Showing papers on "Asymptotic analysis published in 1972"

Compressible corner flow

Abstract: The viscous compressible flow in the vicinity of a right-angle corner, formed by the intersection of two perpendicular flat plates and aligned with the free stream, is investigated. In the absence of viscous-inviscid interactions and imbedded shock waves, a theory is developed that is valid throughout the subsonic and supersonic Mach number range. Within this limitation and the additional assumptions of unit Prandtl number and a linear viscosity-temperature law, a consistent set of governing equations and boundary conditions is derived. The method of matched asymptotic expansions is applied in order to distinguish the relevant regions in the flow field.In the corner region the Crocco integral is shown to apply, even for a three-dimensional flow field. The equations governing the flow in the corner layer consist of four coupled nonlinear elliptic partial differential equations of the Poisson variety. Since they do not lend themselves to analytic solution, numerical methods are employed. Two such methods used here are the Gauss-Seidel explicit technique and the alternating direction implicit method. The merits of both techniques are discussed with regard to convergence rate, accuracy and stability. The calculations show that in cases where the Gauss-Seidel method fails to give converged solutions, owing to instability, the alternating direction implicit method does provide converged solutions. However, in cases where both methods are convergent, there is no appreciable difference in convergence rates. The numerical calculations were done on a CDC 6600 computer.Results of calculations are presented for representative compressible-flow conditions. The extent of the corner disturbance is controlled by the Mach number and wall temperature ratio in a manner analogous to the two-dimensional boundary layer. A swirling motion is noted in the corner layer which is influenced to a great extent by the asymptotic cross-flow profiles. The skin-friction coefficient is shown to increase monotonically from zero at the corner point to its asymptotic two-dimensional value. For cold wall cases, this value is approached more rapidly. The asymptotic analysis indicates that for even colder wall cases, not considered here, an overshoot is possible.

Asymptotic expansion of integrals occurring in linear wave theory

Abstract: The asymptotic expansion of an integral of the type [formula omitted], is derived in terms of the large parameter t. Functions Φ(k) and ψ(k) are assumed analytic, and ψ(k) may have zeros at a stationary phase point. The usual one dimensional stationary phase and Airy integral terms are found as special cases of a more general result. The result is used to find the leading term of the asymptotic expansion of the double integral. A particular two dimensional Φ(k) relevant to surface water wave problems is considered in detail, and the order of magnitude of the integral is shown to depend on the nature of ψ(k) at the stationary phase point.

The Shallow Arch—General Buckling, Postbuckling, and Imperfection Analysis∗

Abstract: A general discussion of the behavior of the shallow circular arch is presented. It is shown that, irrespective of specific loading or boundary conditions, it is possible to arrive at general conclusions regarding buckling, postbuckling, and imperfection sensitivity. General methods of analysis are established which lead to the determination of points of bifurcation and of postbuckling paths under symmetric loads. Modifications accounting for antisymmetric load components are introduced, with special emphasis on their asymptotic and limit load effect. A typical numerical example is carried through in detail. The solution is “exact” in the sense of shallow arch theory. Its asymptotic behavior conforms to the asymptotic theory of Koiter.

Time-Domain Techniques for Measuring the Conductivity and Permittivity Spectrum of Materials

Abstract: A method is presented for evaluating the conductivity and permittivity spectrum of materials by using time-domain reflectometry. A theoretical analysis of the transient response is made, with emphasis on the asymptotic behavior for large values of time. The results of the asymptotic analysis are the basis of the presented method and are essential for the evaluation of the permittivity spectrum of conductive materials. Quite satisfactory experinental results are presented.

Asymptotic Behavior of Vacuum Space-Times

Abstract: Newman and Penrose have given conditions on the asymptotic form of the Weyl tensor in empty space‐time that are sufficient to insure that the space‐time is asymptotically flat at null infinity and has the peeling property. We give considerably weaker conditions and show them to be sufficient for asymptotic flatness. Under the weaker conditions the asymptotic behavior of the Weyl tensor is more general than the case where the peeling property holds. The asymptotic dependence on a suitably defined radial coordinate is given for the basis null tetrad, the spin coefficients, and the tetrad components of the Weyl tensor.

Asymptotic expansions of double-continuum Coulomb wavefunction

Abstract: Various forms of the asymptotic expansion of the wavefunction describing two outgoing electrons in the field of the nucleus are considered for a simple model problem. The connection with the asymptotic behaviour of the Fourier expansion is determined. Numerical calculations are carried out to determine the region where the asymptotic expansion becomes valid.

