Shuchang Zhang

11 Questions 20 Answers 0 Followers

Questions related from Shuchang Zhang

What are general ways to handle simplex dynamics?

I want to know if there's any general method to investigate a linear system restrained by a standard simplex. It's hard for me to start with such a system because if I directly regard it as...

24 March 2014 2,691 3 View

Does Clifford algebra depend on the topology of the manifold?

We know the greatest feature of Clifford algebra is coordinate-free. One can do vector operations without knowing the representation of vectors. And due to this very characteristic, Clifford or...

18 September 2013 4,103 4 View

Can someone advise on a proof of Poincare lemma?

Poincare lemma states that every smooth closed form in contractible subset is exact. The assumption actually represents a set of pdes that dd=0. Could Frobenius theorem be used to say that the...

29 August 2013 2,372 1 View

What form does a skew-symmetric matrix decompose to?

If any, please provide explanation (examples are best welcomed) and/or references.

18 June 2013 6,957 3 View

What tools are generally employed in classical mechanics describing dissipative systems?

It seems Hamiltonian systems handle conservative systems because of invariant Hamiltonian and Lagrangian mechanics does so for it is equivalent to Hamiltonian mechanics. Is there anything a like...

10 May 2013 416 7 View

The relationship between Fokker-Planck equation (FPE) and Stochastic differential equation (SDE)?

Feynman-Kac formula points out an SDE corresponds to a FPE. Given an SDE, I can simulate numerically by following the equation, then I can plot the histogram of the simulated single particle....

10 May 2013 3,980 8 View

Why shall we introduce Hamiltonian system in statistical mechanics?

I believe nearly all books concerning statistical mechanics cover Hamiltonian system. Then naturally Liouville's theorem and Boltzmann-Gibbs distribution are discussed. I don't see the connection...

10 May 2013 2,901 9 View

Does Markov process have something to do with thermodynamics?

I want to know if a Markov process far from equilibrium corresponds to a non-equilibrium thermodynamics process or whether they have something in common?

10 May 2013 8,395 7 View

Symmetry analysis on dynamic system

There are lots of textbooks discussing symmetry analysis on differential equations such as Applications of Lie group to differential equations. All of the methods (at least all of them I have...

11 April 2013 4,283 17 View

Why don't people care about inner product of vectors in symplectic geometry?

I'm a little confused about Riemannian geometry which mainly concerns Riemannian metric (a positive-definite symmetric rank-2 covariant tensor) and symplectic geometry which mainly concerns...

07 April 2013 8,819 5 View

I want to find some simple examples to do simulations on.

Recently I began a project on MCMC and I think it may be helpful if some simple cases are given for me to do some simulations and analyses on. Could someone help introduce several simple,...

25 March 2013 9,500 24 View