Spectral parameter dependent Lax pairs for systems of Calogero–Moser type

Presentation of a method for generating Lax pairs for systems obtained by means of Hamiltonian reduction.     

On thermodynamics and gravity

Physics of Atomic Nuclei - A new entropic gravity inspired derivation of general relativity from thermodynamics is presented. This generalizes the “Thermodynamics of Spacetime” approach...     

Axisymmetric jets impinging on porous walls

The flow of axisymmetric turbulent jets impinging on porous walls has been studied experimentally. It is shown how the overall flow structure depends on the porosity of the surface. For high porosities (open area ratios, β, in excess of around 40% say) the porous wall, or screen, leads to a sudden increase in jet width and decrease in mean and fluctuating velocities, a direct consequence of the momentum flux extracted because of the screen drag. Lower porosities can lead to the appearance of radial wall jets on the upstream side of the screen but, in contrast to the corresponding case of planar jet impingement (Cant et al. in Exp Fluids 32:16–26, 2002), such wall jets never occur on the downstream side. The axial downstream velocities thus remain positive for all porosities. Jet growth rates for are initially increased by the screen, but once β≤0.4 momentum extraction by the screen is virtually complete, so that velocities become very small. Again, unlike in the corresponding planar case (for β≈0.4), recirculating regions upstream of the screen never occur. A simple argument is suggested to explain the fundamental differences in flow behaviour between planar and axisymmetric jet impingement onto porous screens and it is concluded that in the latter case the effects of the screen are generally more benign and unsurprising. Nonetheless, these axisymmetric flows, like the corresponding planar ones, provide a serious challenge for computational modelling.     

Thermal boundary condition effects on heat transfer in turbulent rough-wall boundary layers

Measurements and predictions are presented which investigate the effects of thermal boundary condition on heat transfer in the turbulent rough-wall boundary layer. Stanton number measurements are reported for the turbulent flow of air over rough plates with a variety of thermal boundary conditions on two separate rough surfaces. The cases considered are constant wall temperature, constant wall heat flux, step wall temperature, and piecewise linear wall temperature distributions. These measurements and data from other sources are compared with predictions using finite difference solutions of the discrete element roughness model and with superposition solutions. The predictions and the measurements are in good to excellent agreement.In dieser Arbeit werden Messungen und Berechnungen gezeigt, die den Einfluß der thermischen Randbedingungen auf die Wärmeübertragung in turbulenten Grenzschichten an rauhen Wänden untersuchen. Es werden Messungen der Stanton Zahl für turbulente Luftströmung über rauhe Platten an zwei separaten Oberflächen unter einer Reihe von thermischen Randbedingungen dargestellt. Die betrachteten Fälle sind konstante Wandtemperatur, konstanter Wärmestrom durch die Wand, abgestufte Wandtemperatur und stückweise konstante Wandtemperatur. Diese Messungen, sowie Daten anderer Untersuchungen, werden mit Berechnungen durch Finite-Differenzen Lösungen des Diskrete-Elemente-Rauhheits-Modells und Superpositionslösungen verglichen. Berechnungen und Messungen liegen in guter bis ausgezeichneter Übereinstimmung.     

Rheological and diffusion properties of a dextran-con A polymer in the presence of Insulin and Magnesium

Previous work carried out in our laboratories has focused on the formation and investigation of a dextran and concanavalin A (con A) based gel, which has the ability to alter its conformational structure in the presence and absence of free and terminal glucoses such that a gel–sol phase transition occurs. Here we report the diffusion and rheological investigations in to the effects of the addition of insulin and varyingconcentrations of magnesium chloride hexahydrate (Mg₂Cl₂6H₂O) at 20 and 37 °C. Rheological examination of glucose-sensitive (dextran-con A) gels were conducted using a cone and plate viscometer used in continual rotation and oscillatory modes. The results are interpreted in terms of the structure of the gel network and suggest rheological assessment provides an effective method of assessing the properties of gel systems. The subsequent testing of such formulations in in-vitro diffusion experiments revealed a reduction in the rate of diffusivity in the insulin marker, poly R-478 dye. The performance of this self-regulating drug delivery system has been examined and the addition of insulin and magnesium chloride may alter the way in which the gel operates as a drug delivery device and in the delivery of insulin. This may have implications for other ligands.     

