Vicinity Of Poles Research Articles

Reverse buckling disks under liquid pressure and temperature

Nonlinear bending and stability of reverse buckling disks, i.e., spherical segments under the pressure of heated or cooled fluid (working environment of an explosive device) on the convex shell surface, are analyzed. The results of numerical calculations are obtained in relation to the temperature of the active environment, material properties, and segmental thinning in the pole vicinity.

Numerical Methods for Calculating Poles of the Scattering Matrix With Applications in Grating Theory

Waveguide and resonant properties of diffractive structures are often explained through the complex poles of their scattering matrices. Numerical methods for calculating poles of the scattering matrix with applications in grating theory are discussed. A new iterative method for computing the matrix poles is proposed. The method takes account of the scattering matrix form in the pole vicinity and relies upon solving matrix equations with use of matrix decompositions. Using the same mathematical approach, we also describe a Cauchy-integral-based method that allows all the poles in a specified domain to be calculated. Calculation of the modes of a metal-dielectric diffraction grating shows that the iterative method proposed has the high rate of convergence and is numerically stable for large-dimension scattering matrices. An important advantage of the proposed method is that it usually converges to the nearest pole.

On irregular oscillatory structures in resonant vibrational excitation cross-sections in diatomic molecules

We examine in detail the origin of irregular oscillatory structures in the cross-sections of low-energy resonant vibrational excitation of several diatomic molecules by electron impact. We show that these irregularities are caused by a combination of two phenomena: enhancing of the magnitude of the nuclear wave function in the vicinity of poles in the complex energy plane corresponding to quasi-bound vibrational states of the molecular anion, and energy variations of the phase of the nuclear wave function which corresponds to the reflection in the potential well of the molecular anion and which are sometimes called boomerang oscillations. These two phenomena are usually both involved in the nuclear dynamics. The former one is usually dominant at lower energies (NO molecule) and in systems where the potential energy of the molecular anion ( H 2 in high rotational states) possesses an outer potential well. The latter one dominates if the width of the quasi-bound vibrational states of the molecular anion is relatively large (e.g. at higher energies for NO and N 2 molecule, H 2 in ground state).

Interfacial debonding of a spherical inclusion embedded in an infinite medium under remote stress

In the study of strength of particle reinforced composites, it is important to understand the energy release rate due to interfacial debonding between the particle and the matrix which is induced by manufacturing imperfection. This paper is aimed at the investigation of the critical condition for growth of the interfacial debonding and the corresponding volume increase due to void formation. The model used in the study is an isotropic elastic spherical inclusion embedded in an infinite isotropic elastic matrix under remote stress. Initial axisymmetrical interfacial debondings are assumed to exist in the vicinity of poles of the spherical inclusion. Axisymmetrical deformations of the matrix and the inclusion are analyzed based on the theory of three-dimensional elasticity in spherical coordinates. In order to avoid oscillatory stress singularity at the interfacial debonding front between two dissimilar materials, a condition of free slipping without friction at the interface is imposed. A Fredholm integral equation of the first kind is formulated based on the continuity conditions in the normal components of stress and displacement at the contact interface. The kernel function of the integral equation is expressed in terms of an infinite series of Legendre functions. Two types of remote stresses are considered in this study. The first type is the remote tension in the axial direction of the spherical inclusion and the second type is the remote compression in the transverse direction with respect to the axis of the spherical inclusion. Energy release rate is determined according to the rate of change of work done by remote stresses. In this paper, energy release rate and volume of the deformed void due to debonding are computed for any given size of initial interfacial debonding.

Erratum: “Precession of a freely rotating rigid body. Inelastic relaxation in the vicinity of poles” [J. Math. Phys. 41, 1854 (2000)

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Precession of a freely rotating rigid body. Inelastic relaxation in the vicinity of poles

When a solid body is freely rotating at an angular velocity Ω, the ellipsoid of constant angular momentum, in the space Ω1,Ω2,Ω3, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from principal. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behavior, because an infinitesimally small deviation of the body’s shape from a rotational symmetry (i.e., a small difference between the largest and second largest moments of inertia) yields libration: the precession trajectory is not a circle but an ellipse. In this article we show that often the most effective internal dissipation takes place at twice the frequency of the body’s precession. Applications to precessing asteroids, cosmic-dust alignment, and rotating satellites are discussed.

Two-Body T -Matrices Without Angular-Momentum Decomposition: Energy and Momentum Dependences

The two-body t-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in forward direction. In contrast the corresponding partial wave contributions, whose number increases with increasing energy, become more and more oscillatory with increasing energy. The angular and momentum dependence of the full amplitude is studied and displayed on as well as off the energy shell as function of positive and negative energies. The behavior of the t-matrix in the vicinity of bound state poles and resonance poles in the second energy sheet is studied. It is found that the angular dependence of T exhibits a very characteristic behavior in the vicinity of those poles, which is given by the Legendre function corresponding to the quantum number either of the bound state or the resonance (or virtual) state. This behavior is illustrated with numerical examples.

A palaeomagnetic survey of South American rock formations - Palaeomagnetic studies on rock formations from Northwest Argentina

Cambrian, Cambro-Ordovician and Ordovician formations of red sandstones and siltstones from the sub-Andean regionso f the Provinces of Salta and Jujuy have been studied. The grouping of n.r.m . directions suggests partial remagnetization after folding in the Tertiary or Quaternary geomagnetic field. Thermal cleaning at 300 °C and higher temperatures destroys this secondary magnetization leaving a magnetization which is accepted as representing the lower Palaeozoic geomagnetic field. Palaeomagnetic south pole positions have been computed and lie in the Atlantic Ocean to the NNE of Brazil. The period between the Carboniferous and Triassic is covered by the Paganzo formation which is exposed in La Rioja Province. The older part (Paganzo II) is reversely magnetized with a south p.m . pole in the South Atlantic, while the upper part (Paganzo III) is normally magnetized with a south palaeomagnetic pole in the vicinity of poles obtained for Triassic rock formations from elsewhere in S. America. Formations of red beds from Salta province regarded as Upper Palaeozoic or Mesozoic yield a south palaeomagnetic pole in the South Atlantic corresponding to a Triassic age. Ore microscope and thermal decay curves suggest that the remanent magnetism is due to haematite.