scholarly journals Slender-body theory for plasmonic resonance

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190294 ◽  
Author(s):  
Matias Ruiz ◽  
Ory Schnitzer
Keyword(s):  
Eigenvalue Problem ◽  
Surface Plasmon ◽  
Metallic Nanoparticles ◽  
Liouville Problem ◽  
Slender Body ◽  
Localized Surface Plasmon ◽  
Plasmonic Resonance ◽  
Slender Body Theory ◽  
Matched Asymptotics ◽  
Body Theory

We develop a slender-body theory for plasmonic resonance of slender metallic nanoparticles, focusing on a general class of axisymmetric geometries with locally paraboloidal tips. We adopt a modal approach where one first solves the plasmonic eigenvalue problem, a geometric spectral problem which governs the surface-plasmon modes of the particle; then, the latter modes are used, in conjunction with spectral-decomposition, to analyse localized-surface-plasmon resonance in the quasi-static limit. We show that the permittivity eigenvalues of the axisymmetric modes are strongly singular in the slenderness parameter, implying widely tunable, high-quality-factor, resonances in the near-infrared regime. For that family of modes, we use matched asymptotics to derive an effective eigenvalue problem, a singular non-local Sturm–Liouville problem, where the lumped one-dimensional eigenfunctions represent axial voltage profiles (or charge line densities). We solve the effective eigenvalue problem in closed form for a prolate spheroid and numerically, by expanding the eigenfunctions in Legendre polynomials, for arbitrarily shaped particles. We apply the theory to plane-wave illumination in order to elucidate the excitation of multiple resonances in the case of non-spheroidal particles.

Inviscid separated flow over a non-slender delta wing

1995 ◽  
Vol 305 ◽  
pp. 307-345 ◽  
Author(s):  
D. W. Moore ◽  
D. I. Pullin
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Delta Wing ◽  
Nonlinear Eigenvalue Problem ◽  
Vortex Sheet ◽  
Slender Body ◽  
Normal Velocity ◽  
Slender Body Theory ◽  
Closed Set ◽  
Body Theory

We consider inviscid incompressible flow about an infinite non-slender flat delta wing with leading-edge separation modeled by symmetrical conical vortex sheets. A similarity solution for the three dimensional steady velocity potential Φ is sought with boundary conditions to be satisfied on the line which is the intersection of the wing sheet surface with the surface of the unit sphere. A numerical approach is developed based on the construction of a special boundary element or ‘winglet’ which is effectively a Green function for the projection of ∇2Φ = 0 onto the spherical surface under the similarity ansatz. When the wing semi-apex angle γo is fixed satisfaction of the boundary conditions of zero normal velocity on the wing and zero normal velocity and pressure continuity across the vortex sheet then leads to a nonlinear eigenvalue problem. A method of ensuring a condition of zero lateral force on a lumped model of the inner part of the rolled-up vortex sheet gives a closed set of a equations which is solved numerically by Newton's method. We present and discuss the properties of solutions for γ0 in the range 1.30 < γ <89.50. The dependencies of these solutions on γ0 differs qualitatively from predictions of slender-body theory. In particular the velocity field is in general not conical and the similarity exponent must be calculated as part of the global eigenvalue problem. This exponent, together with the detailed flow field including the position and structure of the separated vortx sheet, depend only on γ0. In the limit of small γ0, a comparison with slender-body theory is made on the basis of an effective angle of incidence.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

Application of Slender-Body Theory

1957 ◽  
Vol 1 (04) ◽  
pp. 40-49
Author(s):  
Paul Kaplan
Keyword(s):  
Slender Body ◽  
Vertical Force ◽  
Regular Waves ◽  
Slender Body Theory ◽  
Surface Theory ◽  
Surface Ship ◽  
Submerged Body ◽  
Dynamic Forces ◽  
Body Theory

The vertical force and pitching moment acting on a slender submerged body and on a surface ship moving normal to the crests of regular waves are found by application of slender-body theory, which utilizes two-dimensional crossflow concepts. Application of the same techniques also results in the evaluation of the dynamic forces and moments resulting from the heaving and pitching motions of the ship, which corrected previous errors in other works, and agreed with the results of specialized calculations of Havelock and Has-kind. An outline of a rational theory, which unites slender-body theory and linearized free-surface theory, for the determination of the forces, moments and motions of surface ships, is also included.

A Wave Resistance Formulation for Slender Bodies at Moderate to High Speeds

2012 ◽  
Vol 56 (04) ◽  
pp. 207-214
Author(s):  
Brandon M. Taravella ◽  
William S. Vorus
Keyword(s):  
General Solution ◽  
High Speed ◽  
Near Field ◽  
Wave Resistance ◽  
Slender Body ◽  
Slender Body Theory ◽  
Rates Of Change ◽  
Order Of Magnitude ◽  
Flow Variables ◽  
Body Theory

T. Francis Ogilvie (1972) developed a Green's function method for calculating the wave profile of slender ships with fine bows. He recognized that near a slender ship's bow, rates of change of flow variables axially should be greater than those typically assumed in slender body theory. Ogilvie's result is still a slender body theory in that the rates of change in the near field are different transversely (a half-order different) than axially; however, the difference in order of magnitude between them is less than in the usual slender body theory. Typical of slender body theory, this formulation results in a downstream stepping solution (along the ship's length) in which downstream effects are not reflected upstream. Ogilvie, however, developed a solution only for wedge-shaped bodies. Taravella, Vorus, and Givan (2010) developed a general solution to Ogilvie's formulation for arbitrary slender ships. In this article, the general solution has been expanded for use on moderate to high-speed ships. The wake trench has been accounted for. The results for wave resistance have been calculated and are compared with previously published model test data.

Side Forces on a Ship’s Hull

1988 ◽  
Vol 32 (03) ◽  
pp. 203-207
Author(s):  
W. S. Hunter ◽  
P. N. Joubert
Keyword(s):  
Froude Number ◽  
Asymptotic Expansions ◽  
Experimental Results ◽  
Slender Body ◽  
Flat Plates ◽  
Slender Body Theory ◽  
Towing Tank ◽  
Side Force ◽  
Low Froude Number ◽  
Body Theory

Side forces on a ship traveling at small yaw angles are predicted using slender-body theory. The approach uses the method of matched asymptotic expansions, with a cascade of flat plates as a model for the submarine portion of the ship's hull. Resulting predictions of side force coefficients are then compared with experimentally measured values derived from towing tank tests of a typical (tanker) hull. Correlation between theoretical and experimental results was very good for yaw angles less than 8 deg at low Froude number (Fn = 0.134).

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