Recent content by gato_

More on http://math.stackexchange.com/questions/634890/has-prof-otelbaev-shown-existence-of-strong-solutions-for-navier-stokes-equatio http://francis.naukas.com/2014/01/18/la-demostracion-de-otelbaev-del-problema-del-milenio-de-navier-stokes/

source: http://ru-facts.com/news/view/30934.html I understand the source means to say Mujtarbay Otelbayev has found a solution to Navier-Stokes equations. The only reference I've found is the article itself (in Russian), so I don't understand a word...

I would like to leave a question arising from the book on nonlinear quantum mechanics referenced above. There, the specific equations chosen have the particularity of being integrable, and having a well defined inverse scattering method (IST). While this is very useful, I don't know if this...

Hi Jarek. I too am very interested in the soliton approach to particles. While the paticle/wave duality has not gone unnoticed, I have not found too much material. As this is not my current field, my "review" of the material will be quite basic, because I didn't go through it First I stumbled...

Look for the stationary points \dot{x}=\dot{y}=0 You have two algebraic equations depending on the parameters

True. Also, I think it is better to consider evaporation rate to be proportional to the surface area rather than constant, the reason being only molecules in the interface can evaporate. That results in a linearly varying radius with time.

the problem will be harder the more detail you get into, but roughly, both mass and friction coefficients will vary in time because of the change in volume/geometry of the drop. You need to model too the process of evaporation. The rate is constant in time? does it depend on velocity? (on...

I honestly don't think the laplace transform will help very much if the field varies with time, the reason being there will be terms like v(t)B(t) making the equation nonlinear, which make linear transforms useless. The problem (assumming B depends on time, but NOT on space coordinate) is...

So, correct me if I am wrong, you are trying to solve the Schrödinger equation with a potential V(r)=-K/r^{3}, and 0 angular momentum and energy. Without making the substitution \psi=exp(\phi), that is: \frac{d}{dr}(r^{2}\frac{d\psi}{dr})+\frac{K}{r^3}\psi=0 for which a solution is...

Well, I have to warn you that the domain does not need to go to 0 to imply a problem. Any arbitrary neighbourhood of 0 contains singularities... I think, in that case the approximation is not valid. If this has been derived from a perturbation expansion, I'm affraid the solution is telling you...

any available boundary conditions? I only find consistent solutions for K<0. That said, if the domain of application includes r->0, I have reasons to think the solution does not apply. After some trial, I tried brute force, and it turns out that maple gives an exact solution. redefining r as...

Sorry. I read d^{2}f/dx^{2} instead of (df/dx)^{2}

Actually, maple does give a solution: f \left( r \right) =1/4\,\ln \left( r \right) +5/4\,\ln \left( r-1 \right) \left( r-1 \right) -r+5/4-1/4\,r\ln \left( r \right) -1/8\, {r}^{-1}+{\it \_C1}\,r+{\it \_C2} The equation is autonomous , so you can reduce it to a quadrature. I...

the command is [x,y]=ode45(@(x,y)[y(2);y(3);(1-y(1))/y(1)^3],[50 0],[1;0;0]); I've tried, and obtained the same result as you. This is an equilibrium point of the system. if you try y(50)=1+1e-15, it blows up. If you try y(0)=1-1e-15, it blows up too (when reaching y=0).

Take for example, the forward Euler: y_{n+1}-y_{n}=-hy_{n} Now, Taylor expand y_{n+1}\equiv y(t_{n}+h) (y_{n}+hy_{n}'+h^{2}y_{n}''/2+..)-y_{n}=-hy_{n} so: (y_{n}'+hy_{n})=-h^{2}y_{n}''/2+... And then, you can say the error of the method is of order O(h^{2})