Trapping of biological random walkers Part 3: Two-dimensional heat equation as the foundation for translating catch number into absolute pest density

2016 ◽  
Author(s):  
James R. Miller
Keyword(s):  
Heat Equation ◽  
Two Dimensional ◽  
Random Walkers ◽  
Pest Density

Continuous quaternion fourier and wavelet transforms

2014 ◽  
Vol 12 (04) ◽  
pp. 1460003 ◽  
Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino ◽  
Rémi Vaillancourt
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Equation ◽  
Wavelet Transforms ◽  
Quaternion Algebra ◽  
Two Dimensional ◽  
Quaternion Fourier Transform ◽  
Fundamental Properties

A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel [Formula: see text] is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.

Measurement of Pointwise Juncture Condition of Temperature at the Interface of Two Bodies in Sliding Contact

1963 ◽  
Vol 85 (3) ◽  
pp. 481-485 ◽  
Author(s):  
F. F. Ling ◽  
T. E. Simkins
Keyword(s):  
Experimental Data ◽  
Heat Equation ◽  
Normal Load ◽  
Frictional Resistance ◽  
Flow Fields ◽  
Sliding Contact ◽  
Two Dimensional ◽  
Temperature Distributions ◽  
Typical Data ◽  
Two Bodies

An apparatus is described for bringing a rider specimen and a slider specimen into continuous sliding contact so that significant temperatures at the interface are achievable. The design is such that the flow fields of heat in the specimens would be at most two-dimensional, i.e., within engineering approximations; this fact makes possible the measurement of temperatures of the specimens without disrupting the flow fields of heat. Typical data are presented of speed, normal load, frictional resistance, and temperatures at strategic locations on the specimens. Using the heat-equation solutions obtained previously for the configurations concerned, contact-surface temperature distributions of both specimens are calculated from experimental data. Results give the pointwise, temperature juncture condition at the interface.

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