401 reputation
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location Brisbane
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visits member for 3 years, 6 months
seen 5 hours ago

I'm an undergraduate Engineering/Mathematics Student down in Brisbane, Australia. Interested in learning as much as I possibly can about maths, particularly the ideas/constructions/history/motivation behind the classic undergraduate concepts.


21h
awarded  Yearling
21h
comment Historical Survey of Statistical Mechanics
I was unaware of that site, sorry. I'm not sure it should be moved though - I'm looking for an historically motivated textbook (like Lanczos for CM or Bohm for QM) rather than a pure history book.
21h
asked Historical Survey of Statistical Mechanics
Apr
14
comment Reading the Feynman lectures in 2012
@RonMaimon OK, that sounds about right. Using the exact two particle solution is a good idea - the problem gets quite stiff when two planets get close. Thanks.
Apr
14
comment Reading the Feynman lectures in 2012
@RonMaimon Your answer inspired me to make an 2D $n$-body simulation to look for this KAM stability. But my naive approach of directly integrating Newton's equation with ode23s is so slow :( I get some great results for <10 planets, but I can't get much more. Do you have any tips for practically implementing such a simulation?
Apr
13
awarded  Critic
Apr
13
comment Calculating temperature from molecular dynamics simulation
thanks. Could you link a reference for how one derive this, and shows it is consistent with macroscopic definitions in the limit? Also does it only apply to free particles?
Apr
13
awarded  Custodian
Apr
13
reviewed Approve Calculating temperature from molecular dynamics simulation
Apr
13
asked Calculating temperature from molecular dynamics simulation
Mar
27
awarded  Editor
Mar
27
revised Geometry of Hamilton-Jacobi Equation
added 86 characters in body
Mar
27
answered Geometry of Hamilton-Jacobi Equation
Mar
27
comment Geometry of Hamilton-Jacobi Equation
Actually, I don't think such general solutions could exist in this case, as every solution satisfies $S[\gamma_{ext}] = S(t_1,y_1)-S(t_0,y_0)$. This is a little surprising, but I know so little of the theory of FOPDEs I really have no right to be surprised here :)
Mar
27
comment Geometry of Hamilton-Jacobi Equation
@Qmechanic Thankyou once again! You've been very helpful, and I now feel my initial suspicions were completely vindicated: the converse is true, and solutions of the H-J equation do correspond to the minimal action from some particular point in phase space (or at least elements of the complete solution - there may be general solutions derived from envelopes of the complete solution which behave otherwise.) I'll explain my error (as usual, very silly) in an answer below. :)
Mar
26
asked Geometry of Hamilton-Jacobi Equation
Mar
19
comment What's the interpretation of Feynman's picture proof of Noether's Theorem?
This is excellent, thanks, but I have a question: You say the virtual path $A^* -> A' -> B' -> B^*$ is an infinitesimal variation of the classical path $A^* -> A -> B -> B^*$, but the derivatives of the paths are not close at all. My understanding is that the Euler-Lagrange equations are only necessary for a weak extrema - i.e. the functional is stationary relative to all the curves 'close' to it, where we define 'close' in terms of both the value of $y$ and it's derivative $\dot{y}(t)$. But doesn't your proof assume that we have a strong extrema?
Jan
2
awarded  Teacher
Nov
8
awarded  Tumbleweed
Nov
1
answered Exact Relation between voltage and current