Journal ArticleDOI
Statistical mechanics far from equilibrium
Sam F. Edwards,W. D. McComb +1 more
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In this article, the case of randomly excited fluid turbulence is studied and it is argued that there is a strong mathematical analogy between the classical (turbulent) cascade of energy and the quantum field or many-body problem.Abstract:
The statistical mechanics of systems in which the dominant process is a flow of energy through the modes of the system is studied. The case of randomly excited fluid turbulence is studied and it is argued that there is a strong mathematical analogy between the classical (turbulent) cascade of energy and the quantum field or many-body problem. The energy has an analogue in the one-particle Green function, and entropy can be defined, the latter being the information content in the case of the probability distribution function for the turbulence. General operations in Hilbert space can be carried out with at most two functions, and the energy equation and the maximization of the entropy give two equations which determine the two chosen unknown functions. The case of a random long-wave input of energy is studied and shown to lead to the Kolmogoroff spectrum, and the Kolmogoroff constant is evaluated for the approximation system used.read more
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Book ChapterDOI
QM/MM Methods for Biological Systems
Hans Martin Senn,Walter Thiel +1 more
TL;DR: In this article, the state of the art of combined quantum-mechanics/molecular mechanics (QM/MM) methods with a focus on biomolecular systems is reviewed.
Journal ArticleDOI
Probability density function approach for a turbulent axisymmetric heated jet. Centerline evolution
Abstract: The equation describing the evolution of the probability density function of the temperature field in a turbulent axisymmetric heated jet is presented. A closure problem is present and some possible ways of attacking it are suggested. A closure at the first‐order level is then tentatively tried and similarity arguments are exploited. A hyperbolic first‐order variable‐coefficient quasi‐self‐preserving partial differential equation is obtained. The constants appearing in those coefficients are evaluated from available experiments. Some questions are raised on the uncertainty of the computed constants due to the experimental scattering of the velocity‐temperature correlation at the centerline. The probability density function is obtained analytically as a function of downstream location along the centerline if it is prescribed at a reference centerline position. In particular, the probability density function is taken as Gaussian at ten diameters downstream. The computed mean and variance are compared with existing experiments and display a reasonably good agreement. Values for the skewness and flatness factor tend to indicate that deviations from Gaussianity along the centerline are very small.
Journal ArticleDOI
Statistical Treatment of Non-Isothermal Chemical Reactions in Turbulence
C. Dopazo,E. E. O'brien +1 more
TL;DR: In this paper, the authors link reactive flow studies to simple mixing of passive scalar fields, which can be used to translate experimental or theoretical information from relatively simple non-reactive turbulent diffusion systems to useful reactive flow information.
Journal ArticleDOI
Convergents to turbulence functions
TL;DR: In this article, a method for constructing approximations, to statistical functions, that are uniformly convergent in time, starting with the expansion of the functions as Taylor series in time is described.
Journal ArticleDOI
H theorems in statistical fluid dynamics
TL;DR: In this paper, it was shown that the second-order Markovian closure of inviscid flow with an ultraviolet spectral cut-off implies a certain functional of the energy spectrum (namely entropy) increases monotonically in time to a maximum value at absolute equilibrium.
References
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Journal ArticleDOI
A mathematical theory of communication
TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Journal ArticleDOI
Quantum theory of solids
Rudolf Peierls,Louis D. Roberts +1 more
TL;DR: In this article, the interaction of light with non-conducting crystals has been studied in the context of crystal lattices and its applications in general theory and applications, such as semi-conductivity and superconductivity.