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So as a proper, over ambitious programmer, I decided to tackle a problem that is at least 3-6 years worth of education above my head, delving into big scary math where nobody my age (nor my teachers for that matter) have dared bury their heads in equations before. For context, this is where my problem comes from : http://www-evasion.imag.fr/Membres/Fabrice.Neyret/NaturalScenes/fluids/water/waves/fluids-nuages/waves/Jonathan/articlesCG/simulating-ocean-water-01.pdf I want to try to simulate ocean waves before I get into other scary water related math problems. I currently have two problems, they both involve programming the equation: The equation h(x, t) = Ʃ mean_h(k, t) exp (ik · x) k where h is the height, x is the wave direction vector (2d vector), mean_h is h with a line over it (I believe it is the mean height, hence the name) , t is time, k is another 2d vector that I think I've defined in programming. (this is more clearly on the article at 4.3, equation 36 in the article) But some parts of the equation raise questions... such as what to do with the exp(ik * x) , I can do the exp(I * x) just fine (its obviously a dot product), but how do I treat the i, it appears to indicate the complex number, but what should I do ? supposing that just means (0,1) (since it can mean that), what do I do between it and the I (ik * x), should I do a cross product or a dot product seeing as it doesn't have a dot unlike the other term. The second problem I have is putting the sigma into programming, the person who wrote the equation does not give everything that summation normally does, it uses a vector of all things as the start point, gives no end... It also leaves me clueless as to the mean height, how do I obtain it ? it doesn't indicate in the article, is it just a product of the summation ? tl;dr : I have math problems with that equation involving just about everything after the = sign.
http://www.redorbit.com/news/science/1113411769/for-the-first-time-scientists-observe-a-two-phonon-quantum-interference-123015/ This is kinda of a science dead period for the forum and just about anywhere. Phonons are simply waveform quanta. If we remeber everything has a wavelength, the more massive the object the smaller the wavelength.