Some Primitive Concepts in Continuum Mechanics Regarded in Terms of Objective Space-Time Molecular Averaging: The Key Rôle Played by Inertial Observers

In Continuum Mechanics the notions of body, material point, and motion, are primitive. Here these concepts are derived for any (possibly time-dependent) material system via mass and momentum densities whose values are local spacetime averages of molecular quantities. The averaging procedure necessary to ensure molecular-based densities can be agreed upon by all observers (that is, are objective) has implications for constitutive relations. Specifically, such relations should first be expressed in terms of Galilean-invariant functions of the motion relative to an inertial frame. Thereafter such relations can be re-phrased for general observers, thereby yielding general-frame constitutive relations compatible with material frame-indifference. Two postulates concerning observer agreement (which together constitute a statement of material frame-indifference) are shown to imply that any stress response function which is assumed to depend upon the motion in an inertial (general) frame must be Galilean-invariant (invariant under superposed rigid body motions). Accordingly, invariance under superposed rigid body motions is not a fundamental tenet of continuum physics, but rather a consequence of material frame-indifference whenever constitutive dependence upon motion in a general observer frame is postulated.     

Temperature profiles in a controlled-stress parallel plate rheometer

Actual melt temperatures are rarely measured directly when conducting rheological characterisations of materials in non-ambient conditions despite the potentially large influence temperature may have on the rheological data. For rheometers that use only a temperature-regulated lower plate, it is likely that the set point and true melt temperatures differ, an effect that becomes significant when characterising melts or suspensions close to phase-change events like crystallisation. This work investigates the magnitude of these effects for a controlled-stress rheometer featuring a temperature-controlled lower plate. The lower plate was fitted with a serrated cover disc that was found to exacerbate temperature deviations from the desired set point. Steady-state radial and vertical temperature profiles within the sample were measured and compared with the predictions of a finite element analysis model. The deviations between set point and measured temperatures were successfully predicted by the simulation for two typical gap heights for a thermoplastic, ceramic paste. The non-ideal heat transfer characteristics were also investigated numerically for a representative polymer system that demonstrated the increased deviations from ideal values for lower thermal conductivity materials.

Experimental study of the shock response of an HMX-based explosive

Experiments have been fired in which the HMX-based explosive EDC37 was subjected to one-dimensional shocks generated by plate impact. The response of the explosive to sustained shocks, double shocks and a short-pulse shock was monitored using embedded particle velocity gauges and shock tracker gauges. The final stages of the growth to detonation process were similar for all of the different input profiles. A strong reactive wave grows and accelerates to overtake and dominate the initial shock. It is shown that the curves showing the growth of the shock and the reactive wave in the sustained shock experiments can be normalised to give universal curves. These curves provides a reference against which to compare the explosive's response, not only to single sustained shocks, but also to double shock and short-pulse inputs. The treatment provides an empirical route for predicting the effects of sustained and more complex shocks on EDC37. PACS 47.40.-x; 82.33.Vx     

Computerized fringe analysis in photomechanics

A generalized method is presented for analyzing the fringe patterns frequently encountered in experimental mechanics. By utilizing digital-image-processing and computer-graphics techniques, a set of menu-driven software is developed for interactively implementing the fringe processing. Tests of this software on the images obtained experimentally by photoelasticity, holographic interferometry and speckle interferometry demonstrate its usefulness. Good agreement between the experimental and theoretical results is established.     

Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time‐independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi–Babuska condition. The k–l model is used to complete the turbulence closure problem. The non‐symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a ‘V‐cycling’ schedule. These methods are all compared to the non‐symmetric frontal solver. Copyright © 1999 John Wiley & Sons, Ltd.