scholarly journals Added Masses and Forces on Two Bodies Approaching Central Impact in an Inviscid Fluid

1992 ◽  
Vol 36 (02) ◽  
pp. 99-122
Author(s):  
L. Landweber ◽  
A. Shahshahan
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Infinite Series ◽  
Numerical Differentiation ◽  
The Other ◽  
Asymptotic Formulas ◽  
Inviscid Fluid ◽  
Interaction Forces ◽  
Added Masses ◽  
Two Bodies

An integral-equation procedure has been developed to determine interaction forces on two bodies approaching central impact in an inviscid fluid. The accuracy of the results from that procedure is evaluated by applying it to a pair of circles and a pair of spheres for which exact solutions are available. A second purpose was to refine the procedure so that accurate solutions could be obtained at closer distances between the bodies. In the first part of this work, the classical theory is extended by deriving truncation corrections for the infinite series representing the exact solution and asymptotic formulas for computing interaction forces at small gaps. In the second part, two problems were resolved: one on the treatment of the sharp peaks of the integrands when the gap between the bodies was small, the other on reducing the errors in the numerical differentiation required to evaluate the forces. Results for various combinations of circle pairs, for equal spheres, and for an elliptical cylinder approaching a circular one are presented. A new relation between the interaction forces on a wall and on a body moving normal to it is presented. Addendum published in 1994 Volume 38, Issue 2 (June), pages 172–173, is included.

Interaction Between Two Bodies Translating in an Inviscid Fluid

1991 ◽  
Vol 35 (01) ◽  
pp. 1-8
Author(s):  
L. Landweber ◽  
A. T. Chwang ◽  
Z. Guo
Keyword(s):  
Translational Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Circular Cylinders ◽  
Integral Approach ◽  
Inviscid Fluid ◽  
Added Masses ◽  
Two Bodies ◽  
Good Agreement

The equations of motion of two bodies in translational motion in an inviscid fluid at rest at infinity are expressed in Lagrangian form. For the case of one body stationary and the other approaching it in a uniform stream, an exact, closed-form solution in terms of added masses is obtained, yielding simple expressions for the velocity of the moving body as a function of its relative position and for the interaction forces. This solution is applied to the case of a rectangular cylinder approaching a cylindrical one, for which the added-mass coefficients had been previously obtained in a companion paper by an integral-equation procedure. In order to compare results with those in the literature, and to evaluate the accuracy of the present procedures, results were calculated for a pair of circular cylinders by these methods as well as by successive images. Very good agreement was found. Comparison with published results showed good agreement with the added mass but very poor agreement on the forces, including disagreement as to whether the forces were repulsive or attractive. The discrepancy is believed to be due to the omission of terms in the Bernoulli equation which was used to obtain the pressure distribution and then the force on a body. The Lagrangian formulation is believed to be preferable to the pressure-integral approach because it yields the hydrodynamic force directly in terms of the added masses and their derivatives, thus requiring the calculation of many fewer coefficients.

On the Exact Solution for the Two-Sphere Problem in Axisymmetrical Potential Flow

1978 ◽  
Vol 45 (3) ◽  
pp. 463-468 ◽  
Author(s):  
M. Bentwich ◽  
T. Miloh
Keyword(s):  
Exact Solution ◽  
Kinetic Energy ◽  
Stream Function ◽  
General Expression ◽  
Infinite Series ◽  
Potential Flow ◽  
Flow Problem ◽  
Integral Form ◽  
The Other ◽  
Limit Process

The authors obtain an exact solution for the stream function representing the title flow problem when the gaps, the radii, and the velocities of the two spheres are arbitrary. For spheres spaced apart it is in the form of infinite series. For touching spheres that solution reduces by a suitable limit process to an integral form. A general expression is then obtained for the kinetic energy of the system, and using Lagranges equation, the forces experienced by the spheres are calculated. It is thus found that the interactive force between them does not vanish when one is stationary and the other is accelerating at an infinite distance away. Another interesting result concerns the logarithmically singular dependence of the interactive force on the gap when the latter is very small.

