Interactive Statistical Mechanics and Nonlinear Filtering

This paper connects non-equilibrium statistical mechanics and optimal nonlinear filtering. The latter concerns the observation-conditional behaviour of Markov signal processes, and thus provides a tool for investigating statistical mechanics with partial observations. These allow entropy reduction, illustrating Landauer’s Principle in a quantitative way. The joint process comprising a signal and its nonlinear filter is irreversible in its invariant distribution, which therefore corresponds to a non-equilibrium stationary state of the associated joint system. Macroscopic entropy and energy flows are identified for this state. Since these are driven by observations internal to the system, they do not cause entropy increase, and so the joint system makes statistical mechanical sense in reverse time. Time reversal yields a dual system in which the signal and filter exchange roles. Despite the structural similarity of the original and dual systems, there is a substantial asymmetry in their complexities. This reveals the direction of time, despite the systems being in stationary states that do not produce entropy. This work was partially supported by Leverhulme Trust Research Fellowship 2003/0426, by MURI Grant F49620-02-1-0325 (Complex Adaptive Networks for Co-operative Control), by ARO-MURI Grant DAAD19-00-1-0466 (Data Fusion in Large Arrays of Microsensors (sensor web)) and by NSF-ITR Grant CCR-0325774 Collaborative Research: New Approaches to Experimental Design and Statistical Analysis of Genomic and Structural Biological Data from Multiple Sources.     

Effect of viscosity upon liquid velocity in axi-symmetric sheets

Zusammenfassung Die nach aussen gerichtete axialsymmetrische Strömung einer viskosen Flüssigkeitsschicht wird untersucht und eine exakte Lösung der Impulsgleichung angegeben. Durch Linearisierung dieser Gleichung lässt sich eine einfache Lösung finden, die eine sehr gute Näherung des Geschwindigkeitsverlaufs gibt. In allen praktisch wichtigen Fällen ist der Geschwindigkeitsverlust der Reynoldsschen Zahl annähernd umgekehrt proportional.

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Nomenclature A, B arbitrary constants - C constant of integration, evaluated in Equation (9), - I ₀,I ₁ modified Bessel functions of the first kind, of zeroth and first order, respectively, - K ₀,K ₁ modified Bessel functions of the second kind, of zeroth and first order, respectively, - Re Reynolds number of the flow,r ₀ u ₀/v, - r radial coordinate, - s ( ^-1–)/2 - t thickness of sheet - u velocity of sheet, - y transformeds, given by Equation (10), - dimensionless radial coordinate,r/r ₀, - dimensionless velocity,u r _o/v, - v kinematic viscosity. - l denoting a linearized result, - o denoting evaluation made at inner boundary of sheet, - denoting an evaluation made as . This work has been supported in part by the College of Agriculture Research Center.     

Geminal coupling constants in methylene groups α to nitrogen in indolizidine,quinolizidine and related systems

Values of J(5a—5e) for indolizidine and related systems show that, contrary to results described in an earlier communication, these couplings do not differ markedly from the corresponding geminal coupling constant in quinolizidine.     

Liquid scintillators X. Some aryl substituted phenanthrenes and dihydrophenanthrenes,and relatedp-terphenyls andp-quaterphenyls determination of Kallmann parameters

A number of new 2- and 2,7-aryl substituted phenanthrenes, 3,4-dihydrophenanthrenes, and 9,10-dihydrophenanthrenes, as well as some relatedp-quaterphenyls andp-terphenyls, were tested as liquid scintillation solutes. Also determined were the compounds' ultraviolet absorption spectra, ultraviolet-induced fluorescence spectra, and Kallmann parameters. On the basis of these measurements, it was possible to correlate to some degree structure and scintillation ability. Some interesting results regarding conjugation and co-planarity in the linear polyphenyls were also obtained.     

Overcompleteness in the theory of chemisorption

The overcompleteness of the basis states when Anderson's Hamiltonian is applied to chemisorption is allowed for by using a pseudopotential to describe the atom-metal coupling. Some calculations for hydrogen on free-electron Al are reported.     

The exponential decay law of unstable systems

It is shown that associated with any sufficiently sharp resonance there is a delayed emergence of particles that under suitable conditions follows an exponential law of decay to an excellent approximation over many lifetimes. The dependence of the duration of the exponential curve on the resonance width, on the excitation width, and on the observation distance, is examined in detail.