Better heat-dissipating systems were found in the use of narrow bore tubes. The small volume of the tube has a large surface of the internal wall to dissipate the produced heat. The lower the ratio of the volume to surface of a tube (Eq. 17.2), the better the heat dissipation and thus higher the separation efficiency. [Pg.579]

In this notation the general linear dissipative system is described by [Pg.490]

U. Weiss, Quantum Dissipative Systems, 2nd ed., World Scientific, Singapore, 1999. [Pg.367]

Strategies for Spectral Analysis in Dissipative Systems Filter Diagonalization in the Lanczos Representation and Harmonic Inversion of the Chebychev Order Domain Autocorrelation Function. [Pg.347]

MSN.52.1. Prigogine, Quantum theory of Dissipative Systems, Nobel Symposium 5, S. Claesson, ed.. Interscience, New York, 1967, pp. 99-129. [Pg.55]

Both QTST and MQCLT can be extended to deal with dissipative systems, whose classical dynamics is described by a GTE. " The main difficulty is that [Pg.32]

Poliak E 1993 Variational transition state theory for dissipative systems Acf/Vafed Barrier Crossinged G Fleming and P Hanggi (New Jersey World Scientific) p 5 [Pg.896]

MSN.79. C. George and 1. Prigogine, Quantum mechanics of dissipative systems and noncano-nical formalism, Int. J. Quantum Chem. Symp. 8, 335—346 (1974). [Pg.56]

Evans D G, Coalson R D, Kim H J and Dakhnovskii Y 1995 Inducing coherent oscillations in an electron transfer dynamics of a strongly dissipative system with pulsed monochromatic light Phys. Rev. Lett. 75 3649 [Pg.2996]

The semiclassical theory of rates has along history.Here, we will just review briefly the final product, a unified theory for the rate in a dissipative system, at all temperatures and for arbitrary damping. Two major routes have been used to derive the semiclassical theory. One is based on the so called ImF method, whereby, one derives a semiclassical limit for the imaginary part of the free energy. This route has the drawback that the semiclassical limit is treated differently for temperatures above and below the crossover temperature. - [Pg.33]

Prigogine I and Lefever R 1968 Symmetry breaking instabilities in dissipative systems J. Chem. Phys. 48 1695-700 [Pg.1118]

Since V(t) = V(0) for all times t in conservative systems, Ap = 0. The presence of attractors in dissipative systems, on the other hand, implies that the available phase space volume is contracting, and thus that Ap < 0. Since chaotic motion (either in conservative or dissipative systems) yields Ai > 0, this therefore also means that, in dissipative systems, the phase space volume is both expanding along certain directions and contracting along others. [Pg.202]

ASR provides an open EM system far from thermodynamic equilibrium in its violent energy exchange with the active vacuum. As is well known, an open dissipative system in disequilibrium with an active environment is permitted to [Pg.643]

The general nexus between fluctuation and dissipation was examined by Callen and Welton [122] in terms of the fluctuations of appropriate generalized forces and the impedance in a linear dissipative system. A system is considered to be dissipative if capable of absorbing energy when subjected to a time-periodic perturbation, e.g. an electrical resistor that absorbs energy from an impressed periodic potential. [Pg.487]

Poliak E, Tucker S C and Berne B J 1990 Variational transition state theory for reaction rates in dissipative systems Phys. Rev. Lett. 65 1399 [Pg.897]

Those are, in fact, the requirements for electrical power systems exhibiting COP > 1.0. Such open systems in disequilibrium with their active vacuum are permitted indeed, every dipolar circuit already is in such disequilibrium. Such a system can also be close-looped to power itself and its load. For instance, an open dissipative system with COP = 2.0, can use 1.0 of its COP to power itself, and the other 1.0 to power the loads and losses [98]. This is no different from the operation of a windmill, except that the electrical system operates in an EM energy wind initiated from the vacuum by the source dipole. We point out that powering a system actually need only be powering its internal losses if the source dipole is maintained. [Pg.669]

Once the door was opened to these new perspectives, the works multiplied rapidly. In 1968 an important paper by Prigogine and Rene Lefever was published On symmetry-breaking instabilities in dissipative systems (TNC.19). Clearly, not any nolinear mechanism can produce the phenomena described above. In the case of chemical reactions, it can be shown that an autocatalytic step must be present in the reaction scheme in order to produce the necessary instability. Prigogine and Lefever invented a very simple model of reactions which contains all the necessary ingerdients for a detailed study of the bifurcations. This model, later called the Brusselator, provided the basis of many subsequent studies. [Pg.13]

Results for two types of model systems are shown here, each at the two different inverse temperatures of P = 1 and P = 8. For each model system, the approximate correlation functions were compared with an exact quantum correlation function obtained by numerical solution of the Schrodinger equation on a grid and with classical MD. As noted earlier, testing the CMD method against exact results for simple one-dimensional non-dissipative systems is problematical, but the results are still useful to help us to better imderstand the limitations of the method imder certain circumstances. [Pg.61]

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877 [Pg.897]

Assuming that the pj (t) and Qj (t) can be interpreted as a TS trajectory, which is discussed later, we can conclude as before that ci = ci = 0 if the exponential instability of the reactive mode is to be suppressed. Coordinate and momentum of the TS trajectory in the reactive mode, if they exist, are therefore unique. For the bath modes, however, difficulties arise. The exponentials in Eq. (35b) remain bounded for all times, so that their coefficients q and q cannot be determined from the condition that we impose on the TS trajectory. Consequently, the TS trajectory cannot be unique. The physical cause of the nonuniqueness is the presence of undamped oscillations, which cannot be avoided in a Hamiltonian setting. In a dissipative system, by contrast, all oscillations are typically damped, and the TS trajectory will be unique. [Pg.211]

The quote is from the third volume of Henri Poincare s New Methods of Celestial Mechanics, and is a description of his discovery of homoclinic orbits (see below) in the restricted three-body problem. It is also one of the earliest recorded formal observations that very complicated behavior may be found even in seemingly simple classical Hamiltonian systems. Although Hamiltonian (or conservative) chaos often involves fractal-like phase-space structures, the fractal character is of an altogether different kind from that arising in dissipative systems. An important common thread in the analysis of motion in either kind of dynamical system, however, is that of the stability of orbits. [Pg.188]

Poliak and Eckhardt have shown that the QTST expression for the rate (Eq. 52) may be analyzed within a semiclassical context. The result is though not very good at very low temperatures, it does not reduce to the low temperature ImF result. The most recent and best resultthus far is the recent theory of Ankerhold and Grabert," who study in detail the semiclassical limit of the time evolution of the density matrix and extract from it the semiclassical rate. Application to the symmetric one dimensional Eckart barrier gives very good results. It remains to be seen how their theory works for asymmetric and dissipative systems. [Pg.33]

Electrophoresis in narrow bore tubes, as performed by Hjerten in 1967, provides a better heat dissipating system. He described an application using glass tubes with an internal diameter (I.D.) of +3 mm. The small volume of the narrow bore tube improves the dissipation of heat due to a lower ratio of the inner volume to the wall surface of a tube (Equation (1)). The better the heat dissipation the higher will be the separation efficiency [Pg.10]

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