Showing papers on "Distribution (differential geometry) published in 1997"
Patent•
28 Aug 1997
TL;DR: In this article, an exhaust gas recirculation manifold (EGR) is proposed to deliver recirculated exhaust gas within the flowpath of the intake manifold, and both linear and round shapes are considered for the EGR manifold.
Abstract: An exhaust gas recirculation (EGR) manifold received within an intake manifold. The EGR manifold includes a plurality of holes for delivery of recirculated exhaust gas within the flowpath of the intake manifold. Both linear and round shapes are contemplated for the EGR manifold.
37 citations
TL;DR: The authors showed that the distribution of the squared length of the projection of the normal variate to any smooth convex cone is a mixture of chi-squared distributions and gave the explicit formulas for the weights.
27 citations
TL;DR: In this article, the authors studied the holonomy and the horizontal holonomy of sub-Riemannian manifolds of contact type relative to an adapted connection, and obtained an Ambrose-Singer type theorem for the horizontal Holonomy.
Abstract: A sub-Riemannian manifold is a smooth manifold which carries a distribution equipped with a metric We study the holonomy and the horizontal holonomy (ie holonomy spanned by loops everywhere tangent to the distribution) of sub-Riemannian manifolds of contact type relative to an adapted connection In particular, we obtain an Ambrose–Singer type theorem for the horizontal holonomy and we classify the holonomy irreducible sub-Riemannian symmetric spaces (ie homogeneous sub-Riemannian manifolds admitting an involutive isometry whose restriction to the distribution is a central symmetry)
26 citations
TL;DR: In this article, the authors explore the global unique continuation property of distribution solutions of a locally integrable vector subbundle of the complexified tangent bundle of a smooth manifold, i.e., the distributionsu onM such thatLu = 0 wheneverL is a section ofV.
Abstract: SupposeM is a smooth manifold andV is a locally integrable vector subbundle of the complexified tangent bundle ofM. This paper explores the global unique continuation property of distribution solutions ofV, i.e., the distributionsu onM such thatLu = 0 wheneverL is a section ofV, and the closely related problem of the structure of the Sussmann orbits ofHV.
15 citations
TL;DR: In this paper, the authors studied the low-temperature dynamics of an elastic manifold driven through a random medium and developed a scaling theory of the thermally activated dynamics (creep) and found a nonlinear glassy response for the driven manifold.
5 citations
14 Jul 1997
TL;DR: It is demonstrated here that fibre bundles occur naturally in specifications and models associated with formal methods, one critical aspect of which is the fibre bundle, and more generally the sheaf.
Abstract: The act of distributing and the resulting distribution are notions which lie at the kernel of any distributed system. The basic algebra of such distributions and their use in formal specifications has already been developed in terms of indexed monoids (i.e., function spaces with valuations in monoids) and their morphisms. Complementary to such algebra is a body of emerging geometry/topology of formal specifications, one critical aspect of which is the fibre bundle, and more generally the sheaf.
Fibre bundles are used to model the nature and shape of geometrical objects and to associate a field with points in a space. They find particular application in theoretical physics, for example. We demonstrate here that fibre bundles occur naturally in specifications and models associated with formal methods.
5 citations
TL;DR: In this article, a new numerical method for constructing a pressure distribution to calculate surface elastic deformation caused by normal contact pressure is developed, where the pressure distribution over one of nonequidistant rectangles is fitted by an approximate tangent plane (ATP), which is formed by five pressure samples.
Abstract: A new numerical method for constructing a pressure distribution to calculate surface elastic deformation caused by normal contact pressure is developed in this paper. The pressure distribution over one of nonequidistant rectangles is fitted by an approximate tangent plane(ATP), which is formed by five pressure samples. Because the pressure distribution could be expressed as an one order linear polynomial, the iterative expression of elastic deformation deduced by this method is simple, and the numerical accuracy is higher.
01 Feb 1997
TL;DR: In this paper, the fractal structures of three-dimensional simplicial quantum gravity were studied by the Monte-Carlo method and they were classified into three types: (i) a crumpled manifold in the strong coupling (hot) phase with a large Hausdorff dimension dH ⋍ 5, (ii) a pseudo-fractal manifold at the critical point with a Hausdorff dimension DH ⌈ 4, and (iii) a branched polymer structure in the weak coupling (cold) phase having a small
Abstract: Phases and fractal structures of three-dimensional simplicial quantum gravity are studied by the Monte-Carlo method. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution (LLD) in two-dimensional quantum gravity, we classify the fractal structures into three types: (i) a crumpled manifold in the strong coupling (hot) phase with a large Hausdorff dimension dH ⋍ 5. (ii) a pseudo-fractal manifold at the critical point with a Hausdorff dimension dH ⋍ 4. We observe some scaling behaviors for the cross-sections of the manifold. (iii) a branched-polymer structure in the weak coupling (cold) phase with a small Hausdorff dimension dH ⋍ 2.
