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.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Implicit and explicit functions in the acquisition of a phonics rule in the word recognition of learning disabled and non learning disabled students /

One group of 12 non learning disabled students and two groups of 12 learning disabled students between the ges of 10 and 12 were measured on implicit and explicit knowledge cquisition. Students in each group implicitly cquired knowledge bout I of 2 vocabulary rules. The vocabulary rules governed the pronunciation of 2 types of pseudowords. After completing the implicit acquisition phase, all groups were administered a test of implicit knowledge. The non learning disabled group and I learning disabled group were then asked to verbalize the knowledge acquired during the initial phase. This was a test of explicit knowledge. All 3 groups were then given a postlest of implicit knowledge. This tcst was a measure of the effectiveness of the employment of the verbalization technique. Results indicate that implicit knowledge capabilities for both the learning disabled and non learning disabled groups were intact. However. there were significant differences between groups on explicit knowledge capabilities. This led to the conclusion that implicit functions show little individual differences, and that explicit functions are affected by ability difference. Furthermore, the employment of the verbalization technique significantly increased POStlest scores for learning disabled students. This suggested that the use of metacognitive techniques was a beneficial learning tool for learning disabled students.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Absolute versus relative difference measures of priming: Which is appropriate when baseline scores change with age?

It is often of theoretical interest to know if implicit memory (repetition priming) develops across childhood under a given circumstance. Methodologically, however, it is difficult to determine whether development is present when baseline performance for unstudied items improves with age. Calculation of priming in absolute (priming=studied - unstudied) or relative-to-baseline terms can lead to different conclusions. In first noting this problem, Parkin (1993) suggested using the Snodgrass (1989a) calculation of relative priming [priming=(studied - unstudied)/(maximum - unstudied)], and most developmental studies have since adopted this procedure. Here, we question the Snodgrass method because the Snodgrass method's results are not replicated in the picture identification task when baselines are equated experimentally across age groups. Instead, results support an absolute measure of priming. Theoretically, we argue against its core assumption; namely, that children and adults always lie on the same learning curve, with an equal maximum performance level and equal rate of learning.

Computing in a social context : gender difference in participation

The thesis reviews the literature relating to girls and computing within a framework which is structured around three specific questions. First, are there differences between girls and boys in their participation in class computing activities and/or in non-class computing activities? Second, do these differences in participation in computing activities have broader implications which justify the growing concern about the under-representation of girls? Third, wahy are girls under-represented in these activities? Although the available literature is predominantly descriptive, the underlying implicit theoretical model is essentially a social learning model. Girl's differential participation is attributed to learned attitudes towards computing rathan to differences between girls and boys in general ability. These attitudes, which stress the masculine, mathematical, technological aspects of computing are developed through modelling, direct experience, intrinsic and extrinsic reinforcement and generalisation from pre-existing, attitudes to related curriculum areas. In the literature it is implicitly assumed that these attitudes underlie girl's decisions to self-select out of computing activities. In this thesis predictions from a social learning model are complemented by predictions derived from expectancy-value, cognitive dissonance and self-perception theories. These are tested in three separate studies. Study one provides data from a pretest-posttest study of 24 children in a year four class learning BASIC. It examines pre- and posttest differences between girls and boys in computing experience, knowledge and achievement as well as the factors relating to computing achievement. Study two uses a pretest-posttest control group design to study the gender differences in the impact of the introduction of Logo into years 1, 3, 5 and 7 in both a coeducational and single-sex setting using a sample of 222 children from three schools. Study three utilises a larger sample of 1176 students, drawn from three secondary schools and five primary schools, enabling an evaluation of gender differences in relation to a wide range of class computing experiences and in a broader range of school contexts. The overall results are consistent across the three studies, supporting the contention that social factors, rather than ability differences influence girls' participation and achievement in computing. The more global theoretical framework, drawing on social learning, expectancy-value, cognitive dissonance and self-perception theories, provides a more adequate explanation of gender differences in participation than does any one of these models.

Identification of five fundamental implicit theories underlying cognitive distortions in child abusers : a preliminary study

Qualitative analysis of interviews with 22 child abusers found strong evidence for Ward and Keenan's (1999) proposal that there are five implicit theories in child abusers that account for the majority of their cognitive distortions/thinking errors. These implicit theories are: Child as a sexual being where children are perceived as being able to and wanting to engage in sexual activity with adults and also are not be harmed by such sexual contact; Nature of harm where the offender perceives that sexual activity does not cause harm (and may in fact be beneficial) to the child; Entitlement where the child abuser perceives that he is superior and more important than others: and hence is able to have sex with whoever, and whenever, he wants; Dangerous world where the offender perceives that that others are abusive and rejecting and he must fight to regain control; and Uncontrollable where the offender perceives the world as uncontrollable and hence he believes that circumstances are outside of his control. There was no evidence for any other type of implicit theory. Results of the study also indicated that there was a significant difference in terms of the endorsement of the Dangerous world implicit theory between participants reporting a history of child sexual abuse and those who did not. Offenders against male victims were significantly more likely to endorse the Child as a sexual being and Dangerous world implicit theories compared to men who had offended against female children.

A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier-Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110: 171-186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199-210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright (c) 2006 John Wiley & Sons, Ltd.

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Numerical simulation of viscous three-dimensional flow over aerospace vehicles using Euler/boundary-layer zonal approach

This paper presents a viscous three-dimensional simulations coupling Euler and boundary layer codes for calculating flows over arbitrary surfaces. The governing equations are written in a general non orthogonal coordinate system. The Levy-Lees transformation generalized to three-dimensional flows is utilized. The inviscid properties are obtained from the Euler equations using the Beam and Warming implicit approximate factorization scheme. The resulting equations are discretized and approximated by a two-point fmitedifference numerical scheme. The code developed is validated and applied to the simulation of the flowfield over aerospace vehicle configurations. The results present good correlation with the available data.