General tooth boundary conditions for equation free modelling

We are developing a framework for multiscale computation which enables models at a ``microscopic'' level of description, for example Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators, to perform modelling tasks at ``macroscopic'' length scales of interest. The plan is to use the microscopic rules restricted to small "patches" of the domain, the "teeth'', using interpolation to bridge the "gaps". Here we explore general boundary conditions coupling the widely separated ``teeth'' of the microscopic simulation that achieve high order accuracy over the macroscale. We present the simplest case when the microscopic simulator is the quintessential example of a partial differential equation. We argue that classic high-order interpolation of the macroscopic field provides the correct forcing in whatever boundary condition is required by the microsimulator. Such interpolation leads to Tooth Boundary Conditions which achieve arbitrarily high-order consistency. The high-order consistency is demonstrated on a class of linear partial differential equations in two ways: firstly through the eigenvalues of the scheme for selected numerical problems; and secondly using the dynamical systems approach of holistic discretisation on a general class of linear \textsc{pde}s. Analytic modelling shows that, for a wide class of microscopic systems, the subgrid fields and the effective macroscopic model are largely independent of the tooth size and the particular tooth boundary conditions. When applied to patches of microscopic simulations these tooth boundary conditions promise efficient macroscale simulation. We expect the same approach will also accurately couple patch simulations in higher spatial dimensions.Comment: 22 page

Modelling and simulation framework for reactive transport of organic contaminants in bed-sediments using a pure java object - oriented paradigm

Numerical modelling and simulation of organic contaminant reactive transport in the environment is being increasingly relied upon for a wide range of tasks associated with risk-based decision-making, such as prediction of contaminant profiles, optimisation of remediation methods, and monitoring of changes resulting from an implemented remediation scheme. The lack of integration of multiple mechanistic models to a single modelling framework, however, has prevented the field of reactive transport modelling in bed-sediments from developing a cohesive understanding of contaminant fate and behaviour in the aquatic sediment environment. This paper will investigate the problems involved in the model integration process, discuss modelling and software development approaches, and present preliminary results from use of CORETRANS, a predictive modelling framework that simulates 1-dimensional organic contaminant reaction and transport in bed-sediments

Wavelet-based voice morphing

This paper presents a new multi-scale voice morphing algorithm. This algorithm enables a user to transform one person's speech pattern into another person's pattern with distinct characteristics, giving it a new identity, while preserving the original content. The voice morphing algorithm performs the morphing at different subbands by using the theory of wavelets and models the spectral conversion using the theory of Radial Basis Function Neural Networks. The results obtained on the TIMIT speech database demonstrate effective transformation of the speaker identity

Voice morphing using the generative topographic mapping

In this paper we address the problem of Voice Morphing. We attempt to transform the spectral characteristics of a source speaker's speech signal so that the listener would believe that the speech was uttered by a target speaker. The voice morphing system transforms the spectral envelope as represented by a Linear Prediction model. The transformation is achieved by codebook mapping using the Generative Topographic Mapping, a non-linear, latent variable, parametrically constrained, Gaussian Mixture Model

Movement and stretching imagery during flexibility training

The aim of this study was to examine the effect of movement and stretching imagery on increases in flexibility. Thirty volunteers took part in a 4 week flexibility training programme. They were randomly assigned to one of three groups: (1) movement imagery, where participants imagined moving the limb they were stretching; (2) stretching imagery, where participants imagined the physiological processes involved in stretching the muscle; and (3) control, where participants did not engage in mental imagery. Active and passive range of motion around the hip was assessed before and after the programme. Participants provided specific ratings of vividness and comfort throughout the programme. Results showed significant increases in flexibility over time, but no differences between the three groups. A significant relationship was found, however, between improved flexibility and vividness ratings in the movement imagery group. Furthermore, both imagery groups scored significantly higher than the control group on levels of comfort, with the movement imagery group also scoring significantly higher than the stretching imagery group. We conclude that the imagery had stronger psychological than physiological effects, but that there is potential for enhancing physiological effects by maximizing imagery vividness, particularly for movement imagery

An Expansion Term In Hamilton's Equations

For any given spacetime the choice of time coordinate is undetermined. A particular choice is the absolute time associated with a preferred vector field. Using the absolute time Hamilton's equations are $- (\delta H_{c})/(\delta q)=\dot{\pi}+\Theta\pi,$+ (\delta H_{c})/(\delta \pi)=\dot{q}$, where$\Theta = V^{a}_{.;a}$is the expansion of the vector field. Thus there is a hitherto unnoticed term in the expansion of the preferred vector field. Hamilton's equations can be used to describe fluid motion. In this case the absolute time is the time associated with the fluid's co-moving vector. As measured by this absolute time the expansion term is present. Similarly in cosmology, each observer has a co-moving vector and Hamilton's equations again have an expansion term. It is necessary to include the expansion term to quantize systems such as the above by the canonical method of replacing Dirac brackets by commutators. Hamilton's equations in this form do not have a corresponding sympletic form. Replacing the expansion by a particle number$N\equiv exp(-\int\Theta d \ta)$and introducing the particle numbers conjugate momentum$\pi^{N}$the standard sympletic form can be recovered with two extra fields N and$\pi^N$. Briefly the possibility of a non-standard sympletic form and the further possibility of there being a non-zero Finsler curvature corresponding to this are looked at.Comment: 10 page