium, and ammonium, tetramethyl, tetraethyl, and tetra-n-propyl ammonium has been measured with high precision. The salting out at infinite dilution of salt, estimated by extrapolation from data for salt concentrations below 0.1 molal, conforms in a general way to the Debye theory, with some discrepancies. Data for high salt concentrations are also given.

Sign in / Sign up

Export Citation Format

Share Document