Three-dimensional, shock-on-shock interaction problem

This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number of quasi-periodic incident acoustic waves. The proposed method depends only on a fundamental a priori estimate established for the acoustic and elastic wave fields and a new mixed-reciprocity relation established in this paper for the solutions of the fluid-solid interaction scattering problem.

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Integral transforms for shock-shock interaction — Three dimensional planar wings

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/bf01595563 ◽

1969 ◽

Vol 20 (2) ◽

pp. 244-260 ◽

Cited By ~ 1

Author(s):

Narendra L. Arora

Keyword(s):

Three Dimensional ◽

Integral Transforms ◽

Shock Interaction

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Existence for a Three-Dimensional Steady State Fluid-Structure Interaction Problem

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-002-8536-9 ◽

2002 ◽

Vol 4 (1) ◽

pp. 76-94 ◽

Cited By ~ 37

Author(s):

C. Grandmont

Keyword(s):

Steady State ◽

Fluid Structure Interaction ◽

Three Dimensional ◽

Fluid Structure ◽

Structure Interaction ◽

Interaction Problem

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EFFECTIVE DIPOLE-RADIATION-FIELD THEORY I: ONE-DIMENSIONAL OSCILLATOR BEYOND STANDARD COUPLING

International Journal of Modern Physics B ◽

10.1142/s0217979294000944 ◽

1994 ◽

Vol 08 (17) ◽

pp. 2307-2325 ◽

Cited By ~ 1

Author(s):

H. DEKKER

Keyword(s):

Dimensional Space ◽

Three Dimensional ◽

Dipole Interaction ◽

Quantum Mechanical ◽

Renormalization Procedure ◽

One Dimensional ◽

Dipole Radiation ◽

Consistent Treatment ◽

Interaction Problem ◽

Three Dimensional Space

A novel generalization is given of the standard dipole interaction between a charged particle and the electromagnetic field in the radiation gauge. The resulting nonlinear interaction problem is statistically linearized. The ensuing dynamics is solved exactly for a harmonically bound nonrelativistic electron in a finite region of three-dimensional space. The solution involves a generalized renormalization procedure and is free of runaway modes. The theory is particularly suited for a self-consistent treatment of the system's quantum mechanics. As a consequence of the generalized coupling an earlier noted ultraviolet quantum mechanical divergence is absent.

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Soil–pipeline interaction along unstable slopes: a coupled three-dimensional approach. Part 1: Theoretical formulation

Canadian Geotechnical Journal ◽

10.1139/t09-028 ◽

2009 ◽

Vol 46 (11) ◽

pp. 1289-1304 ◽

Cited By ~ 27

Author(s):

Giuseppe Cocchetti ◽

Claudio di Prisco ◽

Andrea Galli ◽

Roberto Nova

Keyword(s):

Piecewise Linear ◽

Three Dimensional ◽

Linear Formulation ◽

Constitutive Relationship ◽

Dimensional Approach ◽

Theoretical Formulation ◽

State Of Stress ◽

Displacement Profile ◽

Interaction Problem ◽

Soil Movements

Pipelines buried along potentially unstable slopes are often monitored because soil movements can induce an evolution of the state of stress within the pipe that can eventually result in the loss of the serviceability of the system or even in its failure. In the present paper, the pipeline is discretised by means of a series of three-dimensional beam finite elements and the soil–pipeline interaction is reproduced by means of macroelements independent from each other, but characterized by a failure condition in which coupling among the different loading components is taken into account. The soil–pipeline interaction problem is formulated by accounting for the geometry of the slope, the soil and pipe mechanical properties, and the imposed soil displacement profile. A convenient piecewise linear formulation for the macroelement constitutive relationship is adopted and a large displacements scheme is also formulated.

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