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if you write the recurrence as a homogeneous linear system $A\mathbf x=0$, a necessary and sufficient condition for proportionality of (nonzero) solutions is that $\dim\ker A=1$. For a simple ...

If one moves a plate through the air at a uniform velocity $v$, the pressure exerted on the area $A$ of the plate is: $$p=\frac{1}{2}\rho_{air}v^2 \space .$$ This pressure is measured by the ...

Im a 7th grader so I'm not good in physics that much, but I'm just a curious boy which wants to become a cosmologist.Can the amount of energy or particles run out? For example pizza dough can be ...

I am currently reflecting a bit on the formal structure of the theory presented in Callen's classic text Thermodynamics and an Introduction to Thermostatistics. I was originally going to post a more ...

I'm reading Renato Portugal's "Quantum Walks and Search Algorithms". In The Postulates of Quantum Mechanics, under the heading 'Evolution Postulate', there is the Mach Zehnder experiment, with the ...

In a hypothetical scenario where the coupling of the fermions to the gauge fields were extremely small, would it be possible to observe quark and charged leptons oscillate in the same manner as we ...

I've noticed that if I rub a plastic spoon with some fabric for ~20 seconds and hold it near a compass, it will attract its nearest pole. However, if I keep the spoon stationary, the needle will drift ...

A system made of an even number of fermions behaves like a boson in terms of quantum statistics. One example for that would be the hydrogen atom consisting of one proton (spin-1/2) and one electron (...

Reading Schutz's book on GR: On page 9, there's a derivation (reproduced in the picture below) that I don't follow. If all the barred coordinates are combinations of the unbarred coordinates, then ...

Recently I've been reading up a bit on inflation and the subsequent reheating of the early universe. What has left me a bit confused, however, is that in all of the notes/papers that I've read so far ...

I'm having trouble understanding how two entangled particles stay correlated once they are measured. As an example, if they are anti-correlated in their spins, and one particle is measured to have a ...

Pauli repulsion and Bose--Einstein condensation (BEC) arise from quantum statistics and are not considered fundamental forces. That is, they are neither gravitational nor electrostatic in nature, ...

I have seen in many textbooks the following equation for a combustion chamber $$ \eta \, m_{fuel} LHV = m_{out}h_{out}(T_{out}) - m_{in}h_{in}(T_{in}). \quad (1) $$ Consider now the stoichiometric ...

I am trying to understand static structure factors, $S(Q)$, for liquids. This function represents pairwise correlations in reciprocal space and can be measured experimentally using X-ray or neutron ...

In a Fermi liquid the momentum distribution shows a jump at the Fermi surface, i.e. \begin{equation}\langle n_{k_F-\delta k} - n_{k_F+\delta k}\rangle = Z_{k_F}\end{equation} with $Z_k$ the strength ...