help understanding weird math symbols...
Community Forums/General Help/help understanding weird math symbols...
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| I was reading a pdf file on fluid dynamics and MPM and I came accross some math I do not understand. Im sure it is a simple concept but I am not farmiliar with the symbols and notation of physics. I simply cant figure out what the equations are saying on page 110 and 111 of this document (it starts on 107 so its not that far down) http://www.cs.utah.edu/~kirby/Publications/Kirby-37.pdf I would copy them to this forum but the forum doesnt like those special characters. So does anyone that is farmilliare with physics and the symbols used in it have an explanation of what the symbols and equations mean? |
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| My spidey-sense tingled, and now I'm here. Ok, they're all greek letters. Have a look at that link to find the names for the letters. Omega represents the object, or space you're simulating. A load of particles are created to represent points in the object. Each particle p has a position x_p, a velocity v_p, a mass m_p, volume V_p, and deformation gradient F_p (this sort of means the direction it's being squashed in). The first step is to work out for each cell in the grid a mass and a velocity (the position and volume are known, of course!) Equation (1) says that the mass of each cell is the sum of the mass of each particle multiplied by a basis function 'phi'. Some definitions of basis functions are given in 3, with discussion of which ones are most suitable for different situations. Equation (2) says that to work out the velocity of each cell, you sum up the velocities of all the particles multiplied by their mass and the basis function, and then divide the whole lot by the mass of the cell, which you just worked out. Equations (3) and (4) give the internal forces in each cell, in terms of the stress function sigma. The stress seems to depend on the material being modelled, and section 5.1 says something about how it's calculated, but I think it will involve reading some references. Going to start skipping ahead now - the triangle pointing downwards stands for 'divergence' - an operation from calculus which is sort of like the gradient of a curve in many dimensions. The triangle pointing upwards followed by a t represents the time 'delta' - the size of the time step. This is a very technical paper, and I don't think you'll get very far with it if it's all you're using. Have you seen this open source MPM code? |
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| Thanks Warpy! Somehow I had a feeling you would comment on this, with all of your math skills. ok, got the first equation, so phi can be whatever I want it to be so thats just trial and error (right?) so for the mass I just do (m1 + m2 + m3... )*phi for the velocity (m1*v1+m2*v2 ...)*phi its not all im using but it has a lot I dont understand, another pdf i am using is this one http://faculty.cns.uni.edu/~rothm/MPM1.pdf and thanks for the link to the open source mpm, I will be sure to check it out! |
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| no, phi is a function which changes with each particle - it's something like a measure of the distance of the particle from the cell's centre. So the mass is more like m1*phi1 + m2*phi2 + ... Same idea with the velocity. |
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| no, phi is a function which changes with each particle - it's something like a measure of the distance of the particle from the cell's centre. So the mass is more like well that changes things for sure... I found a guy thats trying to explain how he does simulations on youtube. |
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