The Rational Overhauser: an Interpolating Rational Cubic Curve.

A rational interpolating cubic curve which implicitly maintains first order geometric continuity in splines has been developed. The curve is formed by blending two rational quadratic curves. Since the blending method used was originally introduced by Overhauser, this curve is referred to as the Rational Overhauser (Rover) curve. The curve formulation utilizes four shape factors to provide control of the curve. A geometrical and analytical interpretation of these shape factors and their relationship to each other is discussed. Procedures for representing conic sections using the rational Overhauser curve are presented. Also included are techniques for mapping between the Rover curve and rational forms of the Hermite, Bezier, and B-Spline curves

Continuous boundary elements for potential problems

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Shape Optimisation of Curved Interconnecting Ducts

Practical ducting layout in process plants needs to satisfy a number of on-site constraints. The search for an optimal flow path around the obstructions is a multi-parameter problem and is computationally prohibitively expensive. In this study, authors proposed a rapid and efficient methodology for the optimal linkage of arbitrarily oriented fluid flow ducts using a single-parameter quadratic/cubic Bézier curves in two/three dimensions to describe the centreline of the curved duct. A smooth interconnecting duct can then be generated by extruding the duct face along the curve. By varying the parameter either along the angular bisector or along the axes of the ducts, a family of Bézier curves is generated. Computational fluid dynamics simulations show that the relationship between pressure drop and the adjustable parameter is a unimodal curve and the optimal connecting duct is the one which has the least pressure drop while satisfying on-site constraints can be used for linking the ducts. The efficacy of the method is demonstrated by applying it to some cases of practical interest.Defence Science Journal, Vol. 65, No. 4, July 2015, pp. 300-306, DOI: http://dx.doi.org/10.14429/dsj.65.8353

Enriched and Isogeometric Boundary Element Methods for Acoustic Wave Scattering

This thesis concerns numerical acoustic wave scattering analysis. Such problems have been solved with computational procedures for decades, with the boundary element method being established as a popular choice of approach. However, such problems become more computationally expensive as the wavelength of an incident wave decreases; this is because capturing the oscillatory nature of the incident wave and its scattered field requires increasing numbers of nodal variables. Authors from mathematical and engineering backgrounds have attempted to overcome this problem using a wide variety of procedures. One such approach, and the approach which is further developed in this thesis, is to include the fundamental character of wave propagation in the element formulation. This concept, known as the Partition of Unity Boundary Element Method (PU-BEM), has been shown to significantly reduce the computational burden of wave scattering problems. This thesis furthers this work by considering the different interpolation functions that are used in boundary elements. Initially, shape functions based on trigonomet- ric functions are developed to increase continuity between elements. Following that, non-uniform rational B-splines, ubiquitous in Computer Aided Design (CAD) soft- ware, are used in developing an isogeometric approach to wave scattering analysis of medium-wave problems. The enriched isogeometric approach is named the eXtended Isogeometric Boundary Element Method (XIBEM). In addition to the work above, a novel algorithm for finding a uniform placement of points on a unit sphere is presented. The algorithm allows an arbitrary number of points to be chosen; it also allows a fixed point or a bias towards a fixed point to be used. This algorithm is used for the three-dimensional acoustic analyses in this thesis. The new techniques developed within this thesis significantly reduce the number of degrees of freedom required to solve a problem to a certain accuracy—this reduc- tion is more than 70% in some cases. This reduces the number of equations that have to be solved and reduces the amount of integration required to evaluate these equations

Workshop on Aircraft Surface Representation for Aerodynamic Computation

Papers and discussions on surface representation and its integration with aerodynamics, computers, graphics, wind tunnel model fabrication, and flow field grid generation are presented. Surface definition is emphasized

Comparison of pulsed three-dimensional CEST acquisition schemes at 7 tesla: steady state versus pseudosteady state

Purpose: To compare two pulsed, volumetric chemical exchange saturation transfer (CEST) acquisition schemes: steady state (SS) and pseudosteady state (PS) for the same brain coverage, spatial/spectral resolution and scan time. Methods: Both schemes were optimized for maximum sensitivity to amide proton transfer (APT) and nuclear Overhauser enhancement (NOE) effects through Bloch McConnell simulations, and compared in terms of sensitivity to APT and NOE effects, and to transmit field inhomogeneity. Five consented healthy volunteers were scanned on a 7 Tesla Philips MRsystem using the optimized protocols at three nominal B1 amplitudes: 1 mT, 2 mT, and 3 mT. Results: Region of interest based analysis revealed that PS is more sensitive (P < 0.05) to APT and NOE effects compared with SS at low B1 amplitudes (0.7–1.0 mT). Also, both sequences have similar dependence on the transmit field inhomogeneity. For the optimum CEST presaturation parameters (1 mT and 2 mT for APT and NOE, respectively), NOE is less sensitive to the inhomogeneity effects (15% signal to noise ratio [SNR] change for a B1 dropout of 40%) compared with APT (35% SNR change for a B1 dropout of 40%). Conclusion: For the same brain coverage, spatial/spectral resolution and scan time, at low power levels PS is more sensitive to the slow chemical exchange-mediated processes compared with SS

