Search results for "Mathematica"

New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation

2011

An independent derivation of solutions to the Camassa-Holm equation in terms of multi-dimensional theta functions is presented using an approach based on Fay's identities. Reality and smoothness conditions are studied for these solutions from the point of view of the topology of the underlying real hyperelliptic surface. The solutions are studied numerically for concrete examples, also in the limit where the surface degenerates to the Riemann sphere, and where solitons and cuspons appear.

On the number of singularities of a generic surface with boundary in a 3-manifold

1998

INITIAL PARAMETRIC REPRESENTATION OF BLOBS

2009

Blobs, developed by J.F. Blinn in 1982, are the implicit surfaces obtained by composition of a real numerical function and a distance function. Since, many authors (C. Murakami, H. Nishimura, G. Wyvill…) defined their own function of density, from these implicit surfaces are interesting from several points of view. In particular, their fusion makes it possible to easily obtain an implicit equation of resulting surface. However, these surfaces do not admit a parametric equation yet. In this article, we will establish the parametric equation of two blobs in fusion, defined by the function of density of C. Murakami, by using an algebraic method. Then, we will develop another method, based on …

Curves as measured foliation on noncompact surfaces

1993

In the present work, that regards the Thurston's theory, we prove that, if we choose a closed curve, how we wish, on a noncompact surface, it is always possible to construct a particular masured foliation that has the choosed curve like a leaf; we also prove this foliation has a remarkable property that makes very easy to mesure all homotopy classes of closed curves of our surface. To prove this statement we need some Propositions and some Lemma that we also demonstre.

The limit state of indefinite plates on elastoplastic continuum

1972

The limit analysis of indefinite plates resting on a continuous elastoplastic medium and subjected to a load distributed over a partial surface with a circular boundary yields the fundamental equation governing the problem. Minimum conditions are set and the solution that supplies the collapse load of the plate-soil system is found by variational calculus.

Atomistic Calculations of Positron Surface States

1983

We report on the results of an atomistic, discrete-lattice calculation of positron surface states on the three principal surfaces of Al and Cu. We are able to (i) accurately reproduce the observed values and anisotropy of the binding energies, and (ii) predict the surface state life times. Furthermore, we calculate (iii) the positron lateral diffusion constant, and find it considerably enhanced over the bulk value. We also investigate (iv) the positron trapping at surface vacancies, and (v) the effect of ordered chemisorbed monolayers of oxygen. We find that the oxidation lowers the binding energy and makes the surface state unstable with respect to positronium emission on Al (100) and Al (…

Sodium Adsorption on the TiO2110 Surface an XAFS Structural Study

2005

The adsorption site of sodium atoms deposited onto a clean TiO2(110) surface has been determined by EXAFS. The best result is obtained for an 'in-between' site where the sodium is bound to two bridging oxygen atoms at 2.25 A and one in-plane one at 2.40 A in full agreement with DFT calculations. At higher coverage the site becomes a hollow site where Na is equidistant to the three oxygen atoms at 2.30 A.

Wavelet-like efficient analysis of two-dimensional arbitrarily shaped radomes using a surface formulation

2007

[1] Radomes are usually made of lossy dielectric materials, and their accurate analysis is often cumbersome because of their typical large electrical size and geometrical complexity. In real reflector antenna structures, there are always complex interactions between the radome, the reflector surfaces and the directional feeds, which are typically neglected for the sake of simplicity. In this paper we will consider all such interactions in a very accurate way, thus requiring a high number of unknowns for the numerical solution of the problem. To overcome such drawback, an integral equation formulation based on the Equivalence Principle in combination with the wavelet transform has been emplo…

Measuring Multiple Residual-Stress Components using the Contour Method and Multiple Cuts

2009

The conventional contour method determines one component of residual stress over the cross section of a part. The part is cut into two, the contour (topographic shape) of the exposed surface is measured, and Bueckner’s superposition principle is analytically applied to calculate stresses. In this paper, the contour method is extended to the measurement of multiple residual-stress components by making multiple cuts with subsequent applications of superposition. The theory and limitations are described. The theory is experimentally tested on a 316L stainless steel disk with residual stresses induced by plastically indenting the central portion of the disk. The multiple-cut contour method resu…

MESH COMPARISON USING ATTRIBUTE DEVIATION METRIC

2004

We propose a mesh comparison method using a new attribute deviation metric. The considered meshes contain geometrical and appearance attributes (material color, texture, temperature, etc.). The proposed deviation metric computes local differences between the attributes of two meshes. A mesh comparison assessment can be done easily and quickly using this metric. The techniques proposed are applicable in a number of ways, e.g. 3D matching and registration, and the example described in the paper is the simplification of a surface by iteratively reducing its complexity according to an error metric. The results are presented showing the success of the algorithm through comparisons with other me…