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17

There is a great paper from the group of Howard Stone on this subject: Wetting of flexible fibre arrays (freely available here, but for some reason I am not allowed to link to it normally: http://211.144.68.84:9998/91keshi/Public/File/34/482-7386/pdf/nature10779.pdf) They specifically study when 2 closely positioned parallel fibers (i.e. hairs) clump ...


7

No. There is nothing wrong with perturbation theory, or with theories with known, restricted accuracy. The point of theory is to explain the results of observation from as simple an initial theoretical standpoint as possible. Therefore: Since experiment always has a finite uncertainty, one can only ask that theory match the experimental value within its ...


7

This is what I think the first bit of the calculation does. Suppose you start with a spherical eye with a hole in it (e.g. the pupil in the human eye): The radius of the eye is $ER$ and the radius of the hole is $AR$, and with the length $DA$ these form a right angled triangle. Pythagoras' theorem tells us: $$ DA^2 + AR^2 = ER^2 $$ so: $$ DA = ...


5

In physics and engineering, we often abstract and idealize a physical problem to gain insight into the physics, e.g., infinite plane of charge, infinite line of charge, point charge, etc. Now, it goes without saying that if these idealizations didn't represent good approximations of relevant physical systems, they wouldn't be used. With regards to your ...


4

The article looks indeed wrong. In fact, there are two mistakes. First, you're right that the acceptance-rejection method has to be applied to $\rho(r)$, and not to $m(r)$. To understand how this idea works, suppose we want to generate a one-dimensional normalized distribution function $p(y)$. Now, let's assume we can rewrite this distribution function in ...


3

Yes, and this question filled a semester in my 4th year of Physics. The Schrödinger's equation describes the problem exactly... with the caveat that it is impossible to solve exactly for more than one electron. A typical atomic physics course will then proceed to try to develop different methods and heuristics to solve this problem. The basic idea of the ...


2

I could give an example of what people mean when they "say": ... metric tensor depend on the local coordinate system and therefore are not intrinsic to the surface Take for example the Schwarzschild metric. We have $$ds^2 = -\left(1-\frac{2m}{r}\right)dt^2 + \left(1-\frac{2m}{r}\right)^{-1}dr^2 +r^2(d\theta^2 +\sin^2\theta d\phi^2) $$ If you read this ...


2

I suspect you have misunderstood what is meant by acceleration in the context of circular motion. Acceleration is the rate of change of velocity, but remember that velocity is a vector so it has both direction and magnitude. You are probably thinking that acceleration means a change in the magnitude of the velocity, e.g. speeding up from 1 m/s to 2 m/s, but ...


2

You have to split the time domains into the gears needed to reach 60mph. For each gear, there have to be assumptions on the power delivery of the car. Typically 1st gear is traction limited, so you can assume constant acceleration up to the speed where peak power occurs. The relationship between power speed and acceleration is $P(v) = m \,v\, a(v)$. So run ...


2

Yes! There is such a model or equation governing the electron configuration of an atom! It is Schrödinger's Wave Equation. You need to solve it for electrons surrounding an atom, and it is the reason why the Aufbau principle works. (If you want to do it yourself, I suggest starting with Hydrogen, as it is the easiest potential to work in. You'll need to ...


2

There are three reasons why mathematics is stated as an incomplete description of physics. I list them in order from pragmatically physical to more philosophical. Any calculation, any actual prediction of physics is based on a mathematical description that is known to be a mere approximation. You could conjecture that you have the complete list of ...


1

Classical physics describes the movement of the center of gravity of extended bodies, which, when poorly taught, in the mind of the student becomes equivalent with "classical physics being a theory of point particles". That, of course, is utterly false, even on the level of the classical description. A center of gravity is a vector, not a point. ...


1

This might be unusual, but I will now give an answer to my own question. Maybe somebody who reads this has the same problem and finds this interesting. After all, I have been able to successfully solve also problem (2), and both algorithms actually work quite well. The approach was to calculate both beam and diffuse parts on the horizontal for all ...


1

There are strong constraints on antigravitating antimatter, because it could, in principle, be used, to create a perpetual motion machine. 1) Use energy $E$ to create a particle/antiparticle pair at height $h_{i}$ 2) Raise the particle/antiparticle pair to a height $h_{f}$. This takes zero work, because the antiparticle will be pushed up in the ...


1

Astrophysicists have been looking at electron positron annihilations in the cosmos The Universe viewed trough INTEGRAL: the first complete map of the sky at the electron-positron annihilation energy (Credits J. Knödlseder - CESR - September 2005). If there existed regions in the sky where antimatter was aggregating, the interface between matter and ...


1

Whenever you come up with a theory (eg: Newtonian mechanics), it has some physical domain of validity, and then you come up with the next (better) theory (eg: relativity), and so on. This process might not have a "fixed point". At least if you had a fixed number of things to explain, then you might be able to consider iteratively simplifying it to an ...


1

From http://en.wikipedia.org/wiki/Scientific_theory: "Scientific theories are testable and make falsifiable predictions. They describe the causal elements responsible for a particular natural phenomenon, and are used to explain and predict aspects of the physical universe or specific areas of inquiry[...]. Scientists use theories as a foundation to gain ...


1

The CDF, $F(x)$, is related to the PDF, $f(x)$, via the relation: $$F(x) = \int_{-\infty}^xdx'\,f(x')$$ In the case of radial distributions, your lower limit is obviously 0 and not $-\infty$. Thus, your CDF is $m(r)$ and the PDF is $4\pi(r')^2\rho(r')$ (technically should be $\rho(r')$ with the $4\pi(r')^2$ coming from $dx\to dr$ and spatial isotropy, but ...


1

There will always be solutions that can't be analytical. For example, any model of more than two bodies without any special constraints, cannot be solved analytically. From the gravitational interactions between three planets to three particles interacting (electromagnetically or otherwise) in quantum theory. To have mathematically analytical solutions, ...



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