On second-order formulas in anisotropic stereology

1995 ◽  
Vol 27 (2) ◽  
pp. 326-343 ◽  
Author(s):  
Viktor Beneš
Keyword(s):  
Stochastic Optimization ◽  
Second Order ◽  
Surface Processes ◽  
Original Process ◽  
Order Quantities

Formulas for anisotropic stereology of fibre and surface processes are presented. They concern the relation between second-order quantities of the original process and its projections and sections. Various mathematical tools for handling these formulas are presented, including stochastic optimization. Finally applications in stereology are discussed, relating to intensity estimators using anisotropic sampling designs. Variances of these estimators are expressed and evaluated for processes with the Poisson property.

On second-order formulas in anisotropic stereology

1995 ◽  
Vol 27 (02) ◽  
pp. 326-343 ◽  
Author(s):  
Viktor Beneš
Keyword(s):  
Stochastic Optimization ◽  
Second Order ◽  
Surface Processes ◽  
Original Process ◽  
Order Quantities

Formulas for anisotropic stereology of fibre and surface processes are presented. They concern the relation between second-order quantities of the original process and its projections and sections. Various mathematical tools for handling these formulas are presented, including stochastic optimization. Finally applications in stereology are discussed, relating to intensity estimators using anisotropic sampling designs. Variances of these estimators are expressed and evaluated for processes with the Poisson property.

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.

Second-order stereology for planar fibre processes

1994 ◽  
Vol 26 (04) ◽  
pp. 906-918 ◽  
Author(s):  
V. Weiss ◽  
W. Nagel
Keyword(s):  
Second Order ◽  
Unbiased Estimators ◽  
Order Quantities ◽  
Geometric Formula

Three different stereological methods for the determination of second-order quantities of planar fibre processes which have been suggested in the literature are considered. Proofs of the formulae are given (also by using a new integral geometric formula), relations between the methods are derived and the prerequisites are discussed. Furthermore, edge-corrected unbiased estimators for the second-order quantities are given.

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.

A Comparison of Different Approximations for Computation of Second Order Roll Motions for a FLNG

2013 ◽  
Author(s):  
Flavia C. Rezende ◽  
Allan C. de Oliveira ◽  
Xiao-bo Chen ◽  
Fabio Menezes
Keyword(s):  
Gas Production ◽  
Second Order ◽  
Plant Performance ◽  
Production Plant ◽  
Surface Boundary ◽  
Natural Period ◽  
Oil Companies ◽  
First Order ◽  
Exploration And Production ◽  
Order Quantities

The use of FLNG units for gas exploration and production offshore is a subject in study by some oil companies. More complex and sophisticated than a FPSO production plant, a gas production plant has strict motion criteria in order to have an optimal operational performance. Due to this, designers have been trying hull concepts with small initial stability and higher roll motion periods in order to reduce the unit motions and improve the plant performance. Indeed, the increase of roll natural period dramatically reduces the first order roll motions. However, the unit still responds at its resonance due to second order excitation. These kinds of loads are also more complex and require a great computational power to be evaluated. Due to its complexity, which would involve the solution of a non-homogeneous free surface boundary condition, some approximations are used in order to assess the second order loads and motions. In this paper, the different formulations for the first part of QTF, contributed by first order quantities, are revisited and the differences are highlighted. Furthermore the approximations for the computation of the second part of the QTF, contributed by the second order potential, are benchmarked for the case of a FLNG operating in deep water depth.

scholarly journals On pressure perpendicular to the shear planes in finite pure shears , and on the lengthening of loaded wires when twisted

1909 ◽  
Vol 82 (557) ◽  
pp. 546-559 ◽  
Keyword(s):  
Pure Shear ◽  
Second Order ◽  
Philosophical Magazine ◽  
Order Quantities ◽  
Open Question ◽  
Definite Result ◽  
Shear Planes

In the ‘ Philosophical Magazine,' vol. 9, 1905, p. 397, I gave an analysis of the stresses in a pure shear which appeared to show that if ε is the angle of shear and if n is the rigidity, then a pressure n ε 2 exists perpendicular to the planes of shear. That analysis is, I believe, faulty in that the diagonals of the rhombus into which a square is sheared are not the lines of greatest elongation and contraction, and are not at right angles after the shear, when second order quantities are taken into account, i . e ., quantities of the order of ε 2 ; I think the following analysis is more correct, and though it does not give a definite result, it leaves the existence of a longitudinal pressure an open question. The question appears to be answered in the affirmative by some experiments, described in the second part of the paper, in which loaded wires were found to lengthen when twisted by a small amount proportional to the square of the twist. I.— Stresses in a Pure Shear . Let a square ABCD (fig. 1) of side a be sheared into EFCD by motion through AE = d , the volume being constant. The angle of shear is ADE = ε, and tan ε = d / a exactly ; neglecting ε 3 , we may put ε = d / a .

Sign in / Sign up

Export Citation Format

Share Document