Effective temperature, dissipative

With a reaction enthalpy of A RH = -170 kJ/g mol the sulfonation with S03 is strongly exothermic. As the color of the acid is dependent not only on the residence time but also to a considerable extent on the reaction temperature, it is necessary to have an effective thermal dissipation. This applies to all of the reactors listed in Table 13. The falling film reactors, of which there are various designs, have the advantage that a very short residence time can be realized [152]. 

The concept of a nonequilibrium temperature has stimulated a lot of research in the area of glasses. This line of research has been promoted by Cugliandolo and Kurchan in the study of mean-held models of spin glasses [161, 162] that show violations of the fluctuation-dissipation theorem (FDT) in the NEAS. The main result in the theory is that two-time correlations C t,t ) and responses R t, f ) satisfy a modihed version of the FDT. It is customary to introduce the effective temperature through the fluctuation-dissipation ratio (FDR) [163] dehned as... 

S. M. Eielding and P. Sollich, Observable dependence of fluctuation-dissipation relations and effective temperatures. Phys. Rev. Lett. 88, 050603 (2002). 

The combustion reaction rate is controlled both by the availability of fuel and oxygen kinetic effects (temperature). In full-scale fire modeling, the resolvable length and time scales are usually much larger than those associated with the scales of the chemical combustion reaction, and it is common to assume that the reactions are infinitely fast. The local reaction rate depends on the rate at which oxygen and fuel are transported toward the surface of stoichiometric mixture fraction, shown in Figure 20.2 as a point where both oxygen and fuel mass fractions go to zero. For almost 20 years, the EBU or eddy dissipation models were the standard models used by the combustion CFD community. With the EBU, in its simplest form, the local rate of fuel consumption is calculated as [3] ... 

The above analysis dealt with the effects of dissipation on the flow over an adiabatic flat plate. Attention is now turned to flow over a plate that is kept at a uniform temperature of Tw. 

Behavior of the Fluctuation-Dissipation Ratio and of the Effective Temperature in the Langevin Model... 

The aim of this chapter is to show how the concepts of FDT violation and effective temperature can be illustrated in the framework of the above quoted system, as done experimentally in Ref. 12 and theoretically in Refs. 15-19. We do not discuss here the vast general domain of aging effects in glassy systems, which are reviewed in Refs. 2-4. Since the present contribution should be understood by beginners in the field, some relevant fundamental topics of equilibrium statistical physics—namely, on the one hand, the statistical description of a system coupled to an environment and, on the other hand, the fluctuation-dissipation theorem (in a time domain formulation)—are first recalled. Then, questions specifically related to out-of-equilibrium dynamics, such as the description of aging effects by means of an effective temperature, are taken up in the framework of the above-quoted model system. 

Summing up, the fluctuation-dissipation ratio X(t, t to) and the associated inverse effective temperature (3g(f(f, t to) allow one to write a modified FDT relating Xxxih t ) to cCxx(t. t fo)/8f with to < t < t, this latter quantity taking into account even those fluctuations of the displacement which take place during the waiting time. 

In the quantum case, the effective temperature Teff = ( peff)-1 can be obtained from Eq. (130), an equation which also allows one to define 7 err at T 0 for 1 < 8 < 2. Since Dit) is a monotonic increasing function of T, Eq. (130) yields for reff(T, tw) a uniquely defined value, as in the Ohmic dissipation case. 

The fully general situation of a particle diffusing in an out-of-equilibrium environment is much more difficult to describe. Except for the particular case of a stationary environment, the motion of the diffusing particle cannot be described by the generalized Langevin equation (22). A more general equation of motion has to be used. The fluctuation-dissipation theorems are a fortiori not valid. However, one can try to extend these relations with the help of an age- and frequency-dependent effective temperature, such as proposed and discussed, for instance, in Refs. 5 and 6. 

Interestingly, due to the linearity of the generalized Langevin equation (22), the same effective temperature T,eff(( ) can consistently be used in the modified Nyquist formula linking the noise spectral density C/ /- ([Pg.313]

In this chapter, we have showed that a particle undergoing normal or anomalous diffusion constitutes a system conveniently allowing one to illustrate and to discuss the concepts of FDT violation and effective temperature. Our study was carried out using the Caldeira-Leggett dissipation model. Actually this model, which is sufficiently versatile to give rise to various normal or anomalous diffusion behaviors, constitutes an appropriate framework for such a study, in quantum as well as in classical situations. 

For a particle evolving in a thermal bath, we focused our interest on the particle displacement, a dynamic variable which does not equilibrate with the bath, even at large times. As far as this variable is concerned, the equilibrium FDT does not hold. We showed how one can instead write a modified FDT relating the displacement response and correlation functions, provided that one introduces an effective temperature, associated with this dynamical variable. Except in the classical limit, the effective temperature is not simply proportional to the bath temperature, so that the FDT violation cannot be reduced to a simple rescaling of the latter. In the classical limit and at large times, the fluctuation-dissipation ratio T/Teff, which is equal to 1 /2 for standard Brownian motion, is a self-similar function of the ratio of the observation time to the waiting time when the diffusion is anomalous. 

Fig. 6 Calculated contributions to the pressure rise in a manometric temperature measurement experiment. Calculations were made for a typical product with an initial ice temperature of —20°C, corresponding to an initial vapor pressure of 775mTorr. Open circles = effect 1, sublimation open triangles = effect 2, dissipation of temperature gradient open squares = effect 3, heat flow from shelf to product filled circles = sum of all effects. (Adapted from Ref...

From the angle-dependence of the XPS signal, Muller el al. conclude that Au remains to a large extent at the surface of 5T films if Au is evaporated in short intervals [39], This guarantees an effective heat dissipation with negligible temperature increase. There is a strong dependence of the Au diffusion into the anT film on the film structure. As expected, the diffusion is much smaller in densely packed crystalline films if compared to only z-oriented films (compare Section 3.3). 

When given to a normal individual (one without nerve agent intoxication), a dose of 2 mg of atropine will cause an increase in heart rate of about 35 beats per minute (which usually is not noticed by the recipient), a dry mouth, dry skin, mydriasis, and some paralysis of accommodation. Most of these effects will dissipate by 4 to 6 hours, but near vision may be blurred for 24 hours, even in healthy young men. The decrease in sweating caused by 2 mg of atropine is a major, potentially harmful side effect that may cause some people who work in the heat to become casualties. For example, when 35 soldiers were given 2 mg of atropine and asked to walk for 115 minutes at 3.3 mph at a temperature of about 83°F (71°F wet bulb), more than half dropped out because of illness or were removed from the walk because of body temperature of 103.5°F or above on another day, without atropine, they all successfully completed the same march.129... 

Chen Q, Hou M Effective temperature and fluctuation-dissipation theorem in athermal granular systems a review. Chin Phys B 23 074501, 2014. 

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