A relaxation function with distribution of relaxation times
Dispersion function model based on mixed second order kinetics with distributed relaxation times
Fang, P. H.↗
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Cole-cole diagram and the distribution of relaxation times.
Cole-Cole diagram in analysis of dielectric relaxation, giving correspondence to Deybe relaxation function
DISTRIBUTION FUNCTION↗
Analysis of shear-relaxation processes in liquid.
Shear relaxation in liquids, criticizing Knollman, Miles and Hamamoto relaxation time distribution measurement method
RELAXATION TIME↗
The distribution of stars in galactic nuclei - Loaded polytropes
We consider the structure of a galactic nucleus in which a compact supermassive object (e.g., a black hole or spinar) is embedded. The surrounding stars are assumed to satisfy a polytropic or isothermal equation of state. The density distribution of these loaded polytropes has a sharp central spike in which the time scale for stellar collisions can be short. Other properties of loaded polytropes, such as their masses, radii, projected density distribution, relaxation times, and stability, can also differ significantly from those of normal polytropes.
Huntley, J. M.↗
Vibrational relaxation in expanding N2 and air
New N2 vibrational temperature data, obtained in expanding N2 and air using the electron beam technique, are analyzed permitting the vibrational relaxation times to be determined as a function of temperature. In addition, the effects on N2 vibrational relaxation times of direct vibrational energy transfer between N2 and H2O, between N2 and O2, and between N2 and free electrons introduced from arc contaminants are analyzed. The vibrational relaxation times determined from the present measurements agree with those measured in the expanding flows of shock tunnels and impact tubes. These expanding data also agree with relaxation times observed in acoustical resonant cavities where alternating compressions and expansions take place. The relaxation times in expanding flows (vib-tran exchange process) are found to be approximately 50 times faster than those measured in the compressing flow of shock tubes (tran-vib exchange process). This evidence strongly supports the concept that one relaxation time distribution cannot be applied to both exchange processes.
Sebacher, D. I.↗
Symmetry relation in relaxation dispersions.
Symmetry relation between dispersion function of frequency variable and distribution function of relaxation time variable
RELAXATION TIME↗
Gaseous electronics
Electron-electron relaxation rates determined from time-dependent electron velocity distribution
VELOCITY DISTRIBUTION↗
Time-domain approach for the transient responses in stratified viscoelastic Earth models
We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a constrast of O(100) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(100) and O(exp 4) years. The principal mode is embedded within this continuous spectrum. From this initial-value approach we have found that for the low degree harmonics the non-modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time-domain and normal-mode results are found to decrease strongly with increasing angular order. These calculations also show that a time-dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.
Hanyk, L.↗
The frequency dependence of the viscous component of the magnetic susceptibility of lunar rock and soil samples
The susceptibility of two lunar samples (a soil and a low metamorphic grade breccia) has been measured in a weak field - 0.001 Oe - and as a function of frequency from 0.032 to 1.0 Hz. The measurements were made using a superconducting magnetometer. The results show that the susceptibility decreases linearly with the log of frequency. This observation is in agreement with a theoretical model for viscous decay based on the Neel theory of single-domain and superparamagnetic grains. The relation derived agrees with a model in which there is a uniform distribution of relaxation times.
Hanneken, J. W.↗
Creep Life of Ceramic Components Using a Finite-Element-Based Integrated Design Program (CARES/CREEP)
The desirable properties of ceramics at high temperatures have generated interest in their use for structural application such as in advanced turbine engine systems. Design lives for such systems can exceed 10,000 hours. The long life requirement necessitates subjecting the components to relatively low stresses. The combination of high temperatures and low stresses typically places failure for monolithic ceramics in the creep regime. The objective of this paper is to present a design methodology for predicting the lifetimes of structural components subjected to creep rupture conditions. This methodology utilizes commercially available finite element packages and takes into account the time-varying creep strain distributions (stress relaxation). The creep life, of a component is discretized into short time steps, during which the stress and strain distributions are assumed constant. The damage is calculated for each time step based on a modified Monkman-Grant creep rupture criterion. Failure is assumed to occur when the normalized accumulated damage at any point in the component is greater than or equal to unity. The corresponding time will be the creep rupture life for that component. Examples are chosen to demonstrate the Ceramics Analysis and Reliability Evaluation of Structures/CREEP (CARES/CREEP) integrated design program, which is written for the ANSYS finite element package. Depending on the component size and loading conditions, it was found that in real structures one of two competing failure modes (creep or slow crack growth) will dominate. Applications to benchmark problems and engine components are included.
