DIVISIBLE LOAD DISTRIBUTION IN A NETWORK OF PROCESSORS

The paper presents a closed form solution for an optimum scheduling of a divisible job on an optimum number of processor arranged in an optimum sequence in a multilevel tree networks. The solution has been derived for a single divisible job where there is no dependency among subtasks and the root processor can either perform communication and computation at the same time. The solution is carried out through three basic theorems. One of the theorems selects the optimum number of available processors that must participate in executing a divisible job. The other solves the sequencing problem in load distribution by which we are able to find the optimum sequence for load distribution in a generalized form. Having the optimum number of processors and their sequencing for load distribution, we have developed a closed form solution that determines the optimum share of each processor in the sequence such that the finish time is minimized. Any alteration of the number of processors, their sequences, or their shares that are determined by the three theorems will increase the finish time.

Download Full-text

Scattering by hard and soft parallel half-planes

Canadian Journal of Physics ◽

10.1139/p81-248 ◽

1981 ◽

Vol 59 (12) ◽

pp. 1879-1885 ◽

Cited By ~ 14

Author(s):

R. A. Hurd ◽

E. Lüneburg

Keyword(s):

Plane Wave ◽

Closed Form ◽

Half Plane ◽

Diffraction Problem ◽

Closed Form Solution ◽

Normal Derivative ◽

Form Solution ◽

The Other ◽

Total Field

We consider the diffraction of a scalar plane wave by two parallel half-planes. On one half-plane the total field vanishes whilst on the other its normal derivative is zero. This is a new canonical diffraction problem and we give an exact closed-form solution to it. The problem has applications to the design of acoustic barriers.

Download Full-text

CLOSED-FORM TRIGONOMETRIC SOLUTIONS FOR INHOMOGENEOUS BEAM-COLUMNS ON ELASTIC FOUNDATION

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455404001112 ◽

2004 ◽

Vol 04 (01) ◽

pp. 139-146 ◽

Cited By ~ 22

Author(s):

IVO CALIÒ ◽

ISAAC ELISHAKOFF

Keyword(s):

Closed Form ◽

Elastic Foundation ◽

Load Distribution ◽

Flexural Rigidity ◽

Closed Form Solution ◽

Form Solution ◽

Material Density ◽

Buckling Modes ◽

Beam Columns ◽

Closed Form Solutions

In this study, a special class of closed-form solutions for inhomogeneous beam-columns on elastic foundations is investigated. Namely the following problem is considered: find the distribution of the material density and the flexural rigidity of an inhomogeneous beam resting on a variable elastic foundation so that the postulated trigonometric mode shape serves both as vibration and buckling modes. Specifically, for a simply-supported beam on elastic foundation, the harmonically varying vibration mode is postulated and the associated semi-inverse problem is solved that result in the distributions of flexural rigidity that together with a specific law of material density, an axial load distribution and a particular variability of elastic foundation characteristics satisfy the governing eigenvalue problem. The analytical expression for the natural frequencies of the corresponding homogeneous beam-column with a constant characteristic elastic foundation is obtained as a particular case. For comparison the obtained closed-form solution is contrasted with an approximate solution based on an appropriate polynomial shape, serving as trial function in an energy method.

Download Full-text

Bi-BCM: A Closed-Form Solution for Fixed-Guided Beams in Compliant Mechanisms

Journal of Mechanisms and Robotics ◽

10.1115/1.4035084 ◽

2016 ◽

Vol 9 (1) ◽

Cited By ~ 19

Author(s):

Fulei Ma ◽

Guimin Chen

Keyword(s):