Skyrme's interaction in the asymptotic basis

Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Skyrme’s interaction in the asymptotic basis P. Quentin

On asymptotic behavior of perturbed nonlinear systems

Abstract: A version of the variation of constants formula for nonlinear systems is used to study the comparative asymptotic behavior of the systems x'=f(t, x) and y'=f(t, y)+g(t, y).

The rate of convergence in limit theorems for service systems with finite queue capacity

Abstract: The paper deals with the asymptotic analysis of waiting time distribution for service systems with finite queue capacity. First an M/MIm system is considered and the rate of approximation is given. Then the case of the M/G/1 system is studied for traffic intensity p > 1. In the last section a condition is given under which an estimate can be derived for the remainder term in central limit theorems for randomly stopped sums. QUEUEING THEORY; SERVICE SYSTEM WITH FINITE CAPACITY; CENTRAL LIMIT THEOREM; RANDOMLY STOPPED SUMS; RATE OF CONVERGENCE

Variable Mesh Numerical Method for Solving the Orr-Sommerfeld Equation

Abstract: A numerical method using a nonuniform mesh spacing has been developed for solving the Orr‐Sommerfield equation and has been used to explore a puzzling detail in the curve of neutral stability at large values of the Reynolds number. The numerical method consists of the usual finite‐difference method, an automatically determined variable mesh, and a modified eigenvalue‐search‐procedure. For plane Poiseuille flow it is demonstrated that the kink in the curve of neutral stability is a feature of solutions of the Orr‐Sommerfeld equation and not just a deficiency in the asymptotic analysis as previously suggested.

On the Asymptotic Behavior of Certain Dynamical Systems

Abstract: The asymptotic behavior at large times for certain dynamical systems arising in the Hamiltonian formulation of classical mechanics is investigated. It is shown that for potentials which die out sufficiently fast at large distances the unbounded states of the system are asymptotically free. This result complements the corresponding result for quantum mechanical systems, and is obtained by analogous methods. In addition, the existence, differentiability, and asymptotic completeness of the associated wave mappings is established under appropriate further assumptions by classical methods.

Progress in nonlinear finite element analysis using asymptotic solution techniques.

Abstract: The existence of standard forms of finite element equations for nonlinear analysis is observed. These are noted to provide a sufficiently special circumstance to admit the construction of asymptotic solution techniques. Although efforts in this direction have been made only recently, a number of distinct approaches to asymptotic solution techniques for finite element analysis have been put forward and are examined herein. Consideration is given to the differences and similarities of the approaches and the resulting methods of solution. Special characteristics regarding applicability, accuracy and efficiency are delineated.

Short-wave asymptotic behaviour of the solution of the problem of diffraction by a circular disk

Abstract: A METHOD making it possible to obtain and rigorously justify the short-wave asymptotic solution of the scalar problem of the diffraction by an ideally rigi4 infinitely thin, circular disk of a plane wave normally incident on it is presented.

An asymptotic fundamental solution of the reduced wave equation on a surface

Abstract: The physical problem of steady-state heat conduction in a thin shell is described by the \"reduced wave equation\" in which the differential operator is the (generally noneuclidean) Laplacian for the surface. A similar equation gives the approximation for steady-state waves in a prestressed curved membrane. A modification of the \"geometric optics\" asymptotic expansion, involving a Bessel function, is given for the fundamental point source solution. This is proven to be uniformly valid in the large, until a \"caustic\" is reached. Various features of the solution for a surface, which do not occur for the plane, are discussed.

Asymptotic behaviour of the chain molecule distribution function

Abstract: An asymptotic expansion for the distribution density Wz of the length h of a freely jointed polymer chain neglecting volume effects is derived up to order Z-2; Z-1 is the number of chain bonds. The derivation is performed on the basis of the exact Chandrasekhar form of this distribution. The relationship between the asymptotic expansion and the original and amended Langevin distribution has been found as well as the values of these distributions for h = 0. These values lead in turn to a better agreement of the approximations with the exact distribution than do the values determined from normalizing conditions. Further, the relationship of asymptotics to the gaussian distribution is shown and the range of its applicability is determined. In this way the topic of the exact distribution and its approximation is completed.

On the asymptotic expansion of green's function for the heat conduction equation with small parameter

Abstract: This work is devoted to an investigation of the asymptotic expansion for α→0 of Green's function Γ(x, t; x0) for the first boundary value problem for the equation Γt(x, t; x0) = α2 Γxx(x, t; x0) for the case of a moving boundary. The asymptotic expansion is obtained by means of a modification of the method of heat potentials. Bibliography: 5 items.