Periodic motion of a piecewise homogeneous medium with complex damping

Geophysics ◽  
1987 ◽  
Vol 52 (3) ◽  
pp. 335-341 ◽  
Author(s):  
H. L. Langhaar ◽  
A. P. Boresi
Keyword(s):  
Periodic Motion ◽  
Displacement Vector ◽  
Homogeneous Medium ◽  
One Dimensional ◽  
Work Input ◽  
Piecewise Homogeneous Medium ◽  
Space Coordinate ◽  
The One ◽  
Energy Dissipated ◽  
Complex Damping

A piecewise homogeneous medium with complex damping (Q damping) is excited by a prescribed periodic motion at the origin. The differential equations for the associated periodic motion of the medium are shown to be of second order in terms of the space‐dependent displacement components. The continuity conditions at an interface between disparate parts require specific conditions on the stress vector and the displacement components. We solve the one‐dimensional case completely, in which the displacement vector depends upon a single space coordinate, for a bilayered medium. An explicit formula for the energy dissipation in a layer, based upon the work input to the medium, shows that the energy dissipated is zero when no damping is present and is positive for positive damping.

Zur Theorie der Gegenstromelektrolyse

1970 ◽  
Vol 25 (7) ◽  
pp. 1007-1017
Author(s):  
H. Gaus
Keyword(s):  
Aqueous Solution ◽  
Diffusion Coefficient ◽  
Dimensional Space ◽  
One Dimensional ◽  
First Order ◽  
Space Coordinate ◽  
The One ◽  
Space Dependence ◽  
Common Anion ◽  
First Order Differential Equations

In the case of stationary countercurrent electrolysis the one dimensional space dependence of the different concentrations is governed by a system of nonlinear first order differential equations. Here one takes into account the dependence of the electric field on the concentrations. One considers a mixture of completely dissociating salts with a common anion solved in an aqueous solution of the completely dissociating acid with the same anion. The equations are solved rigorously both in the homogeneous and the inhomogeneous case. One gets the concentrations and the space coordinate explicitly as a function of a parameter w, which is the electric potential divided by the diffusion coefficient. For infinitely long tubes the Kohlrausch-condition remains valid also in regions, where the profiles of the concentrations are influenced by diffusional transport. The results are applied to a process investigated by other authors

Nondestructive Depth Profiling of a Diffuse Interface

1988 ◽  
Vol 142 ◽  
Author(s):  
Anthony N. Sinclair ◽  
Phineas Dickstein ◽  
Michael A. Graf
Keyword(s):  
Wave Equation ◽  
Reflection Coefficient ◽  
Theoretical Calculations ◽  
Homogeneous Medium ◽  
Depth Profiling ◽  
Diffuse Interface ◽  
One Dimensional ◽  
Frequency Comparison ◽  
The One ◽  
Dimensional Wave

AbstractA numerical solution of the one-dimensional wave equation is used to find the characteristics of wave propagation in a non-homogeneous medium. The solution is used to determine the magnitude and phase of the reflection coefficient at a diffuse interface. The result is found to be strongly dependent on sonic frequency. Comparison is made between theoretical calculations and measurements of the reflection coefficient at a copper-to-nickel diffusion bond.

Optimization of the Axial Porosity Distribution of Porous Inserts in a Liquid-Piston Gas Compressor Using a One-Dimensional Formulation

2013 ◽  
Author(s):  
Chao Zhang ◽  
Terrence W. Simon ◽  
Perry Y. Li
Keyword(s):  
Porous Media ◽  
Piston Compressor ◽  
High Porosity ◽  
Porosity Distribution ◽  
One Dimensional ◽  
Piston Speed ◽  
Work Input ◽  
The One ◽  
Liquid Piston ◽  
D Model

A One-Dimensional (One-D) numerical model to calculate transient temperature distributions in a liquid-piston compressor with porous inserts is presented. The liquid-piston compressor is used for Compressed Air Energy Storage (CAES), and the inserted porous media serve the purpose of reducing temperature rise during compression. The One-D model considers heat transfer by convection in both the fluids (gas and liquid) and convective heat exchange with the solid. The Volume of Fluid (VOF) method is used in the model to deal with the moving liquid-gas interface. Solutions of the One-D model are validated against full CFD solutions of the same problem but within a two-dimensional computation domain, and against another study given in the literature. The model is used to optimize the porosity distribution, in the axial direction, of the porous insert. The objective is to minimize the compression work input for a given piston speed and a given overall pressure compression ratio. The model equations are discretized and solved by a finite difference method. The optimization method is based on sensitivity calculations in an iterative procedure. The sensitivity is the partial derivative of compression work with respect to the porosity value at each optimization node. In each optimization round, the One-D model is solved as many times as there are optimization nodes, and each time the porosity value at a single optimization node is changed by a small amount. From these calculations, the sensitivity of changing the porosity distribution to the total work input (objective) is obtained. Based on this, the porosity distribution is updated in the direction that favors the objective. Then, the optimization procedure marches to the next round and the same calculations are completed iteratively until an optimum solution is reached. The optimization shows that porous media with high porosity should be used in the lower part of the chamber and porous media with low porosity should be used in the upper part of the chamber. An optimal distribution of porosity over the chamber is obtained.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Method of first integrals and interface, surface waves

2010 ◽  
Vol 32 (2) ◽  
pp. 107-120
Author(s):  
Pham Chi Vinh ◽  
Trinh Thi Thanh Hue ◽  
Dinh Van Quang ◽  
Nguyen Thi Khanh Linh ◽  
Nguyen Thi Nam
Keyword(s):  
Rayleigh Waves ◽  
Displacement Vector ◽  
Attenuation Factor ◽  
Electrical Potential ◽  
Polarization Vector ◽  
First Integrals ◽  
Dispersion Equations ◽  
Interface Surface ◽  
Electric Induction ◽  
The One

The method of first integrals (MFI) based on the equation of motion for the displacement vector, or  based on the one for the traction vector was introduced  recently in order to find explicit secular equations of Rayleigh waves whose characteristic equations (i.e the equations determining the attenuation factor) are fully quartic or are of higher order (then the classical approach is not applicable). In this paper it is shown that, not only to Rayleigh waves,  the MFI can be applicable also to other waves by running it on the equations for mixed vectors. In particular: (i) By applying the MFI  to the equations for the displacement-traction vector we get the explicit dispersion equations of Stoneley waves in twinned crystals (ii)  Running the MFI on the equations for the traction-electric induction vector and the traction-electrical potential vector provides the explicit dispersion equations of SH-waves in piezoelastic materials. The obtained dispersion equations are identical with the ones previously derived using the method of polarization vector, but the procedure of driving them is more simple.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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