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Thursday, 19 August 2010 22:47 |
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For a vector function V(x,y,z) in space, let vx, vy, and vz denote the components of V. The circulation of the vector field V around any simple closed path S is defined as the integral of the tangential component of V
around that path (in the "right-handed" direction). If the path is
defined parametrically as a function of the path length parameter s by
equations for xp(s), yp(s), zp(s), then the unit tangent vector as a function of s is
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Thursday, 19 August 2010 22:46 |
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One of the most common representations of
dynamic coupling between two variables x and y is the "lead-lag"
transfer function, which is based on the ordinary first-order
differential equation |
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Thursday, 19 August 2010 22:42 |
The  velocity of a wave can be defined in many
different ways, partly because there many different kinds of waves, and
partly because we can focus on different aspects or components of any
given wave. The ambiguity in the definition of "wave velocity" often
leads to confusion, and we frequently read stories about experiments
purporting to demonstrate "superluminal" propagation of electromagnetic
waves (for example). Invariably, after looking into the details of these
experiments, we find the claims of "superluminal communication" are
simply due to a failure to recognize the differences between phase,
group, and signal velocities.
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Page 2 of 65 |
The Hofstadter Butterfly
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