Comparison of the Rayleigh and T‐matrix theories of scattering of sound from an elastic shell

Abstract The scattering of plane steady-state sound waves from a viscous fluid-filled thin cylindrical shell weak- ened by a long linear slit and submerged in an ideal fluid is studied. For the description of vibrations of elastic objects the Kirchhoff-Love shell-theory approximation is used. An exact solution of this problem is obtained in the form of series with cylindrical harmonics. The numerical analysis is carried out for a steel shell filled with oil and immersed in seawater. The modules and phases of the scattering amplitudes versus the dimensionless wavenumber of the incident sound wave as well as directivity patterns of the scattered field are investigated taking into consideration the orientation of the slit on the elastic shell surface. The plots obtained show a considerable influence of the slit and viscous fluid filler on the diffraction process.

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T-Matrix Simulation of Plasmon Resonances of Particles on or near a Surface

PIERS Online ◽

10.2529/piers050906085003 ◽

2006 ◽

Vol 2 (5) ◽

pp. 450-454

Author(s):

Norbert Riefler ◽

Thomas Wriedt

Keyword(s):

Plasmon Resonances ◽

T Matrix

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ASYMPTOTIC BEHAVIOR OF TWO-PARTICLE T-MATRIX ELEMENTS IN CONTINUOUS AND DISCRETE SPECTRAL REGIONS

Izvestia Ufimskogo Nauchnogo Tsentra RAN ◽

10.31040/2222-8349-2020-0-3-17-22 ◽

2020 ◽

Vol 0 (3) ◽

pp. 17-22

Author(s):

R.F. AKHMETYANOV ◽

◽

E.S. SHIKHOVTSEVA ◽

Keyword(s):

Asymptotic Behavior ◽

Matrix Elements ◽

T Matrix

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Systems with Condensates and Pairing

10.1093/oso/9780198797241.003.0012 ◽

2018 ◽

Author(s):

Klaus Morawetz

Keyword(s):

Critical Parameters ◽

Einstein Condensation ◽

Cooper Pairs ◽

Pair Breaking ◽

Systematic Theory ◽

Bose Einstein Condensation ◽

T Matrix ◽

The Stability ◽

Bose Einstein

The Bose–Einstein condensation and appearance of superfluidity and superconductivity are introduced from basic phenomena. A systematic theory based on the asymmetric expansion of chapter 11 is shown to correct the T-matrix from unphysical multiple-scattering events. The resulting generalised Soven scheme provides the Beliaev equations for Boson’s and the Nambu–Gorkov equations for fermions without the usage of anomalous and non-conserving propagators. This systematic theory allows calculating the fluctuations above and below the critical parameters. Gap equations and Bogoliubov–DeGennes equations are derived from this theory. Interacting Bose systems with finite temperatures are discussed with successively better approximations ranging from Bogoliubov and Popov up to corrected T-matrices. For superconductivity, the asymmetric theory leading to the corrected T-matrix allows for establishing the stability of the condensate and decides correctly about the pair-breaking mechanisms in contrast to conventional approaches. The relation between the correlated density from nonlocal kinetic theory and the density of Cooper pairs is shown.

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Target metric and Shell Shaping

Curved and Layered Structures ◽

10.1515/cls-2021-0002 ◽

2021 ◽

Vol 8 (1) ◽

pp. 13-25

Author(s):

Gloria Rita Argento ◽

Stefano Gabriele ◽

Luciano Teresi ◽

Valerio Varano

Keyword(s):

Elastic Energy ◽

Elastic Shell ◽

The Other ◽

The One

Abstract We exploit the possibility of deforming a shell by assigning a target metric, which, for 2D structures, is decomposed into the first and second target fundamental-forms. As well known, an elastic shell may change its shape under two different kinds of actions: one are the loadings, the other one are the distortions, also known as the pre-strains. Actually, the target fundamental forms prescribe a sought shape for the solid, and the metric effectively realized is the one that minimizes the distance, measured through an elastic energy, between the target and the actual fundamental forms. The proposed method is very effective in deforming shells.

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An Incompressible Polymer Fluid Interacting with a Koiter Shell

Journal of Nonlinear Science ◽

10.1007/s00332-021-09678-5 ◽

2021 ◽

Vol 31 (1) ◽

Author(s):

Dominic Breit ◽

Prince Romeo Mensah

Keyword(s):

Moving Boundary ◽

Classical Model ◽

Elastic Shell ◽

Planck Equation ◽

Navier Stokes ◽

Flexible Shell ◽

Navier Stokes Equation ◽

Shell System ◽

Forward Equation ◽

Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

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