Numerical and asymptotic solutions of generalised Burgers’ equation

The generalised Burgers’ equation has been subject to a considerable amount of research on how the equation should behave according to asymptotic analysis, however there has been limited research verifying the asymptotic analysis. In order to verify the asymptotic analysis, this paper aims to run long time and detailed numerical simulations of Burgers’ equation by employing suitable rescalings of Burgers’ equation. It is hoped that this technique will make it possible to notice subtle changes in the shock structure which would otherwise be impossible to observe. The main aim of this paper is to validate the numerical methods used in order to allow further research into shock evolution where further relaxation effects will be included

Effect of molecular relaxation on nonlinear evolution of n-waves

The propagation of an initially antisymmetric disturbance through a relaxing medium in one-dimension is considered. If dissipation and dispersion effects are small compared with the effect of nonlinearity, the disturbance approaches the classic N-wave profile with narrow shocks controlled by relaxation processes. As the N-wave propagates it spreads and decays in amplitude, affecting key balances between competing physical processes. In this paper we analyse the change in the shock structure as the outer solution evolves, using asymptotic analysis supplemented by numerical results. Two numerical schemes are described - an implicit scheme with variable spatial mesh which allows good resolution of the shock structure, and a pseudospectral scheme which is used when multiple relaxation modes are considered. Experimental measurements (Pawlowski et al 2005 and Yuldashev et al 2008) reveal the appearance of a slowly decaying shock tail previously unexplained by analysis of the augmented Burgers equation. In this paper we demonstrate that this phenomenon occurs when one of the relaxation timescales is comparable to the time of pulse duration

A Multiple Migration and Stacking Algorithm Designed for Land Mine Detection

This paper describes a modification to a standard migration algorithm for land mine detection with a ground-penetrating radar (GPR) system. High directivity from the antenna requires a significantly large aperture in relation to the operating wavelength, but at the frequencies of operation of GPR, this would result in a large and impractical antenna. For operator convenience, most GPR antennas are small and exhibit low directivity and a wide beamwidth. This causes the GPR image to bear little resemblance to the actual target scattering centers. Migration algorithms attempt to reduce this effect by focusing the scattered energy from the source reflector and consequentially improve the target detection rate. However, problems occur due to the varying operational conditions, which result in the migration algorithm requiring vastly different calibration parameters. In order to combat this effect, this migration scheme stacks multiple versions of the same migrated data with different velocity values, whereas some other migration schemes only use a single velocity value

Asymptotic and numerical analysis of pulse propagation in relaxation media

We consider the case of disturbances propagating in one-dimension through a medium with multiple relaxation modes and thermoviscous diffusion. Each relaxation mode is characterized by two parameters and the evolution of the disturbance is governed by an augmented Burgers equation. We begin by considering travelling wave solutions for the propagation of a pressure step, of amplitude P, in the small viscosity limit. For a single relaxation mode, if the amplitude P is less than a certain critical value then the transition is controlled entirely by the relaxation mode whereas for larger P, a thin viscous sub-shock arises. We then consider the propagation of a rectangular pulse. We establish parameter ranges in which the waveform is described by an outer solution (obtained using characteristics) and a thin shock region. Analysis of the shock region then reveals the same richness of structure seen in the travelling wave case, with subtle changes in shock structure as the disturbance decays. This is illustrated by numerical results using a pseudospectral method. Finally, analysis of the case of two relaxation modes is presented demonstrating that in some parameter regimes the transition region consists of three separate sub-regions governed by the three different physical processes

Efficient description of shape perturbations

Airbus wish to have efficient ways of describing perturbations of a manu- factured aerofoil from its design shape. The typical kind of perturbations expected are waves, steps, and bumps, and automatic classification into the classes is desired. Various possible methods of analysis were pro- posed and studied in some detail, including projection onto suitable basis functions, wavelets, and radial basis functions. Other methods were studied in less detail, but with the aim of giving a digital signature of defects that could be used to classify them

Childhood trauma as a mediator of the association between autistic traits and psychotic experiences evidence from the ALSPAC birth cohort

