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5

Typically, this situation is handled by: Using an "event function" or something to that effect to stop the integration when $P_{1} = P_{2}$. LSODA (the backend for scipy.integrate.odeint) does not have this capability, but other integrators, such as CVODE (part of SUNDIALS) do. Reformulating the right-hand side so it's continuously differentiable when $P_{1}...


5

Take a look at active subspaces, e.g., Active Subspace Methods in Theory and Practice: http://epubs.siam.org/doi/abs/10.1137/130916138 And a PDF here: http://inside.mines.edu/~pconstan/docs/constantine-asm.pdf I have a SIAM book (Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies) coming out in March. Suppose $f$ maps $\mathbb{...


3

Each of your subsystems -- and likely also each coupling between subsystems -- will have an intrinsic time scale. What that is of course depends on your system. The spin up time will then be a small multiple of the maximum of all of the time scales that are relevant in the transition you are considering.


3

CESM and COSMOS have been mentioned. A group in Japan has their own model, although I forget what it's called. If you really need a comprehensive list and a comparison, I'd recommend taking a look at any of the papers published in CMIP project. Our's (COSMOS) is in there and you can see where each model has its weaknesses. Just as a clarification question, ...


2

That is known as 3D reconstruction. I don't know if there is anything better in the bookstores these days but Multiple-view geometry by Hartley and Zisserman is a good textbook on the subject.


1

As, $J2 = -21 meV$ is more dominant than $J1 = 2.3meV$, the system is antiferromagnetic in nature. The expected ground state energy per moelcule(NiO) is $-42meV$. When the state reaches equilibirum, two of the nearest neighbors are alike and two are opposite, cancelling the energy contirbutions of each other. The energy contribution is from the second ...


1

Hint: The value $\max(x_1,x_2)$ is the smallest value $t$ for which $t\geq x_1$ and $t\geq x_2$.


1

If you need to terminate the ODE solver at some point (P1==P2) you can use odespy. The solve method of the solvers accepts a terminate function that accepts the state u, the time t and the integration step step_no and returns a boolean. I used it today to stop the integration when any of the state elements is too low: u,t = solver.solve(linspace(0,100,1000),...


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