Exponential integrators and a dual-scale model for wood drying

For the timber industry, the ability to simulate the drying of wood is invaluable for manufacturing high quality wood products. Mathematically, however, modelling the drying of a wet porous material, such as wood, is a diffcult task due to its heterogeneous and anisotropic nature, and the complex geometry of the underlying pore structure. The well{ developed macroscopic modelling approach involves writing down classical conservation equations at a length scale where physical quantities (e.g., porosity) can be interpreted as averaged values over a small volume (typically containing hundreds or thousands of pores). This averaging procedure produces balance equations that resemble those of a continuum with the exception that effective coeffcients appear in their deffnitions. Exponential integrators are numerical schemes for initial value problems involving a system of ordinary differential equations. These methods differ from popular Newton{Krylov implicit methods (i.e., those based on the backward differentiation formulae (BDF)) in that they do not require the solution of a system of nonlinear equations at each time step but rather they require computation of matrix{vector products involving the exponential of the Jacobian matrix. Although originally appearing in the 1960s, exponential integrators have recently experienced a resurgence in interest due to a greater undertaking of research in Krylov subspace methods for matrix function approximation. One of the simplest examples of an exponential integrator is the exponential Euler method (EEM), which requires, at each time step, approximation of φ(A)b, where φ(z) = (ez - 1)/z, A E Rnxn and b E Rn. For drying in porous media, the most comprehensive macroscopic formulation is TransPore [Perre and Turner, Chem. Eng. J., 86: 117-131, 2002], which features three coupled, nonlinear partial differential equations. The focus of the first part of this thesis is the use of the exponential Euler method (EEM) for performing the time integration of the macroscopic set of equations featured in TransPore. In particular, a new variable{ stepsize algorithm for EEM is presented within a Krylov subspace framework, which allows control of the error during the integration process. The performance of the new algorithm highlights the great potential of exponential integrators not only for drying applications but across all disciplines of transport phenomena. For example, when applied to well{ known benchmark problems involving single{phase liquid ow in heterogeneous soils, the proposed algorithm requires half the number of function evaluations than that required for an equivalent (sophisticated) Newton{Krylov BDF implementation. Furthermore for all drying configurations tested, the new algorithm always produces, in less computational time, a solution of higher accuracy than the existing backward Euler module featured in TransPore. Some new results relating to Krylov subspace approximation of '(A)b are also developed in this thesis. Most notably, an alternative derivation of the approximation error estimate of Hochbruck, Lubich and Selhofer [SIAM J. Sci. Comput., 19(5): 1552{1574, 1998] is provided, which reveals why it performs well in the error control procedure. Two of the main drawbacks of the macroscopic approach outlined above include the effective coefficients must be supplied to the model, and it fails for some drying configurations, where typical dual{scale mechanisms occur. In the second part of this thesis, a new dual{scale approach for simulating wood drying is proposed that couples the porous medium (macroscale) with the underlying pore structure (microscale). The proposed model is applied to the convective drying of softwood at low temperatures and is valid in the so{called hygroscopic range, where hygroscopically held liquid water is present in the solid phase and water exits only as vapour in the pores. Coupling between scales is achieved by imposing the macroscopic gradient on the microscopic field using suitably defined periodic boundary conditions, which allows the macroscopic ux to be defined as an average of the microscopic ux over the unit cell. This formulation provides a first step for moving from the macroscopic formulation featured in TransPore to a comprehensive dual{scale formulation capable of addressing any drying configuration. Simulation results reported for a sample of spruce highlight the potential and flexibility of the new dual{scale approach. In particular, for a given unit cell configuration it is not necessary to supply the effective coefficients prior to each simulation.

Nonresonant power transfer in plasma-surface interactions via two-surface wave decay

The excitation of pairs of electron surface waves via nonresonant decay of plasma waves incident onto a solid surface is studied in the context of controlling the interaction of pulsed electromagnetic radiation with plasma-exposed solid surfaces. The role of the plasma-exposed surfaces in nonlinear heating of the plasma edge and related power transfer is discussed. It is shown that the maximum efficiency of the power transfer at solid surfaces with dielectric permittivity εd <3 corresponds to the resonant two-surface wave decay. On the other hand, for solids with εd >3 the maximum power transfer efficiency is achieved through nonresonant excitation of the quasistatic surface waves. In this case the plasma waves generated by external radiation dissipate their energy into the plasma periphery most effectively.

