The Relaxation Process

While various approaches are suggested in the literature to describe and generalize relaxation processes concerning to several objectives, the wider problem addressed here is to find the best-suited relaxation process for a given assignment problem, or better still, to construct a task-dependent relaxation process. For this, we develop a general framework for the theoretical foundations of relaxation processes in pattern recognition. The resulting structure enables 1) a description of all known relaxation processes in general terms and 2) the design of task-dependent relaxation processes. We show that the well-known standard relaxation formulas verify our approach. Referring to the common problem of generating a generalized description of a contour we demonstrate the applicability of the suggested generalization in detail. Important characteristics of the constructed task-dependent relaxation process are: 1) the independency of the segmentation from any parameters, 2) the invariance to geometric transformations, 3) the simplicity, and 4) efficiency.

Relaxation and consolidation processes in solids (stress relaxation, physical aging) exhibit a number of similarities, especially with regard to the kinetics involved. In this paper, we derive a kinetic formula representing the time-domain equivalent of a Bose-Einstein (BE) distribution. The approach is based on the master equation supplemented with a BE enhancement factor. The plausibility of the underlying physical mechanism is discussed, especially with regard to the clustering of the elementary transitions involved in such a process.

We examine the density–density correlation function in a model recently proposed to study the effect of entropy barriers in glassy dynamics. We find that the relaxation proceeds in two steps with a fast beta process followed by alpha relaxation. The results are physically interpreted in the context of an adiabatic approximation which allows one to separate the two processes and define an effective temperature in the off-equilibrium dynamics of the model. We investigate the behaviour of the response function associated with the density and find violations of the fluctuation dissipation theorem. The relaxation in supercooled liquids near the glass transition has a characteristic twostep form. Experiments on very different materials reveal the existence of a first fast relaxation process, called beta relaxation, followed by a much slower one, called alpha relaxation [1]. One of the most striking successes of mode coupling theory [2] is its ability to capture this phenomenon and to give a correct prediction for the relation among the exponents characterizing the two relaxations. However, we believe that comprehension of the basic mechanisms underlying the relaxation in glasses is missing. Experiments in glasses have been recently interpreted in terms of traps models [3, 4]. In these models, the system evolves among traps—or metastable states—which have a lifetime that grows with decreasing temperature, and finally diverges at the glass transition. The two-step relaxation follows naturally from the hypothesis that equilibration inside a trap occurs much faster than ‘jumps’ among different traps. How a trap may be defined and described for real systems or microscopic models is an interesting open problem. If the traps have to be interpreted as the result of energy barriers in a rough energy landscape, one finds the difficulty that the relaxation should appear as a random process even on a large scale. A ‘jump’ among two different traps should imply a discontinuity in various quantities as the energy or the correlation function. This problem was already noted in [4], where it was proposed, as a way out, that real systems could be composed of a large number of quasi-independent subsystems leading to the observed self-averaging properties for the different quantities. In this direction, it can be instructive to investigate a different mechanism for slow relaxation and, in particular, the role of entropy barriers.



Nanosecond relaxation processes of phospholipid bilayers in the transition zone

Abstract
Ultrasonic relaxation spectra of dipalmitoyl lecithin vesicles have been recorded as a function of temperature over the frequency range 14-265 MHz. A relaxation process is observed with a time constant of about 10(-8) sec. At the mid-point of the crystalline-liquid crystalline transition (about 41.3 degrees), the relaxation amplitude is maximal. This suggests that the relaxation process is intimately associated with the order-disorder transition. Further support for this conclusion comes from the finding that the volume change of the reaction, as calculated from the relaxation amplitude at the transition midpoint, agrees with that determined independently by equilibrium dilatometry measurements of the deltaV of the transition. The results show that a major step in the transition occurs on a far shorter time scale than previously recognized. Similar fast processes have also been detected in dimyristoyl and distearoyl lecithin vesicles. From a consideration of various lines of evidence, it appears that the relaxation monitors the elementary step associated with the isomerization of lipid chains, such as kink formation through internal bond rotations, as the bilayer transforms between ordered and disordered phases.

In the cylindrical pore geometry of inorganic Anopore membranes the collective relaxation processes observed in a bulk antiferroelectric liquid crystal change considerably under confinement. The frequency degeneration of the soft and Goldstone modes present at the smectic A* (SmA*)-chiral smectic C (SmC*) phase transition in the bulk phase is removed under geometrical restrictions. The relaxation rate of the soft mode is strongly modified due to the deformation of the smectic layers in the curved geometry of the pores and is superimposed by the molecular relaxation process in the SmA* and SmC* phases. The soft mode in confinement splits into two relaxation processes, which are present through all other mesophases (SmC* and SmCa*). One of them is nearly temperature independent and slightly decreases in frequency in the SmCa* phase. This Goldstone-like process can be assigned to the highly deformed helical structure fluctuations. The second one exhibits the characteristic features for the molecular and soft mode relaxation processes depending on the temperature range. The biquadratic and the piezoelectric coupling between the tilt angle and spontaneous polarization are revealed in their temperature dependence.