A Simple Model for Solar Isorotational Contours

The solar convective zone, or SCZ, is nearly adiabatic and marginally convectively unstable. But the SCZ is also in a state of differential rotation, and its dynamical stability properties are those of a weakly magnetized gas. This renders it far more prone to rapidly growing rotational baroclinic instabilities than a hydrodynamical system would be. These instabilities should be treated on the same footing as convective instabilites. If isentropic and isorotational surfaces coincide in the SCZ, the gas is marginally (un)stable to {\em both} convective and rotational disturbances. This is a plausible resolution for the instabilities associated with these more general rotating convective systems. This motivates an analysis of the thermal wind equation in which isentropes and isorotational surfaces are identical. The characteristics of this partial differential equation correspond to isorotation contours, and their form may be deduced even without precise knowledge of how the entropy and rotation are functionally related. Although the exact solution of the global SCZ problem in principle requires this knowledge, even the simplest models produce striking results in broad agreement with helioseismology data. This includes horizontal (i.e. quasi-spherical) isorotational contours at the poles, axial contours at the equator, and approximately radial contours at midlatitudes. The theory does not apply directly to the tachocline, where a simple thermal wind balance is not expected to be valid. The work presented here is subject to tests of self-consistency, among them the prediction that there should be good agreement between isentropes and isorotational contours in sufficiently well-resolved large scale numerical MHD simulations.Comment: Final version: 21 pages, 4 figures, to appear in MNRAS; thorough revision, typos and minor errors corrected, expanded development and reordering of the material. Conclusions unchanged from origina

Minimal area surfaces in AdS_{n+1} and Wilson loops

The AdS/CFT correspondence relates the expectation value of Wilson loops in N=4 SYM to the area of minimal surfaces in AdS_5 In this paper we consider minimal area surfaces in generic Euclidean AdS_{n+1} using the Pohlmeyer reduction in a similar way as we did previously in Euclidean AdS_3. As in that case, the main obstacle is to find the correct parameterization of the curve in terms of a conformal parameter. Once that is done, the boundary conditions for the Pohlmeyer fields are obtained in terms of conformal invariants of the curve. After solving the Pohlmeyer equations, the area can be expressed as a boundary integral involving a generalization of the conformal arc-length, curvature and torsion of the curve. Furthermore, one can introduce the \lambda-deformation symmetry of the contours by a simple change in the conformal invariants. This determines the \lambda-deformed contours in terms of the solution of a boundary linear problem. In fact the condition that all \lambda deformed contours are periodic can be used as an alternative to solving the Pohlmeyer equations and is equivalent to imposing the vanishing of an infinite set of conserved charges derived from integrability.Comment: 29 pages, LaTeX, 1 figur

Modeling Surfaces from Volume Data Using Nonparallel Contours

Magnetic resonance imaging: MRI) and computed tomography: CT) scanners have long been used to produce three-dimensional samplings of anatomy elements for use in medical visualization and analysis. From such datasets, physicians often need to construct surfaces representing anatomical shapes in order to conduct treatment, such as irradiating a tumor. Traditionally, this is done through a time-consuming and error-prone process in which an experienced scientist or physician marks a series of parallel contours that outline the structures of interest. Recent advances in surface reconstruction algorithms have led to methods for reconstructing surfaces from nonparallel contours that could greatly reduce the manual component of this process. Despite these technological advances, the segmentation process has remained unchanged. This dissertation takes the first steps toward bridging the gap between the new surface reconstruction technologies and bringing those methods to use in clinical practice. We develop VolumeViewer, a novel interface for modeling surfaces from volume data by allowing the user to sketch contours on arbitrarily oriented cross-sections of the volume. We design the algorithms necessary to support nonparallel contouring, and we evaluate the system with medical professionals using actual patient data. In this way, we begin to understand how nonparallel contouring can aid the segmentation process and expose the challenges associated with a nonparallel contouring system in practice

Modelling of Surfaces of Engineering Products on the Basis of Array of Points

The method of designing elements of the surfaces\u27 frames based on array of points is suggested in the work. Elements of frames are contours that are received via interpolation of sets of points, which are selected from the initial array of points. The algorithms have been developed for design plane and spatial contours that represent the curves with specified geometrical properties with prescribed accuracy. Formed contours are used as elements of «Profile» and «Guide Curves» at forming the model of surface by means of function of «Lofted Surface» in CAD system. Using the method of designing elements of frames of the surfaces is actual for modeling of surfaces of technical items that function-interact with the environment. The developed method was proven while modelling functional surfaces that bound an impeller blade channel of a turbine compressor

VolumeViewer: An Interactive Tool for Fitting Surfaces to Volume Data

Recent advances in surface reconstruction algorithms allow surfaces to be built from contours lying on non-parallel planes. Such algorithms allow users to construct surfaces of similar quality more efficiently by using a small set of oblique contours, rather than many parallel contours. However, current medical imaging systems do not provide tools for sketching contours on oblique planes. In this paper, we take the first steps towards bridging the gap between the new surface reconstruction technologies and putting those methods to use in practice. We develop a novel interface for modeling surfaces from volume data by allowing the user to sketch contours on arbitrarily oriented cross-sections of the volume, and we examine the users\u27 ability to contour the same structures using oblique cross-sections with similar consistency as they can using parallel cross-sections. We measure the inter-observer and intra-observer variability of trained physicians contouring on oblique cross-sections of real patient data as compared to the traditional parallel cross-sections, and show that the variation is much higher for oblique contouring. We then show that this variability can be greatly reduced by integrating a collection of training images into the interface

Computing and Displaying Isosurfaces in R

This paper presents R utilities for computing and displaying isosurfaces, or three-dimensional contour surfaces, from a three-dimensional array of function values. A version of the marching cubes algorithm that takes into account face and internal ambiguities is used to compute the isosurfaces. Vectorization is used to ensure adequate performance using only R code. Examples are presented showing contours of theoretical densities, density estimates, and medical imaging data. Rendering can use the rgl package or standard or grid graphics, and a set of tools for representing and rendering surfaces using standard or grid graphics is presented.

Design of thrust vectoring exhaust nozzles for real-time applications using neural networks

Thrust vectoring continues to be an important issue in military aircraft system designs. A recently developed concept of vectoring aircraft thrust makes use of flexible exhaust nozzles. Subtle modifications in the nozzle wall contours produce a non-uniform flow field containing a complex pattern of shock and expansion waves. The end result, due to the asymmetric velocity and pressure distributions, is vectored thrust. Specification of the nozzle contours required for a desired thrust vector angle (an inverse design problem) has been achieved with genetic algorithms. This approach is computationally intensive and prevents the nozzles from being designed in real-time, which is necessary for an operational aircraft system. An investigation was conducted into using genetic algorithms to train a neural network in an attempt to obtain, in real-time, two-dimensional nozzle contours. Results show that genetic algorithm trained neural networks provide a viable, real-time alternative for designing thrust vectoring nozzles contours. Thrust vector angles up to 20 deg were obtained within an average error of 0.0914 deg. The error surfaces encountered were highly degenerate and thus the robustness of genetic algorithms was well suited for minimizing global errors