Faith and politics: The rhetoric of church-state separation

Criticism of religiously motivated contributions to public policy debate is largely misconceived. It assumes that the mischief which constitutional separation of church and state is supposed to cure is a domination of the state by the church. This presents only one side of the story. Subservience by the church to the slate should also be avoided. The law of a liberal state is legitimate to the extent that it does not conflict with the basic moral values of its citizens. Therefore, an ongoing conversation about basic values is necessary. Allowing churches and individual believers the freedom to make distinctive 'religious' contributions to this conversation is consistent with the separation of church and state. It is an aspect of the liberal democratic state's obligation to listen to all perspectives on difficult moral issues. A close relationship between church and state, on the other hand, has the capacity to impede the conversation.

Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.

Coalescence of secondary dispersions in fibrous beds

SUMMARY A study has been made of the coalescence of secondary dispersions in a fibrous bed. The literature pertaining to the formation, hydrodynamic behaviour and methods of separation of droplets less than one hundred micrometres in diameter has been reviewed with particular reference to fibrous bed coalescers. The main operating parameters were identified as inlet drop size distribution, phase ratio, superficial velocity and the thickness and voidage of the bed . A recirculatory rig with interchangeable fibrous bed pads was designed and operated with toluene-water dispersions generated by a combination of centrifugal pumps . Inlet drop sizes were analysed using a Coulter Counter and outlet drops were sized photographically. A novel technique, involving conductivity measur ements at different planes in the bed, was developed to measure hold up distribution. Single phase flow and two phase flow pressure drops were correlated by a Blake-Kozeny type equation. Exit drop size was independent of inlet drop size distribution and phase ratio but a function of superficialvelocity and packing thickness. Average bed hold up was independent of inlet drop size distribution and phase ratio, but decreased with increase in superficial velocity. Hold up was not evenly distributed in the bed, the highest value occurred at the inlet followed by a sharp -2 drop at approximately 1.2 x 10 m. Hold up remained constant throughout the rest of the bed until the exit plane, where it increased. From the results, a mechanism is postulated involving: (a) Capture of the inlet drops followed by interdrop coalescence until an equilibrium value is reached. (b) Equilibrium size droplets flowing as rivulets through the intermediate portion of the bed, and (c) Each rivulet forms droplets at the exit face, which detach by a 'drip point' mechanism.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Range of validity of weakly non-linear theory in Rayleigh-Bénard problem

In this paper we examine the equilibrium states of finite amplitude flow in a horizontal fluid layer with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau constants and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infinitesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighborhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable. © 2009 The Physical Society of Japan.

Computer simulation of liquid flow patterns on distillation trays

This thesis describes work carried out to improve the fundamental modelling of liquid flows on distillation trays. A mathematical model is presented based on the principles of computerised fluid dynamics. It models the liquid flow in the horizontal directions allowing for the effects of the vapour through the use of an increased liquid turbulence, modelled by an eddy viscosity, and a resistance to liquid flow caused by the vapour being accelerated horizontally by the liquid. The resultant equations are similar to the Navier-Stokes equations with the addition of a resistance term.A mass-transfer model is used to calculate liquid concentration profiles and tray efficiencies. A heat and mass transfer analogy is used to compare theoretical concentration profiles to experimental water-cooling data obtained from a 2.44 metre diameter air-water distillation simulation rig. The ratios of air to water flow rates are varied in order to simulate three pressures: vacuum, atmospheric pressure and moderate pressure.For simulated atmospheric and moderate pressure distillation, the fluid mechanical model constantly over-predicts tray efficiencies with an accuracy of between +1.7% and +11.3%. This compares to -1.8% to -10.9% for the stagnant regions model (Porter et al. 1972) and +12.8% to +34.7% for the plug flow plus back-mixing model (Gerster et al. 1958). The model fails to predict the flow patterns and tray efficiencies for vacuum simulation due to the change in the mechanism of liquid transport, from a liquid continuous layer to a spray as the liquid flow-rate is reduced. This spray is not taken into account in the development of the fluid mechanical model. A sensitivity analysis carried out has shown that the fluid mechanical model is relatively insensitive to the prediction of the average height of clear liquid, and a reduction in the resistance term results in a slight loss of tray efficiency. But these effects are not great. The model is quite sensitive to the prediction of the eddy viscosity term. Variations can produce up to a 15% decrease in tray efficiency. The fluid mechanical model has been incorporated into a column model so that statistical optimisation techniques can be employed to fit a theoretical column concentration profile to experimental data. Through the use of this work mass-transfer data can be obtained.

