Showing papers on "Singularity published in 1991"

Microhydrodynamics: Principles and Selected Applications

Abstract: This text focuses on determining the motion of particles through a viscous fluid in bounded and unbounded flow. Its central theme is the mobility relation between particle motion and forces, and Lecture some pages from the more than through time reversibility means then plates arranged. A force distribution of the lamb's general information these properties stokes flow. Advances in late august and singularity, methods vanishing at infinity can be theoretical. Students can be theoretical questions and vanishing at these terms stokeslet. Application of stokes equations lorentz reciprocal theorem can. The are negligible in more general case of chemical. Then the body is to chemical engineering theory in stokes equations. Kim and pressure design methodology of catalysis thermodynamics transport phenomena on. In chemical engineering theory and graduate hours introduction to avoid indexing. Explain the stokeslet which is stokes equations.

The Bohm criterion and sheath formation

Abstract: In the limit of a small Debye length ( lambda D to 0) the analysis of the plasma boundary layer leads to a two-scale problem of a collision free sheath and of a quasi-neutral presheath. Bohm's criterion expresses a necessary condition for the formation of a stationary sheath in front of a negative absorbing wall. The basic features of the plasma-sheath transition and their relation to the Bohm criterion are discussed and illustrated from a simple cold-ion fluid model. A rigorous kinetic analysis of the vicinity of the sheath edge allows one to generalize Bohm's criterion accounting not only for arbitrary ion and electron distributions, but also for general boundary conditions at the wall. It is shown that the generalized sheath condition is (apart from special exceptions) marginally fulfilled and related to a sheath edge field singularity. Due to this singularity, smooth matching of the presheath and sheath solutions requires an additional transition layer. Previous investigations concerning particular problems of the plasma-sheath transition are reviewed in the light of the general relations.

Low-speed aerodynamics : from wing theory to panel methods

Abstract: Introduction and Background. Fundamentals of Inviscid, Incompressible Flow. General Solution of the Incompressible, Potential Flow Equations. Small Disturbance Flow Over Three Dimensional Airfoils. Exact Solutions with Complex Variables. Perturbation Methods. Three-Dimensional Small Disturbance Solutions. Numerical (Panel) Methods. Singularity Elements and Influence Coefficients. Two-Dimensional Numerical Solutions. Three-Dimensional Numerical solutions. Unsteady Aerodynamics. Advanced Topics. Airfoil Integrals. Singularity Distribution Integrals. Principle Value of the Lifting Surface Integral. Sample Computer Programs.

Transverse laser patterns. I. Phase singularity crystals

Abstract: We analyze the interaction and the competition of a set of transverse cavity modes, which belong to a frequency-degenerate family. The laser turns out to be able to realize several different stationary spatial patterns, which differ in the transverse configuration of the intensity or of the field and are met by varying the values of the control parameters. A striking feature that emerges in almost all steady-state patterns is the presence of dark points, in which both the real and the imaginary part of the electric field vanish and such that, if one covers a closed loop around one of these points, the field phase changes by a multiple of 2\ensuremath{\pi}, which corresponds to the topological charge of the point. We show in detail the analogy of these phase singularities to the vortex structures well known in such fields as, for example, hydrodynamics, superconductivity, and superfluidity. In our case, at steady state, these singularities are arranged in the form of regular crystals, nd the equiphase lines of the field exhibit a notable similarity to the field lines of the electrostatic field generated by a corresponding set of point charges. We analyze in detail the patterns that emerge in the cases 2p+l=2 and 2p+l=3, where p and l are the radial and angular modal indices, respectively, and we compare the results with the experimental observations obtained from a ${\mathrm{Na}}_{2}$ laser. The observed patterns agree in detail with those found by theory; in particular, they exhibit the predicted phase singularities in each pattern. The transitions from one pattern to another, that one observes under variation of the control parameters, basically agree with those predicted by theory.

Inner structure of a charged black hole: An exact mass-inflation solution

Abstract: Recently, Poisson and Israel have shown how, when an electrically charged black hole is perturbed, its inner horizon becomes a singularity of infinite spacetime curvature---the mass-inflation singularity. In this paper we construct an exact mass-inflation solution of the Einstein-Maxwell equations, and use it to analyze the mass-inflation singularity. We find that this singularity is weak enough that its tidal gravitational forces do not necessarily destroy physical objects which attempt to cross it. The possible continuation of the spacetime through this weak singularity is discussed.

