Location Of Singular Points Research Articles

Surface Flow Visualization of MIRA Notchback Reference Car

A surface flow visualization of a MIRA notchback reference car was conducted using a 1/4 -scale model in the POSTECH wind tunnel. The flow separation and reattachment phenomen a around A-pillar, C-pillar, backlight, and trunk were discussed with the help of the distributions of singular points such as nodes, saddles, and spiral foci. The locations of the singular points on the trunk and the backlight from experimental results are compared with those of CFD results using the turbulence modeling of RNG k - and RSM.

パラレルメカニズムの機構剛性解析 特異点近傍における剛性特性の解析

Parallel manipulators have many useful characteristics, that is high speed motion as the inertia is light, rigid structure and full 6 degrees of freedom. There are many different type parallel manipulators. Stewart platform. is the most typical type which has 6 linear actuators called struts, A new type parallel manipulator named PSSP has been proposed, which is moved with three pentagon type SCARA robots. Parallel manipulators have many singular points in the working space, on the points the stiffness of the structure becomes zero. It is very important to study the location of singular points and characteristics. The standard approach of the study on singular points is to find the zero points of jacobian matrix determinant. In this study a new approach to analyze the singular configuration of parallel mechanism to resolve the eigenvalue and eigenvectors of stiffness matrix. PSSP robot is analyzed by the method.

A bifurcation study of natural convection in porous media with internal heat sources: the non-Darcy effects

Multiplicity features of natural convection flow in porous media, generated and sustained by a uniform internal heat source are investigated. The flow, in a two-dimensional enclosure, is described by the Brinkman's extension of the Darcy equation. No-slip boundary conditions are used. The focus is on the role of the Brinkman viscous term in influencing the location of singular points. The behavior of the system is regulated by two control parameters, the Rayleigh number (the dynamic parameter) and the Darcy number. The singular solutions are constructed using algorithms from bifurcation theory. Multiple solutions consisting of symmetric and nonsymmetric solution branches, are revealed as the control parameters change. The range of the Rayleigh number for which a unique solution exists is enlarged when the Darcy number is increased.

Chern-Simons gauge theory on orbifolds: Open strings from three dimensions

Chern-Simons gauge theory is formulated on three-dimensional Z 2 orbifolds. The locus of singular points on a given orbifold is equivalent to a link of Wilson lines. This allows one to reduce any correlation function on orbifolds to a sum of more complicated correlation functions in the simpler theory on manifolds. Chern-Simons theory on manifolds is known to be related to two-dimensional (2D) conformal field theory (CFT) on closed-string surfaces; here it is shown that the theory on orbifolds is related to 2D CFT of unoriented closed- and open-string models, i.e. to worldsheet orbifold models. In particular, the boundary components of the worldsheet correspond to the components of the singular locus in the 3D orbifold. This correspondence leads to a simple identification of the open-string spectra, including their Chan-Paton degeneration, in terms of fusing Wilson lines in the corresponding Chern-Simons theory. The correspondence is studied in detail, and some exactly solvable examples are presented. Some of these examples indicate that it is natural to think of the orbifold group Z 2 as a part of the gauge group of the Chern-Simons theory, thus generalizing the standard definition of gauge theories.

On the structure and multipole moments of axially symmetric stationary metrics

The structure of the stationary metrics [1], generated from Laplace’s solutions as seed, is investigated. The expressions for the equatorial and polar circumferences, the surface area of the event horizon, location of singular points and the Gaussian curvatures of the metrics [1] are derived and their variations with the field parameter α0 are studied. The multipole moments are calculated with the help of coordinate invariant Geroch-Hansen technique. These investigations expose some interesting properties of the metrics, some of which are known in the literature and some deserve a new interpretation.

Multiplicity analysis of intraparticle char combustion

This study presents a detailed investigation of the steady-state multiplicity structure of the combustion of porous char particles in an environment of oxygen and nitrogen. Particular emphasis was placed on the effects of thermal radiation on the steady-state features of the problem. A shooting method and a method based on B-spline collocation were employed for the solution of the model equations and the direct location of singular points of the solution loci. Our extensive numerical computations showed that the key parameters for the appearance of multiplicity of solutions higher than three, up to five steady states, are the effective diffusivity and effective thermal conductivity in the porous medium. however, multiplicity of five steady states is found only in a rather small region of the parametric space which lies outside the domain of “feasible” parameter values for low and intermediate porosity values.