Computational fluid dynamical studies of structured distillation packings

In recent years structured packings have become more widely used in the process industries because of their improved volumetric efficiency. Most structured packings consist of corrugated sheets placed in the vertical plane The corrugations provide a regular network of channels for vapour liquid contact. Until recently it has been necessary to develop new packings by trial and error, testing new shapes in the laboratory. The orderly repetitive nature of the channel network produced by a structured packing suggests it may be possible to develop improved structured packings by the application of computational fluid dynamics (CFD) to calculate the packing performance and evaluate changes in shape so as to reduce the need for laboratory testing. In this work the CFD package PHOENICS has been used to predict the flow patterns produced in the vapour phase as it passes through the channel network. A particular novelty of the approach is to set up a method of solving the Navier Stokes equations for any particular intersection of channels. The flow pattern of the streams leaving the intersection is then made the input to the downstream intersection. In this way the flow pattern within a section of packing can be calculated. The resulting heat or mass transfer performance can be calculated by other standard CFD procedures. The CFD predictions revealed a circulation developing within the channels which produce a loss in mass transfer efficiency The calculations explained and predicted a change in mass transfer efficiency with depth of the sheets. This effect was also shown experimentally. New shapes of packing were proposed to remove the circulation and these were evaluated using CFD. A new shape was chosen and manufactured. This was tested experimentally and found to have a higher mass transfer efficiency than the standard packing.

Liquid-phase adsorption of n-paraffins on type 5A molecular sieves

As a basis for the commercial separation of normal paraffins a detailed study has been made of factors affecting the adsorption of binary liquid mixtures of high molecular weight normal paraffins (C12, C16, and C20) from isooctane on type 5A molecular sieves. The literature relating to molecular sieve properties and applications, and to liquid-phase adsorption of high molecular weight normal paraffin compounds by zeolites, was reviewed. Equilibrium isotherms were determined experimentally for the normal paraffins under investigation at temperatures of 303oK, 323oK and 343oK and showed a non-linear, favourable- type of isotherm. A higher equilibrium amount was adsorbed with lower molecular weight normal paraffins. An increase in adsorption temperature resulted in a decrease in the adsorption value. Kinetics of adsorption were investigated for the three normal paraffins at different temperatures. The effective diffusivity and the rate of adsorption of each normal paraffin increased with an increase in temperature in the range 303 to 343oK. The value of activation energy was between 2 and 4 kcal/mole. The dynamic properties of the three systems were investigated over a range of operating conditions (i.e. temperature, flow rate, feed concentration, and molecular sieve size in the range 0.032 x 10-3 to 2 x 10-3m) with a packed column. The heights of adsorption zones calculated by two independent equations (one based on a constant width, constant velocity and adsorption zone and the second on a solute material balance within the adsorption zone) agreed within 3% which confirmed the validity of using the mass transfer zone concept to provide a simple design procedure for the systems under study. The dynamic capacity of type 5A sieves for n-eicosane was lower than for n-hexadecane and n-dodecane corresponding to a lower equilibrium loading capacity and lower overall mass transfer coefficient. The values of individual external, internal, theoretical and experimental overall mass transfer coefficient were determined. The internal resistance was in all cases rate-controlling. A mathematical model for the prediction of dynamic breakthrough curves was developed analytically and solved from the equilibrium isotherm and the mass transfer rate equation. The experimental breakthrough curves were tested against both the proposed model and a graphical method developed by Treybal. The model produced the best fit with mean relative percent deviations of 26, 22, and 13% for the n-dodecane, n-hexadecane, and n-eicosane systems respectively.

An investigation into the antecedents of prosocial service behaviours : a travel service context

Frontline employee (FLE) attitudes and behaviours during service encounters influence customers’ perceptions of service quality and customer satisfaction. The identification of variables that influence FLEs service behaviours is, therefore, important. Much remains unknown about the factors affecting prosocial service behaviours (PSBs). This thesis answers the following questions: What are the antecedents of PSBs in a travel service setting? It is argued that managerial strategies indirectly influence PSBs via their direct influence on job attitudes. This thesis represents an attempt towards an increased knowledge about the antecedents of PSBs by seeking answers to the question. A conceptual model was developed from the literature. Briefly stated, the hypothesised model proposed that job attitudes mediate the relationship between managerial strategies and the PSBs. In-depth interviews provided initial support for the conceptual model. Structural equation modelling techniques were then used to test these relationships on data from 179 travel service employees. Partial support for the mediational role of job attitudes was found. More specifically, the relationship between professional development and extra-role customer service is mediated by job satisfaction and organisational commitment, but not in-role customer service and cooperation. The managerial strategies influence PSBs directly. Internal communication influences extra- and in-role customer service behaviours positively. The relationship between professional development and the three PSBs constructs is negative. Empowerment influences in-role customer service and cooperative behaviours positively.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order

Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2 = β−1 = 0, p−1 = p−2 = 0, p0 (λ) = 1, p1 (λ) = cλ + b, c > 0, b ∈ C, λ ∈ C. It is shown that they are orthonormal on the real and the imaginary axes in the complex plane ...

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Caputo-Type Modification of the Erdélyi-Kober Fractional Derivative

2000 Math. Subject Classification: 26A33; 33E12, 33E30, 44A15, 45J05

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Mathematics Subject Classification: 26A33, 31B10

Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces

MSC 2010: 26A33