17,383 reputation
13473
bio website ilorentz.org/beenakker
location Leiden, The Netherlands
age
visits member for 3 years, 9 months
seen 28 mins ago
physicist at Leiden University

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revised Use a graphic tablet to write in Latex or MathML
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revised Use a graphic tablet to write in Latex or MathML
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revised Use a graphic tablet to write in Latex or MathML
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answered Use a graphic tablet to write in Latex or MathML
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revised Taking matrix derivative with MATLAB or Wolfram Alpha
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comment Mathematics of volleyball
"mathematics of volleyball"? don't you mean "physics of volleyball"? there's an extensive literature on that.
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answered Taking matrix derivative with MATLAB or Wolfram Alpha
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comment Taking matrix derivative with MATLAB or Wolfram Alpha
en.wikipedia.org/wiki/Matrix_calculus#Other_matrix_derivatives
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answered Making a system of second-order ODEs chaotic
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comment Helmholtz equation Poynting vector integral
I like to think about this in mechanical terms: the domain $\Omega$ is a box filled with photons, sloshing around periodically with period $2\pi/\omega$; their total momentum oscillates with the same period, why would the amplitude of this oscillation be zero? Momentum conservation just says that forces on the boundary of the box have to appear if the momentum oscillates, so there will be some net force on the boundaries that oscillates with the same period. Why do you see a conflict with conservation of momentum?
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comment Helmholtz equation Poynting vector integral
physics.stackexchange.com/questions/131509/… --- researchgate.net/post/…
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revised Trapping a particle
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comment Trapping a particle
To determine $C$ in equation (1) one will have to solve a diffusion equation and there is no closed-form expression, unlike for the ergodic case in equations (2)-(4). The proof by Lewenkopf and Vallejos applies to the ergodic case, when the particle explores the whole phase space before exiting. Then $\tau$ is simply a ratio of phase space areas, without any shape dependence. A Brownian walk inside $Y$ is not ergodic, so their proof does not apply.
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revised Trapping a particle
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comment Trapping a particle
@BorisBukh -- I have added a figure and included a reference where the result for the average dwell time is derived in some detail.
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