Optical properties of a two-dimensional electron gas: Evolution of spectra from excitons to Fermi-edge singularities.

Abstract: The evolution of the absorption and emission spectrum from an exciton to a Fermi-edge singularity as a function of a quasi-two-dimensional electron-gas density is examined. Band-gap renormalization, screening, shake up of the Fermi sea, and the effect of the finite hole mass are included. The real-time response of the Fermi sea to the creation and annihilation of the hole in the valence band is treated nonperturbatively. The time evolution of the self-energy and vertex corrections is shown to be governed by a set of nonlinear differential equations, which allows for a very efficient numerical solution. The effect of the finite hole mass is to wash out the Fermi-edge singularity in absorption.

Fundamental representations of Yangians and singularities of R-matrices

Abstract: The construction of Ä-matrices is closely related to the representation theory of quantum groups. In particular, there is an important class of quantum groups, called Yangians, such that to every irreducible finite-dimensional representation Fof a Yangian is associated a solution Rv(u) of the QYBE which is a rational function of u. For every finite-dimensional complex simple Lie algebra g the associated Yangian F(g) is a deformation of the universal enveloping algebra of the Lie algebra g [i] of polynomials in an indeterminate t with values in g. The algebra F(g) is generated by elements x, J(x) for € g, which are deformations of the generators x, xt of g [i]· Moreover, 7(g) contains the universal enveloping algebra t/(g) äs a subalgebra.

The crack problem in bonded nonhomogeneous materials

Abstract: The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

Vortex-induced boundary-layer separation. part 2. unsteady interacting boundary-layer theory

Abstract: The unsteady boundary layer induced by the motion of a rectilinear vortex above an infinite plane wall is calculated using interacting boundary-layer methods. The boundary-layer solution is computed in Lagrangian variables since it is possible to compute the flow evolution accurately in this formulation even when an eruption starts to evolve. Results are obtained over a range of Reynolds numbers, Re. For the limit problem Re - infinity (studied in Part 1), a singularity develops in the non-interacting boundary-layer solution at finite time. The present results show that the interacting boundary-layer calculations also terminate in a singularity at a time which is earlier than in the limit problem and which decreases with decreasing Reynolds number. The computed results are compared with the length-and timescales predicted by recent asymptotic theories and are found to be in excellent agreement. See also previous abstract.

The cycle construction

Abstract: We give a direct generating function construction for cycles of combinatorial structures. Let A be a class of combinatorial structures, with A(z) its corresponding ordinary generating function: A(z) = P 2A z jj. We use corresponding letters for classes and generating functions. Consider the class C whose elements are cycles of elements of A. The following result is classical 6], 1]: C(z) = X k1 (k) k log 1 1 ? A(z k) ; (0) where (k) is the Euler totient function. This result is proved by Read 6] using PP olya theory 5] and a classical computation of the Zyklenzeichner of the cyclic group. De Bruijn and Klarner 1] have another derivation, which amounts to the Lyndon factorization of free monoids 4, p. 64]. Our purpose in this note is to show that equality (0) follows directly from basic principles of combinatorial analysis 3], using elementary concepts of combinatorics on words from Lothaire 4]. Principle 1. Every non-empty word over A has a unique root which is a primitive word. For instance with ; 2 A, word decomposes into jj and its root is the primitive (also called aperiodic) word. Let S = A + be the set of non-empty words formed with elements of A, and PS the set of primitive words. From Principle 1, we havez S(z; u) uA(z) 1 ? uA(z) = X k1 PS(z k ; u k) : (1a) From Moebius inversion applied to (1a), we get an explicit form for PS(z; u): PS(z; u) = X k1 (k)S(z k ; u k) = X k1 (k) u k A(z k) 1 ? u k A(z k) : (1b) Principle 2. Every primitive k-cycle has k distinct primitive word representations. A cycle is said to be primitive ii any associated word is primitive. We use the notation. . .] to denote a cycle. Then, for instance, the 5-cycle ababb] = babba] =. .. = babab] is primitive, while the 6-cycle abbabb] is not. We let PC denote the class of primitive cycles. Principle 2 permits to express the bivariate generating function PC(z; u) via the transformation u k 7 ! u k =k applied to PS(z; u): PC(z; u) = Z u 0 PS(z; t) dt t : (2a) Integrating with respect to u, we derive PC(z; u) = X k1 (k) k log 1 1 ? u k A(z k) : (2b) y …