Two-surface wave decay : controlling power transfer in plasma-surface interactions

Controlled interaction of high-power pulsed electromagnetic radiation with plasma-exposed solid surfaces is a major challenge in applications spanning from electron beam accelerators in microwave electronics to pulsed laser ablation-assisted synthesis of nanomaterials. It is shown that the efficiency of such interaction can be potentially improved via an additional channel of wave power dissipation due to nonlinear excitation of two counterpropagating surface waves, resonant excitations of the plasma-solid system.Physics.

Coherent phonon decay and the boron isotope effect for MgB2

Ab-initio DFT calculations for the phonon dispersion (PD) and the Phonon Density Of States (PDOS) of the two isotopic forms (10B and 11B) of MgB2 demonstrate that use of a reduced symmetry super-lattice provides an improved approximation to the dynamical, phonon-distorted P6/mmm crystal structure. Construction of phonon frequency plots using calculated values for these isotopic forms gives linear trends with integer multiples of a base frequency that change in slope in a manner consistent with the isotope effect (IE). Spectral parameters inferred from this method are similar to that determined experimentally for the pure isotopic forms of MgB2. Comparison with AlB2 demonstrates that a coherent phonon decay down to acoustic modes is not possible for this metal. Coherent acoustic phonon decay may be an important contributor to superconductivity for MgB2.

Adaptive estimation of hidden semi-Markov chains with parameterised transition probabilities and exponential decaying states

This paper develops maximum likelihood (ML) estimation schemes for finite-state semi-Markov chains in white Gaussian noise. We assume that the semi-Markov chain is characterised by transition probabilities of known parametric from with unknown parameters. We reformulate this hidden semi-Markov model (HSM) problem in the scalar case as a two-vector homogeneous hidden Markov model (HMM) problem in which the state consist of the signal augmented by the time to last transition. With this reformulation we apply the expectation Maximumisation (EM ) algorithm to obtain ML estimates of the transition probabilities parameters, Markov state levels and noise variance. To demonstrate our proposed schemes, motivated by neuro-biological applications, we use a damped sinusoidal parameterised function for the transition probabilities.

GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Efficient simulation of unsaturated flow in heterogeneous soils using an exponential integrator

- Provided a practical variable-stepsize implementation of the exponential Euler method (EEM). - Introduced a new second-order variant of the scheme that enables the local error to be estimated at the cost of a single additional function evaluation. - New EEM implementation outperformed sophisticated implementations of the backward differentiation formulae (BDF) of order 2 and was competitive with BDF of order 5 for moderate to high tolerances.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Less popular but more democratic? Corrie, Clarkson and the dancing Cru

The central cultural experience of modernity has been change, both the ‘creative destruction’ of existing structures, and the growth, often exponential, of new knowledge. During the twentieth century, the central cultural platform for the collective experience of modernising societies changed too, from page and stage to the screen – from publishing, the press and radio to cinema, television and latterly computer screens. Despite the successive dominance of new media, none has lasted long at the top. The pattern for each was to give way to a successor platform in popularity, but to continue as part of an increasingly crowded media menu. Modern media are supplemented not supplanted by their successors.

The comprehensive Australian Study of entrepreneurial emergence (CAUSEE) high potential nascent entrepreneurs : some preliminary findings

