Arbitrary Three-dimensional Objects Research Articles

Three-Dimensional Elastic Scattering Coefficients and Enhancement of the Elastic Near Cloaking

This paper is concerned with the elastic near cloaking for the Lamé system in three-dimensions using the notion of elastic scattering coefficients (ESC). Accordingly, the ESC of arbitrary three-dimensional objects are designed and some of their properties are discussed using elements of the elastic layer potential theory. Then, near-cloaking structures, coined as ESC-vanishing-structures, are constructed for the elastic cloaking at a fixed frequency or a band of frequencies. These multi-layered structures are designed so that their first few significant ESC vanish ahead of transformation-elastodynamics. The invisibility effect is achieved as the arbitrary elastic object inside the cloak has near-zero scattering cross-section for a band of frequencies. The cloaking effect for the Lamé system is significantly enhanced by the proposed near-cloaking structures.

CASIMIR FORCE FOR ARBITRARY OBJECTS USING THE ARGUMENT PRINCIPLE AND BOUNDARY ELEMENT METHODS

Recent progress in the simulation of Casimir forces between various objects has allowed traditional computational electromagnetic solvers to be used to flnd Casimir forces in arbitrary three-dimensional objects. The underlying theory to these approaches requires knowledge and manipulation of quantum fleld theory and statistical physics. We present a calculation of the Casimir force using the method of moments via the argument principle. This simplifled derivation allows greater freedom in the moment matrix where the argument principle can be used to calculate Casimir forces for arbitrary geometries and materials with the use of various computational electromagnetic techniques.

Inverse Problems in Aerodynamics, Heat Transfer, Elasticity and Materials Design

A number of existing and emerging concepts for formulating solution algorithms applicable to multidisciplinary inverse problems involving aerodynamics, heat conduction, elasticity, and material properties of arbitrary three-dimensional objects are briefly surveyed. Certain unique features of these algorithms and their advantages are sketched for use with boundary element and finite element methods.

Computation of Casimir interactions between arbitrary three-dimensional objects with arbitrary material properties

We extend a recently introduced method for computing Casimir forces between arbitrarily shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett. 103 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface-surface separation at which finite-size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.

Optical forces in time domain on arbitrary objects

We develop a general theoretical and computational framework to describe, in time domain, the exchange of momentum between light and arbitrary three-dimensional objects. Our formulation can be used to study the time evolution of optical forces on any object with linear material response, including inhomogeneous, dispersive, and absorbing dielectrics and metals. We illustrate our approach by studying the behavior of the Abraham force on an object illuminated by a sequence of electromagnetic pulses.

Generation of Point-Based 3D Statistical Shape Models for Anatomical Objects

A novel method that allows the development of surface point-based three-dimensional statistical shape models is presented. Given a set of medical objects, a statistical shape model can be obtained by principal component analysis. This technique requires that a set of complex shaped objects is represented as a set of vectors that uniquely determines the shapes of the objects and at the same time is suitable for a statistical analysis. The correspondence between the vector components and the respective shape features has to be identical in order for all shape parameter vectors to be considered. We present a novel approach to the correspondence problem for arbitrary three-dimensional objects which involves developing a template shape and fitting this template to all objects to be analyzed. The method is successfully applied to obtain a statistical shape model for the lumbar vertebrae.

The degree of similarity of three-dimensional bodies: Application to molecular shape analysis

Similarity of shape features of three-dimensional bodies is of importance in many fields. Computational methods that are suitable to provide numerical measures for such similarities are expected to find applications in a wide variety of areas. Whereas relative measures based on direct pair comparisons are useful, nevertheless, methods that involve absolute shape descriptors are expected to be more universally applicable. The general “grade of similarity” concept proposed in this study is based on such absolute shape descriptors of three-dimensional bodies. The study of similarity of the three-dimensional shapes of molecules as represented, for example, by their electronic charge distributions, or electrostatic potentials, or simply by their fused spheres Van der Waals surfaces, is an important component of modem drug design. A family of topological methods, the shape group methods (SGM), have been proposed recently for the study of the shapes of formal molecular bodies, evaluating and comparing numerical shape codes for the non-visual comparison of molecules by the computer. In this contribution a new, and conceptually simpler numerical measure of shape similarity is proposed, applicable for the computer evaluation of similarity of arbitrary three-dimensional objects of closed surfaces. The technique is suggested for the non-visual, numerical evaluation of shape similarity of formal molecular bodies and contour surfaces.

Surface-Deformation Measurement Using the Wavefront Reconstruction Technique

This paper describes a new method for the measurement of minute deformations of arbitrary three-dimensional objects, such as might occur due to applied stress. The method is an application of the wavefront reconstruction technique, as developed by Leith and Upatnieks, to the interferometry of three-dimensional diffusely reflecting objects. The theory of wavefront reconstruction is sketched. A detailed theory for the interpretation of the interference phenomena observed in terms of the translations and rotations undergone by a point on the object is presented. Experimental results verifying the method and the theory are shown.