Continuous time crystal in an electron-nuclear spin system: stability and melting of periodic auto-oscillations

Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time. Originally suggested for closed thermodynamic systems in equilibrium, no-go theorems prevent the existence of time crystals. Proposals for open systems out of equilibrium led to the observation of discrete time crystals subject to external periodic driving to which they respond with a sub-harmonic response. A continuous time crystal is an autonomous system that develops periodic auto-oscillations when exposed to a continuous, time-independent driving, as recently demonstrated for the density in an atomic Bose-Einstein condensate with a crystal lifetime of a few ms. Here we demonstrate an ultra-robust continuous time crystal in the nonlinear electron-nuclear spin system of a tailored semiconductor with a coherence time exceeding hours. Varying the experimental parameters reveals huge stability ranges of this time crystal, but allows one also to enter chaotic regimes, where aperiodic behavior appears corresponding to melting of the crystal. This novel phase of matter opens the possibility to study systems with nonlinear interactions in an unprecedented way.Comment: 12 figures, 17 page

The z-spectrum from human blood at 7T

Chemical Exchange Saturation Transfer (CEST) has been used to assess healthy and pathological tissue in both animals and humans. However, the CEST signal from blood has not been fully assessed. This paper presents the CEST and nuclear Overhauser enhancement (NOE) signals detected in human blood measured via z-spectrum analysis. We assessed the effects of blood oxygenation levels, haematocrit, cell structure and pH upon the z-spectrum in ex vivo human blood for different saturation powers at 7T. The data were analysed using Lorentzian difference (LD) model fitting and AREX (to compensate for changes in T1), which have been successfully used to study CEST effects in vivo. Full Bloch-McConnell fitting was also performed to provide an initial estimate of exchange rates and transverse relaxation rates of the various pools. CEST and NOE signals were observed at 3.5 ppm, -1.7ppm and -3.5 ppm and were found to originate primarily from the red blood cells (RBCs), although the amide proton transfer (APT) CEST effect, and NOEs showed no dependence upon oxygenation levels. Upon lysing, the APT and NOE signals fell significantly. Different pH levels in blood resulted in changes in both the APT and NOE (at -3.5ppm), which suggests that this NOE signal is in part an exchange relayed process. These results will be important for assessing in vivo z-spectra

Use of the conventional and tangent derivative boundary integral equations for the solution of problems in linear elasticity

Regularized forms of the traction and tangent derivative boundary integral equations of elasticity are derived for the case of closed regions. The hypersingular and strongly singular integrals of the displacement gradient representation are regularized independently, through identities of the fundamental solution and its various derivatives, before the boundary integral equations are formed. Besides the displacements and the tractions, only the tangential derivatives of the displacements evaluated at the singular point appear in the regularized equations making them well suited for numerical treatment. The regularization of the hypersingular integrals demands that the displacement components have Holder continuous first derivatives at the singular point. Consistent with this requirement, the regularization of the strongly singular integrals is effective if the tractions and the unit vectors normal and tangent to the surface are continuous at that location.;Higher order elements for two and three dimensional elastostatic problems are implemented through the coincident collocation of regularised forms of the displacement and the tangent derivative equations. The nodal values of the displacements, the fractions and their tangential derivatives are used as the degrees of freedom associated with the functional representation of the boundary variables. The tangential derivatives of the displacements and the tractions at the functional nodes are directly recovered from the boundary solution with comparable accuracy as the primative variables. Hence, the nodal values of the stress components are directly obtained through Hooke\u27s law and need not be determined in a post processing manner. Several numerical examples demonstrate the advantages of the higher order elements versus the conventional ones. In two dimensions, four degrees of freedom per node Hermitian elements are used for functional interpolation only on those portions of the boundary where the gradients are high and quadratic Lagrangian elements are employed for the remaining parts of the modelled region. In three dimensions, nine degrees of freedom per node, incomplete quartic elements are employed for the approximation of the displacements and the tractions. Finally, the methodology presented here is general and can be extended to other problems amenable to a boundary integral formulation