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The spectral finite element method is an advanced implementation of the finite element method in which the solution over each element is expressed in terms of a priori unknown values at carefully selected spectral nodes. These methods are naturally chosen to solve problems in regular rectangular, cylindrical or spherical regions. However in a general irregular region it would be unwise to turn awa
An important topic in the area of airborne sound propagation is the prediction of sound propagation above an impedance ground with an atmospheric profile whose sound speed varies with height. Even if this problem is simple in concept, it leads to complications for general velocity profiles. This work illustrates the existence of a large class of realistic atmospheric profiles for which analytical
A waveguide boundary spectral finite element method (SFEM) is developed for the study of acoustical wave propagation in non-uniform waveguide-like geometries. The formulation is based on a variational approach using a mixture of non-internal node element shape functions and wave solutions. The numerical method provides solutions to acoustic duct or fluid waveguide environments which may be divided
We study the codimension-one and -two bifurcations of the Ornstein-Zernike equation with hypernetted chain (HNC) closure with Lennard-Jones intermolecular interaction potential. The main purpose of the paper is to present the results of a numerical study undertaken using a suite of algorithms implemented in MATLAB and based on pseudo arc-length continuation for the codimension-one case and a Newto
Motivated by the large number of solutions obtained when applying bifurcation algorithms to the Ornstein-Zernike (OZ) equation with the hypernetted chain (HNC) closure from liquid state theory, we provide existence and bifurcation results for a computationally-motivated version of the problem. We first establish the natural result that if the potential satisfies a short-range condition then a low-
This paper considers elastic wave propagation and vibration transmission in lightweight composite structures. Specifically a spectral finite element method (SFEM) is developed as an effective numerical tool for the analysis of wave motion in uniform laminated elastic media. In short, SFEM combines a standard finite element method in the direction of layering together with analytical solutions for
The transmission and reduction of vibrations in the far-field of the surface of the ground due to a surface load is investigated theoretically and validated with given field measurement data. The performance of a given stabilization column, located directly underneath the load, at a number of receiver positions is studied and measured in terms of insertion loss. A numerical model is presented, whi
The dynamic response of the vibrating structures are studied with the standard finite element method against the more computationally efficient spectral finite element method. First a simple beam structure is modelled with the standard method and newly developed spectral elements; which has the advantage that dispersion relations for all beam structures may be developed. Some numerical examples ar
The prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions over a noise-screen onto surrounding flat grassland is presented. It is well known that over flat ground the spectra for single-noise screens have significant marked differences for propagation over absorbing ground where the screen obstructs surface wave attenuation ove
In this paper we study the application of boundary integral equation methods to the solution of the Helmholtz equation in a locally perturbed half-plane with Robin or impedance boundary conditions. This problem models outdoor noise propagation from a cutting onto a surrounding flat plane, and also the harbour resonance problem in coastal engineering. We employ Green's theorem to derive a system of
The asymptotic states of numerical methods for initial value problems are examined. In particular, spurious steady solutions, solutions with period 2 in the timestep, and spurious invariant curves are studied. A numerical method is considered as a dynamical system parameterised by the timestep h. It is shown that the three-kinds of spurious solutions can bifurcate from genuine steady solutions of
We consider second kind integral equations of the form x(s) - ʃΩ k(s, t)x(t) dt = y(s) (abbreviated x - Kx = y), in which Ω is some unbounded subset of Rn Let Xp denote the weighted space of functions x continuous on Ω and satisfying x(s) = O(|s| -p), s → ∞. We show that if the kernel k(s, t) decays like | s - t | -q as | s - t | → ∞ for some sufficiently large q (and some other mild conditions on
In this paper we present a semi-analytical model which enables the acoustic pressure field created by two spheres radiating close together to be predicted at any point outside the spheres. By representing the pressure field from each sphere as a finite sum of spherical harmonics and satisfying the boundary conditions at a finite number of points on the surface of each sphere, the problem reduces t
A spectral element method is described which enables reduced wave equation problems defined in regular, arbitrary length regions to be solved as a set of coupled problems over neighbouring domains. A combination of trial functions are considered, namely the specific eigenfunctions of a differential operator and a set of hierarchical polynomials. The coefficients in the representation of the acoust
A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding Hat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. The numerica
A super-spectral finite element method is developed for the study of acoustical wave propagation in nonuniform waveguides. The formulation is based on a finite-element approach using a mixture of high order element shape functions and wave solutions. The numerical method provides solutions to acoustic duct or fluid waveguide environments which may be divided into rectangular sectors. Examples of i
A measurement of event-shape variables in proton-proton collisions at large momentum transfer is presented using data collected at s = 13 TeV with the ATLAS detector at the Large Hadron Collider. Six event-shape variables calculated using hadronic jets are studied in inclusive multijet events using data corresponding to an integrated luminosity of 139 fb−1. Measurements are performed in bins of je
Research on children's literature mainly involves literary texts. This article focuses on the underresearched genre of information books, and analyses the Swedish translation of a French information book intended for children aged 4-7. The source and target texts are studied from a Hallidayan perspective by situating the texts in their respective contexts of situation and culture, and comparing th
Background Good nutrition is essential for individual health, a notion that is particularly true during pregnancy. We have used a nutrition index that measures the adequacy of one's diet relative to the unique nutritional needs of individuals due to, for example, their activity level, dietary restrictions, lifestyle and body size. The use of this personalised metric of dietary nutritiousness in th
MI, motivational interviewing, is a counseling method for increasing a person's motivation for behavior change with a large prevalence in social work. MI emphasizes building trusting social worker-client relationships and is presented as concrete and simple to follow. MI's benefit is limited by actual opportunities for change through poverty, the labor market and health. The article aims to criticMI, motivational interviewing, is a counseling method for increasing a person's motivation for behavior change with a large prevalence in social work. MI emphasizes building trusting social worker-client relationships and is presented as concrete and simple to follow. MI's benefit is limited by actual opportunities for change through poverty, the labor market and health. The article aims to critic
