Axial symmetry

About: Axial symmetry is a research topic. Over the lifetime, 6496 publications have been published within this topic receiving 100626 citations. The topic is also known as: line symmetry & axisymmetry.

Symmetry-seeking models and 3D object reconstruction

Abstract: We propose models of 3D shape which may be viewed as deformable bodies composed of simulated elastic material. In contrast to traditional, purely geometric models of shape, deformable models are active—their shapes change in response to externally applied forces. We develop a deformable model for 3D shape which has a preference for axial symmetry. Symmetry is represented even though the model does not belong to a parametric shape family such as (generalized) cylinders. Rather, a symmetry-seeking property is designed into internal forces that constrain the deformations of the model. We develop a framework for 3D object reconstruction based on symmetry-seeking models. Instances of these models are formed from monocular image data through the action of external forces derived from the data. The forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2D silhouette of an object of interest. The effectiveness of our approach is demonstrated using natural images.

RMS Envelope Equations with Space Charge

Abstract: Envelope equations for a continuous beam with uniform charge density and elliptical cross-section were first derived by Kapchinsky and Vladimirsky (K-V). In fact, the K-V equations are not restricted to uniformly charged beams, but are equally valid for any charge distribution with elliptical symmetry, provided the beam boundary and emittance are defined by rms (root-meansquare) values. This results because (i) the second moments of any particle distribution depend only on the linear part of the force (determined by least squares method), while (ii) this linear part of the force in turn depends only on the second moments of the distribution. This is also true in practice for three-dimensional bunched beams with ellipsoidal symmetry, and allows the formulation of envelope equations that include the effect of space charge on bunch length and energy spread. The utility of this rms approach was first demonstrated by Lapostolle for stationary distributions. Subsequently, Gluckstern proved that the rms version of the K-V equations remain valid for all continuous beams with axial symmetry. In this report these results are extended to continuous beams with elliptical symmetry as well as to bunched beams with ellipsoidal form, and also to one-dimensional motion.

Point‐source representation for laser‐generated ultrasound

Abstract: The stress‐free thermal strain corresponding to the temperature rise induced in a target by an incident laser pulse constitutes a volume source of ultrasound. In the present work, the appropriate point‐source representation is derived by starting from a general representation theorem for volume sources. A formal solution for the double (Hankel–Laplace) transform of the displacement potentials is obtained for axially symmetric configurations, with the point‐source lying within or on the surface of a half‐space or a plate. The Cagniard‐de Hoop technique is used to invert these double transforms. For the source on the surface of a half‐space, detailed results are presented for the wave‐front expansions, the displacement along the axis of symmetry and on the surface, the directivity pattern, and the partition of energy between longitudinal, transverse, and surface waves. For the source within or on the surface of a plate, only the epicentral displacement is considered in detail.