Random generation of coherent solitary waves from incoherent waves

The random generation of coherent solitary waves from incoherent waves in a medium with an instantaneous nonlinearity has been observed. One excites a propagating incoherent spin wave packet in a magnetic film strip and observes the random appearance of solitary wave pulses. These pulses are as coherent as traditional solitary waves, but with random timing and a random peak amplitude.     

Modification of solitary waves by third-harmonic generation

The effect of phase-matched third-harmonic generation on the structure and stability of spatial solitary waves is investigated. A power threshold for the existence of two-frequency spatial solitons is found, and the multistability of solitary waves in a Kerr medium owing to a higher-order nonlinear phase shift caused by cascaded third-order processes is revealed.     

On the generation of internal solitary marine waves

Summary A nonlinear model of generation of internal ?solitary? marine waves is discussed: when a large surface wave—for instance a superficial wave or a bore of tidal origin—passes over a submarine mountain or crosses a strait, packets of internal waves may often be detected. We study this phenomenon taking into account the effect of the air-sea surface; we show that the phenomenon can be schematized, in an approximate but realistic way, by using the solutions of an inhomogeneous KdV equation. The forcing term depends on the air-sea surface elevation and on the bottom topography. We then apply our model to the marine currents, of tidal origin, flowing through the straits of Gibraltar.

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Riassunto Si studia un modello non lineare della generazione di onde interne marine. Quando una grande onda superficiale passa sopra una montagna sottomarina o attraversa uno stretto si osservano pacchetti di onde interne. Si studia questo fenomeno tenendo conto della interfaccia aria-mare, si mostra che il fenomeno può essere rappresentato in maniera approssimata dalle soluzioni di un'equazione di KdV non omogenea. Il termine forzante dipende dalla superficie aria-mare e dalla topografia del fondo. Infine il modello proposto è applicato alle correnti di marea dello stretto di Gibilterra.

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Резюме Обсуждается нелинейная модель образования внутренних ?одиночных? морских волн: когда большая поверхностная волна проходит над подводной горой или приливная волна пересекает пролив, часто могут детектироваться пакеты внутренних волн. Мы исследуем зто явление, учитывая влияние границы раздела воздух-море. Мы показываем, что это явление может быть схематизировано приближенным, но реалистическим способом, используя решения неоднородного уравнения Кортевега-де Вриса. Силовой член зависит от возвышения границы раздела воздух-море и от топографии дна. Затем мы применяем нашу модель для морских течений (приливного происхождения), проходязих через Гибралтарский пролив.

     

Difference equations in statistical mechanics. I. Cluster statistics models

A review and some new results are presented for several cluster statistics models, solutions of which can be reduced to difference equations. Mathematical techniques suitable for solving these equations are surveyed.     

Spatial solitary waves and patterns in type II second-harmonic generation

The existence of Turing patterns and of spatial solitary waves that arise from a polarization instability of the fundamental field is predicted in type II second-harmonic generation in a quadratically nonlinear optical cavity. The analogy between these dissipative structures and those studied in absorptive optical bistability is pointed out.     

On the nonequilibrium statistical mechanics of a binary mixture. I. The distribution functions

In this paper, we obtain the generalization of the BBGKY hierarchy for a binary mixture of chemically neutral particles. Using modified boundary conditions different from the ones proposed by Bogoliubov, we solve the hierarchy, and obtain explicitly the set of two-particle distribution functions for the several species of the mixture, up to first order in the density.     

The time-local view of nonequilibrium statistical mechanics. I. Linear theory of transport and relaxation

The various approaches to nonequilibrium statistical mechanics may be subdivided into convolution and convolutionless (time-local) ones. While the former, put forward by Zwanzig, Mori, and others, are used most commonly, the latter are less well developed, but have proven very useful in recent applications. The aim of the present series of papers is to develop the time-local picture (TLP) of nonequilibrium statistical mechanics on a new footing and to consider its physical implications for topics such as the formulation of irreversible thermodynamics. The most natural approach to TLP is seen to derive from the Fourier-Laplace transform ) of pertinent time correlation functions, which on the physical sheet typically displays an essential singularity at z= and a number of macroscopic and microscopic poles in the lower half-plane corresponding to long- and short-lived modes, respectively, the former giving rise to the autonomous macrodynamics, whereas the latter are interpreted as doorway modes mediating the transfer of information from relevant to irrelevant channels. Possible implications of this doorway mode concept for socalled extended irreversible thermodynamics are briefly discussed. The pole structure is used for deriving new kinds of generalized Green-Kubo relations expressing macroscopic quantities, transport coefficients, e.g., by contour integrals over current-current correlation functions obeying Hamiltonian dynamics, the contour integration replacing projection. The conventional Green-Kubo relations valid for conserved quantities only are rederived for illustration. Moreover, may be expressed by a Laurent series expansion in positive and negative powers ofz, from which a rigorous, general, and straightforward method is developed for extracting all macroscopic quantities from so-called secularly divergent expansions of as obtained from the application of conventional many-body techniques to the calculation of . The expressions are formulated as time scale expansions, which should rapidly converge if macroscopic and microscopic time scales are sufficiently well separated, i.e., if lifetime (memory) effects are not too large.     

