Measuring the Effects of Artificial Viscosity in SPH Simulations of Rotating Fluid Flows

A commonly cited drawback of SPH is the introduction of spurious shear viscosity by the artificial viscosity term in situations involving rotation. Existing approaches for quantifying its effect include approximate analytic formulae and disc-averaged be- haviour in specific ring-spreading simulations, based on the kinematic effects produced by the artificial viscosity. These methods have disadvantages, in that they typically are applicable to a very small range of physical scenarios, have a large number of simplifying assumptions, and often are tied to specific SPH formulations which do not include corrective (e.g., Balsara) or time-dependent viscosity terms. In this study we have developed a simple, generally applicable and practical technique for evaluating the local effect of artificial viscosity directly from the creation of specific entropy for each SPH particle. This local approach is simple and quick to implement, and it al- lows a detailed characterization of viscous effects as a function of position. Several advantages of this method are discussed, including its ease in evaluation, its greater accuracy and its broad applicability. In order to compare this new method with ex- isting ones, simple disc flow examples are used. Even in these basic cases, the very roughly approximate nature of the previous methods is shown. Our local method pro- vides a detailed description of the effects of the artificial viscosity throughout the disc, even for extended examples which implement Balsara corrections. As a further use of this approach, explicit dependencies of the effective viscosity in terms of SPH and flow parameters are estimated from the example cases. In an appendix, a method for the initial placement of SPH particles is discussed which is very effective in reducing numerical fluctuations.Comment: 15 pages, 9 figures, resubmitted to MNRA

Aortic Coarctation: Recent Developments in Experimental and Computational Methods to Assess Treatments for this Simple Condition

Coarctation of the aorta (CoA) is often considered a relatively simple disease, but long-term outcomes suggest otherwise as life expectancies are decades less than in the average population and substantial morbidity often exists. What follows is an expanded version of collective work conducted by the authors\u27 and numerous collaborators that was presented at the 1st International Conference on Computational Simulation in Congenital Heart Disease pertaining to recent advances for CoA. The work begins by focusing on what is known about blood flow, pressure and indices of wall shear stress (WSS) in patients with normal vascular anatomy from both clinical imaging and the use of computational fluid dynamics (CFD) techniques. Hemodynamic alterations observed in CFD studies from untreated CoA patients and those undergoing surgical or interventional treatment are subsequently discussed. The impact of surgical approach, stent design and valve morphology are also presented for these patient populations. Finally, recent work from a representative experimental animal model of CoA that may offer insight into proposed mechanisms of long-term morbidity in CoA is presented

Form discrimination in young children and the concept of similarity

A brief account is given of differentiation theory as it relates to form discrimination studies, and relevant experimental work is reviewed. Some preliminary comments on the concept of similarity, arising out of this and pertaining to the extent to which children can be said to possess an adequate grasp of what is implied by "the same as," are made as an introduction to the first experiment. This examines the performance of a group of children twice, at mean ages 3-8 and 4-9, in matching-from-sample discrimination tasks with stimulus material varying in orientation only, and in form and orient¬ ation. Considerable improvement in terms of increased number of correct responses is shown. A sequence of three stages is described. In the first, characterised by a small number of correct responses and a small number of multiple responses (MR), that is responses where more than one comparison figure are matched to the standard, performance is affected as much by extraneous factors such as position of a figure in the comparison array as by stimulus features. The second stage shows an increase in both MR and number of correct matches; here global features of similarity appear to be being detected and used. The final stage, with most responses being correct and few MRs being given, represents the most competent level. It is indicated that failure to detect stimulus features, rather than the presence of a deviant notion of the meaning of "same, "/"same," is responsible for the error patterns shown. The concept of similarity is then examined in greater detail. A number of distinctions are drawn, in particular, between the specification of similarity relations between members of a stimulus set in terms of its attribute structure and the perceived similarity of the same set as expressed by subjects' judgements. The importance of providing a normative model as a baseline for the assessment of perfomnance is emphasised. A number of ways of specifying stimuli are described, together with methods of analysing similarities data. The use of a model to link perceived and physical structure, and thus to give some indication of the processes underlying discrimination performance, is considered. A set of experiments is then described which embody these ideas, and it is shown that even in four-year-old children errors in a matching-from-sample task systematically reflect features of the v/hole stimulus set. It is also shown that this does not hold with pair comparison presentation. The capacity of children for redefining the attribute structure of stimulus sets is brought out. It is concluded that much more attention should be given to stimulus speci¬ fication in formal terms if the processes involved in form discrimination are to be elucidated, as opposed to the discriminability of a particular set of stimuli under particular circumstances

Renormalization in Coulomb gauge QCD

In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.Comment: 23 pages, 26 figure

Energy Dependence of Scattering Ground State Polar Molecules

We explore the total cross section of ground state polar molecules in an electric field at various energies, focusing on RbCs and RbK. An external electric field polarizes the molecules and induces strong dipolar interactions leading to non-zero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total M to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low field temperature dependence. To understand the scattering of the polar molecules we compare a semi-classical cross section with quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy.Comment: Accepted PRA, 10 pages, 5 figure

Inverse Scattering and Acousto-Optic Imaging

We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes use of the principle of interior control of boundary measurements by an external wave field.Comment: 10 page