17 Questions 27 Answers 0 Followers
Questions related from Shuchang Zhang
Noether's (first) theorem states that if a Lagrangian L admits a continuous symmetry, then some quantities are conserved. So I want to know if there's any inverse problem like this: Given one or...
03 March 2014 6,945 17 View
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...
03 March 2014 1,751 3 View
Navier-Stokes equation describes the evolutionary law of fluid velocity. Essentially, it is a special form of Newton's second law. But why not position here? People don't care about trajectories...
03 March 2014 874 5 View
In Helmholtz original thesis On integrals of the hydrodynamical equations, which express vortex-motion, he mentioned in the first section that the change undergone by an arbitrary infinitesimal...
09 September 2013 2,883 3 View
The Taylor expansion of a vector field $f(x)$ to the order of one is $$f(x)=f(x_0)+Jf(x_0)\cdot\Delta x+o(\Delta x)$$ where $Jf$ is Jacobian of the vector field and $\Delta x=x-x_0$. Suppose we...
09 September 2013 4,858 0 View
We know that a higher-order ode can be converted to a dynamical system by replacing each higher-order derivative by a new variable. What about the inverse problem? Does a dynamical system convert...
08 August 2013 9,066 11 View
∂f/∂x+∂g/∂y=0 and ∂f/∂y-∂g/∂x=0
08 August 2013 2,020 4 View
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...
08 August 2013 392 1 View
If any, please provide explanation (examples are best welcomed) and/or references.
06 June 2013 1,217 3 View
In physics, continuity equation often reads as ∂ρ/∂t+∇⋅(ρu)=0. Obviously, if velocity field u is solenoidal, the equation degenerates to dρ/dt=∂ρ/∂t+u⋅∇ρ=0. That is, the total derivative of...
05 May 2013 4,354 2 View
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...
05 May 2013 3,485 8 View
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...
05 May 2013 8,723 9 View
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?
05 May 2013 9,980 7 View
Retrospect the whole history of physics, we could see that lots of branches eventually are formulated using the language of geometry. For example, Newton uses geometry to set the foundation of...
04 April 2013 5,504 17 View
People usually talk about arrow of time. But this implies an implicit assumption that time is one dimensional. I'd like to know if it is possible that time is two dimensional or higher? What will...
04 April 2013 627 14 View
I'm wondering if anyone knows a good introductory book where differential geometry is naturally brought into Maxwell's equation? Some textbooks are too straightforward to describe it in geometric...
04 April 2013 8,695 4 View
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...
04 April 2013 6,441 18 View