Retarded learning: rigorous results from statistical mechanics

We study learning of probability distributions characterized by an unknown symmetry direction. Based on an entropic performance measure and the variational method of statistical mechanics we develop exact upper and lower bounds on the scaled critical number of examples below which learning of the direction is impossible. The asymptotic tightness of the bounds suggests an asymptotically optimal method for learning nonsmooth distributions.     

Large-eddy simulation of the generation and propagation of internal solitary waves

A modified large-eddy simulation model,the dynamic coherent eddy model(DCEM)is employed to simulate the generation and propagation of internal solitary waves(ISWs)of both depression and elevation type,with wave amplitudes ranging from small,medium to large scales.The simulation results agree well with the existing experimental data.The generation process of ISWs is successfully captured by the DCEM method.Shear instabilities and diapycnal mixing in the initial wave generation phase are observed.The dissipation rate is not equal at different locations of an ISW.ISW-induced velocity field is analyzed in the present study.The structure of the bottom boundary layer(BBL)of internal wave packets is found to be different from that of a single ISW.A reverse boundary jet instead of a separation bubble exists behind the leading internal wave while separation bubbles appear in other parts of the wave-induced velocity field.The boundary jet flow resulting from the adverse pressure gradients has distinctive dynamics compared with free shear jets.     

A theory of the bion in the one-dimensional sine-Gordon system: I. Quantum statistical mechanics

Introducing an appropriate renormalization to the phase space of the bion, we study the quantum statistical mechanics of the bion in the one-dimensional sine-Gordon system. A bion representation is found for the partition function of the system in the limit of weak coupling, i.e., the free field. From the partition function, the bion distribution is calculated and an approximate analytic formula is obtained both at low and intermediate temperatures. The obtained bion distribution is neither the Bose distribution nor the Fermi distribution, nor the Boltzmann distribution at low temperatures. The self-energy of the bion at finite temperature is also discussed.     

The cluster expansion in statistical mechanics

The Glimm-Jaffe-Spencer cluster expansion from constructive quantum field theory is adapted to treat quantum statistical mechanical systems of particles interacting by finite range potentials. The HamiltonianH ₀+V need be stable in the extended sense thatH ₀+4V+BN0 for someB. In this situation, with a mild technical condition on the potentials, the cluster expansion converges and the infinite volume limit of the correlation functions exists, at low enough density. These infinite volume correlation functions cluster exponentially. We define a class of interacting boson and fermion particle theories with a matter-like potential, 1/r suitably truncated at large distance. This system would collapse in the absence of the exclusion principle—the potential is unstable—but the Hamiltonian is stable. This provides an example of a system for which our method proves existence of the infinite volume limit, that is not covered by the classic work of Ginibre, which requires stable potentials.One key ingredient is a type of Holder inequality for the expectation values of spatially smeared Euclidean densities, a special interpolation theorem. We also obtain a result on the absolute value of the fermion measure, it equals the boson measure.This work was supported in part by NSF Grant MPS 75-10751Michigan Junior Fellow     

Principles of statistical mechanics: The energy duality

We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces. We show general theorems and their implications and apply the approach to the particle confinement in fields of rotational symmetry. Misleading associations with the theories of quasienergy and generalized thermodynamic potential are exposed.     

Nonequilibrium statistical mechanics in the general theory of relativity I. A general formalism

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The object here is the development of a tractable theory for self-gravitating systems. It is argued that the “state” of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. by mapping the true physics onto a fictitious “background” spacetime, which may be chosen to satisfy some “average” field equations, one then obtains a useful covariant notion of “evolution” in response to a fluctuating “gravitational force.” For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as “localized” in space and time, one obtains a tractable kinetic equation which reduces, in the newtonian limit, to the standard Landau equation.     

Nonequilibrium statistical mechanics. I. Mathematical formalism. Theorem of N. S. Krylov

Based on an algebraic formulation of quantum mechanics we introduce concepts playing a fundamental role in the constructionof the statistical mechanics of systems having direct classical analogs. We give the definition of a macrostate, mixing in the quantum version, and also demonstrate the existence of an upper bound to the relaxation time for an isolated system. It is shown that the theory constructed here contains both quantum and classical mechanics as limiting cases, but these two cases are not reducible to each other. The existence of a transition range not describable by the Schrodinger equation is noted.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 11, pp. 42–45, November, 1981.     

RNA分子折叠的统计力学

RNA分子折叠对决定分子（基因）水平上的生命活动是至关重要的．文章对RNA分子折叠（特别是二级结构的折叠）的热力学和动力学性质作一简单回顾与介绍．因为静电相互作用在RNA折叠过程中的特殊重要作用，文章作者对RNA（与DNA）折叠的电相互作用单独作较为详细的讨论．