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You are asking how to numerically solve a second order initial value problem. An initial value problem involves advancing some initial state over time given an ordinary differential equation (ODE) that describes the time evolution of the state. There are many books, journal articles, and college classes about this topic. There is no one perfect technique. ...


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Your equation in the Liouville form is elementary for numerical integration, it is structurally just a linear advection equation with spatially varying coefficients. The transformed equation with the kernel F is not useful at all for numerical solution, don't bother with it. All we have here is a 2D advection equation (I use y instead of p): $ \partial_{t} ...


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Yes, I'm doing research with exactly such a concept right now. It is called molecular dynamics. It works exactly as you stated: you feed atom types and positions into it and get the time evolution of the system. I am also using what is known as a reactive potential, which allows chemical reactions, and the formation of bonds and ions (specifically, I am ...


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I am not sure what the exact system is from the description. However, if you are considering the Hamiltonian of the form $\mathcal{H} \sim J_{ex}\sum \sigma_i \sigma_j$ or something similar, then the corresponding partition function will be $Z \sim \sum e^{-\frac{J_{ex}}{k_B T}\sum \sigma_i \sigma_j}$. It is pretty clear that the physics only depends on the ...


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As some other materials in addition of those definitely helpful references proposed by Michiel, I found the following very useful resources: a full review of many concepts in droplet dynamics has been presented in this book: Ashgriz, N. Handbook of Atomization and Sprays. Vol. 11. Springer New York, 2010. for droplet collision: Rein, Martin. ...


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Hints: OP's eq. (1) is the equation for a constant of motion $\frac{df}{dt}=\{f,H\}_{PB}+\frac{\partial f}{\partial t}=0$ of a harmonic oscillator $H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2 x^2$. Let us assume for simplicity that $m\omega=1$, and leave it to the reader to generalize to arbitrary $m$ and $\omega$. Complexify $z=x+ip\in\mathbb{C}$. Then the ...


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As far as I understand, detailed theory knowledge of ray optics will only ever take you so far, because in real laboratory situations the setups are much too complex to deal with using pen and paper. This means that, in practice, all the relevant physics gets implemented by an appropriate ray-tracing software package. As a beginner, it is therefore ...


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Check out Richard Feynman's QED lectures. It's not quantum gravity yet but it might be what you're after.


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Books For fundamentals I prefer books over papers, because they are typically more thorough and a little bit more 'slow' in the introduction of concepts. There are many books that will cover, some of, the topics that you mention. I will mention below the 3 books that where most useful to me in the past. 1) An excellent resource for a theoretical foundation ...


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i would like to provide another answer (despite my comments on top or complementary to them) i would propose to use a historical account of the evolution of the concepts and ideas/methods in physics from Newtonian mechanics to Relativistic mechanics, including the specific problems that arised (this provides two things: 1. a perspective on the methods and ...


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I created this site early in 2014: SpecialRelativity.net The site was built specifically for people who aren't keen on math.


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You don't say at what level you are studying this. Before you get stuck into the intricacies of exotic neutron star equations of state you need a good grounding in statistical mechanics and nuclear physics. A good place to start is the first few chapters of Shapiro & Teukolsky; "White Dwarfs, Neutron Stars and Black Holes" ...



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