Closed Form ◽

Compliant Mechanisms ◽

Closed Form Solution ◽

Form Solution ◽

The Other ◽

Boundary Line ◽

Final Solution ◽

Second Mode ◽

Design Calculations ◽

Constraint Model

A fixed-guided beam, with one end is fixed while the other is guided in that the angle of that end does not change, is one of the most commonly used flexible segments in compliant mechanisms such as bistable mechanisms, compliant parallelogram mechanisms, compound compliant parallelogram mechanisms, and thermomechanical in-plane microactuators. In this paper, we split a fixed-guided beam into two elements, formulate each element using the beam constraint model (BCM) equations, and then assemble the two elements' equations to obtain the final solution for the load–deflection relations. Interestingly, the resulting load–deflection solution (referred to as Bi-BCM) is closed-form, in which the tip loads are expressed as functions of the tip deflections. The maximum allowable axial force of Bi-BCM is the quadruple of that of BCM. Bi-BCM also extends the capability of BCM for predicting the second mode bending of fixed-guided beams. Besides, the boundary line between the first and the second modes bending of fixed-guided beams can be easily obtained using a closed-form equation. Bi-BCM can be immediately used for quick design calculations of compliant mechanisms utilizing fixed-guided beams as their flexible segments (generally no iteration is required). Different examples are analyzed to illustrate the usage of Bi-BCM, and the results show the effectiveness of the closed-form solution.

Download Full-text

Closed form Solution for Scheduling Arbitrarily Divisible Load Model in Data Grid Applications: Multiple Sources

American Journal of Applied Sciences ◽

10.3844/ajassp.2009.626.630 ◽

2009 ◽

Vol 6 (4) ◽

pp. 626-630

Author(s):

Abdullah

Keyword(s):

Closed Form ◽

Closed Form Solution ◽

Data Grid ◽

Form Solution ◽

Multiple Sources ◽

Load Model ◽

Divisible Load ◽

Grid Applications

Download Full-text

Spontaneous potential log response expressed as convolution

Geophysics ◽

10.1190/1.1441395 ◽

1982 ◽

Vol 47 (9) ◽

pp. 1335-1337

Author(s):

E. A. Nosal

Keyword(s):

Closed Form ◽

Signal Analysis ◽

Closed Form Solution ◽

Form Solution ◽

The Other ◽

Individual Contribution ◽

Spontaneous Potential ◽

The Earth ◽

The Individual ◽

Special Case

A special case of spontaneous potential (SP) logging, which has a closed‐form solution, will be expressed as a convolutional operation. Such a formal demonstration serves two purposes. First, it separates the individual contribution of the tool from that of the earth. Second, it places this logging device within the mathematical context of signal analysis. The special case for which a closed‐form solution is known is that where all resistivities are equal. Fourier analysis applied to this solution leads to a product of two functions, of which one is identified as the contribution of the earth and the other of the tool.

Download Full-text

An Inverse Force Analysis of a Tetrahedral Three-Spring System

Journal of Mechanical Design ◽

10.1115/1.2826136 ◽

1995 ◽

Vol 117 (2A) ◽

pp. 286-291 ◽

Cited By ~ 6

Author(s):

P. Dietmaier

Keyword(s):

Closed Form ◽

Closed Form Solution ◽

Form Solution ◽

The Other ◽

Force Analysis ◽

Equilibrium Configurations ◽

Spring System ◽

The Common ◽

The Stability ◽

Inverse Force

A tetrahedral three-spring system under a single load has been analyzed and a closed-form solution for the equilibrium positions is given. Each of the three springs is attached at one end to a fixed pivot in space while the other three ends are linked by a common pivot. The springs are assumed to behave in a linearly elastic way. The aim of the paper at hand was to find out what the maximum number of equilibrium positions of such a system might be, and how to compute all possible equilibrium configurations if a given force is applied to the common pivot. First a symmetric and unloaded system was studied. For such a system it was shown that there may exist a maximum of 22 equilibrium configurations which may all be real. Second the general, loaded system was analyzed, revealing again a maximum of 22 real equilibrium configurations. Finally, the stability of this three-spring system was investigated. A numerical example illustrates the theoretical findings.

Download Full-text

Diffraction by an infinite set of soft/hard parallel half-planes: the Riemann approach

Canadian Journal of Physics ◽

10.1139/p82-153 ◽

1982 ◽

Vol 60 (8) ◽

pp. 1125-1138 ◽

Cited By ~ 2

Author(s):

E. Lüneburg

Keyword(s):

Plane Wave ◽

Boundary Value Problem ◽

Closed Form ◽

Closed Form Solution ◽

Normal Derivative ◽

Form Solution ◽

The Other ◽

Bragg Angle ◽

Total Field ◽

Infinite Set

We consider the diffraction of a plane wave by an infinite set of parallel equidistant half-planes. On each plate the total field vanishes on one side and the normal derivative vanishes on the other side. A closed-form solution for Bragg angle incidence is obtained by reducing the boundary value problem to a solvable Riemann problem.

Download Full-text