Recent content by motherh

That Wiki helps a little but I'm still confused by this. So the Reynolds number is given by Re = ρUL/µ? As U is the velocity scale it makes to take U as V here. But after this I don't know how G comes into the Reynolds number.

Homework Statement I don't fully understand the Reynolds number and it has arisen in a problem. It says: Fluid with viscosity µ and density ρ fills the gap between two parallel plates at z = 0 and z = h. The upper plate at z = h moves with speed V in the x direction, while the lower plate at...

I've got it! Thanks so much for all of the help, I certainly needed it!

So far I have \frac{\partial I_2}{\partial t} = \frac{\partial}{\partial t}\int_{-\infty}^{\infty}(u^3+\frac{1}{2}u_x^2)dx = 3\int_{-\infty}^{\infty}u^2u_tdx + \int_{-\infty}^{\infty}u_xu_{xt} = 3\int_{-\infty}^{\infty}u^2u_tdx - \int_{-\infty}^{\infty}u_{xx}u_tdx...

I'm really sorry, I don't follow what you're saying. How is u_{xt} = u_{tx} useful and what should be integrated by parts?

Right, I got it thanks! There's another part to the question, it's pretty much the same as part one but now for I_2 = \int_{-\infty}^{\infty}(u^3+\frac{1}{2}u_x^2)dx . I got it down to \frac{\partial I_2}{\partial t}=3\int_{-\infty}^{\infty}u^2u_tdx + \int_{-\infty}^{\infty}u_xu_{xt} ...

Right, I got it thanks! There's another part to the question, it's pretty much the same as part one but now for I_2=\int_{-\infty)^{\infty}(u^3+\frac{1}{2}u_x^2)dx . I got it down to \frac{\partial I_2}{\partial t}=3\int_{-\infty)^{\infty}u^2u_tdx + \int_{-\infty)^{\infty}u_xu_{xt} . Now...

I thought about subbing in u_t=6uu_x-u_{xxx} to get 6\int_{-\infty}^{\infty}u^2u_xdx-\int_{-\infty}^{\infty}uu_{xxx}dx . I can compute the first integral to get \frac{1}{3}u^3 evaluated at -\infty to \infty (so that integral is equal to 0) but I can't do anything with the second...

Thanks guys. I've given your advice a go. So far I have used Leibniz integral rule and f=u^2 : \frac{\partial I_1}{\partial t} = \frac{\partial}{\partial t}(\int_{-\infty}^{\infty} f(x,t)dx) = \int_{-\infty}^{\infty} \frac{\partial f}{\partial t} dx = \int_{-\infty}^{\infty} uu_tdx. Where...

Homework Statement Given that u(x,t) satisfies u_t-6uu_x+u_{xxx}=0 (*) and u, u_x, u_{xx} \to 0 as |x| \to \infty show that I_1 = \int_{-\infty}^{\infty}u^2dx is independent of time ( \frac{\partial I_1}{\partial t}=0 ). Homework Equations - The Attempt at a Solution I...

Take f = 2x^2 + 1. When I run coeffs(f) in Matlab it outputs [2,1]. However I want it to output all the zero coefficients as well, for example [2 0 1] here. How do I do that?

Hi, I am trying to answer the following question: Consider a geometric Brownian motion S(t) with S(0) = S_0 and parameters μ and σ^2. Write down an approximation of S(t) in terms of a product of random variables. By taking the limit of the expectation of these compute the expectation of S(t)...

Hi, I'm trying to answer the following question: In each time period, a certain stock either goes down 1 with probability 0.39, remains the same with probability 0.20, or goes up 1 with probability 0.41. Assuming that the changes in successive time periods are independent, approximate the...

Suppose that \dot{x} = f(x) in \Re^{n}. There exists a bounded 2D invariant manifold M for this system. There are no critical points in M. Does it follow that there is a periodic orbit in M? I've realized that this has it's similarities to Poincare-Bendixon's theorem but I don't believe that...

Anybody?