Search results for "Geometric"
showing 10 items of 652 documents
Optical studies of laser-induced gray-tracking in KTP
1999
We have studied gray-tracking induced by a pulsed and polarized 532-nm laser beam in flux grown KTiOPO/sub 4/ (KTP) crystals. Transmission spectra measured under polarized light give different results: gray-tracking leads to an increase in the initial anisotropy of the linear optical properties of KTP, and the polar axis is the most sensitive to this process. The dynamics of relaxation of gray-tracking is anisotropic and depends on the wavelength under analysis. We show a possible induced modification of the crystal surface and also the existence of an intensity above which gray-tracking reaches the saturation point. We then measure the temperature above which gray-tracking no longer exists.
Geometric characterization and simulation of planar layered elastomeric fibrous biomaterials
2015
An important class of biomaterials is composed of layered networks of elastomeric fibers. While there is a growing interest in modeling and simulation of the mechanical response of these biomaterials, a theoretical foundation for such simulations has yet to be firmly established. The present work addresses this issue in two ways. First, using methods of geometric probability we develop theoretical estimates for the linear and areal fiber intersection densities for two-dimensional fibrous networks. These are expressed in terms of the fiber density and orientation distribution function, both of which are relatively easy to measure properties. Secondly, we develop a random walk algorithm for g…
Temperature dependence of slow-positron production and of positronium formation on untreated surfaces
1987
Low-energy positron emission from tungsten moderators, placed at a electron accelerator beam stop slows down with increasing moderator temperature. Efficient positronium formation is reported on untreated and unoriented metal surfaces at higher target temperatures.
MUTUAL INDUCTANCE FOR AN EXPLICITLY FINITE NUMBER OF TURNS
2011
Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly flnite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an integral of a single analytical expression. Sample numerical results are given for some representative cases and the approach to the limit where the turns are considered to be smeared ou…
Qualitative Theory of Differential Equations, Difference Equations, and Dynamic Equations on Time Scales
2016
We are pleased to present this special issue. This volume reflects an increasing interest in the analysis of qualitative behavior of solutions to differential equations, difference equations, and dynamic equations on time scales. Numerous applications arising in the engineering and natural sciences call for the development of new efficient methods and for the modification and refinement of known techniques that should be adjusted for the analysis of new classes of problems. The twofold goal of this special issue is to reflect both the state-of-the-art theoretical research and important recent advances in the solution of applied problems.
Approximate survival probability determination of hysteretic systems with fractional derivative elements
2018
Abstract A Galerkin scheme-based approach is developed for determining the survival probability and first-passage probability of a randomly excited hysteretic systems endowed with fractional derivative elements. Specifically, by employing a combination of statistical linearization and of stochastic averaging, the amplitude of the system response is modeled as one-dimensional Markovian Process. In this manner the corresponding backward Kolmogorov equation which governs the evolution of the survival probability of the system is determined. An approximate solution of this equation is sought by employing a Galerkin scheme in which a convenient set of confluent hypergeometric functions is used a…
Detecting All Dependences in Systems of Geometric Constraints Using the Witness Method
2007
In geometric constraints solving, the detection of dependences and the decomposition of the system into smaller subsystems are two important steps that characterize any solving process, but nowadays solvers, which are graph-based in most of the cases, fail to detect dependences due to geometric theorems and to decompose such systems. In this paper, we discuss why detecting all dependences between constraints is a hard problem and propose to use the witness method published recently to detect both structural and non structural dependences.We study various examples of constraints systems and show the promising results of the witness method in subtle dependences detection and systems decomposi…
Solving the pentahedron problem
2015
Nowadays, all geometric modelers provide some tools for specifying geometric constraints. The 3D pentahedron problem is an example of a 3D Geometric Constraint Solving Problem (GCSP), composed of six vertices, nine edges, five faces (two triangles and three quadrilaterals), and defined by the lengths of its edges and the planarity of its quadrilateral faces. This problem seems to be the simplest non-trivial problem, as the methods used to solve the Stewart platform or octahedron problem fail to solve it. The naive algebraic formulation of the pentahedron yields an under-constrained system of twelve equations in eighteen unknowns. Even if the use of placement rules transforms the pentahedron…
Using the witness method to detect rigid subsystems of geometric constraints in CAD
2010
International audience; This paper deals with the resolution of geometric constraint systems encountered in CAD-CAM. The main results are that the witness method can be used to detect that a constraint system is over-constrained and that the computation of the maximal rigid subsystems of a system leads to a powerful decomposition method. In a first step, we recall the theoretical framework of the witness method in geometric constraint solving and extend this method to generate a witness. We show then that it can be used to incrementally detect over-constrainedness. We give an algorithm to efficiently identify all maximal rigid parts of a geometric constraint system. We introduce the algorit…
Corrigendum to ``A smooth foliation of the 5-sphere by complex surfaces"
2011
International audience