Perturbation response

In other cases, the inherent flaws or perturbations responsible for fracture are less easily recognized. The internal spalling of glass or the cavitation of a rapidly expanding liquid are examples although even here, some form of imperfection such as impurities, dislocations, or thermal fluctuations are expected to play an important role in nucleating the fracture process. 

A second limiting physical/hydrodynamic case is the soil as a porous bed. Often others simulate undisturbed soils in the lab with soil columns, however we have chosen to use a slice of such a column a differential volume reactor (DVR)-as the experimental design (22). This approach offers advantages in the ability to develop a more spatially homogeneous system and also contributes to the perturbation/response analysis needed for systems identification. 

Pseudospin representation and the perturbative estimates of the bond-geminal ESVs. To provide the required explanation, we notice that the effective Hamiltonians for the bond geminals can be represented as a sum of the unperturbed part which, when diagonalized yields invariant, i.e. exactly transferable, values of the ESVs, and of a perturbation responsible for the specificity of electronic structure for different chemical compositions and environments of the bond. 

The decay of the CO stretch is a single exponential when W(CO)6 has substantial interactions with a solvent. A single exponential (aside from orientational relaxation in liquids) is observed even when very fast pulses are used in the experiments (81). In the gas phase, the transition frequency of the CO stretch evolves over a range of frequencies because of its time-dependent interaction with the low-frequency modes. When a buffer gas or solvent is added, collisions cause the coherent evolution of the slow modes to be interrupted frequently, possibly averaging away the perturbation responsible for the observed fast time dependence. Thus, the fastest and slowest components of the tri-exponential decay are inherently low-pressure, gas phase phenomena. 

We characterize the adsorbed layer by a density perturbation response function ... 

In the case of the [N —> p) = p -representation the perturbations — responses transformation similarly reads ... 

When the constituent subsystems are mutually closed (in molecular fragment resolution), the corresponding matrices of charge sensitivities replace the global quantities in the corresponding four perturbation —> response transformations ... 

Fig. 8.22. The vanishing radiative width in the Ba spectrum. Experimental data are shown which correspond to oscillator strength measurements below the ionisation threshold by the magneto-optical method described in chapter 4, which also gives an overview of the Ba spectrum including the broad 5d8p perturber responsible for the vanishing radiative width. The inset shows a comparison between measured values (squares) and an MQDT extrapolation (triangles) on a logarithmic scale (see also fig. 4.3 - after J.-P. Connerade et al. [136]).

Perturbation Response Type of transfer function (units)... 

Pulse-response and step-funetion-response experiments are perhaps the easiest to carry out and analyze however, any perturbation-response technique can be used to determine age distributions. Kramers and Alberda [H. Kramers and G. Alberda, Chem. Eng. Sci., 2, 173 (1953)) describe a frequency-response analysis, and a general treatment of arbitrary input functions. Errors associated with input and... 

In Fig. 2A we show that the response of a nonlinear system (of the form Eq. (5)) in steady state to a small perturbation is linear (with parameter predictable from Eq. (6)). In Fig. 2B we demonstrate the effect of non steady state on the response. In Fig. 2C we see the effect of an excessively large perturbation on the response. Further, in Fig. 2D we see the effect of the degree of nonlinearity of the system on the perturbation response. 

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