Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces

In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces. Novel FDTD formulations of frequency-independent and simple frequency-dependent impedance boundaries are proposed for 2D and 3D acoustic systems, including a full treatment of corners and boundary edges. The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on a rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital waveguide mesh (K-DWM) methods. In addition, new analytic evaluation methods that accurately predict the reflectance of numerical boundary formulations are proposed. numerical experiments and numerical boundary analysis (NBA) are analysed in time and frequency domains in terms of the pressure wave reflectance for different angles of incidence and various impedances. The results show that the proposed boundary formulations structurally adhere well to the theoretical reflectance. In particular, both reflectance magnitude and phase are closely approximated even at high angles of incidence and low impedances. Furthermore, excellent agreement was found between the numerical boundary analysis and the experimental results, validating both as tools for researching FDTD boundary formulations.

Room acoustics simulation using 3-D compact explicit FDTD schemes

This paper presents methods for simulating room acoustics using the finite-difference time-domain (FDTD) technique, focusing on boundary and medium modeling. A family of nonstaggered 3-D compact explicit FDTD schemes is analyzed in terms of stability, accuracy, and computational efficiency, and the most accurate and isotropic schemes based on a rectilinear grid are identified. A frequency-dependent boundary model that is consistent with locally reacting surface theory is also presented, in which the wall impedance is represented with a digital filter. For boundaries, accuracy in numerical reflection is analyzed and a stability proof is provided. The results indicate that the proposed 3-D interpolated wideband and isotropic schemes outperform directly related techniques based on Yee's staggered grid and standard digital waveguide mesh, and that the boundary formulations generally have properties that are similar to that of the basic scheme used.

Crossing Thresholds and Expanding Conceptual Spaces: Using Arts-Based Methods to Extend Teachers’ Perceptions of Literacy

The context for this paper is a teacher education program for adult literacy practitioners at Queen’s University Belfast in Northern Ireland. This paper describes and reflects on the use of arts-based approaches to enhance these practitioners’ conceptualizations of literacy, presenting their arts-based responses and their evaluations of the methods and their contrasting definitions of literacy at the start and the end of the course. The discussion raises questions about the inclusion of visual literacy in adult literacy teacher education programmes.

Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

Food-web structure in low- and high-dimensional trophic niche spaces

A question central to modelling and, ultimately, managing food webs concerns the dimensionality of trophic niche space, that is, the number of independent traits relevant for determining consumer-resource links. Food-web topologies can often be interpreted by assuming resource traits to be specified by points along a line and each consumer's diet to be given by resources contained in an interval on this line. This phenomenon, called intervality, has been known for 30 years and is widely acknowledged to indicate that trophic niche space is close to one-dimensional. We show that the degrees of intervality observed in nature can be reproduced in arbitrary-dimensional trophic niche spaces, provided that the processes of evolutionary diversification and adaptation are taken into account. Contrary to expectations, intervality is least pronounced at intermediate dimensions and steadily improves towards lower- and higher-dimensional trophic niche spaces.

Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.