Quasistatic

Generai principies, representative appiications, fluctuations and irreversibie thermodynamics. Chapter 4 discusses quasistatic processes, reversibie work and heat sources, and thermodynamic engines. 

Therefore, the absorjDtion line is massively inlromogeneously broadened at low temperature. An inliomogeneous lineshape can be used to detennine the static or quasistatic frequency spread of oscillators due to a distribution of environments, but it provides no dynamical infonnation whatsoever [94, 95]. As T is increased to 300 K, the absorjDtion linewidth decreases and increases. At 300 K, the lineshape is nearly homogeneously broadened and dominated by vibrational dephasing, because fast dephasing wipes out effects of inliomogeneous environments, a well known phenomenon tenned motional narrowing [951. 

In the domain we consider the following equations describing quasistatic deformation of a plate ... 

The magnitude and nature of the load are considered in formulating the design. The load may be essentially quasistatic, cycHc, or impact. Many stmctural failures, for example, have been caused by supposedly innocuous stmctural details welded in place without any consideration given to their effect on fatigue properties. The service temperatures are also important, since they affect the fracture resistance of a material. 

Mechanical wave-propagation problems are analyzed on the basis of quasistatic electromagnetic conditions. This is an excellent approximation since the electromagnetic wavespeed greatly exceeds the mechanical wavespeed and the particle velocity is typically only about one-tenth of the mechanical wavespeed. (See the discussion by Thurston [74T01].)... 

Table 3.3. Comparison of results from torsion pendulum and from tensile tests (quasistatic) at T = 500 K...

The Hubbard straight line corresponds to rotational diffusion, and quasistatic straight lines (6.65) to quasi-free rotation. One type of motion substitutes for the other in the vicinity of the minimum point of curve xe,2 (tj) and is accompanied by collapse of the anisotropic scattering spectrum. 

Kinetic friction in the quasistatic limit of v 0 exhibits a similar dependence on a and b. Friction disappears if the strength b is less than a critical value bf, but above this threshold it is the instability similar to that discussed in the... 

The purpose of this section is to show how the previous theory can be applied in practical calculations. For the time being only quasistatic processes have been... 

A second equation is needed to determine the surface tension as a function of axial position. We adopt the quasistatic assumption that a is a unique equilibrium function of the surface excess concentration, T, even during dynamic events (17). A surface species continuity balance dictates how T varies along the interface. Upon neglect of surface diffusion and for h <1, the steady state form of this balance is... 

The above expression and the quasistatic adsorption assumption provide the additional information necessary to establish both the bubble profile, h(x) from Equation 1, and the surfactant distribution, T(x) from Equation 3. 

The rate of rewarming is especially critical. One has to differentiate between quasistatic situations, which are independent of time and all other dynamic states, in which the history of the present situation and the rate of the further changes play an important role. 

Quasi-Static Parameters. We noted earlier that the longer-term gas pressures which develop for explosions in vented or unvented structures can be characterized by three parameters the peak quasistatic pressure Pqs, the duration and the gas impulse ig. For... 

In the problem of pulse diffraction on waveguide junctions, the quasistatic approximation is feasible if the diffraction length of the light beam is much shorter than the characteristic length of the pulse variation owing to the mentioned above MD, FTNR and SS effects which influence the pulse envelope. Then the results obtained for stationary light beam can be used in the analysis of the non-stationary beam self-focusing. 

It is seen that longitudinal dependences of the variation in the pulse duration plotted for 2 of the same modulus but different signs are approximately symmetrical with respect to the curve obtained in the quasistatic approximation. Hence, at normal GVD, the pulse duration is shorter than the initial one as a result of the self-focusing effect until, owing to GVD, this duration continuously increases to its initial value (denoted by asterisks) and then exceeds it. The size of the region within which the pulse compression is observed at decreases with increasing 2 - In turn,... 

The most spectacular success of the theory in its quasistatic limit is to show how to film atomic motions during a physicochemical process. As is widely known, photographing atomic positions in a liquid can be achieved in static problems by Fourier sine transforming the X-ray diffraction pattern [22]. The situation is particularly simple in atomic liquids, where the well-known Zernicke-Prins formula provides g(r) directly. Can this procedure be transfered to the quasistatic case The answer is yes, although some precautions are necessary. The theoretical recipe is as follows (1) Build the quantity F q)q AS q,x), where F q) = is the sharpening factor ... 

The purpose of this section is to show how the above theory can be applied in practical calculations. For the time being, only quasistatic processes have been studied in detail the subsequent discussion will thus focus on this limit. Two sorts of quantities enter into the theory the atom-atom distribution functions r) in a given electronic state j and the corresponding populations nj t). The total atom-atom distribution function gnv(r, t) is then... 

Another interesting limit is the quasistatic limit r 0. Based on the numerical solution of the saddle point equations (160)-(162), it was suggested in Ref. 117 that T q) converged to a constant value over a finite range of work values. Figure 15a shows the results obtained for the heat distributions, whereas the path temperature is shown in Fig. 15b. A more detailed analysis [134] has shown that a plateau is never fully reached for a finite interval of heat values when r 0. The presence of a plateau has been interpreted as the occurrence of a first-order phase transition in the path entropy s q) [134]. 

Indentation hardness determinations were performed in dynamic mode ( 1500 mm/sec impact speed) using a pendulum impact device and in quasistatic mode ( 0.008 mm/sec impact speed) with a custom-built indentation tester. The spherical indenters were of 2.54 cm diameter and 65.6 g mass, and the pendulum length was 92.3 cm with a release angle of 30°. Quasistatic indentation forces were selected to produce indentations of a similar size to the dynamic indentation test (1.5 to 2.0 mm radius). The compact indentations were measured using a white light interferometer (Zygo Corporation, Middlefield, Connecticut, U.S.A.) and the dent depth, dent diameter, apparent radius of curvature, and pendulum initial and rebound heights were used to calculate the indentation hardness of the compacts. 

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