Spontaneous noise

The second block is the solution of the wave equation for ASE intensity developing out of uniform spontaneous noise (see Section 3.2.3). The final, third, block of the code gives the solution to differential equations for populations with pump and ASE intensities evaluated in the previous two blocks. All three blocks are looped with respect to time while the space dependence is vectorized. The orientational... 

Another area of concern is the occurrence of spontaneous noise spikes and the presence of man made and natural debris around the earth and in the solar system. Both phenomena could potentially affect the reliability of the survey since they are indistinguishable from astronomical infrared objects. For this reason there is considerable emphasis on repetition of the survey. In the survey instrument coincidence of source detections will be required. Moreover, scans in consecutive orbits will have a fifty percent overlap. 

In liquid crystals, laser induced director axis reorientations lead to the possibility of another type of stimulated scattering process,in which the spontaneous noise... 

If there are no reactions, the conservation of the total quantity of each species dictates that the time dependence of is given by minus the divergence of the flux ps vs), where (vs) is the drift velocity of the species s. The latter is proportional to the average force acting locally on species s, which is the thermodynamic force, equal to minus the gradient of the thermodynamic potential. In the local coupling approximation the mobility appears as a proportionality constant M. For spontaneous processes near equilibrium it is important that a noise term T] t) is retained [146]. Thus dynamic equations of the form... 

The principle of electrochemical noise experiments is to monitor, without perturbation, the spontaneous fluctuations of potential or current which occur at the electrode surface. The stochastic processes which give rise to the noise signals are related to the electrode kinetics which govern the corrosion rate of the system. Much can be learned about the corrosion of the coated substrate from these experiments. The technique of these measurements is discussed elsewhere (A). 

Electrochemical noise is the name given to spontaneous fluctuations of parameters in an electrochemical system. Difierent types of such noise are encountered (1) fluctuations of an electrode s potential at zero external current (2) fluctuations of electrode potential when the system is galvanostatically controlled (a current of constant density passes through the electrode), (3) fluctuations around a theoretical zero value of the current flowing between two perfectly identical electrodes, (4) fluctuations of the imposed current when the system is potentiostatically controlled, and (5) fluctuations of the potential difference AE between unlike electrodes, and similar phenomena. 

We only had to add one more term - spontaneous emission - to the equation. Well, we did that, and then I had a hard time solving the equation, but a mathematician, Dr. [G.] Takahashi solved it. So Takahashi, Shimoda and I then wrote a paper on the maser amplifier, what the noise had to be, the theory of the noise fluctuations, and so on. Again, just trading ideas back and forth. 

The stability of scarred states to external noise and other environmental disturbances was the next natural issue that was raised and partially addressed earlier (L. Sirko, et.al., 1993 R. Scharf, et.al., 1994). The main conclusion was that scarred states are quite robust to reasonable levels of noise. This question took on added relevance with the coming of age of mesoscopic systems where, be it spontaneous emission in atom optics or leads or scattering and other forms of dissipation in heterostructures, the open nature of the system must be accounted for. These new experiments also provided non-ideal realizations of simple theoretical paradigms such as stadium billiards and the kicked rotor, with additional issues that had to be accounted for in the theory. 

Signal-to-noise ratio the ratio of the magnitude of the response due to the pollutant concentration to the magnitude of unwanted, spontaneous, short-term responses not caused by variations in pollutant concentration. 

The spectral line shape in CARS spectroscopy is described by Equation (6.14). In order to investigate an unknown sample, one needs to extract the imaginary part of to be able to compare it with the known spontaneous Raman spectrum. To do so, one has to determine the phase of the resonant contribution with respect to the nonreso-nant one. This is a well-known problem of phase retrieval, which has been discussed in detail elsewhere (Lucarini et al. 2005). The basic idea is to use the whole CARS spectrum and the fact that the nonresonant background is approximately constant. The latter assumption is justihed if there are no two-photon resonances in the molecular system (Akhmanov and Koroteev 1981). There are several approaches to retrieve the unknown phase (Lucarini et al. 2005), but the majority of those techniques are based on an iterative procedure, which often converges only for simple spectra and negligible noise. When dealing with real experimental data, such iterative procedures often fail to reproduce the spectroscopic data obtained by some other means. 

A closed-form result involving only matrix solution and substitution operations was obtained. Under certain circumstances, particularly in the low-noise case, application of the Burg method results in spurious resolution or spontaneous line splitting (Fougere et al., 1976). One solution to this problem (Fougere, 1977) introduces iteration. 

Quantum-state decay to a continuum or changes in its population via coupling to a thermal bath is known as amplitude noise (AN). It characterizes decoherence processes in many quantum systems, for example, spontaneous emission of photons by excited atoms [35], vibrational and collisional relaxation of trapped ions [36] and the relaxation of current-biased Josephson junctions [37], Another source of decoherence in the same systems is proper dephasing or phase noise (PN) [38], which does not affect the populations of quantum states but randomizes their energies or phases. 

In a chemical system, spatial patterns can spontaneously arise from an initial spatially homogeneous concentration profile by the selection from noise and amplification of perturbations with wavelengths in the neighborhood of some preferred wavelength. To determine the conditions under which this occurs, the behavior of the system in the vicinity of the spatially homogeneous steady state A" = Xs, Y = T, where F(XS, Ys) = G(XS, Ys) = 0, is analyzed using a standard linearization procedure. 

I have made this model a little more complicated than the model in Chapter 2 by adding an arrow labeled Internal Stimuli within each possible information process to reflect the fact that more events are occurring in the agent s mind and nervous system than the experimenter s request to influence the target. This is also true for our clairvoyance and precognition model. For example, there may be spontaneous neural discharges or noises within your brain that interfere with the flow of information between the various processes. Or you may consciously dislike the experimenter, so that when he tells you to make the dice come up fours, you say (mentally), Nuts to you, and consciously try for a different target face. Or you may... 

Fig. 6.9. A Spontaneous Raman spectrum of d62-DPPC lipids and its decomposition into Lorentzian line profiles. B Normalized multiplex CARS spectra (dots) of a planar-supported bilayer and monolayer formed by d62-DPPC on a glass-water interface for parallel-polarized input beams, together with the fit using the center frequency and line width parameters extracted from the decomposition analysis in (A) (solid line). The spectrum exposure time was 0.64 s. Error bars indicate the shot-noise standard deviation (Copyright American Chemical Society [70])...

Spontaneous Raman spectroscopy has the ability to provide clinically relevant chemical concentration measurements of multiple analytes in biofluids. Blood serum, whole blood, and urine have all been studied. The detection limit (assuming a few hundred seconds of spectral acquisition) appears, based upon fundamental noise considerations, to be around 0.1 mM for most biochemicals this places several important analytes within reach but certainly precludes... 

Large-scale domains feature a larger spontaneous polarization Ps than small ones. Thus larger amplitudes of tin, and larger intensities of the initial noise result. 

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