POLAR-SYMMETRIC PROBLEM OF ELASTIC DIFFUSIONFOR A MULTICOMPONENT MEDIUM

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

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The Classical-to-Semiclassical Connection

Rays, Waves, and Scattering ◽

10.23943/princeton/9780691148373.003.0021 ◽

2017 ◽

Author(s):

John A. Adam

Keyword(s):

Electromagnetic Waves ◽

Wave Radiation ◽

Physical Optics ◽

Incident Plane Wave ◽

Potential Well ◽

Intermediate Region ◽

Symmetric Problem ◽

Classical Domain ◽

Incident Plane ◽

Semiclassical Scattering

This chapter discusses the connection between the classical and semiclassical domains of scattering. Scattering phenomena may be described via three regimes: the scattering of waves by objects with small, large, or comparable sizes with the wavelength of the incident (plane wave) radiation. All three regions can be related to three domains: the classical domain (geometrical optics, particle and particle/ray-like trajectories); the wave domain (physical optics, acoustic and electromagnetic waves, quantum mechanics); and the semiclassical domain (the vast intermediate region between the first and second domain). The chapter first provides an overview of classical and semiclassical scattering domains before beginning with an analysis of the semiclassical formulation. It also considers the radial equation, scattering by a one-dimensional potential barrier, and the radially symmetric problem. Solutions for phase shifts and the potential well are presented.

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4D STATIC SOLUTIONS WITH INTERACTING PHANTOM FIELDS

International Journal of Modern Physics D ◽

10.1142/s0218271808013753 ◽

2008 ◽

Vol 17 (11) ◽

pp. 2125-2142 ◽

Cited By ~ 5

Author(s):

VLADIMIR DZHUNUSHALIEV ◽

VLADIMIR FOLOMEEV

Keyword(s):

Scalar Fields ◽

Spherically Symmetric ◽

Symmetric Problem ◽

Regular Solutions ◽

Traversable Wormhole ◽

Static Solutions ◽

Static Models ◽

Phantom Fields

Three static models with two interacting phantom and ghost scalar fields are considered: a model of a traversable wormhole, a branelike model and a spherically symmetric problem. It is shown numerically that regular solutions exist for all three cases.

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