The Representation of Ship Hulls by Conformal Mapping Functions: Fractional Maps

1983 ◽  
Vol 27 (03) ◽  
pp. 158-159
Author(s):  
C. von Kerczek
Keyword(s):  
Conformal Mapping ◽  
Cross Sections ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Longitudinal Direction ◽  
Interpolation Scheme ◽  
Mapping Functions ◽  
Ship Hulls ◽  
The Cross ◽  
High Degree

The method for analytically representing ship hulls by conformal mapping functions of the cross sections and lengthwise polynomial interpolation of the mappings, which was developed by von Kerczek and Tuck [1], has found useful applications to ship hydrodynamics (see references [2] and [3]) as well as ship design [4]. In both such applications, however, there have been two major criticisms of this type of representation of the underwater portion of the ship hull. The first criticism concerned the occurrence of undesirable waviness in the longitudinal direction of the cross sections of the ship. This waviness is due to fitting high-degree polynomials to very slowly varying data. This defect of the surface representation can be removed easily by abandoning the polynomial interpolation and substituting some form of spline interpolation. It has been found that interpolation by simple Hermite cubic splines works very well. Such modifications of the lengthwise interpolation scheme are well known and need no elaboration.

The Representation of Ship Hulls by Conformal Mapping Functions

1969 ◽  
Vol 13 (04) ◽  
pp. 284-298
Author(s):  
C. von Kerczek ◽  
E. O. Tuckk
Keyword(s):  
Conformal Mapping ◽  
Cross Sections ◽  
Design Procedure ◽  
Mapping Function ◽  
Polynomial Functions ◽  
Mapping Functions ◽  
Ship Hulls ◽  
Longitudinal Coordinate ◽  
Hydrodynamic Calculations ◽  
Hull Design

A method is described by which an arbitrary hull surface may be approximated by ananalytic function. The cross sections of the ship are represented by conformal mapping functions whose coefficients are polynomial functions of the longitudinal coordinate of the ship. Such a representation is intended to be used primarily for hydrodynamic calculations. However, the procedure used in generating the mapping function representation of the hull surface can, with some slight modifications, be used to freely form a hull surface. This could possibly be the basis of a mathematical hull design procedure.

Streamlines and Pressure Distribution on Arbitrary Ship Hulls at Zero Froude Number

1968 ◽  
Vol 12 (03) ◽  
pp. 231-236
Author(s):  
E. O. Tuck ◽  
C. von Kerczek
Keyword(s):  
Conformal Mapping ◽  
Froude Number ◽  
Potential Flow ◽  
Hydrodynamic Pressure ◽  
Polynomial Functions ◽  
Forward Motion ◽  
Mapping Functions ◽  
Ship Hulls ◽  
Longitudinal Coordinate ◽  
Quantities Of Interest

A method is presented for computing the streamlines and the hydrodynamic pressure along the streamlines on a slender ship in steady forward motion at zero Froude number. The ship is represented by conformal mapping functions whose coefficients are polynomial functions of the longitudinal coordinate of the ship. The potential flow about the ship is obtained in terms of the coefficients of the surface equation of the ship and all flow quantities of interest are computed directly from these coefficients.

High Order Cubic-Polynomial Interpolation Schemes on Triangular Meshes

2012 ◽  
Vol 12 (5) ◽  
pp. 1588-1602
Author(s):  
Renzhong Feng
Keyword(s):  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
High Order ◽  
Triangular Meshes ◽  
Interpolation Scheme ◽  
Irregular Domains ◽  
Numerical Examples ◽  
Cubic Polynomial ◽  
Interpolation Techniques

Abstract The Cubic-Polynomial Interpolation scheme has been developed and applied to many practical simulations. However, it seems the existing Cubic-Polynomial Interpolation scheme are restricted to uniform rectangular meshes. Consequently, this scheme has some limitations to problems in irregular domains. This paper will extend the Cubic-Polynomial Interpolation scheme to triangular meshes by using some spline interpolation techniques. Numerical examples are provided to demonstrate the accuracy of the proposed schemes.

