Three Problems in the Asymptotic Order of Group Elements

2020 ◽  
Author(s):  
James Thomas
Keyword(s):  
Asymptotic Order

scholarly journals Analysis and compilation of the statement into machine code and execute that the machine code for discarding the degree to which performance changes between prototype and production system

2016 ◽  
Vol 2 (1) ◽  
pp. 52
Author(s):  
Bhubneshwar Sharma
Keyword(s):  
Production System ◽  
Order Of Growth ◽  
Machine Code ◽  
Improve Performance ◽  
General Technique ◽  
Asymptotic Order

Beyond asymptotic order of growth, the constant factors matter: an asymptotically slower algorithm may be faster or smaller (because simpler) than an asymptotically faster algorithm when they are both faced with small input, which may be the case that occurs in reality. Often ahybrid algorithmwill provide the best performance, due to this tradeoff changing with size. A general technique to improve performance is to avoid work. A good example is the use of afast pathfor common cases, improving performance by avoiding unnecessary work

Size Dependent Orientation of Knudsen Force

2012 ◽  
Author(s):  
Taishan Zhu ◽  
Wenjing Ye ◽  
Jun Zhang
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Thermal Gradient ◽  
Rarefied Gas ◽  
Mechanical Force ◽  
Thermal Gradients ◽  
Free Molecule ◽  
Asymptotic Order ◽  
Size Dependent ◽  
Leading Term

Knudsen force acting on a heated microbeam adjacent to a cold substrate in a rarefied gas is a mechanical force created by unbalanced thermal gradients. The measured force has its direction pointing towards the side with a lower thermal gradient and its magnitude vanishes in both continuum and free-molecule limits. In our previous study, negative Knudsen forces were discovered at the high Knudsen regime before diminishing in the free-molecule limit. Such a phenomenon was however not observed in the experiment. In this paper, the existence of such a negative Knudsen force is further confirmed using both numerical simulation and theoretical analysis. The asymptotic order of the Knudsen force near the collisionless limit is analyzed and the analytical expression of its leading term is provided, from which approaches for the enhancement of negative Knudsen forces are proposed.

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