Powers, L. M.↗
Creep Life of Ceramic Components Using a Finite-Element-Based Integrated Design Program (CARES/CREEP)
The desirable properties of ceramics at high temperatures have generated interest in their use for structural applications such as in advanced turbine systems. Design lives for such systems can exceed 10,000 hours. The long life requirement necessitates subjecting the components to relatively low stresses. The combination of high temperatures and low stresses typically places failure for monolithic ceramics in the creep regime. The objective of this paper is to present a design methodology for predicting the lifetimes of structural components subjected to creep rupture conditions. This methodology utilized commercially available finite element packages and takes into account the time-varying creep strain distributions (stress relaxation). The creep life of a component is discretized into short time steps, during which the stress and strain distributions are assumed constant. The damage is calculated for each time step based on a modified Monkman-Grant creep rupture criterion. Failure is assumed to occur when the normalized accumulated damage at any point in the component is greater than or equal to unity. The corresponding time will be the creep rupture life for that component. Examples are chosen to demonstrate the CARES/CREEP (Ceramics Analysis and Reliability Evaluation of Structures/CREEP) integrated design programs, which is written for the ANSYS finite element package. Depending on the component size and loading conditions, it was found that in real structures one of two competing failure modes (creep or slow crack growth) will dominate. Applications to benechmark problems and engine components are included.
Gyekenyesi, J. P.↗
Creep Life Prediction of Ceramic Components Using the Finite Element Based Integrated Design Program (CARES/Creep)
The desirable properties of ceramics at high temperatures have generated interest in their use for structural applications such as in advanced turbine systems. Design lives for such systems can exceed 10,000 hours. Such long life requirements necessitate subjecting the components to relatively low stresses. The combination of high temperatures and low stresses typically places failure for monolithic ceramics in the creep regime. The objective of this work is to present a design methodology for predicting the lifetimes of structural components subjected to multiaxial creep loading. This methodology utilizes commercially available finite element packages and takes into account the time varying creep stress distributions (stress relaxation). In this methodology, the creep life of a component is divided into short time steps, during which, the stress and strain distributions are assumed constant. The damage, D, is calculated for each time step based on a modified Monkman-Grant creep rupture criterion. For components subjected to predominantly tensile loading, failure is assumed to occur when the normalized accumulated damage at any point in the component is greater than or equal to unity.
Jadaan, Osama M.↗
Random walk study of electron motion in helium in crossed electromagnetic fields
Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.
Englert, G. W.↗
A correlation of N sub 2 vibrational goes to translational relaxation times.
Correlation of nitrogen vibrational-translational relaxation times for various measuring methods, noting temperature distribution of rate
VIBRATIONAL RELAXATION↗
High order finite difference and multigrid methods for spatially evolving instability in a planar channel
The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.
Liu, C.↗
Variable thermal properties and thermal relaxation time in hyperbolic heat conduction
Numerical solutions were obtained for a finite slab with an applied surface heat flux at one boundary using both the hyperbolic (MacCormack's method) and parabolic (Crank-Nicolson method) heat conduction equations. The effects on the temperature distributions of varying density, specific heat, and thermal relaxation time were calculated. Each of these properties had an effect on the thermal front velocity (in the hyperbolic solution) as well as the temperatures in the medium. In the hyperbolic solutions, as the density or specific heat decreased with temperature, both the temperatures within the medium and the thermal front velocity increased. The value taken for the thermal relaxation time was found to determine the 'hyperbolicity' of the heat conduction model. The use of a time dependent relaxation time allowed for solutions where the thermal energy propagated as a high temperature wave initially, but approached a diffusion process more rapidly than was possible with a constant large relaxation time.
Glass, David E.↗
The H + OCS hot atom reaction - CO state distributions and translational energy from time-resolved infrared absorption spectroscopy
Time-resolved infrared diode laser spectroscopy has been used to probe CO internal and translational excitation from the reaction of hot H atoms with OCS. Product distributions should be strongly biased toward the maximum 1.4 eV collision energy obtained from 278 nm pulsed photolysis of HI. Rotations and vibrations are both colder than predicted by statistical density of states theory, as evidenced by large positive surprisal parameters. The bias against rotation is stronger than that against vibration, with measurable population as high as v = 4. The average CO internal excitation is 1920/cm, accounting for only 13 percent of the available energy. Of the energy balance, time-resolved sub-Doppler line shape measurements show that more than 38 percent appears as relative translation of the separating CO and SH fragments. Studies of the relaxation kinetics indicate that some rotational energy transfer occurs on the time scale of our measurements, but the distributions do not relax sufficiently to alter our conclusions. Vibrational distributions are nascent, though vibrational relaxation of excited CO is unusually fast in the OCS bath, with rates approaching 3 percent of gas kinetic for v = 1.
Nickolaisen, Scott L.↗
Diffusion of charged particles in a random magnetic field
When charged particles move in a random magnetic field superimposed upon a relatively large constant field, their pitch angle distribution can be calculated to any desired precision by an iterative approximation procedure. Improved knowledge of the pitch angle distribution and of the characteristic time for relaxation of anisotropy leads to an accurate expression for the coefficient of diffusion parallel to the mean field.
Earl, J. A.↗