Stochastic susceptibilities

O, produces the stochastic susceptibilities. .. Fourier transformation over... 

In our approach [1, 2] termed the dynamic method the complex susceptibility x = x — ix" is determined by a law of undamped motion of a dipole in a given potential well and by dissipation mechanism often described as stosszahlansatz in the underlying kinetic or Boltzmann equation. In this review we shall refer to this (dynamic) method as the ACF method, since it is actually based on calculation of the spectrum of the dipolar autocorrelation function (ACF). Actually we use a one-particle approximation, in which the form of an employed potential well (being in many cases rectangular or close to it) is taken a priori. Correlation of the particles coordinates is characterized implicitly by the Kirkwood correlation factor g, its value being taken from the experimental data. The ACF method is simple and effective, because we do not employ the stochastic equations of motions. This feature distinguishes our method from other well-known approaches—for example, from those described in books [13, 14]. 

C. An analogous model was considered in Ref. 12b, but an important new step was made. Now it was assumed that the stochastic processes with two different relaxation times correspond to types of motion described by two wells. Two different complex susceptibilities were calculated, which have split Eq. (235) by two similar expressions for reorientation and vibration processes ... 

In Section IV.B.4 we have shown that the quadratic dynamic susceptibilities of a superparamagnetic system display temperature maxima that are sharper than those of the linear ones. If the maximum occurs as well at the temperature dependence of the signal-to-noise ratio, this should be called the nonlinear stochastic resonance. However, before discussing this phenomenon, one has to define what should be taken as the signal-to-noise ratio in a nonlinear case. 

Heterogeneity of values over time, space or different members of a population, including stochastic variability and controllable variability. Variability implies real differences among members of that population. For example, different individual persons have different intake and susceptibility. In relation to human exposure assessment, differences over time for a given individual are referred to as intraindividual variability differences over members of a population at a given time are referred to as interindividual variability. 

Garcia-Palacios JL, Lazaro FJ (1997) Anisotropy effects on the nonlinear magnetic susceptibilities of superparamagnetic particles. Phys Rev B 55 1006-1010 Garcia-Palacios JL, Svedlindh P (2000) Large nonlinear dynamical response of superparamagnets Interplay between precession and thermoactivation in the stochastic Landau-Lifshitz equation. Phys Rev Lett 85 3724-3727... 

Equation (4.2.11) describes the response to three delta pulses separated by ti =oi — 02 >0, t2 = 02 — 03 > 0, and t3 = 03 > 0. Writing the multi-pulse response as a function of the pulse separations is the custom in multi-dimensional Fourier NMR [Eml ]. Figure 4.2.3 illustrates the two time conventions used for the nonlinear impulse response and in multi-dimensional NMR spectroscopy for n = 3. Fourier transformation of 3 over the pulse separations r, produces the multi-dimensional correlation spectra of pulsed Fourier NMR. Foinier transformation over the time delays <7, produces the nonlinear transfer junctions known from system theory or the nonlinear susceptibilities of optical spectroscopy. The nonlinear susceptibilities and the multi-dimensional impulse-response functions can also be measured with multi-resonance CW excitation, and with stochastic excitation piul]. 

J. Q. Boedicker, L. Li, T. R. Kline, and R. F. Ismagilov, Detecting bacteria and determining their susceptibility to antibiotics by stochastic confinement in nanoliter droplets using plug-based microfluidics. Lab on A Chip, vol. 8, no. 8, pp. 1265-1272, 2008. 

A predictive model formulates a stochastic process representing the presence of a microbiological, chemical or physical load in food, which depends on a set of intrinsic parameters (e.g. pH, water-activity, acids, salt and preservatives), extrinsic parameters (e.g. chilling, modified atmosphere) or processing parameters (e.g. heat treatment, pressurisation and irradiation). It is clear that these parameters are susceptible to the variability inherent to the characteristics of the products and the operational equipment, and predictive modelling can represent such variability. 

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