BACKGROUND: Little is known on whether associations between childhood autistic traits and psychotic experiences persist into adulthood and whether genetic confounding and childhood trauma influence them. Here we investigate the associations between childhood autistic traits and psychotic experiences until young adulthood and assess the influence of schizophrenia polygenic risk and childhood traumatic experiences, using the Avon Longitudinal Study of Parents and Children (ALSPAC) population-based birth cohort. STUDY DESIGN: We used a measure of broad autistic traits (autism factor mean score), and four dichotomised measures of autistic traits capturing social communication difficulties (age 7), repetitive behaviours (age 5), sociability (age 3), and pragmatic language (age 9). Psychotic experiences were assessed at ages 18 and 24 using the semi-structured Psychosis-Like Symptoms interview (PLIKSi). Traumatic experiences between ages 5 and 11 were assessed with questionnaires and interviews administered to children and parents at multiple ages. STUDY RESULTS: Broad autistic traits, as well as social communication difficulties, were associated with psychotic experiences that were distressing and/or frequent until age 24 (autism factor mean score, n = 3707: OR 1.19, 95%CI 1.01-1.39; social communication difficulties, n = 3384: OR 1.54, 95%CI 0.97-2.45). Childhood trauma mediated a substantial proportion of the identified associations (~28% and 36% respectively, maximum n = 3577). Schizophrenia polygenic risk did not appear to confound the associations. Multiple imputation analyses (maximum n = 13 105) yielded comparable results. CONCLUSIONS: Childhood trauma may be an important, potentially modifiable pathway between autistic features and later onset of psychotic psychopathology

Valorising cassava peel waste into plasticized polyhydroxyalkanoates blended with polycaprolactone with controllable thermal and mechanical properties

Approximately 99% of plastics produced worldwide were produced by the petrochemical industry in 2019 and it is predicted that plastic consumption may double between 2023 and 2050. The use of biodegradable bioplastics represents an alternative solution to petroleum-based plastics. However, the production cost of biopolymers hinders their real-world use. The use of waste biomass as a primary carbon source for biopolymers may enable a cost-effective production of bioplastics whilst providing a solution to waste management towards a carbon–neutral and circular plastics economy. Here, we report for the first time the production of poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) with a controlled molar ratio of 2:1 3-hydroxybutyrate:3-hydroxvalerate (3HB:3HV) through an integrated pre-treatment and fermentation process followed by alkaline digestion of cassava peel waste, a renewable low-cost substrate, through Cupriavidus necator biotransformation. PHBV was subsequently melt blended with a biodegradable polymer, polycaprolactone (PCL), whereby the 30:70 (mol%) PHBV:PCL blend exhibited an excellent balance of mechanical properties and higher degradation temperatures than PHBV alone, thus providing enhanced stability and controllable properties. This work represents a potential environmental solution to waste management that can benefit cassava processing industries (or other crop processing industries) whilst developing new bioplastic materials that can be applied, for example, to packaging and biomedical engineering

Phenotypic Characterization of EIF2AK4 Mutation Carriers in a Large Cohort of Patients Diagnosed Clinically With Pulmonary Arterial Hypertension.

BACKGROUND: Pulmonary arterial hypertension (PAH) is a rare disease with an emerging genetic basis. Heterozygous mutations in the gene encoding the bone morphogenetic protein receptor type 2 (BMPR2) are the commonest genetic cause of PAH, whereas biallelic mutations in the eukaryotic translation initiation factor 2 alpha kinase 4 gene (EIF2AK4) are described in pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Here, we determine the frequency of these mutations and define the genotype-phenotype characteristics in a large cohort of patients diagnosed clinically with PAH. METHODS: Whole-genome sequencing was performed on DNA from patients with idiopathic and heritable PAH and with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis recruited to the National Institute of Health Research BioResource-Rare Diseases study. Heterozygous variants in BMPR2 and biallelic EIF2AK4 variants with a minor allele frequency of <1:10 000 in control data sets and predicted to be deleterious (by combined annotation-dependent depletion, PolyPhen-2, and sorting intolerant from tolerant predictions) were identified as potentially causal. Phenotype data from the time of diagnosis were also captured. RESULTS: Eight hundred sixty-four patients with idiopathic or heritable PAH and 16 with pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis were recruited. Mutations in BMPR2 were identified in 130 patients (14.8%). Biallelic mutations in EIF2AK4 were identified in 5 patients with a clinical diagnosis of pulmonary veno-occlusive disease/pulmonary capillary hemangiomatosis. Furthermore, 9 patients with a clinical diagnosis of PAH carried biallelic EIF2AK4 mutations. These patients had a reduced transfer coefficient for carbon monoxide (Kco; 33% [interquartile range, 30%-35%] predicted) and younger age at diagnosis (29 years; interquartile range, 23-38 years) and more interlobular septal thickening and mediastinal lymphadenopathy on computed tomography of the chest compared with patients with PAH without EIF2AK4 mutations. However, radiological assessment alone could not accurately identify biallelic EIF2AK4 mutation carriers. Patients with PAH with biallelic EIF2AK4 mutations had a shorter survival. CONCLUSIONS: Biallelic EIF2AK4 mutations are found in patients classified clinically as having idiopathic and heritable PAH. These patients cannot be identified reliably by computed tomography, but a low Kco and a young age at diagnosis suggests the underlying molecular diagnosis. Genetic testing can identify these misclassified patients, allowing appropriate management and early referral for lung transplantation