Canonical and non-canonical equilibrium distribution

We address the problem of the dynamical foundation of non-canonical equilibrium. We consider, as a source of divergence from ordinary statistical mechanics, the breakdown of the condition of time scale separation between microscopic and macroscopic dynamics. We show that this breakdown has the effect of producing a significant deviation from the canonical prescription. We also show that, while the canonical equilibrium can be reached with no apparent dependence on dynamics, the specific form of non-canonical equilibrium is, in fact, determined by dynamics. We consider the special case where the thermal reservoir driving the system of interest to equilibrium is a generator of intermittent fluctuations. We assess the form of the non-canonical equilibrium reached by the system in this case. Using both theoretical and numerical arguments we demonstrate that Levy statistics are the best description of the dynamics and that the Levy distribution is the correct basin of attraction. We also show that the correct path to non-canonical equilibrium by means of strictly thermodynamic arguments has not yet been found, and that further research has to be done to establish a connection between dynamics and thermodynamics.Comment: 13 pages, 6 figure

Holder exponent spectra for human gait

The stride interval time series in normal human gait is not strictly constant, but fluctuates from step to step in a complex manner. More precisely, it has been shown that the control process for human gait is a fractal random phenomenon, that is, one with a long-term memory. Herein we study the Holder exponent spectra for the slow, normal and fast gaits of 10 young healthy men in both free and metronomically triggered conditions and establish that the stride interval time series is more complex than a monofractal phenomenon. A slightly multifractal and non-stationary time series under the three different gait conditions emerges.Comment: 23 pages, 12 figures, 9 Table

Galaxy Orientations in the Coma Cluster

We have examined the orientations of early-type galaxies in the Coma cluster to see whether the well-established tendency for brightest cluster galaxies to share the same major axis orientation as their host cluster also extends to the rest of the galaxy population. We find no evidence of any preferential orientations of galaxies within Coma or its surroundings. The implications of this result for theories of the formation of clusters and galaxies (particularly the first-ranked members) are discussed.Comment: Accepted for publication in the Astrophysical Journal Letters. 4 pages, 4 figure

Non-Poisson dichotomous noise: higher-order correlation functions and aging

We study a two-state symmetric noise, with a given waiting time distribution $\psi (\tau)$, and focus our attention on the connection between the four-time and the two-time correlation functions. The transition of $\psi (\tau)$ from the exponential to the non-exponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties, and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process

Anomalous isotopic predissociation in the F³Πu(v=1) state of O₂

Using a tunable, narrow-bandwidth vacuum-ultraviolet source based on third-harmonic generation from excimer-pumped dye-laser radiation, the F³Πu←X³Σg-(1,0)photoabsorption cross sections of ¹⁶O₂ and ¹⁸O₂ have been recorded in high resolution. Rotational analyses have been performed and the resultant F(v=1) term values fitted to the ³Π Hamiltonian of Brown and Merer [J. Mol. Spectrosc. 74, 488 (1979)]. A large rotationless isotope effect is observed in the F(v=1)predissociation, wherein the Lorentzian linewidth component for ¹⁸O₂ is a factor of ∼50 smaller than the corresponding ¹⁶O₂linewidth. This effect, a consequence of the nonadiabatic rotationless predissociation mechanism, is described using a coupled-channel treatment of the strongly Rydberg-valence-mixed 3Πu states. Significant J, e/f-parity, and sublevel dependencies observed in the isotopic F(v=1) rotational widths are found to derive from an indirect predissociation mechanism involving an accidental degeneracy with the E³Σ−u(v=3) level, itself strongly predissociated by ³Σ−u Rydberg-valence interactions, together with L-uncoupling (rotational) interactions between the Rydberg components of the F and E states. Transitions into the E(v=3) level are observed directly for the first time, specifically in the ¹⁸O₂ spectrumPartial support was provided by an NSF International Opportunities for Scientists and Engineers Program Grant No. INT-9513350, and Visiting Fellowships for G.S. and J.B.W. at the Australian National University

DEKAS - An evolutionary case-based reasoning system to support protection scheme design

This paper describes a decision support system being developed in conjunction with two UK utility companies to aid the design of electrical power transmission protection systems. A brief overview of the application domain is provided, followed by a description of the work carried out to date concerning the development and deployment of the Design Engineering Knowledge Application System (DEKAS). The paper then discusses the provision of intelligent decision support to the design engineer through the application of case-based reasoning (CBR). The key benefits from this will be outlined in conjunction with a relevant case study

Aging and Rejuvenation with Fractional Derivatives

We discuss a dynamic procedure that makes the fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment and divergent second moment, namely with the power index mu in the interval 2<mu <3, yields a generalized master equation equivalent to the sum of an ordinary Markov contribution and of a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, ord, is given by ord=3-mu . A brand new system is characterized by the degree ord=mu -2. If the system is prepared at time -ta<0$ and the observation begins at time t=0, we derive the following scenario. For times 0<t<<ta the system is satisfactorily described by the fractional derivative with ord=3-mu . Upon time increase the system undergoes a rejuvenation process that in the time limit t>>ta yields ord=mu -2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.Comment: 11 pages, 4 figure