Modelling the mechanical response of the reed-mouthpiece-lip system of a clarinet. Part II: A lumped model approximation

A non-linear lumped model of the reed-mouthpiece-lip system of a clarinet is formulated, in which the lumped parameters are derived from numerical experiments with a finite-difference simulation based on a distributed reed model. The effective stiffness per unit area is formulated as a function of the pressure signal driving the reed, in order to simulate the effects of the reed bending against the lay, and mass and damping terms are added as a first approximation to the dynamic behaviour of the reed. A discrete-time formulation is presented, and its response is compared to that of the distributed model. In addition, the lumped model is applied in the simulation of clarinet tones, enabling the analysis of the effects of using a pressure-dependent stiffness per unit area on sustained oscillations. The analysed effects and features are in qualitative agreement with players' experiences and experimental results obtained in prior studies.

A Phase Grating Approach to Modeling Surface Diffusion in FDTD Room Acoustics Simulations

In this paper, a method for modeling diffusive boundaries in finite difference time domain (FDTD) room acoustics simulations with the use of impedance filters is presented. The proposed technique is based on the concept of phase grating diffusers, and realized by designing boundary impedance filters from normal-incidence reflection filters with added delay. These added delays, that correspond to the diffuser well depths, are varied across the boundary surface, and implemented using Thiran allpass filters. The proposed method for simulating sound scattering is suitable for modeling high frequency diffusion caused by small variations in surface roughness and, more generally, diffusers characterized by narrow wells with infinitely thin separators. This concept is also applicable to other wave-based modeling techniques. The approach is validated by comparing numerical results for Schroeder diffusers to measured data. In addition, it is proposed that irregular surfaces are modeled by shaping them with Brownian noise, giving good control over the sound scattering properties of the simulated boundary through two parameters, namely the spectral density exponent and the maximum well depth.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

Strong-field approximation for Coulomb explosion of H-2(+) and D-2(+) by short intense laser pulses

We present a simple quantum mechanical model to describe Coulomb explosion of H-2(+) and D-2(+) by short, intense infrared laser pulses. The model is based on the length gauge version of the molecular strong-field approximation and is valid when the process of dissociation prior to ionization is negligible. The results are compared with recent experimental data for the proton kinetic energy spectrum [Th. Ergler , Phys. Rev. Lett. 95, 093001 (2005); D. S. Murphy , J. Phys. B 40, S359 (2007)]. Using a Franck-Condon distribution over initial vibrational states, the theory reproduces the overall shape of the spectrum with only a small overestimation of slow protons. The agreement between theory and experiment can be made perfect by using a non-Frank-Condon initial distribution characteristic for H-2(+) (D-2(+)) targets produced by strong-field ionization of H-2 (D-2). For comparison, we also present results obtained by two different tunneling models for this process.

The distorted-wave impulse approximation for electron capture into excited states

Total cross sections for electron capture are calculated for collisions of fast protons and a-particles with atomic hydrogen. The distorted-wave impulse approximation is applied over the energy range 10-1500 keV/u. State-selective results are given for the 1s, 2s and 2p levels. Both the post and prior forms of the model are calculated and compared with results from other theories and experimental measurements. In general the model performs very well in comparison with experiment over this energy range though discrepancies arise at lower energies.

Finite difference time domain modeling of phase grating diffusion

In this paper, a method for modeling diffusion caused by non-smooth boundary surfaces in simulations of room acoustics using finite difference time domain (FDTD) technique is investigated. The proposed approach adopts the well-known theory of phase grating diffusers to efficiently model sound scattering from rough surfaces. The variation of diffuser well-depths is attained by nesting allpass filters within the reflection filters from which the digital impedance filters used in the boundary implementation are obtained. The presented technique is appropriate for modeling diffusion at high frequencies caused by small surface roughness and generally diffusers that have narrow wells and infinitely thin separators. The diffusion coefficient was measured with numerical experiments for a range of fractional Brownian diffusers.

Theoretical and experimental correlations of gas dissolution, diffusion, and thermodynamic properties in determination of gas permeability and selectivity in supported ionic liquid membranes