scholarly journals The capture of neutrons by deuterons

1948 ◽  
Vol 192 (1029) ◽  
pp. 156-166 ◽  
Keyword(s):  
Magnetic Dipole ◽  
Cross Section ◽  
Cross Sections ◽  
Group Structure ◽  
Wave Functions ◽  
Fast Neutrons ◽  
Dipole Radiation ◽  
Exchange Character ◽  
The Cross ◽  
High Degree

The cross-sections for capture of neutrons by deuterons, involving emission of both electric and magnetic dipole radiation, are calculated using the wave functions obtained by Buckingham & Massey (1941) in the course of an application of the resonating-group structure method to the elastic scattering of neutrons by deuterons. The value found for capture of neutrons with emission of magnetic dipole radiation is found to be very sensitive to the particular form taken for the various wave functions, owing to a very high degree of cancellation that occurs in the integrations. As a result it is out of the question at present to provide accurate theoretical values for this process. All that can be said is that the cross-section for capture of thermal neutrons by deuterons is likely to be abnormally small. It may well be 10 -28 cm. 2 or less. This is in general agreement with observation. For capture of fast neutrons with emission of electric dipole radiation there is much less uncertainty in the calculated values although the cross-sections are very small, of the order of a few times 10 -29 cm. 2. The actual value of the cross-section in this case depends on the assumed type of nucleonic interaction, i.e. whether it is of exchange character or not. Results are also given for the inverse process—the photodisintegration of the triton.

The cross sections for different channels in heavy ion nuclear reactions

1971 ◽  
Vol 32 (1) ◽  
pp. 7-9 ◽  
Author(s):  
J. Galin ◽  
D. Guerreau ◽  
M. Lefort ◽  
X. Tarrago
Keyword(s):  
Cross Sections ◽  
Nuclear Reactions ◽  
Heavy Ion ◽  
The Cross

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

scholarly journals Total cross sections of eγ → $$ eX\overline{X} $$ processes with X = μ, γ, e via multiloop methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Roman N. Lee ◽  
Alexey A. Lyubyakin ◽  
Vyacheslav A. Stotsky
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Elliptic Integral ◽  
High Energy ◽  
Calculation Methods ◽  
Complete Elliptic Integral ◽  
Total Cross Sections ◽  
Multiloop Calculation ◽  
The Cross ◽  
Analytical Expressions

Abstract Using modern multiloop calculation methods, we derive the analytical expressions for the total cross sections of the processes e−γ →$$ {e}^{-}X\overline{X} $$ e − X X ¯ with X = μ, γ or e at arbitrary energies. For the first two processes our results are expressed via classical polylogarithms. The cross section of e−γ → e−e−e+ is represented as a one-fold integral of complete elliptic integral K and logarithms. Using our results, we calculate the threshold and high-energy asymptotics and compare them with available results.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

ISOSPIN DECOMPOSITION OF pp → NNππ CROSS SECTIONS — DO WE SEE A SIGN OF Δ(1600) EXCITATION IN THE nnπ+π+ CHANNEL?

2009 ◽  
Vol 24 (02n03) ◽  
pp. 450-453
Author(s):  
◽  
T. SKORODKO ◽  
M. BASHKANOV ◽  
D. BOGOSLOWSKY ◽  
H. CALÉN ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Pion Production ◽  
Significant Contribution ◽  
Differential Cross Sections ◽  
Pp Collisions ◽  
Theoretical Predictions ◽  
Order Of Magnitude ◽  
The Cross

The two-pion production in pp-collisions has been investigated in exclusive measurements from threshold up to Tp = 1.36 GeV . Total and differential cross sections have been obtained for the channels pnπ+π0, ppπ+π-, ppπ0π0 and also nnπ+π+. For intermediate incident energies Tp > 1 GeV , i.e. in the region, which is beyond the Roper excitation but at the onset of ΔΔ excitation the total ppπ0π0 cross section falls behind theoretical predictions by as much as an order of magnitude near 1.2 GeV, whereas the nnπ+π+ cross section is a factor of five larger than predicted. A model-unconstrained isospin decompostion of the cross section points to a significant contribution of an isospin 3/2 resonance other than the Δ(1232). As a possible candidate the Δ(1600) is discussed.

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