Generating Raking Matrices: A Fascinating Second-Order Problem

2017 ◽  
pp. 109-137
Author(s):  
Mauro Mangia ◽  
Fabio Pareschi ◽  
Valerio Cambareri ◽  
Riccardo Rovatti ◽  
Gianluca Setti
Keyword(s):  
Second Order ◽  
Order Problem

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

First and Second Order Wave-Current Interactions for Floating Bodies

2012 ◽  
Author(s):  
Charles Monroy ◽  
Yann Giorgiutti ◽  
Xiao-Bo Chen
Keyword(s):  
Field Method ◽  
Boundary Integral ◽  
Second Order ◽  
Boundary Integral Method ◽  
Diffraction Radiation ◽  
Floating Bodies ◽  
Order Problem ◽  
First Order ◽  
Wave Drift Damping ◽  
Order Quantities

The influence of current in sea-keeping problems is felt not only for first order quantities such as wave run-ups in front of the structure, but also mainly for second order quantities. In particular, the wave drift damping (which is expressed as the derivative of drift force with respect to the current) is of special interest for mooring systems. The interaction effects of a double-body steady flow on wave diffraction-radiation is studied through a decomposition of the time-harmonic potential into linear and interaction components. A boundary integral method is used to solve the first order problem. Ultimately, a far-field method is proposed to get access to second order drift forces.

Modeling the Second-Order Problem is not Easy

1990 ◽  
Vol 2 (1) ◽  
pp. 118-122 ◽  
Author(s):  
Pamela E. Oliver
Keyword(s):  
Second Order ◽  
Order Problem

Second-Order Diffraction Forces on an Array of Vertical Cylinders in Bichromatic Bidirectional Waves

1995 ◽  
Vol 117 (1) ◽  
pp. 12-18 ◽  
Author(s):  
J. H. Vazquez ◽  
A. N. Williams
Keyword(s):  
Cross Section ◽  
Finite Depth ◽  
Hydrodynamic Forces ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Order Problem ◽  
First Order ◽  
Wave Directionality ◽  
Vertical Cylinders ◽  
Green Function Approach

A complete second-order solution is presented for the hydrodynamic forces due to the action of bichromatic, bidirectional waves on an array of bottom-mounted, surface-piercing cylinders of arbitrary cross section in water of uniform finite depth. Based on the constant structural cross section, the first-order problem is solved utilizing a two-dimensional Green function approach, while an assisting radiation potential approach is used to obtain the hydrodynamic loads due to the second-order potential. Results are presented which illustrate the influence of wave directionality on the second-order sum and difference frequency hydrodynamic forces on a two-cylinder array. It is found that wave directionality may have a significant influence on the second-order hydrodynamic forces on these arrays and that the assumption of unidirectional waves does not always lead to conservative estimates of the second-order loading.

scholarly journals Existence of Multiple Solutions for Second-Order Problem with Stieltjes Integral Boundary Condition

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Qing-Qing Hu ◽  
Baoqiang Yan
Keyword(s):  
Boundary Condition ◽  
Variational Method ◽  
Multiple Solutions ◽  
Order Equation ◽  
Second Order ◽  
Integral Boundary Condition ◽  
Stieltjes Integral ◽  
Order Problem ◽  
Integral Boundary ◽  
Critical Point Theorem

In this paper, we consider the existence of multiple solutions for second-order equation with Stieltjes integral boundary condition using the three-critical-point theorem and variational method. Firstly, a novel space is established and proved to be Hilbert one. Secondly, based on the above work, we obtain the existence of multiple solutions for our problem. Finally, in order to illustrate the effectiveness of our problem better, the example is listed.

The Von Neumann-Mullins Theory of Grain Growth – Valid or Not?!

2004 ◽  
Vol 467-470 ◽  
pp. 1111-1116 ◽  
Author(s):  
Lasar S. Shvindlerman ◽  
Günter Gottstein ◽  
Anthony D. Rollett
Keyword(s):  
Relative Rate ◽  
Second Order ◽  
Rate Of Change ◽  
Recent Analysis ◽  
Order Problem ◽  
Von Neumann ◽  
First Order ◽  
Dimensional Network ◽  
The Stability ◽  
Grain Topology

We present a new analysis of the relative rate of growth or shrinkage of grains in a two-dimensional network, based on the classical Von Neumann-Mullins (VN-M) analysis. We find that an analysis of the stability of the grain shape during shrinkage or growth shows that any change in the regular 2D grain leads to changes in the shape. We also re-examine a recent analysis that claims to have invalidated the VN-M relationship, but find that it is still valid, and that the cited analysis, in fact, confused a second order correction with a first order problem, partly because their derivation was in error. The erroneous magnitude of the discrepancy led them to use unphysical issues to explain the discrepancy. The way in which the curvature is distributed along the perimeter of a grain only gives rise only to second order corrections to the rate of change of area as a function of grain topology (number of sides).

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