Principal Topic The Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE) represents the first Australian study to employ and extend the longitudinal and large scale systematic research developed for the Panel Study of Entrepreneurial Dynamics (PSED) in the US (Gartner, Shaver, Carter and Reynolds, 2004; Reynolds, 2007). This research approach addresses several shortcomings of other data sets including under coverage; selection bias; memory decay and hindsight bias, and lack of time separation between the assessment of causes and their assumed effects (Johnson et al 2006; Davidsson 2006). However, a remaining problem is that any a random sample of start-ups will be dominated by low potential, imitative ventures. In recognition of this issue CAUSEE supplemented PSED-type random samples with theoretically representative samples of the 'high potential' emerging ventures employing a unique methodology using novel multiple screening criteria. We define new ''high-potential'' ventures as new entrepreneurial innovative ventures with high aspirations and potential for growth. This distinguishes them from those ''lifestyle'' imitative businesses that start small and remain intentionally small (Timmons, 1986). CAUSEE is providing the opportunity to explore, for the first time, if process and outcomes of high potentials differ from those of traditional lifestyle firms. This will allows us to compare process and outcome attributes of the random sample with the high potential over sample of new firms and young firms. The attributes in which we will examine potential differences will include source of funding, and internationalisation. This is interesting both in terms of helping to explain why different outcomes occur but also in terms of assistance to future policymaking, given that high growth potential firms are increasingly becoming the focus of government intervention in economic development policies around the world. The first wave of data of a four year longitudinal study has been collected using these samples, allowing us to also provide some initial analysis on which to continue further research. The aim of this paper therefore is to present some selected preliminary results from the first wave of the data collection, with comparisons of high potential with lifestyle firms. We expect to see owing to greater resource requirements and higher risk profiles, more use of venture capital and angel investment, and more internationalisation activity to assist in recouping investment and to overcome Australia's smaller economic markets Methodology/Key Propositions In order to develop the samples of 'high potential' in the NF and YF categories a set of qualification criteria were developed. Specifically, to qualify, firms as nascent or young high potentials, we used multiple, partly compensating screening criteria related to the human capital and aspirations of the founders as well as the novelty of the venture idea, and venture high technology. A variety of techniques were also employed to develop a multi level dataset of sources to develop leads and firm details. A dataset was generated from a variety of websites including major stakeholders including the Federal and State Governments, Australian Chamber of Commerce, University Commercialisation Offices, Patent and Trademark Attorneys, Government Awards and Industry Awards in Entrepreneurship and Innovation, Industry lead associations, Venture Capital Association, Innovation directories including Australian Technology Showcase, Business and Entrepreneurs Magazines including BRW and Anthill. In total, over 480 industry, association, government and award sources were generated in this process. Of these, 74 discrete sources generated high potentials that fufilled the criteria. 1116 firms were contacted as high potential cases. 331 cases agreed to participate in the screener, with 279 firms (134 nascents, and 140 young firms) successfully passing the high potential criteria. 222 Firms (108 Nascents and 113 Young firms) completed the full interview. For the general sample CAUSEE conducts screening phone interviews with a very large number of adult members of households randomly selected through random digit dialing using screening questions which determine whether respondents qualify as 'nascent entrepreneurs'. CAUSEE additionally targets 'young firms' those that commenced trading from 2004 or later. This process yielded 977 Nascent Firms (3.4%) and 1,011 Young Firms (3.6%). These were directed to the full length interview (40-60 minutes) either directly following the screener or later by appointment. The full length interviews were completed by 594 NF and 514 YF cases. These are the cases we will use in the comparative analysis in this report. Results and Implications The results for this paper are based on Wave one of the survey which has been completed and the data obtained. It is expected that the findings will assist in beginning to develop an understanding of high potential nascent and young firms in Australia, how they differ from the larger lifestyle entrepreneur group that makes up the vast majority of the new firms created each year, and the elements that may contribute to turning high potential growth status into high growth realities. The results have implications for Government in the design of better conditions for the creation of new business, firms who assist high potentials in developing better advice programs in line with a better understanding of their needs and requirements, individuals who may be considering becoming entrepreneurs in high potential arenas and existing entrepreneurs make better decisions.

The mechanism of breath aerosol formation

Background: Aerosol production during normal breathing is often attributed to turbulence in the respiratory tract. That mechanism is not consistent with a high degree of asymmetry between aerosol production during inhalation and exhalation. The objective was to investigate production symmetry during breathing. Methods: The aerosol size distribution in exhaled breath was examined for different breathing patterns including normal breathing, varied breath holding periods and contrasting inhalation and exhalation rates. The aerosol droplet size distribution measured in the exhaled breath was examined in real time using an aerodynamic particle sizer. Results and Conclusions: The dependence of the particle concentration decay rate on diameter during breath holding was consistent with gravitational settling in the alveolar spaces. Also, deep exhalation resulted in a 4 to 6 fold increase in concentration and rapid inhalation produced a further 2 to 3 fold increase in concentration. In contrast rapid exhalation had little effect on the measured concentration. A positive correlation of the breath aerosol concentration with subject age was observed. The results were consistent with the breath aerosol being produced through fluid film rupture in the respiratory bronchioles in the early stages of inhalation and the resulting aerosol being drawn into the alveoli and held before exhalation. The observed asymmetry of production in the breathing cycle with very little aerosol being produced during exhalation, is inconsistent with the widely assumed turbulence induced aerosolization mechanism.

Pornography and erotica: Definitions and prevalence

In this paper, we offer some observations regarding the sex industry, in particular the pornography and erotica sectors. Marketing literature observing pornography and erotica is scant. We find that following exponential growth of the sex industry (given use of the Internet) an evaluation of consumer behaviour and marketing practices is justified. In order to begin a study of these industry sectors, we find it necessary to define both pornography and erotica. Following the development of definitions, we consider these industries from a marketing perspective in the hope that we may encourage research into these areas.