4,435 research outputs found
Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator
It is demonstrated that finite-pressure, approximately quasi-axisymmetric
stellarator equilibria can be directly constructed (without numerical
optimization) via perturbations of given axisymmetric equilibria. The size of
such perturbations is measured in two ways, via the fractional external
rotation and, alternatively, via the relative magnetic field strength, i.e. the
average size of the perturbed magnetic field, divided by the unperturbed field
strength. It is found that significant fractional external rotational transform
can be generated by quasi-axisymmetric perturbations, with a similar value of
the relative field strength, despite the fact that the former scales more
weakly with the perturbation size. High mode number perturbations are
identified as a candidate for generating such transform with local current
distributions. Implications for the development of a general non-perturbative
solver for optimal stellarator equilibria is discussed
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A Local/Global Approach to Mesh Parameterization
We present a novel approach to parameterize a mesh with disk topology to the plane in a shape-preserving manner. Our key contribution is a local/global algorithm, which combines a local mapping of each 3D triangle to the plane, using transformations taken from a restricted set, with a global "stitch" operation of all triangles, involving a sparse linear system. The local transformations can be taken from a variety of families, e.g. similarities or rotations, generating different types of parameterizations. In the first case, the parameterization tries to force each 2D triangle to be an as-similar-as-possible version of its 3D counterpart. This is shown to yield results identical to those of the LSCM algorithm. In the second case, the parameterization tries to force each 2D triangle to be an as-rigid-as-possible version of its 3D counterpart. This approach preserves shape as much as possible. It is simple, effective, and fast, due to pre-factoring of the linear system involved in the global phase. Experimental results show that our approach provides almost isometric parameterizations and obtains more shape-preserving results than other state-of-the-art approaches.
We present also a more general "hybrid" parameterization model which provides a continuous spectrum of possibilities, controlled by a single parameter. The two cases described above lie at the two ends of the spectrum. We generalize our local/global algorithm to compute these parameterizations. The local phase may also be accelerated by parallelizing the independent computations per triangle.Engineering and Applied Science
Shape analysis in shape space
This study aims to classify different deformations based on the shape space concept. A shape space is a quotient space in which each point corresponds to a class of shapes. The shapes of each class are transformed to each other by a transformation group preserving a geometrical property in which we are interested. Therefore, each deformation is a curve on the high dimensional shape space manifold, and one can classify the deformations by comparison of their corresponding deformation curves in shape space. Towards this end, two classification methods are proposed.
In the first method, a quasi conformal shape space is constructed based on a novel quasi-conformal metric, which preserves the curvature changes at each vertex during the deformation. Besides, a classification framework is introduced for deformation classification. The results on synthetic and real datasets show the effectiveness of the metric to estimate the intrinsic geometry of the shape space manifold, and its ability to classify and interpolate different deformations.
In the second method, we introduce the medial surface shape space which classifies the deformations based on the medial surface and thickness of the shape. This shape space is based on the log map and uses two novel measures, average of the normal vectors and mean of the positions, to determine the distance between each pair of shapes on shape space.
We applied these methods to classify the left ventricle deformations. The experimental results shows that the first method can remarkably classify the normal and abnormal subjects but this method cannot spot the location of the abnormality. In contrast, the second method can discriminate healthy subjects from patients with cardiomyopathy, and also can spot the abnormality on the left ventricle, which makes it a valuable assistant tool for diagnostic purposes
A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials
The architecture of mechanical metamaterialsis designed to harness geometry,
non-linearity and topology to obtain advanced functionalities such as shape
morphing, programmability and one-way propagation. While a purely geometric
framework successfully captures the physics of small systems under idealized
conditions, large systems or heterogeneous driving conditions remain
essentially unexplored. Here we uncover strong anomalies in the mechanics of a
broad class of metamaterials, such as auxetics, shape-changers or topological
insulators: a non-monotonic variation of their stiffness with system size, and
the ability of textured boundaries to completely alter their properties. These
striking features stem from the competition between rotation-based
deformations---relevant for small systems---and ordinary elasticity, and are
controlled by a characteristic length scale which is entirely tunable by the
architectural details. Our study provides new vistas for designing, controlling
and programming the mechanics of metamaterials in the thermodynamic limit.Comment: Main text has 4 pages, 4 figures + Methods and Supplementary
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Finite Element Based Tracking of Deforming Surfaces
We present an approach to robustly track the geometry of an object that
deforms over time from a set of input point clouds captured from a single
viewpoint. The deformations we consider are caused by applying forces to known
locations on the object's surface. Our method combines the use of prior
information on the geometry of the object modeled by a smooth template and the
use of a linear finite element method to predict the deformation. This allows
the accurate reconstruction of both the observed and the unobserved sides of
the object. We present tracking results for noisy low-quality point clouds
acquired by either a stereo camera or a depth camera, and simulations with
point clouds corrupted by different error terms. We show that our method is
also applicable to large non-linear deformations.Comment: additional experiment
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