A Hamiltonian approach to simulation of acoustic systems involving nonlinear interactions

Nonlinear interactions take place in most systems that arise in music acoustics, usually as a result of player-instrument coupling. Several time-stepping methods exist for the numerical simulation of such systems. These methods generally involve the discretization of the Newtonian description of the system. However, it is not always possible to prove the stability of the resulting algorithms, especially when dealing with systems where the underlying force is a non-analytic function of the phase space variables. On the other hand, if the discretization is carried out on the Hamiltonian description of the system, it is possible to prove the stability of the derived numerical schemes. This Hamiltonian approach is applied to a series of test models of single or multiple nonlinear collisions and the energetic properties of the derived schemes are discussed. After establishing that the schemes respect the principle of conservation of energy, a nonlinear single-reed model is formulated and coupled to a digital bore, in order to synthesize clarinet-like sounds.

Computing Zeros of Analytic Functions in the Complex Plane without using Derivatives

A new approach to evaluating all multiple complex roots of analytical function f(z) confined to the specified rectangular domain of complex plane has been developed and implemented in Fortran code. Generally f (z), despite being holomorphic function, does not have a closed analytical form thereby inhibiting explicit evaluation of its derivatives. The latter constraint poses a major challenge to implementation of the robust numerical algorithm. This work is at the instrumental level and provides an enabling tool for solving a broad class of eigenvalue problems and polynomial approximations.

Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Two-stage mixed discrete-continuous identification of radial basis function (RBF) neural models for nonlinear systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete-continuous; identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.

A function-based treatment package aiming at decreasing self-injurious behaviour and tantrums.

Self-injurious and aggressive behaviours have often been identified as the cause for students’ lack of academic progress, parental distress, health risks and teachers´ low satisfaction levels. Functional analysis has been identified in the research literature as the benchmark of effective treatments for disruptive and/or inappropriate behaviours. The present study was completed with a girl diagnosed with ASD. An experimental functional analysis was conducted identifying the function of self-injurious behaviours and tantrums to be escaping from tasks. A treatment package was consequently put in place integrating several components that aimed at reducing overall levels of inappropriate behaviours. Results showed a clear and meaningful improvement in the student´s overall health and academic progress, as well as in parental involvement, teachers’ satisfaction and school inclusion. These outcomes are discussed in the light of evidence-based experimental procedures based on applied behaviour analysis and more specifically on the functional-analytic literature, which, if put in place consistently, can bring valuable positive changes in the quality of life of individuals with ASD.