Run off Conditions on Rimming Power Law Fluids

The rimming ?ow of a power-law ?uid in the inner surface of a horizontal rotating cylinder is investigated. Exploiting the fact that the liquid layer is thin, the simplest lubrication theory is applied. The generalized run-off condition for the steady-state ?ow of the power-law liquid is derived. In the bounds implied by this condition, ?lm thickness admits a continuous solution. In the supercritical case when the mass of non-Newtonian liquid exceeds a certain value or the speed of rotation is less than an indicated limit, a discontinuous solution is possible and a hydraulic jump may occur in the steady-state regime. The location and height of the hydraulic jump for the power-law liquid is determined.

Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

A variational approach to the relaxation of single domain magnetic particles based on Brown's model

Brown's model for the relaxation of the magnetization of a single domain ferromagnetic particle is considered. This model results in the Fokker-Planck equation of the process. The solution of this equation in the cases of most interest is non- trivial. The probability density of orientations of the magnetization in the Fokker-Planck equation can be expanded in terms of an infinite set of eigenfunctions and their corresponding eigenvalues where these obey a Sturm-Liouville type equation. A variational principle is applied to the solution of this equation in the case of an axially symmetric potential. The first (non-zero) eigenvalue, corresponding to the largest time constant, is considered. From this we obtain two new results. Firstly, an approximate minimising trial function is obtained which allows calculation of a rigorous upper bound. Secondly, a new upper bound formula is derived based on the Euler-Lagrange condition. This leads to very accurate calculation of the eigenvalue but also, interestingly, from this, use of the simplest trial function yields an equivalent result to the correlation time of Coffey et at. and the integral relaxation time of Garanin. (C) 2004 Elsevier B.V. All rights reserved.

An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Compact operators without extended eigenvalues

A complex number lambda is called an extended eigenvalue of a bounded linear operator T on a Banach space B if there exists a non-zero bounded linear operator X acting on B such that XT = lambda TX. We show that there are compact quasinilpotent operators on a separable Hilbert space, for which the set of extended eigenvalues is the one-point set {1}.

Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

A Novel Packet Marking Function for Real-Time Interactive MPEG-4 Video Applications in a Differentiated Services Network

The future convergence of voice, video and data applications on the Internet requires that next generation technology provides bandwidth and delay guarantees. Current technology trends are moving towards scalable aggregate-based systems where applications are grouped together and guarantees are provided at the aggregate level only. This solution alone is not enough for interactive video applications with sub-second delay bounds. This paper introduces a novel packet marking scheme that controls the end-to-end delay of an individual flow as it traverses a network enabled to supply aggregate- granularity Quality of Service (QoS). IPv6 Hop-by-Hop extension header fields are used to track the packet delay encountered at each network node and autonomous decisions are made on the best queuing strategy to employ. The results of network simulations are presented and it is shown that when the proposed mechanism is employed the requested delay bound is met with a 20% reduction in resource reservation and no packet loss in the network.

An agent-based control mechanism for WFQ in IP networks

This paper presents a new packet scheduling scheme called agent-based WFQ to control and maintain QoS parameters in virtual private networks (VPNs) within the confines of adaptive networks. Future networks are expected to be open heterogeneous environments consisting of more than one network operator. In this adaptive environment, agents act on behalf of users or third-party operators to obtain the best service for their clients and maintain those services through the modification of the scheduling scheme in routers and switches spanning the VPN. In agent-based WFQ, an agent on the router monitors the accumulated queuing delay for each service. In order to control and to keep the end-to-end delay within the bounds, the weights for services are adjusted dynamically by agents on the routers spanning the VPN. If there is an increase or decrease in queuing delay of a service, an agent on a downstream router informs the upstream routers to adjust the weights of their queues. This keeps the end-to-end delay of services within the specified bounds and offers better QoS compared to VPNs using static WFQ. This paper also describes the algorithm for agent-based WFQ, and presents simulation results. (C) 2003 Elsevier Science Ltd. All rights reserved.