scholarly journals Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mohsen Alipour ◽  
Dumitru Baleanu ◽  
Fereshteh Babaei
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Convergence Analysis ◽  
Bernstein Polynomials ◽  
Linear Equations ◽  
The Other ◽  
New Combination ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Block Pulse Functions

We introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

Study of Oscillating Flow of Viscoelastic Fluid With the Fractional Maxwell Model

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Jiu-hong Jia ◽  
Hong-xing Hua
Keyword(s):  
Exact Solution ◽  
Petroleum Chemistry ◽  
Viscoelastic Fluid ◽  
Maxwell Model ◽  
The Other ◽  
Oscillating Flow ◽  
Model Parameters ◽  
Series Approximation ◽  
Phase Lags ◽  
Annular Effect

The oscillating flow of the viscoelastic fluid in cylindrical pipes has been applied in many fields, such as industries of petroleum, chemistry, and bioengineering. It is studied using the fractional derivative Maxwell model in this paper. The exact solution is obtained utilizing a simpler and more reasonable technique. According to this velocity solution, the time-velocity profile of one kind of viscoelastic fluid is analyzed. From analysis, it is found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Moreover, two series approximations for the velocity are obtained and analyzed for different model parameters. In one series approximation, the velocity is parabolic in profile, while in the other series approximation, the velocity presents three characteristics: (1) it is independent of radius and at the centerline is smaller than that of steady Poiseuille flow, (2) the phase lags about 90deg with respect to the imposed pressure gradient, and (3) the Richardson annular effect is found near the wall.

The Circular Cylinder With a Band of Uniform Pressure on a Finite Length of the Surface

1941 ◽  
Vol 8 (3) ◽  
pp. A97-A104 ◽  
Author(s):  
M. V. Barton
Keyword(s):  
Circular Cylinder ◽  
Finite Length ◽  
Infinite Series ◽  
Fundamental Problem ◽  
The Other ◽  
Complete Picture ◽  
Uniform Pressure ◽  
Uniform Tension ◽  
Special Cases ◽  
Stress And Deformation

Abstract The solution to the fundamental problem of a cylinder with a uniform pressure over one half its length and a uniform tension on the other half is found by using the Papcovitch-Neuber solution to the general equations. In this paper, the results, given analytically in terms of infinite-series expressions, are exhibited as curves giving a complete picture of the stress and deformation. The case of a cylinder with a band of uniform pressure of any length, with the exception of very small ones, is then solved by the method of superposition. The stresses and displacements are evaluated for the special cases of a cylinder with a uniform pressure load of 1 diam and 1/2 diam in length. The problem of a cylinder heated over one half its length is solved by the same means.

Buckling of Rectangular Plates With Built-In Edges

1942 ◽  
Vol 9 (4) ◽  
pp. A171-A174
Author(s):  
Samuel Levy
Keyword(s):  
Exact Solution ◽  
Rectangular Plate ◽  
Infinite Series ◽  
Numerical Results ◽  
Buckling Load ◽  
Rectangular Plates

Abstract This paper presents an exact solution in terms of infinite series of the problem of buckling by compressive forces in one direction of a rectangular plate with built-in edges (zero slope, zero displacement in the direction normal to the plane of the plate). The buckling load is calculated for 14 ratios of length to width, ranging in steps of 0.25 from 0.75 to 4. On the basis of convergence, as the number of terms used in the infinite series is increased, it is estimated that the possible error in the numerical results presented is of the order of 0.1 per cent. A comparison is given with the work of other authors.