Identification of observed dynamic bifurcations and development of qualitative models

A systematic study of dynamical systems requires finding a series of bifurcation diagrams instead of just cases with different phase plane behaviour. A scheme is developed for identifying experimentally observed bifurcations (transitions) in the dynamic features of a system characterized by two state variables. Maps of experimentally found bifurcation points in a two parameter (operating conditions) plane may be used to estimate the location of singular points and their nature (defining conditions). This information may be used to predict new types of dynamic behaviour and corresponding operating conditions. Moreover, it can be used to develop a simple (qualitative) mathematical model which predicts all the observed dynamic features and transitions.

The solution of multi-parameter systems of equations with application to problems in nonlinear elasticity

Systems of nonlinear equations governed by more than one parameter are discussed with particular attention to bifurcation behaviour. The procedure adopted is to add to the original system of n equations ( m − 1) further equations, in the case of m parameters, and to seek solution curves in R n+ m to this augmented system. Two types of additional equations are considered: one describes a piecewise linear path in the space of parameters, and the second constrains the solution curve to be a locus of singular points. These ideas are all subsequently applied to the systems of equations arising from finite element approximations of boundary value problems in nonlinear elasticity. The behaviour of a nonlinear elastic thick-walled cylinder subjected to internal pressure and axial extension is discussed.

Matrix displacement mappings in the numerical solution of functional and nonlinear differential equations with the tau method

The use of matrix displacement mappings reduces most matrix operations required in the construction of an approximate solution of a functional or differential equation by means of Ortiz' formulation of the Tau method to index shifts. The coefficient vector of the approximate solution is defined implicitly by a very sparse system of linear algebraic equations. The contributions of the differential or functional operator, and of the supplementary conditions of the problem (initial, boundary, or multipoint conditions) are treated with a single and versatile procedure of remarkable simplicity, which can be easily implemented in a computer. We give two nontrivial examples on the application of this approach: the first is a nonlinear boundary value problem with a continuous locus of singular points and multiple solutions, where stiffness is present, the second is a functional differential equation arising in analytic number theory. In both cases we obtain results of nigh accuracy.

Additional note on plane congruences and fifth incidence theorems

In a recent paper I discussed plane congruences of order two in [4] and obtained congruences of types (2, 6)1, (2, 6)2, (2, 5), (2, 4) and (2, 3). The method employed was due to Segre, who showed that a plane congruence of order two in [4] has in general a curve locus of singular points which is met by each plane in five points. Then, if we can find a curve in [4], composite or not, with an ∞2 system of quadrisecant planes of which two pass through an arbitrary point, the planes must all meet a residual curve, and we shall have obtained a congruence of the second order and a fifth incidence theorem.

V. On the locus of singular points and lines which occur in connection the theory of the locus of ultimate intersections of a system of surfaces

In a paper “On the c - and p -Discriminants of Ordinary Integrable Differential Equations of the First Order,” published in vol. 19 of the ‘Proceedings of the London Mathematical Society,' the factors which occur in the c -discriminant of an equation of the form f ( x, y, c ) = 0, where f ( x, y, c ) is a rational integral function of x, y, c , are determined analytically. It is shown that if E = 0 be the equation of the envelope locus of the curves f ( x, y, c ) = 0; if N = 0 be the equation of their node-locus; if C = 0 be the equation of their cusp-locus, then the factors of the discriminant are E, N 2 , C 3 .

IV. On the locus of singular points and lines which occur in connexion with the theory of the locus of ultimate intersections of a system of surfaces

In a paper "On the c - and p -Discriminants of Ordinary Integrable Differential Equations of the First Order," published in vol. 19 of the ‘Proceedings of the London Mathematical Society,’ the factors which occur in the c -discriminant of an equation of the form f ( x, y, c ) = 0, where f ( x, y, c ) is a rational integral function of x, y, c , are determined analytically.