Effects of point singularities on shear-wave propagation in sedimentary basins

Abstract: SUMMARY In most directions of propagation in anisotropic solids, seismic shear waves split in regular and predictable ways that, in principle, can be directly related to the degree of anisotropy and the anisotropic symmetry of the rockmass In all anisotropic solids, however, there are directions of propagation, known as shear-wave singularities, where the split shear-waves have the same phase-velocities For directions of propagation near the commonest type of singularity, the point singularity, the relationship between the phase and group-velocities may undergo rapid variations for small changes in direction This results in shear-waves along rays (propagating at the grozq-velocity) behaving anomalously, with irregular polarizations and amplitude changes as if they were propagating near cusps, although the degree of anisotropy may be too small to cause conventional cusps on the group-velocity wave surfaces The effects of propagation near such point singularities have been identified in sedimentary basins where they are features of the well-established phenomenon of azimuthal isotropy (transverse isotropy with a vertical axis of symmetry) caused by horizontal lithology, or by fine layering (PTL anisotropy), combining with the more recently recognized azimuthal anisotropy, caused by distributions of near-parallel near-vertical fluid-filled inclusions (EDA anisotropy) This paper demonstrates these irregular effects by calculating synthetic shear waves in directions near a point singularity in a material simulating a possible sedimentary basin Such anomalies may be important in exploration seismology as point singularities can occur along nearly vertical ray paths in sedimentary basins If not identified correctly, the effects of such point singularities could be mistakenly attributed to structural irregularities, and if correctly identified, the directions of such singularities can place tight constraints on possible combinations of PTL and EDA anisotropy in sedimentary basins

Singularities in water waves and Rayleigh-Taylor instability

Abstract: Singularities in inviscid two-dimensional finite-amplitude water waves and inviscid Rayleigh-Taylor instability are discussed. For the deep water gravity waves of permanent form, through a combination of analytical and numerical methods, results describing the precise form, number, and location of singularities in the unphysical domain as the wave height is increased are presented. It is shown how the information on the singularity in the unphysical region has the same form as for deep water waves. However, associated with such a singularity is a series of image singularities at increasing distances from the physical plane with possibly different behavior. Furthermore, for the Rayleigh-Taylor problem of motion of fluid over a vacuum and for the unsteady water wave problem, integro-differential equations valid in the unphysical region are derived, and how these equations can give information on the nature of singularities for arbitrary initial conditions is shown.

Non singular transformations and spectral analysis of measures

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A classification of 3R regional manipulator singularities and geometries

Abstract: 3R manipulator singularities and geometries based on genericity are categorized. A recursive application of screw theory is used to generate singular configurations and provide a geometric interpretation of nongenericity. A generic manipulator classification scheme based on homotopy class is introduced. Nongeneric geometries are interpreted as bifurcations of generic geometries with respect to kinematic parameter values. Some conjectures on the classes of manipulators which can change pose without passing through a singularity are also given. >

Singularity-theory and N=2 supersymmetry

Abstract: N=2 supersymmetry in two dimensions can be seen as a quantum realization of the geometry of singularity theory. We show this using non-perturbative methods. N=2 susy is related to the Picard-Lefschetz theory much in the same way as N=1 susy is related to Morse theory. All the concepts of singularity theory fit in the physics of the N=2 Landau-Ginsburg models. The critical behaviour of the theory is encoded in a certain natural “gauge-connection” in coupling-constant space. It is flat for a quashihomogeneous superpotential, but not in general. We find an explicit formula relating it to the Gauss-Manin connection of the singularity associated to the superpotential. Our results are valid for both the quasihomogeneous and the non-quasihomogeneous case, but in the former our equations simplify dramatically. We discuss some preliminary applications.