Locating Afghan History

2013 ◽  
Vol 45 (1) ◽  
pp. 132-134 ◽  
Author(s):  
Nile Green
Keyword(s):  
20Th Century ◽  
Nation Building ◽  
The Other ◽  
Historical Process ◽  
Historical Scholarship ◽  
History Of ◽  
Missing Middle ◽  
Two Bodies

Afghanistan's 20th century has long been seen through an analytical dichotomy. One concentration of historical scholarship has sought to explain the fraught progress of Afghan nation-building in the 1910s and 1920s. A second has sought to explain the unraveling of the Afghan nation after 1979. Weighted toward the decades at either end of the century, this dichotomized field has been problematic in both chronological (and thereby processual) and methodological terms. On the level of chronology, the missing long mid-section (indeed, half) of the century between the framing coups of 1929 and 1979 has made it difficult to convincingly join together the two bodies of scholarship. Not only has the missing middle further cemented the division of scholarly labor but it also has made it more difficult to connect the history of the last quarter of the century to that of the first quarter (except as a story of parallels), rendering them discrete narratives of development, one ending and the other beginning with a coup. The problems are deeper than this, though, extending from questions of chronology and process to matters of method. For if in its focus on nationalism and nation-building the first-quarter scholarship is framed within the neat boundaries of national spaces and actors, then in its focus on the unraveling of the nation and its peoples through the consequences of Soviet intervention, the last-quarter scholarship elevates nonnational actors as the key agents of historical process.

scholarly journals The use of fractional calculus for the optimal placement of electronic components on a linear array

2015 ◽  
Vol 28 (1) ◽  
pp. 77-84
Author(s):  
Mey de ◽  
Mariusz Felczak ◽  
Bogusław Więcek
Keyword(s):  
Integral Equation ◽  
Fractional Calculus ◽  
Forced Convection ◽  
Linear Array ◽  
The Other ◽  
Simple Solution ◽  
Optimal Placement ◽  
Critical Component ◽  
Electronic Components ◽  
One Dimensional

Cooling of heat dissipating components has become an important topic in the last decades. Sometimes a simple solution is possible, such as placing the critical component closer to the fan outlet. On the other hand this component will heat the air which has to cool the other components further away from the fan outlet. If a substrate bearing a one dimensional array of heat dissipating components, is cooled by forced convection only, an integral equation relating temperature and power is obtained. The forced convection will be modelled by a simple analytical wake function. It will be demonstrated that the integral equation can be solved analytically using fractional calculus.

scholarly journals An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives

2020 ◽  
Vol 8 (2) ◽  
pp. 590-601
Author(s):  
Melani Barrios ◽  
Gabriela Reyero
Keyword(s):  
Exact Solution ◽  
Variational Problem ◽  
Lagrange Equation ◽  
Integral Form ◽  
Variational Problems ◽  
The Other ◽  
Isoperimetric Problems ◽  
Caputo Derivatives ◽  
Fractional Variational Problems ◽  
Derivatives Of

In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputofractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the basic and isoperimetric problems, one in an integral form, and the other that depends only on the Caputo derivatives. The advantage is that Caputo derivatives are more appropriate for modeling problems than the Riemann-Liouville derivatives and makes the calculations easier to solve because, in some cases, its behavior is similar to the behavior of classical derivatives. Finally, anew exact solution for a particular variational problem is obtained.

Further Contributions to the Theory of Peripheral Jets in Ground Proximity

1992 ◽  
Vol 36 (01) ◽  
pp. 88-90
Author(s):  
David S. Tselnik
Keyword(s):  
General Solution ◽  
Infinite Series ◽  
Elliptic Functions ◽  
Jet Flow ◽  
New Method ◽  
Asymptotic Formulas ◽  
Flow Problems ◽  
Complicated Task

A number of plane inviscid jet flow problems of interest in hydrodynamics require the use of elliptic functions theory. Generally speaking, finding the general solution to a problem in terms of elliptic functions is not a complicated task. However, finding solutions as rapidly convergent infinite series or as sound asymptotic formulas is often not as easy, and special ways of treatment may prove to be necessary. In parallel with solving the problem of peripheral jets, the author's earlier paper (1985) proposed some such ways of treatment. In the present paper, a new method of treatment is proposed (and used);this approach may be of help in studies where the methods of elliptic functions theory have to be used.

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