Elasticity. Adiabatic

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

Hugoniot. At low-stress amplitudes pot /o C S c,o, where c,o is the adiabatic longitudinal elastic sound speed at p = pg. 

To plan and fully analyze experimental studies of the effect of adiabatic elastic strain on the electrical conductivity of germanium, C.L. Julian (for-... 

Adiabatic elasticity, Q, measured under such conditions that no heat is allowed to enter, or escape from, the fluid during the volume change. 

Attenuation in solids due to viscosity may be treated by a similar analysis. There may well be other damping mechanisms, such as heat conduction (i.e. imperfectly adiabatic conditions) which also gives an f2 law, and other phenomena associated with solid state defects that may have more complicated frequency and temperature dependence. In polycrystalline solids, especially metals and alloys and also ceramics, elastic grain scattering may cause much greater attenuation than any inelastic damping (Papadakis 1968 Stanke and Kino 1984). 

Pandit and King (1982) and Bathe et al. (1984) presented measurements using transducer techniques, which are somewhat different from the accepted values of Kiefte et al. (1985). The reason for the discrepancy of the sonic velocity values from those in Table 2.8 and above is not fully understood. It should be noted that compressional velocity values can vary significantly depending on the hydrate composition and occupancy. This has been demonstrated by lattice-dynamics calculations, which showed that the adiabatic elastic moduli of methane hydrate is larger than that of a hypothetical empty hydrate lattice (Shpakov et al., 1998). 

To describe the effect of the change of the elastic springs on the optical spectrum of an impurity center, we use the adiabatic approximation. In this approximation, phonons are described by different phonon Hamiltonians in different electronic states. The optical spectrum, which corresponds to a transition between different electronic states is determined by the expression /( >) = const X oj1 1 I(oj) [28], where the — sign corresponds to the absorption spectrum and the + sign stands for the emission spectrum,... 

Katchalsky and Curran [2], for example, consider a system separated from the environment by a rigid adiabatic wall. The system consists of two compartments 1 and 2, separated by a diathermal, elastic barrier that is permeable to one of the components in the system (Figure 4.1). It can be shown that the entropy generation rate is given by... 

This expression clearly has parallels with Equation 5 if we interpret adiabatic compressibility, k, as the reciprocal of the elastic modulus, M. This simple equation is the key to an important class of food measurements because k is related to changes in the tertiary structure of proteins, opening up the possibility of rapid characterization and the detection of denaturation (Apenten et al., 2000). For mixtures of materials, Wood (1941) invoked the idea of an effective medium to represent a mixture consisting of particles suspended in a continuum with compressibility and density given as ... 

There may be, however, another reason why for polymers the results of dynamic and static experiments can differ. Polymers are not really elastic, but viscoelastic materials. The high frequencies of most adiabatic techniques do not allow equilibrium to be reached in viscoelastic materials at high frequencies they will behave more elastic and less viscous. 

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