Wave-type equations of low regularity

We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.Comment: 16 pages, 1 figur

Numerical Modeling of Transient Wave Propagation for High Frequency NDT

Electromagnetic nondestructive testing (NDT) methods use frequencies ranging from low (dc) to high (microwave) frequencies [1]. Applications of numerical methods to model two- and three-dimensional low-frequency (dc or eddy current) nondestructive testing phenomena, where displacement currents can be omitted, were extensively examined, [2,3]. These are all interior boundary value problems. Finite element study of ultrasonic wave propagation and scattering in metals, which is again an interior boundary value problem, was recently reported in [4]. However, modeling of wave propagation for high-frequency NDT problems have not yet been attempted. Recently, finite difference methods in time domain have been successfully applied to solve transient electromagnetic wave propagation problems over the atmosphere and the ground [5], and time-dependent eddy current problems [6]. The method used here is a generalization of this work and is designed for numerical modeling of high-frequency electromagnetic wave propagation arising from nondestructive testing applications. The physical situation includes examination of the scattering effects by cracks inside a piece of material (especially dielectrics) or due to surface variations when the material is illuminated by a TM plane wave. This leads to an interface type problem

An improved method of computing geometrical potential force (GPF) employed in the segmentation of 3D and 4D medical images

The geometric potential force (GPF) used in segmentation of medical images is in general a robustmethod. However, calculation of the GPF is often time consuming and slow. In the present work, wepropose several methods for improving the GPF calculation and evaluate their efficiency against theoriginal method. Among different methods investigated, the procedure that combines Riesz transformand integration by part provides the fastest solution. Both static and dynamic images have been employedto demonstrate the efficacy of the proposed methods

Macular Telangiectasia Type 2: A Classification System Using MultiModal Imaging MacTel Project Report Number 10

Purpose: To develop a severity classification for macular telangiectasia type 2 (MacTel) disease using multimodal imaging. Design: An algorithm was used on data from a prospective natural history study of MacTel for classification development. Subjects: A total of 1733 participants enrolled in an international natural history study of MacTel. Methods: The Classification and Regression Trees (CART), a predictive nonparametric algorithm used in machine learning, analyzed the features of the multimodal imaging important for the development of a classification, including reading center gradings of the following digital images: stereoscopic color and red-free fundus photographs, fluorescein angiographic images, fundus autofluorescence images, and spectral-domain (SD)-OCT images. Regression models that used least square method created a decision tree using features of the ocular images into different categories of disease severity. Main Outcome Measures: The primary target of interest for the algorithm development by CART was the change in best-corrected visual acuity (BCVA) at baseline for the right and left eyes. These analyses using the algorithm were repeated for the BCVA obtained at the last study visit of the natural history study for the right and left eyes. Results: The CART analyses demonstrated 3 important features from the multimodal imaging for the classification: OCT hyper-reflectivity, pigment, and ellipsoid zone loss. By combining these 3 features (as absent, present, noncentral involvement, and central involvement of the macula), a 7-step scale was created, ranging from excellent to poor visual acuity. At grade 0, 3 features are not present. At the most severe grade, pigment and exudative neovascularization are present. To further validate the classification, using the Generalized Estimating Equation regression models, analyses for the annual relative risk of progression over a period of 5 years for vision loss and for progression along the scale were performed. Conclusions: This analysis using the data from current imaging modalities in participants followed in the MacTel natural history study informed a classification for MacTel disease severity featuring variables from SD-OCT. This classification is designed to provide better communications to other clinicians, researchers, and patients. Financial Disclosure(s): Proprietary or commercial disclosure may be found after the references

Algebraic QFT in Curved Spacetime and quasifree Hadamard states: an introduction

Within this chapter (published as [49]) we introduce the overall idea of the algebraic formalism of QFT on a fixed globally hyperbolic spacetime in the framework of unital $*$-algebras. We point out some general features of CCR algebras, such as simplicity and the construction of symmetry-induced homomorphisms. For simplicity, we deal only with a real scalar quantum field. We discuss some known general results in curved spacetime like the existence of quasifree states enjoying symmetries induced from the background, pointing out the relevant original references. We introduce, in particular, the notion of a Hadamard quasifree algebraic quantum state, both in the geometric and microlocal formulation, and the associated notion of Wick polynomials.Comment: v3: better discussion of Unitary Equivalence, thanks to comments of Ko Sanders. v2: minor corrections, added reference to older work by Sahlmann and Verch. v1: 59 pages, 4 figures. arXiv admin note: text overlap with arXiv:1008.1776 by other author

Radiation from a D-dimensional collision of shock waves: first order perturbation theory