Supported ionic liquid membranes (SILMs) has the potential to be a new technological platform for gas/organic vapour separation because of the unique non-volatile nature and discriminating gas dissolution properties of room temperature ionic liquids (ILs). This work starts with an examination of gas dissolution and transport properties in bulk imidazulium cation based ionic liquids [C_nmim][NTf2] (n = 2.4, 6, 8.10) from simple gas H₂, N₂, to polar CO₂, and C₂H₆, leading to a further analysis of how gas dissolution and diffusion are influenced by molecular specific gas-SILMs interactions, reflected by differences in gas dissolution enthalpy and entropy. These effects were elucidated again during gas permeation studies by examining how changes in these properties and molecular specific interactions work together to cause deviations from conventional solution–diffusion theory and their impact on some remarkably contrasting gas perm-selectivity performance. The experimental perm-selectivity for all tested gases showed varied and contrasting deviation from the solution–diffusion, depending on specific gas-IL combinations. It transpires permeation for simpler non-polar gases (H₂, N₂) is diffusion controlled, but strong molecular specific gas-ILs interactions led to a different permeation and selectivity performance for C₂H₆ and CO₂. With exothermic dissolution enthalpy and large order disruptive entropy, C₂H₆ displayed the fastest permeation rate at increased gas phase pressure in spite of its smallest diffusivity among the tested gases. The C₂H₆ gas molecules “peg” on the side alkyl chain on the imidazulium cation at low concentration, and are well dispersed in the ionic liquids phase at high concentration. On the other hand strong CO₂-ILs affinity resulted in a more prolonged “residence time” for the gas molecule, typified by reversed CO₂/N₂ selectivity and slowest CO₂ transport despite CO₂ possess the highest solubility and comparable diffusivity in the ionic liquids. The unique transport and dissolution behaviour of CO₂ are further exploited by examining the residing state of CO₂ molecules in the ionic liquid phase, which leads to a hypothesis of a condensing and holding capacity of ILs towards CO₂, which provide an explanation to slower CO₂ transport through the SILMs. The pressure related exponential increase in permeations rate is also analysed which suggests a typical concentration dependent diffusion rate at high gas concentration under increased gas feed pressure. Finally the strong influence of discriminating and molecular specific gas-ILs interactions on gas perm-selectivity performance points to future specific design of ionic liquids for targeted gas separations.

ON THE UNIVERSALITY OF 2-DIMENSIONAL DIFFUSION-LIMITED DEPOSITION

A history dependent stick probability is introduced to the diffusion-limited deposition model. The exponents in the scaling laws are calculated. The universality class is also discussed.

The Diffusion of Risks in Public Private Partnership Contracts

Purpose The UK government argues that the benefits of public private partnership (PPP) in delivering public infrastructure stem from: transferring risks to the private sector within a structure in which financiers put their own capital at risk; and, the performance based payment mechanism, reinforced by the due diligence requirements imposed by the lenders financing the projects (HM Treasury, 2010). Prior studies of risk in PPPs have investigated ‘what’ risks are allocated and to ‘whom’, that is to the public or the private sector. The purpose of this study is to examine ‘how’ and ‘why’ PPP risks are diffused by their financiers. Design/methodology/approach This study focuses on the financial structure of PPPs and on their financiers. Empirical evidence comes from interviews conducted with equity and debt financiers. Findings The findings show that the financial structure of the deals generates risk aversion in both debt and equity financiers and that the need to attract affordable finance leads to risk diffusion through a network of companies using various means that include contractual mitigation through insurance, performance support guarantees, interest rate swaps and inflation hedges. Because of the complexity this process generates, both procurers and suppliers need expensive expert advice. The risk aversion and diffusion and the consequent need for advice add cost to the projects impacting on the government’s economic argument for risk transfer. Limitations and implications The empirical work covers the private finance initiative (PFI) type of PPP arrangements and therefore the risk diffusion mechanisms may not be generalisable to other forms of PPP, especially those that do not involve the use of high leverage or private finance. Moreover, the scope of this research is limited to exploring the diffusion of risk in the private sector. Further research is needed on how risk is diffused in other settings and on the value for money implication of risk diffusion in PPP contracts. Originality/value The expectation inherent in PPP is that the private sector will better manage those risks allocated to it and because private capital is at risk, financiers will perform due diligence with the ultimate outcome that only viable projects will proceed. This paper presents empirical evidence that raises questions about these expectations. Key words: public private partnership, risk management, diffusion, private finance initiative, financiers

High-performance liquid chromatographic determination of 17 beta-estradiol and 17 beta-estradiol-3-acetate solubilities and diffusion coefficients in silicone elastomeric intravaginal rings

A rapid, sensitive reversed-phase high-performance liquid chromatographic method has been developed for the determination of in vitro release of 17 beta-estradiol and its ester prodrug, 17 beta-estradiol-3-acetate, from silicone intravaginal rings. Partial hydrolysis of the acetate under the aqueous conditions provided by the 1% benzalkonium chloride release medium necessitates its conversion to 17 beta-estradiol prior to HPLC analysis. Both steroid peaks have been fully resolved from the benzalkonium chloride peaks by the reported chromatographic method,which employs a C-18 bonded reversed-phase column, an acetonitrile-water (50:50, v/v) mobile phase and a UV detection wavelength of 281 nm. The peak area versus 17 beta-estradiol concentration was found to be linear over the range of 0.0137-1347 mu g ml(-1) The HPLC method has also been used to determine the silicone solubilities and diffusion coefficients of the two related steroids. The almost 100-fold increase in 17 beta-estradiol-3-acetate release from the silicone core-type intravaginal rings compared to 17 beta-estradiol is shown to be due to a 60-fold increase in silicone solubility and a one and a half-fold increase in diffusitivity. The results demonstrate that an effective estrogen replacement therapy dose of 17 beta-estradiol may be administered from a silicone intravaginal reservoir device containing the labile 17 beta-estradiol-3-acetate prodrug. (C) 2000 Elsevier Science B.V. All rights reserved.