Hysteretic process

Structures made of transforming materials exhibit a striking capacity to hysteretically recover significant deformation with a controllable amount of energy absorbed m the process. The unusual properties of these materials are due to the fact that large deformations and inelastic behavior are accomplished by coordinated migration of mobile phase or domain boundaries. Intensive research in recent years has led to well-defined static continuum theories for some of the transforming materials (see Pitteri and Zanzotto (1997) for a recent review). Within the context of these theories, the main unresolved issues include history and rate sensitivity in the constitutive structure. 

An important feature of combustion phenomena is their hysteretic character for example, extinguishing a high-temperature chemical reaction turns out to be possible only when conditions are provided such that the cold system is far from the threshold of ignition. Realization of a particular combustion regime depends on the history of the process, i.e., whether the initial gas temperature was high or low. 

In this approximation, unlike the general case, the harmonic amplitudes are determined by a single self-similar argument Co/aig. Note also that for the suspensions of ferromagnetic particles, where the hysteretic remagnetization process is possible, Eq. (4.377) holds only if an additional condition... 

Above Eth. the field is sufficiently strong to cause limited translation of the domain wall without disturbing to any significant extent the overall domain structure. This process is described as reversible (more correctly as nearly reversible ) to distinguish it from the very hysteretic and clearly irreversible process evidenced by the hysteresis loop (Fig. 2.46). In this regime the P-E characteristic is a narrow loop, the Rayleigh loop referred to above (c.f. Fig. 6.9). 

Different polysaccharide variable-path processes were observed in a pectin-sugar-water-acid mixture dispersed at 105°C then cooled to 25°C, and a mixture dispersed at 50°C then cooled to 25°C. The higher-temperature gel was relatively stable, but the lower-temperature gel was unstable (Walter and Sherman, 1986). Heated agar sols gel when cooled to approximately 30°C, and they remain dimensionally stable to a reheating temperature of 85°C due to relatively permanent physical crosslinks below Tm (Lips et al., 1988). The reheated gels follow a hysteretic pathway to melting at the... 

The hysteresis loop is considered a dynamic property because the kinetics of activated processes should depend on the observation time. The limit of long observation times is important in geophysics for simulating processes occurring over geological time scales. Kinetics experiments are the most important tool in this respect because the study of hysteretic transitions is otherwise limited to measurements taken under nonequilibrium conditions. 

Upon removal of the light source, the colouring disappears as the molecule remms to its inactivated state, i.e. rest state. Deactivation is usually a slower process than activation and hysteretic behaviour is noted. In terms of the dynamics of deactivation, visible light spectra and heat will increase it, while polar solvents decrease it. Colouring is usually of lower intensity at higher temperamres, i.e. reversely proportionate. 

Sorption by soils and sediments in aquatic surface and subsurface systems functions to retard the transport, regulate the toxicity, and constrain the bioavailability of organic contaminants (1-3). The process is frequently observed to be nonlinear, slow, and apparently hysteretic (4-23). Such behavior is often invoked to explain the ineffectiveness of various technologies to fully cleanup and remediate contaminated... 

The authors collected the test data shown in Table X. From these data it can be noted that the number-average molecular weight, or of a commercial emulsion SBR such as IISRP 1500 or 1712 is typically 90,000 to 175,000. The primary molecular weight of a solution-polymerized polymer produced with an anionic lithium catalyst can, in contrast, be increased toward 250,000 without gelation. In addition, emulsion-polymerized SBR contains only about 92% rubber hydrocarbon as a result of the presence of residues from the production process solution polymers tend to be near 100% hydrocarbon. As a consequence, the authors concluded that the number-average molecular weight can be considered the key parameter of polymer macrostructure, particularly with respect to the hysteretic characteristics of a tread formulation. Hence the differences in macrostructure between emulsion- and solution-polymerized polymers will dictate many of their properties in a tire tread compound. 

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