We study the spacetime obtained by superimposing two equal Aichelburg-Sexl shock waves in D dimensions traveling, head-on, in opposite directions. Considering the collision in a boosted frame, one shock becomes stronger than the other, and a perturbative framework to compute the metric in the future of the collision is setup. The geometry is given, in first order perturbation theory, as an integral solution, in terms of initial data on the null surface where the strong shock has support. We then extract the radiation emitted in the collision by using a D-dimensional generalisation of the Landau-Lifschitz pseudo-tensor and compute the percentage of the initial centre of mass energy epsilon emitted as gravitational waves. In D=4 we find epsilon=25.0%, in agreement with the result of D'Eath and Payne. As D increases, this percentage increases monotonically, reaching 40.0% in D=10. Our result is always within the bound obtained from apparent horizons by Penrose, in D=4, yielding 29.3%, and Eardley and Giddings, in D> 4, which also increases monotonically with dimension, reaching 41.2% in D=10. We also present the wave forms and provide a physical interpretation for the observed peaks, in terms of the null generators of the shocks.Comment: 27 pages, 11 figures; v2 some corrections, including D dependent factor in epsilon; matches version accepted in JHE

Continuous low- to moderate-intensity exercise training is as effective as moderate- to high-intensity exercise training at lowering blood HbA1c in obese type 2 diabetes patients

Aims/hypothesis: Exercise represents an effective interventional strategy to improve glycaemic control in type 2 diabetes patients. However, the impact of exercise intensity on the benefits of exercise training remains to be established. In the present study, we compared the clinical benefits of 6 months of continuous low- to moderate-intensity exercise training with those of continuous moderate- to high-intensity exercise training, matched for energy expenditure, in obese type 2 diabetes patients. Methods: Fifty male obese type 2 diabetes patients (age 59∈±∈8 years, BMI 32∈± ∈4 kg/m2) participated in a 6 month continuous endurance-type exercise training programme. All participants performed three supervised exercise sessions per week, either 55 min at 50% of whole body peak oxygen uptake left(VO2peak) (low to moderate intensity) or 40 min at 75% of VO2peak (moderate to high intensity). Oral glucose tolerance, blood glycated haemoglobin, lipid profile, body composition, maximal workload capacity, whole body and skeletal muscle oxidative capacity and skeletal muscle fibre type composition were assessed before and after 2 and 6 months of intervention. Results: The entire 6 month intervention programme was completed by 37 participants. Continuous endurance-type exercise training reduced blood glycated haemoglobin levels, LDL-cholesterol concentrations, body weight and leg fat mass, and increased VO2peak, lean muscle mass and skeletal muscle cytochrome c oxidase and citrate synthase activity (p∈<∈0. 05). No differences were observed between the groups training at low to moderate or moderate to high intensity. Conclusions/interpretation: When matched for energy cost, prolonged continuous low- to moderate-intensity endurance-type exercise training is equally effective as continuous moderate- to high-intensity training in lowering blood glycated haemoglobin and increasing whole body and skeletal muscle oxidative capacity in obese type 2 diabetes patients. © 2009 Springer-Verlag

Motion in classical field theories and the foundations of the self-force problem

This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and self-torque are derived using simple, non-perturbative arguments. The relevant concepts are developed gradually by considering motion in a series of increasingly complicated theories. Newtonian gravity is discussed first, then Klein-Gordon theory, electromagnetism, and finally general relativity. Linear and angular momenta as well as centers of mass are defined in each of these cases. Multipole expansions for the force and torque are then derived to all orders for arbitrarily self-interacting extended objects. These expansions are found to be structurally identical to the laws of motion satisfied by extended test bodies, except that all relevant fields are replaced by effective versions which exclude the self-fields in a particular sense. Regularization methods traditionally associated with self-interacting point particles arise as straightforward perturbative limits of these (more fundamental) results. Additionally, generic mechanisms are discussed which dynamically shift --- i.e., renormalize --- the apparent multipole moments associated with self-interacting extended bodies. Although this is primarily a synthesis of earlier work, several new results and interpretations are included as well.Comment: 68 pages, 1 figur

The motion of point particles in curved spacetime

This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The field's action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field's singular part and show that it exerts no force on the particle -- its only effect is to contribute to the particle's inertia. What remains after subtraction is a smooth field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free (radiative) field that interacts with the particle; it is this interaction that gives rise to the self-force. The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle's word line (part II). It continues with a thorough discussion of Green's functions in curved spacetime (part III). The review concludes with a detailed derivation of each of the three equations of motion (part IV).Comment: LaTeX2e, 116 pages, 10 figures. This is the final version, as it will appear in Living Reviews in Relativit