Closed Form Solutions for Connectivity of Fixed Radius Random Graphs in One-Dimensional Space

2006 ◽  
Author(s):  
Ai Noshiro ◽  
Masahito Kurihara
Keyword(s):  
Closed Form ◽  
Random Graphs ◽  
Dimensional Space ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Fixed Radius

scholarly journals Transient Solutions for One-Dimensional Problems With Strain Softening

1987 ◽  
Vol 54 (3) ◽  
pp. 513-518 ◽  
Author(s):  
T. Belytschko ◽  
Xiao-Jun Wang ◽  
Z. P. Bazant ◽  
Y. Hyun
Keyword(s):  
Strain Rate ◽  
Closed Form ◽  
Transient Response ◽  
Softening Point ◽  
Strain Softening ◽  
Stress Strain ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Transient Solutions

Closed-form solutions are presented for the transient response of rods in which strain softening occurs and the stress-strain laws exhibit nonvanishing stresses after the strain-softening regime. It is found that the appearance of any strain softening results in an infinite strain rate if the material is inviscid. For a stress-strain law with a monotonically decreasing stress the strains are infinite also. If the stress increases after the strain-softening portion, the strains remain finite and the strain-softening point moves through the rod.

The Use of the Milne-Eddington Absorption Coefficient for Radiative Heat Transfer in Combustion Systems

1977 ◽  
Vol 99 (3) ◽  
pp. 458-465 ◽  
Author(s):  
J. D. Felske ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Absorption Coefficient ◽  
Closed Form ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Wide Band ◽  
One Dimensional ◽  
Soot Particles ◽  
Closed Form Solutions ◽  
Combustion Systems

The applicability of the Milne-Eddington absorption coefficient approximation is discussed in relation to the calculation of radiative transport involving the two distinct types of species produced in combustion systems—gases and soot particles. The approximation is found to apply well to hydrocarbon soot particles and as a result analytical closed-form solutions are derived for the radiative heat transfer inside one-dimensional slab shaped soot clouds. (The applicability of the gray approximation to soot is also discussed.) For the calculation of total band radiation from gases, however, the Milne-Eddington approximation is found to be questionable. The meaning of its assumption is discussed in light of an established Curtis-Godson wide band scaling approximation. Its usefulness for real gases is then assessed through the calculation and comparison of slab radiation by both techniques.

Joint and Cross Acceptances for Cross-Flow-Induced Vibration—Part I: Theoretical and Finite Element Formulations

2000 ◽  
Vol 122 (3) ◽  
pp. 349-354 ◽  
Author(s):  
M. K. Au-Yang
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Cross Flow ◽  
Theoretical Development ◽  
Element Formulation ◽  
Flow Induced Vibration ◽  
Arbitrary Boundary ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Special Cases

The theoretical development of the acceptance integral method to estimate the random vibration of structures subject to turbulent flow is critically reviewed and put onto a firm mathematical basis. Closed-form solutions for the joint acceptances for cross-flow-induced vibration of one-dimensional structures are derived for two special cases of spring-supported and simply supported beams. These are used to check results from a finite element formulation of the acceptance integrals for one-dimensional structures with arbitrary boundary conditions, and for arbitrary correlation lengths. Agreements between the finite element and closed-form solutions are excellent. [S0094-9930(00)02303-9]

Inverse Kinematics Analysis of 5-DOF Robot Manipulators Based on Virtual Joint Method

2011 ◽  
Vol 143-144 ◽  
pp. 265-268
Author(s):  
Zhi Zhong Liu ◽  
Hong Yi Liu ◽  
Zhong Luo
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Kinematics Analysis ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Joint Method

To solve the inverse kinematics problem of a robot manipulator without closed form solutions, one-dimensional iterative method is very useful. However, for a 5-DOF robot manipulator, because of the uncontrolable and uncertain orientation vectors, it's difficult to analytically express all joint variables by one of them, therefore one-dimensional iterative method can not be directedly used. By adding an appropriate virtual joint to it, a 5-DOF manipulator can be changed into a 6-DOF one so that the uncertain orientation vectors can be pre-given, and the difficulty is solved. To illustrate this virtual joint method a 5-DOF serial robot manipulator with prismatic arm joint and offset wrist is discussed in this paper as an example.

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