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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

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 = ...


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 ...


5

No. Notoriously, supersymmetric string theory has to be formulated in 10 dimensions in order to be consistent. Another example is supergravity, which can be formulated in a maximum of 11 dimensions otherwise it predicts particles with spins higher than two.


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

Mathematics is just a systematic way of stating facts about the world. It is only useful inasmuch as it is internally self-consistent. The latter fact means that there is nothing to "assume" about mathematics. It is a relationship between axioms and conclusions that enables one to succinctly summarize many observations. Something like Galileo's ...


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

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

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 ...


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, ...


1

Short answer: that depends on your definition of sound theory. For instance, it is possible to find peer-reviewed papers considering such possibilities. The idea that antimatter can be gravitationally repulsed from ordinary matter is definitely not the most popular one. Nevertheless, some people do try to apply it in astrophysical context. Let us have a ...



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