scholarly journals CORRELATION OF WATER LEVEL VARIATIONS WITH WAVE FORCES ON A VERTICAL PILE FOR NONPERIODIC WAVES

2011 ◽  
Vol 1 (6) ◽  
pp. 46
Author(s):  
Robert O. Reid
Keyword(s):  
Fixed Point ◽  
Velocity Field ◽  
Circular Cylinder ◽  
Water Level ◽  
Linear Combination ◽  
The Other ◽  
Wave Forces ◽  
Independent Functions ◽  
Serial Sequences ◽  
Water Level Variations

This paper describes the design and application of numerical transforms for the estimation of the field of motion associated with irregular, nonperiodic surface waves from measured serial sequences of water level at a fixed point. The design of these transforms is based upon the linear theory for long-crested waves. The method is applied in the analysis of wave forces exerted upon a vertical circular cylinder, where the measured reaction is considered to be expressible as a linear combination of two independent functions of time. One of these functions depends (nonlinearly) upon the velocity field, the other depends (linearly) upon the acceleration field. The covariance of these functions with the measured reaction allows a direct means of evaluation of the drag and inertial coefficients for the cylinder.

scholarly journals WAVE FORCES INDUCED BY IRREGULAR WAVES ON A VERTICAL CIRCULAR CYLINDER

1978 ◽  
Vol 1 (16) ◽  
pp. 144 ◽  
Author(s):  
Hajime Ishida ◽  
Yuichi Iwagaki
Keyword(s):  
Circular Cylinder ◽  
Laboratory Experiments ◽  
Large Diameter ◽  
Small Diameter ◽  
Diffraction Theory ◽  
Irregular Waves ◽  
Wave Forces ◽  
Irregular Wave ◽  
Water Level Variations ◽  
Particle Velocities

In order to examine the irregular wave forces on a small diameter cylinder, laboratory experiments have been conducted on water particle velocities and wave forces with various kinds of irregular waves. As the results, it is indicated that the time variation and the spectral distribution of wave forces can be calculated adequately from the water level variations by using the methods proposed by Reid1' and Borgman2' respectively. Moreover, with respect to the irregular wave forces on a large diameter cylinder, a new calculation method was shown by means of applying Reid's linear filters1' to MacCamy and Fuchs's diffraction theory.

scholarly journals On the Recurrence Properties of Narayana’s Cows Sequence

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 149
Author(s):  
Xin Lin
Keyword(s):  
Linear Combination ◽  
The Other ◽  
Other Hand ◽  
Computation Formula ◽  
The One

In this paper, we consider the recurrence properties of two generalized forms of Narayana’s cows sequence. On the one hand, we study Narayana’s cows sequence at negative indices and express it as the linear combination of the sequence at positive indices. On the other hand, we study the convolved Narayana number and obtain a computation formula for it.

scholarly journals Well-definedness and observational equivalence for inductive–coinductive programs

2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen
Keyword(s):  
Fixed Point ◽  
Modal Logic ◽  
The Other ◽  
Observational Equivalence ◽  
Other Hand ◽  
Inductive Types ◽  
Point Types ◽  
Usual Topology

Abstract We define notions of well-definedness and observational equivalence for programs of mixed inductive and coinductive types. These notions are defined by means of tests formulas which combine structural congruence for inductive types and modal logic for coinductive types. Tests also correspond to certain evaluation contexts. We define a program to be well-defined if it is strongly normalizing under all tests, and two programs are observationally equivalent if they satisfy the same tests. We show that observational equivalence is sufficiently coarse to ensure that least and greatest fixed point types are initial algebras and final coalgebras, respectively. This yields inductive and coinductive proof principles for reasoning about program behaviour. On the other hand, we argue that observational equivalence does not identify too many terms, by showing that tests induce a topology that, on streams, coincides with usual topology induced by the prefix metric. As one would expect, observational equivalence is, in general, undecidable, but in order to develop some practically useful heuristics we provide coinductive techniques for establishing observational normalization and observational equivalence, along with up-to techniques for enhancing these methods.

A modified Runge-Kutta method

SIMULATION ◽  
1968 ◽  
Vol 10 (5) ◽  
pp. 221-223 ◽  
Author(s):  
A.S. Chai
Keyword(s):  
Error Estimate ◽  
Linear Combination ◽  
Experimental Results ◽  
The Other ◽  
New Method ◽  
Kutta Method ◽  
Starting Values ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
A Minor

It is possible to replace k2 in a 4th-order Runge-Kutta for mula (also Nth-order 3 ≤ N ≤ 5) by a linear combination of k1 and the ki's in the last step, using the same procedure for computing the other ki's and y as in the standard R-K method. The advantages of the new method are: It re quires one less derivative evaluation, provides an error estimate at each step, gives more accurate results, and needs a minor change to switch to the RK to obtain the starting values. Experimental results are shown in verification of the for mula.

A Yield Criterion of Porous Materials With Anisotropy Caused by Geometry or Distribution of Pores

1991 ◽  
Vol 113 (4) ◽  
pp. 425-429 ◽  
Author(s):  
T. Hisatsune ◽  
T. Tabata ◽  
S. Masaki
Keyword(s):  
Velocity Field ◽  
Porous Materials ◽  
Upper Bound ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Longitudinal Direction ◽  
Axisymmetric Deformation ◽  
The Other ◽  
The Matrix ◽  
Spherical Cells

Axisymmetric deformation of anisotropic porous materials caused by geometry of pores or by distribution of pores is analyzed. Two models of the materials are proposed: one consists of spherical cells each of which has a concentric ellipsoidal pore; and the other consists of ellipsoidal cells each of which has a concentric spherical pore. The velocity field in the matrix is assumed and the upper bound approach is attempted. Yield criteria are expressed as ellipses on the σm σ3 plane which are longer in longitudinal direction with increasing anisotropy and smaller with increasing volume fraction of the pore. Furthermore, the axes rotate about the origin at an angle α from the σm-axis, while the axis for isotropic porous materials is on the σm-axis.

Presentation and assessment of tides and water level records for geophysical investigations

1970 ◽  
Vol 7 (2) ◽  
pp. 607-625 ◽  
Author(s):  
G. C. Dohler ◽  
L. F. Ku
Keyword(s):  
Water Level ◽  
Power Spectra ◽  
Rate Of Change ◽  
Regression Technique ◽  
Level Data ◽  
Water Level Data ◽  
Geophysical Investigations ◽  
Water Level Variations ◽  
Mean Water Level ◽  
Change In Mean

The methods and problems involved in collecting water level data are explained, and the processing and formats of the data are illustrated. The trend of the change in mean water level is plotted and the corresponding rate of change is estimated by the regression technique. The power spectra of the water level variations are plotted to illustrate these variations in terms of frequencies.

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

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