Assignment methods for incidence calculus

Incidence calculus is a mechanism for probabilistic reasoning in which sets of possible worlds, called incidences, are associated with axioms, and probabilities are then associated with these sets. Inference rules are used to deduce bounds on the incidence of formulae which are not axioms, and bounds for the probability of such a formula can then be obtained. In practice an assignment of probabilities directly to axioms may be given, and it is then necessary to find an assignment of incidence which will reproduce these probabilities. We show that this task of assigning incidences can be viewed as a tree searching problem, and two techniques for performing this research are discussed. One of these is a new proposal involving a depth first search, while the other incorporates a random element. A Prolog implementation of these methods has been developed. The two approaches are compared for efficiency and the significance of their results are discussed. Finally we discuss a new proposal for applying techniques from linear programming to incidence calculus.

Spectrally efficient cooperative diversity protocol for uplink wireless transmission

A spectrally efficient cooperative protocol for uplink wireless transmission in a centralised communication system is proposed, where each of the N users play the relaying and source roles simultaneously by using superposition (SP) modulation. The probability density function of the mutual information between SP-modulated transmitted and received signals of the cooperative uplink channels is derived. Using the high-signal-to-noise ratio (SNR) approximation of this density function, the outage probability formula of the system as well as its easily computable tight upper and lower bounds are obtained and these formulas are evaluated numerically. Numerical results show that the proposed strategy can achieve around 3 dB performance gain over comparable schemes. Furthermore, the multiplexing and diversity tradeoff formula is derived to illustrate the optimal performance of the proposed protocol, which also confirms that the SP relaying transmission does not cause any loss of data rate. Moreover, performance characterisation in terms of ergodic and outage capacities are studied and numerical results show that the proposed scheme can achieve significantly larger outage capacity than direct transmission, which is similar to other cooperative schemes. The superiority of the proposed strategy is demonstrated by the fact that it can maintain almost the same ergodic capacity as the direct transmission, whereas the ergodic capacity of other cooperative schemes would be much worse.

Cooperative transmission protocol with full diversity and iterative detection

The authors propose a three-node full diversity cooperative protocol, which allows the retransmission of all symbols. By allowing multiple nodes to transmit simultaneously, relaying transmission only consumes limited bandwidth resource. To facilitate the performance analysis of the proposed cooperative protocol, the lower and upper bounds of the outage probability are first developed, and then the high signal-to-noise ratio behaviour is studied. Our analytical results show that the proposed strategy can achieve full diversity. To achieve the performance gain promised by the cooperative diversity, at the relays decode-and-forward strategy is adopted and an iterative soft-interference-cancellation minimum mean-squared error equaliser is developed. The simulation results compare the bit-error-rate performance of the proposed protocol with the non-cooperative scheme and the scheme presented by Azarian et al. ( 2005).

Online CORDIC algorithm and VLSI architecture for implementing QR-array processors

A novel most significant digit first CORDIC architecture is presented that is suitable for the VLSI design of systolic array processor cells for performing QR decomposition. This is based on an on-line CORDIC algorithm with a constant scale factor and a latency independent of the wordlength. This has been derived through the extension of previously published CORDIC algorithms. It is shown that simplifying the calculation of convergence bounds also greatly simplifies the derivation of suitable VLSI architectures. Design studies, based on a 0.35-µ CMOS standard cell process, indicate that 20 such QR processor cells operating at rates suitable for radar beamfoming can be readily accommodated on a single chip.

Universal power-law diet partitioning by marine fish and squid with surprising stability–diversity implications

A central question in community ecology is how the number of trophic links relates to community species richness. For simple dynamical food-web models, link density (the ratio of links to species) is bounded from above as the number of species increases; but empirical data suggest that it increases without bounds. We found a new empirical upper bound on link density in large marine communities with emphasis on fish and squid, using novel methods that avoid known sources of bias in traditional approaches. Bounds are expressed in terms of the diet-partitioning function (DPF): the average number of resources contributing more than a fraction f to a consumer's diet, as a function of f. All observed DPF follow a functional form closely related to a power law, with power-law exponents indepen- dent of species richness at the measurement accuracy. Results imply universal upper bounds on link density across the oceans. However, the inherently scale-free nature of power-law diet partitioning suggests that the DPF itself is a better defined characterization of network structure than link density.