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It will rotate arround their center of mass, which can be computed: $$ \mathbf R_{cm} = \iint_S\mathbf r'\sigma(\mathbf r')dS $$ And therefore, the torque: $$ \mathbf \tau = \iint_S (\mathbf r' - \mathbf R_{cm})\times\mathbf F(\mathbf r', t)\sigma(\mathbf r')dS $$ If you know the shape of the object and its density, you can do the integration manually and ...


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A thought experiment: after N steps, each of which create a change in angle $\Delta \theta$, we should end up with a normal distribution of angles with a standard deviation of $\frac{\sigma}{\sqrt{N}}$. When you change the step length, you therefore need to scale the standard deviation by the square root of that change, so that after moving the same distance ...


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You pretty much have the right ideas here. The MC is necessary because the functional dependence of the detector response and the underlying physics is too complex to calculate in any other way. And therein lies the actual analysis problem: it's not enough to simulate the physics based on the standard model (or some other hypothetical interaction). In order ...


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You don't say what simulation technique you are using, but clearly errors are adding energy to the system. A simple one would be to take a starting position $(x,y)$ and velocity $(v_x,v_y)$. Note that if your velocity is not exactly right for a circular orbit, you should just get an ellipse that is close to the circle you are after, so that is not your ...


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Looks like the Astigmatism is measured from the diodes surface as per Stephern Blake's answer. The fast axis divergence is measured from the diodes surfaces and then the astigmatism is the position of the beam source point of the lens behind the diode surface. The fast axis beam waist must be on the diodes surface at Py and the slow axis beam waist at Px. ...


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My impression is the beam is not Gaussian at all, as the beam divergence in two orthogonal planes differs dramatically.


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Yes, you can simulate non-locality in celular automata, even if the rules are local. In such a case, contiguous cells do not represent adjacent points in our space. In these models space is an approximate, macroscopic emergent property (it is discussed in detail in NKS). This emergent space can have, at microspcopic scales, functional links that resemble the ...


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Acceptance is some measure of the fraction of events or the spacial or momentum distributions of events that will be registered in the detector. The exact meaning varies from experiment to experiment and sometimes from analysis to analysis within a single experimental data set. Understanding the acceptance of a experiment for a particular signal can be a ...


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The best way to numerically work with continuous phase transitions is to study observables that have a vanishing length dimension (or mass dimension in the language of QFT). Take for example the Binder's cumulant ($\langle m^4\rangle/\langle m^2\rangle^2$ modulo factors of 3 and constants, where $m$ is the order parameter) or the correlation length scaled by ...


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The planet will follow an elliptical path and as an ellipse is a 2D figure it can only be traced to a plane and from two points infinite planes can pass, so you need to decide first which plane you want which is the missing information, because of which you are not able to do so. If finally you form a plane $\vec r.\vec N=p$ then the direction of the ...



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