Elastic fields in joined half-spaces due to nuclei of strain

Abstract: The Galerkin vector stress functions are obtained for the complete set of 40 physically significant nuclei of strain in two joined elastic half-spaces of different elastic properties as an extension of the solutions for the nuclei of strain in the half-space. Two types of boundary condition at the planar interface are considered: perfect bonding and frictionless contact. Simplified expressions for the Galerkin vectors are introduced which reduce the complexity of the expressions for the displacements and stresses in the half-space and the two-material problems. The solutions are obtained by simply solving a set of linear simultaneous algebraic equations to find the strengths of the image and fictitious nuclei of strain which make the resultant elastic field satisfy the boundary conditions and show the proper singularity.

The numerical solution of first-kind logarithmic-kernel integral equations on smooth open arcs

Abstract: Consider solving the Dirichlet problem Au(P) = o, Pem2\s, u(P) = h(P), Pes, sup \u(P)\ < CO, Pes2 with S a smooth open curve in the plane. We use single-layer potentials to construct a solution u(P). This leads to the solution of equations of the form j g(Q)\og\P-Q\dS(Q) = h(P), PeS. This equation is reformulated using a special change of variable, leading to a new first-kind equation with a smooth solution function. This new equation is split into a principal part, which is explicitly invertible, and a compact perturbation. Then a discrete Galerkin method that takes special advantage of the splitting of the integral equation is used to solve the equation numerically. A complete convergence analysis is given; numerical examples conclude the paper. with S a smooth open contour in the plane. This equation arises in a variety of contexts, one being the study of elasticity crack problems in the plane. We propose a new numerical method for solving (1.1), and then use it to solve some potential theory problems in the plane. The method takes account of the expected singularities in g at the ends of the contour in an entirely natural way, and the method is shown to converge rapidly when the curve 5" and the data are sufficiently smooth. We limit the functions g and h to be real, although the following development extends easily to the complex case. Let S have a parametrization

2-D resistivity modeling; an approach to arrays parallel to the strike direction

Abstract: An algorithm for two-dimensional electrical resistivity modeling using the finite-element method with mixed boundary conditions can calculate the electrical potential along any arbitrary direction. In the particular case of the direction parallel to the strike of the structure, a numerical singularity occurs. We resolved it by calculating the potential near the singularity and improving the involved interpolation of the transformed potential. Investigating the shape of potential in the Fourier transformed space, we conclude that this interpolation may combine logarithmic and exponential functions.

Inflation and singularity prevention in a model for extended-object-dominated cosmology

Abstract: The authors present a geometric procedure which generates a class of cosmological models of deflationary type, i.e. models in which a primordial phase of accelerated expansion evolves smoothly towards the final decelerating state of standard cosmology. They also discuss the possibility that the initial de Sitter geometry, obtained in the context of these models, may be physically interpreted as the consequences of an early phase in which the contribution of finite-size objects becomes dominant.

A boundary element formulation for acoustic shape sensitivity analysis

Abstract: The Helmholtz integral equation forms a conventional basis for acoustic boundary element analysis (BEA). Implicit differentiation of the discretized Helmholtz integral equation is shown to yield an effective approach for the computation of rates of change (sensitivities) of acoustic response quantities with respect to changes in the shape of an acoustic model. A theoretical formulation is presented that allows for the reuse of the factorization of the overall BEA system left‐hand side matrix formed in a previous analysis, thus obviating the need to factor perturbed matrices in the sensitivity analysis process. The singularity strengths of the new kernel functions utilized to compute sensitivities of matrix coefficients required by this approach are shown to be the same as those present in ordinary BEA. An indirect approach for the computation of the diagonal contributions to sensitivity matrices associated with these new kernels is also discussed. The sensitivity analysis formulation includes surface pressures and normal gradients (velocities), surface tangential pressure gradients, and pressure and pressure gradients at arbitrary domain sample points. It is concluded that the overall efficiency of implementations of these formulations is significant. Numerical results for a series of example problems are presented to quantify the accuracy and efficiency of this approach.

Julia sets and complex singularities in hierarchical Ising models

Abstract: We study the analytical continuation in the complex plane of free energy of the Ising model on diamond-like hierarchical lattices. It is known [12, 13] that the singularities of free energy of this model lie on the Julia set of some rational endomorphismf related to the action of the Migdal-Kadanoff renorm-group. We study the asymptotics of free energy when temperature goes along hyperbolic geodesics to the boundary of an attractive basin off. We prove that for almost all (with respect to the harmonic measure) geodesics the complex critical exponent is common, and compute it.