Sampling time scales

In the parallel realization a multi-window sampling time scale is created [86]. The implemented time scale is the piecewise approximation of the logarithmic scale. It includes nw c 16 sites with a uniform discretization step determined by the following formula ... 

At still shorter time scales other techniques can be used to detenuiue excited-state lifetimes, but perhaps not as precisely. Streak cameras can be used to measure faster changes in light intensity. Probably the most iisellil teclmiques are pump-probe methods where one intense laser pulse is used to excite a sample and a weaker pulse, delayed by a known amount of time, is used to probe changes in absorption or other properties caused by the excitation. At short time scales the delay is readily adjusted by varying the path length travelled by the beams, letting the speed of light set the delay. 

Experimentally, tire hard-sphere phase transition was observed using non-aqueous polymer lattices [79, 80]. Samples are prepared, brought into the fluid state by tumbling and tlien left to stand. Depending on particle size and concentration, colloidal crystals tlien fonn on a time scale from minutes to days. Experimentally, tliere is always some uncertainty in the actual volume fraction. Often tire concentrations are tlierefore rescaled so freezing occurs at ( )p = 0.49. The widtli of tire coexistence region agrees well witli simulations [Jd, 80]. 

The flash lamp teclmology first used to photolyse samples has since been superseded by successive generations of increasingly faster pulsed laser teclmologies, leading to a time resolution for optical perturbation metliods tliat now extends to femtoseconds. This time scale approaches tlie ultimate limit on time resolution (At) available to flash photolysis studies, tlie limit imposed by chemical bond energies (AA) tlirough tlie uncertainty principle, AAAt > 2/j. 

New Sampling Methods for the Extrinsic Multiple Time Scale Problem... 

Viscosity is considerably more sensitive to temperature than elasticity. By varying the temperature, the relaxation time of the polymer will be changed. Hence different mechanical response might be expected on a fixed laboratory time scale for samples examined at different temperatures. 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

A promising technique is cavity ringdown laser absorption spectroscopy (307), in which the rate of decay of laser pulses injected into an optical cavity containing the sample is measured. Absorption sensitivities of 5 x 10 have been measured on a ]ls time scale. AppHcations from the uv to the ir... 

Shoiild the particles have a tendency to cohere slightly during sedimentation, each sampling time, representing a different nominal detention time in the clarifier, will produce different suspended-sohds concentrations at similar rates. These data can be plotted as sets of cui ves of concentration versus settling rate for each detention time by the means just described. Scale-up will be similar, except that detention time will be a factor, and both depth and area of the clarifier will influence the results. In most cases, more than one combination of diameter and depth will be capable of producing the same clarification result. 

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