01 Apr 1997
TL;DR: In this paper, the degeneration locus I is defined as the set of points where the distribution has a Lie-bracket growth vector less than or equal I, a xed integer vector.
Abstract: Given a distribution of k-planes on a manifold, consider the degeneration locus I consisting of points where the distribution has Lie-bracket growth vector less than or equal I, a xed integer vector. We calculate the characteristic classes associated to the I for a generic two-plane distribution on a four-manifold. 1. Results and Background. 1.1. Generalities, Setting and Results. A distribution D of k-planes on an n-dimensional manifold Q can be thought of as either a subbundle DTQ of the tangent bundle or as a locally free sheaf of smooth vector elds. We use the same notation for both. Write D 2 = D +[ D ;D] and more generally D j+1 = D j +[ D ;D j ]. These are sheaves of modules of vector elds (over the ring of smooth functions). We are interested in distributions such that for r large enough we obtain all vector elds by this procedure: D r = T
Posted Content•
TL;DR: In this article, it was shown that the degeneration locus of the Engel distribution is a finite union of surfaces, and that these surfaces represent Chern classes associated to the distribution.
Abstract: There is a remarkable type of field of two-planes special to four dimensions known as an Engel distributions. They are the only stable regular distributions besides the contact, quasi-contact and line fields. If an arbitrary two-plane field on a four-manifold is slightly perturbed then it will be Engel at generic points. On the other hand, if a manifold admits an oriented Engel structure then the manifold must be parallelizable and consequently the alleged Engel distribution must have a degeneration loci -- a point set where the Engel conditions fails. By a theorem of Zhitomirskii this locus is a finite union of surfaces. We prove that these surfaces represent Chern classes associated to the distribution.
TL;DR: In this article, the authors derived the areas distribution of random walks of length $ N $ on a two-dimensional square lattice for large contributions, taking into account finite size contributions.
Abstract: Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $ N $ on a two-dimensional square lattice for large $ N $, taking into account finite size contributions.
10 Apr 1997
TL;DR: In this article, the integrability of the one dimensional betatron equation of motion is discussed and the solutions of such integrable equations are investigated numerically and analytically and a rigorous stability analysis of the solutions with respect to their initial conditions is performed.
Abstract: The integrability of the one dimensional betatron equation of motion is discussed. Although it is known that the general time dependent differential equation of second order describing single particle motion in presence of sextupoles is nonintegrable, special cases may be found in which integrability can be proven and first integrals can be written analytically. The present paper introduces a method to find specific sextupole distributions for which integrability can be obtained. The solutions of such integrable equations are investigated numerically and analytically and a rigorous stability analysis of the solutions with respect to their initial conditions is performed. The possibilities of applications of this theory to real machines is discussed.
Patent•
02 Jul 1997
TL;DR: A water manifold is a manifold formed from a number of elements in a flexible manner, in that the elements are assembled as needed for a particular application as mentioned in this paper. The manifold is usable in the construction of a fluid-based heat-transfer system for space heating, the supply and distribution of potable water, and other applications.
Abstract: A water manifold is usable in the construction of a fluid-based heat-transfer system for space heating, the supply and distribution of potable water, and other applications. The water manifold is formed from a number of elements in a flexible manner, in that the elements are assembled as needed for a particular application. A plurality of manifold segments 100, each supporting a pipe directed away from a main pipe, transfer heat to a specific area, and may be be connected in a linear manner, as required by the design of the application. A cross tee segment 300 is attachable to the manifold segments, and may be used to support a thermometer unit 200, an automatic air vent or other apparatus. A spigot 400 is attachable to the cross tee segment, adjacent to the thermometer. An open end cap 500 provides a male plastic fitting connected to a brass female fitting, thereby allowing connection of the manifold to metal plumbing. A closed end cap 600 allows the manifold to be terminated. A support bracket 700 is adapted to connect to the manifold segments for support.