Volume elasticity

Volume change of charge neutralization, ELECTROSTRICTION Volume elasticity,... 

At one end of the spectrum are first-principles methods where the only input requirements are the atomic numbers Za, Zb,. .. the relevant mole fractions and a specified crystal structure. This is a simple extension to the methods used to determine the lattice stability of the elements themselves. Having specified the atomic numbers, and some specific approximation for the interaction of the relevant wave functions, there is no need for any further specification of attractive and repulsive terms. Other properties, such as the equilibrium atomic volumes, elastic moduli and charge transfer, result automatically from the global minimisation of... 

Embedded atom potentials have been extensively used for performing atomistic simulations of point, line and planar defects in metals and alloys (e.g. Vitek and Srolovitz 1989). The pair potential ( ), atomic charge density pBtom(r), and embedding function F(p) are usually fitted to reproduce the known equilibrium atomic volume, elastic moduli, and ground state structure of the perfect defect-free lattice. However, the prediction of ground state structure, especially the competition between the common metallic structure types fee, bcc, and hep, requires a more careful treatment of the pair potential contribution ( ) than that provided by the semiempirical embedded atom potential. This is considered in the next chapter. 

Pulsation dampeners work by fluid friction, reflexion of pressure waves and volume elasticity. They represent an effective measure of controlling pulsation. 

Thus, the volume elastic modulus of the percolation system near the percolation threshold (p —> pc + 0) may be defined as... 

By using this correspondence principle for a connected set, the complex volume elastic modulus K and the complex shear modulus p at the (k + l)th step can be written... 

IV. The volume elasticity of a substance is defined as the ratio of any small increase of pressure to the diminution of volume per unit volume of substance. If the temperature is kept constant... 

Values for tte internal variabtes in thetmodynamic, internal equilibriwn are generally uniquely defined by the values for the external variables. For instance, in a simple, thermomechanical system (i.e. one that reacts mechanically solely volume-elastically) the equilibrium concentrations of the conformational isomers are uniquely described by temperature and pressure. In this case the conformational isomerism is not explicitly percqitible, but causes only overall effects, for example in the system s enthalpy or entropy. Elastic macroscopic effects may, however, occur when the relationship between internal and external variables is not single-valued. Then the response-functions of the system diverge or show discontinuities. The Systran undergoes a thermodynamic transformation. The best-known example of sudi a transformation based on conformational isomerism is the helix-coil transition displayed by sonte polymers in solution. An example in the scdid state is the crystal-to-condis crystal transition discussed in this paper. The conditions under which such transformations occur are dealt with in more detail in Sect 2.2. 

Rock types Modulus of volume elasticity B/Pa Shear modulus S/Pa Angle of internal friction F/° Cohesive force C/Pa Tensile strength T/Pa Density D/kg.m ... 

Parameters Lithology Bulk density (KN/m=) Modulus of volume elasticity (Gpa) Shear modulus (Gpa) Cohesion (MPa) Angle of internal friction (°)... 

Vasl] Measuring of frie resonanee ultrasonic frequency excited by piezoelectrie vibrator Volume elasticity... 

The pair potential atomic charge density and embedding function F(p) are usually fitted to reproduce the known equilibrium atomic volume, elastic moduli, and ground-state structure of the defect-free lattice. 

Bulk modulus n. The modulus of volume elasticity, i.e., the resistance of a solid or liquid to change in volume with change in pressure, at constant temperature. The thermodynamic definition is ... 

Following Hooke s law, only squares of the director deformations (9Li/9xj), where i, Xj = x, y, 2 , are included in the expression for the free energy. At the same time attention is paid only to the pure volume elastic terms L(r), r G V. All the terms which could be expressed via the surface director field L(r), r G 5 are omitted. 

In view of these suggestions the density of the free volume elastic energy (Frank s energy) of a nematic liquid crystal could be written as... 

SAGAWA I also disagree with Dr. Feigl. I don t see any reason why the word elastance should be used strictly as a passive property. Even the so-called passive property of muscle is quite active. It is very difficult to draw a sharp line between passive and active muscle. In addition, in engineering, the suffix ance is not used to represent a material property. Instead it represents a systems property. For example, the elastance of the balloon at a given volume is not a measure of the elasticity of the balloon material. Instead, the term elasticity, or modulus of volume elasticity, is used to describe the material property. So I think it s right to use the term elastance for the ventricular chamber regardless of its state of activation. 

Over the past decade, we (Sagawa, 1978) have measured the ventricular pressure (P)-volume (V) relationship in an isolated and blood perfused canine heart preparation and came to consider that the ventricular end-systolic P-V relationship (ESPVR) is (a) linear as opposed to the highly nonlinear P-V relationship of the frog s ventricle reported by Otto Frank a century ago, (b) rather insensitive to the preload and afterload and (c) changes its slope (E, ) sensitively with inotropic interventions without a significant shift in the volume intercept (Vq). This is to say that our model of the ventricle merely consists of a linear volume elastance E which varies with each heart beat from a smaller end-diastolic value to a larger... 

The mean correlation coefficient was 0.985 0.004 (SE). The result demonstrates that, as far as prediction of 5V is concerned, our linear end-systolic volume-elastance model is reasonably accurate despite its neglection of a slight afterload dependence (a small sift of V with changes in afterload resistance and characteristic impedance) (Maughan et ai, 1984). 

The specific (per unit volume) elastic energy released from PZ fibrils and membranes due to their break is denoted by g,. Thus, the rate of energy release due to crack advance into PZ is g S. The rate of the energy consumed due to crack advance is denoted by 2y, ... 

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