Suppression of fluctuations

X — A/T + B (where A and B are constants) however, the parameters from the fit cannot straightforwardly be interpreted on a molecular basis (Almdal et al. 1996). A transition from shear-induced order to shear-induced disorder on increasing the shear rate has recently been reported in an asymmetric PS-PI diblock in concentrated solution (Balsara and Dai 1996). The low-shear rate ordering was consistent with the suppression of fluctuations, and the high-shear rate disordering was interpreted as arising from fluctuations of the ordered (cylindrical) microstructure (Balsara and Dai 1996). 

The first one is some negative feedback process. In general, the negative feedback can suppress the response as well as the fluctuation. Still, it is not a trivial question how chemical reaction can give rise to suppression of fluctuation, since to realize the negative feedback in chemical reaction, production of some molecules is necessary, which may further add fluctuations. 

Universal Statistics and Control of Fluctuations. Statistics of the number fluctuations of each molecular species is studied. We have found (i) power-law distribution of fast switching molecules, (ii) suppression of fluctuation in the core hypercycle species, and (iii) ubiquity of log-normal distribution for most other molecular species. The origin of log-normal distribution is generally due to multiplicative stochastic process in the catalytic reaction dynamics, as is confirmed in several other reaction network models. On the other hand, suppression of the number fluctuations of the core hypercycle is due to high connections in reaction paths with other molecules. In particular, reduced is the number fluctuations of the minority molecular species that has high catalytic connections with others. This suppression of fluctuation further reinforces the... 

Predictions for the Parameters k and The parameter f is not far from zero, which is to he expected since the surroundings of jimctions cause their deformation to be nearly affine with the macroscopic strain. The primary parameter ic is defined as the ratio of the mean-square junction fluctuations in the equivalent phantom network, ie, in the absence of constraints, to the mean-square jimction fluctuations about the centers of domains of entanglement constraints (in the absence of the network) in the isotropic state. Thus in a phantom network, the absence of constraints leads to /c = 0. In an affine one, the complete suppression of fluctuations is equivalent to /c = oo. It has been proposed that k should be proportional to the degree of interpenetration of chains and junctions (165). Since an increasing number of junctions in a volume pervaded by a chain leads to stronger constraints on these jimctions, k was taken to be... 

Fig.4 Borders of instability in the flow-gradient direction for G = 1, according to the model of Clarke and McLeish (dotted /me), and Criado-Sancho et al. (solid line). The CM model predicts shear-induced suppression of fluctuations, i.e., Axc >0, to the left of the dotted line and shear-induced enhancement to the right, i.e., Axc < 0. The CSJVC model predicts shear-induced suppression of fluctuations to the left of the left-most solid curve and to the right of the right-most solid curve and shear-induced enhancement between the two curves. Reproduced with permission from reference [38]...

In [17] it is stated that oil companies often underestimate risk. Of the many possible causes of such underestimates (from the point of view of this chapter) clearly (i) insufficient numbers of realisations in Monte Carlo studies (ii) suppression of fluctuations caused by upscaling methods are contributors. 

The first term in this equation describes the suppression of the probability of the fluctuation with the correlator Eq. (3.22) (the weight />[//(a)] of the disorder configuration is exp (— J da/2 (x))), while the second term stems from the condition that the energy c+[t/(x)] of the lowest positive-energy single-electron state for the disorder realization t/(x) equals c. The factor /< is a Lagrange multiplier. It can be shown that the disorder fluctuation //(a) that minimizes A [//(a)] has the form of the soliton-anlisolilon pair configuration described by [48] ... 

C (or 15N) NMR signals recorded by both CPMAS and DDMAS NMR, however, could be broadened or suppressed, when fluctuation motions with intermediate frequencies of 104-105 Hz interfere with... 

Ronca and Allegra (12) and Flory ( 1, 2) assume explicitly in their new rubber elasticity theory that trapped entanglements make no contribution to the equilibrium elastic modulus. It is proposed that chain entangling merely serves to suppress junction fluctuations at small deformations, thereby making the network deform affinely at small deformations. This means that the limiting value of the front factor is one for complete suppression of junction fluctuations. 

Comparison of Eqs. (28) and (14) shows that the high temperature expression (28) is recovered, if one drops all the terms except n = 0 in the corresponding Matsubara sum over ojn = 2irinT in Eq. (14). The contribution of v 0 terms to the 2k specific heat given by the first term of (24). Thus in our case one may suppress the frequency dependence of fluctuations only for... 

This refinement of the constrained-junction model is based on re-examination of the constraint problem and evaluation of some neutron-scattering estimates of actual junction fluctuations [158, 159]. It was concluded that the suppression of the fluctuations was over-estimated in the theory, presumably because the entire effect of the inter-chain interactions was arbitrarily placed on the junctions. The theory was therefore revised to make it more realistic by placing the effects of the constraints along the network-chain contours, specifically at their mass centers [4, 160, 161]. This is illustrated in the second portion of Figure 2. Relocating the constraints in this more realistic way provided improved agreement between theory and experiment. 

Remark. It is easily seen that the second term of (5.2) by itself causes the norm of if/ to change. In order that this is compensated by the fluctuating term the two terms must be linked, as is done by the relation U = V V. This resembles the classical fluctuation-dissipation theorem, which links both terms by the requirement that the fluctuations compensate the energy loss so as to establish the equilibrium. The difference is that the latter requirement involves the temperature T of the environment that makes it possible to suppress the fluctuations by taking T = 0 without losing the damping. This is the reason why in classical theory deterministic equations with damping exist, see XI.5. 

Marko (1993) has considered microphase separation in cyclic block copolymers, and found that the spinodal is shifted to higher for a given copolymer composition compared to a diblock. This is due to the suppression of composition fluctuations because of the closed topology of the ring polymer. 

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