On inertial-range scaling laws

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's $k^{-5/3}$ scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.Comment: 16 pages, postscript (uncompressed, not encoded

Large-scale energy spectra in surface quasi-geostrophic turbulence

The large-scale energy spectrum in two-dimensional turbulence governed by the surface quasi-geostrophic (SQG) equation $$\partial_t(-\Delta)^{1/2}\psi+J(\psi,(-\Delta)^{1/2}\psi) =\mu\Delta\psi+f$$ is studied. The nonlinear transfer of this system conserves the two quadratic quantities $\Psi_1=/2$ and $\Psi_2=/2$ (kinetic energy), where $$ denotes a spatial average. The energy density $\Psi_2$ is bounded and its spectrum $\Psi_2(k)$ is shallower than $k^{-1}$ in the inverse-transfer range. For bounded turbulence, $\Psi_2(k)$ in the low-wavenumber region can be bounded by $Ck$ where $C$ is a constant independent of $k$ but dependent on the domain size. Results from numerical simulations confirming the theoretical predictions are presented.Comment: 11 pages, 4 figures, to appear in JF

Modelling Garbage Collection Algorithms --- Extend abstract

We show how abstract requirements of garbage collection can be captured using temporal logic. The temporal logic specification can then be used as a basis for process algebra specifications which can involve varying amounts of parallelism. We present two simple CCS specifications as an example, followed by a more complex specification of the cyclic reference counting algorithm. The verification of such algorithms is then briefly discussed

Analysis of a Multimedia Stream using Stochastic Process Algebra

It is now well recognised that the next generation of distributed systems will be distributed multimedia systems. Central to multimedia systems is quality of service, which defines the non-functional requirements on the system. In this paper we investigate how stochastic process algebra can be used in order to determine the quality of service properties of distributed multimedia systems. We use a simple multimedia stream as our basic example. We describe it in the Stochastic Process Algebra PEPA and then we analyse whether the stream satisfies a set of quality of service parameters: throughput, end-to-end latency, jitter and error rates

A Study of the Low Current Density Electrolysis of Ammonium Thiosulfate Fixers

Determinations of the current tolerences of sodium thiosulfate and ammonium thiosulfate fixers are made and compared. The rate of fixation of ammonium thiosulfate fixer before and after electrolysis is studied. The current efficiency of low current density electrolysis in ammonium thiosulfate is found. Causes and forms of sulfiding are discussed and related to the work of the experimenter

Specifying and Refining Internal Operations in Z

Abstract An important aspect in the specification of distributed systems is the role of the internal (or unobservable) operation. Such operations are not part of the interface to the environment (i.e. the user cannot invoke them), however, they are essential to our understanding and correct modelling of the system. In this paper we are interested in the use of the formal specification notation Z for the description of distributed systems. Various conventions have been employed to model internal operations when specifying such systems in Z. If internal operations are distinguished in the specification notation, then refinement needs to deal with internal operations in appropriate ways. Using an example of a telecommunications protocol we show that standard Z refinement is inappropriate for refining a system when internal operations are specified explicitly. We present a generalization of Z refinement, called weak refinement, which treats internal operations differently from observable operations when refining a system. We discuss the role of internal operations in a Z specification, and in particular whether an equivalent specification not containing internal operations can be found. The nature of divergence through livelock is also discussed. Keywords: Z; Refinement; Distributed Systems; Internal Operations; Process Algebras; Concurrency