175

For organic matter, such as bread and human skin, cutting is a straightforward process because cells/tissues/proteins/etc can be broken apart with relatively little energy. This is because organic matter is much more flexible and the molecules bind through weak intermolecular interactions such as hydrogen bonding and van der Waals forces. For inorganic ...


24

The question isn't silly. The speed of each molecule in the liquid is much higher than the speed of either the piston or the water shooting out from the nozzle. At room temperature, for water molecules the average is on the order of 500m/s. And yet, the speed of sound in water is three times higher than that, which implies that pressure can propagate in ...


22

It depends on what's being cut. When metal is cut, what happens is that, on a small or not so small scale, it shears. That means layers slide over each other. The mechanism by which they slide over each other is that there are imperfections in the crystal structure called dislocations, and the crystal layers can move by making the dislocations move in the ...


22

Adjacent molecules in a liquid all repel each other because of the electron clouds that surround the nuclei that they contain. In that sense these molecules never even 'touch' each other (at least not in the intuitive sense of the word). When you apply pressure to the liquid you're squeezing them into a (very slightly) smaller volume, thereby increasing the ...


20

You are thinking of a lego or a jigsaw puzzle. You have to think of huge numbers and tiny dimensions . There are $10^{23}$ molecules in a mole. The atomic dimensions are less than $10^{-9}$ meters. The lattice that has been broken will not fit the puzzle if it has been moved further than this last small distance because the molecular forces will not match. ...


13

First of all you need to understand how the rubber is held together in the first place. Rubber, plastics, carbon fibre and pretty much all forms of living tissue are held together in the same manner. All, or a large part of the molecules are long strings, either repeating the same simple pattern, or a number of slightly different patterns organised in random ...


8

I have written an answer to Mathoverflow in which explicit formulas for the classical and quantum Hamiltonians of a spin system (Generators of $SU(2))$ were written explicitely. The classical Hamiltonians are given by means of functions on the two sphere and the quantum Hamiltonians by means of holomorphic differential operators (which act on the sections of ...


8

Your question is perfectly valid despite most people may think it's odd as reason looks obvious. There's a property of system called entropy which must not decrease for any process (do some research on web; You may have problem in understanding it as you're in high school). Only those processes in the universe happen in which entropy of system either stays ...


7

Your mistake is to multiply the equation $$\sum_a \int dR \left[ (E_a + T_\text{nuc} + V_\text{nuc-nuc} - \mathcal{E}) \chi_a(R) |E_a(R)\rangle |R\rangle\right] = 0$$ on the left by $\langle E_a(R)|$. The left-hand side is a vector in $\mathcal{S}_\text{mol}$, and while you can project it down to $\mathcal{S}_\text{nuc}$ by multiplying it on the left with a ...


7

A one atom thick wire will not cause any damage to the finger whatsoever. A free hanging one-atom thick wire won’t even be stable. Regardless, let’s examine what happens when you apply tiny force on your finger. Let’s take a special case: you have a scab on your finger. You’re trying to cut your finger with a scab with an “unbreakable” one-atom thick wire; ...


6

Let's simplify things down to the barest minimum: one dimension, one particle, and a wall. O | The particle moves to the right, hits the wall, and rebounds, perfectly elastically. If the wall is fixed in place, the particle will leave the collision with exactly the same kinetic energy as it came in with. But what if the wall is moving to ...


5

This is related to NVE vs NVT. When I once had to do a molecular simulation, the goal was to make the molecule trajectories as accurate as possible. Therefore I did molecular dynamics, initialized with NVT, checked that the pressure was appropriate, then did the production run with NVE. The usual ways to implement NVT--where there are imaginary frictional ...


5

Reading a discussion on this topic on the XKCD forums, it seems there is a whole book dedicated to this question. If you check e.g. page 51, the graph there indicates a much more detailed structure than an uniform one. To be more precise, there are several mechanisms in play: evaporation ice formation ice melting influx of fresh water Several quotes: ...


5

Many of the proposed answers focus on entropy and the low probability of all the microscopic components of the process coming together to result in a reformed band. I'm not convinced these answers get to the second part of your question: given infinite time will the band be reformed? Before coming to my approach to answering your question, a brief look at ...


5

There is a practical and a "theoretical" limit to why you can't just run longer with molecular dynamics simulations. First, the practical limit. If you are looking at an atom and you want to accurately resolve something, you need to have a sufficient number of temporal integration points per time scale of interest. Since we are looking at atoms and ...


5

Alpha particles are only significantly scattered by nuclei. Electrons are so much lighter than an alpha particle that it is hard for the alpha particle to transfer much momentum to them. But nuclei are small. The radius of a nucleus is of the order of $10^{-5}$ times the radius of an atom, so the cross-sectional area of the nucleus is of order $10^{-10}$ ...


5

Static electricity is counter-intuitive, because small charges can lead to high voltages. Once you create a path for the charge to move away, that small charge only produces a small current. And because of the high voltage, it's fairly easy to create such a path. Of course, when the blanket is stuck together because of static electricity, it means there are ...


4

A month (and lots of lines of code) later, I have finally gained a better understanding of what I have been asking here previously. The book by Frenkel and Smit shed some light into this: when you are running an MD simulation, you are doing this in in something that is very close to the NVE ensemble. It is possible to run an MD simulation in something that ...


4

You are right, there is most likely a typo in the paper. Presumably they mean $$U(r_{ij}; \lambda) = 4\epsilon\left(1-\lambda\right)^{n}\left\{ \frac{1}{\left[\alpha\lambda^{2}+\left(\frac{r_{ij}}{\sigma_{ij}}\right)^{6}\right]^{2}}-\frac{1}{\alpha\lambda^{2}+\left(\frac{r_{ij}}{\sigma_{ij}}\right)^{6}}\right\}. $$ This is what's given in their reference (...


4

To amplify on something in the Ron's answer: Fixed energy is hard to maintain numerically; the slight computational errors accumulate over time. The "thermalization" effects serve to fix this, and keep the overall system with a (relatively) stable average energy (large N).


4

You have broken the chemical bonds between the molecules by inserting energy which is then dissipated. You also distorted the molecule structure. To repair this you should again insert energy. Holding the pieces together does not provide the energy, nor reorders the molecule structure. The answer to your second question is this no.


4

Good conductors are materials providing a lot of efficient electric charge transporters. electrons and ions are two kinds of them. But electron are light and in stable phase in metal, while ions in fluids are heavy, slow, and need the fluid to be there, contained, not changed too much in partial densities of components, and this for a very long time if it's ...


4

I'm presuming your question isn't whether this could be done at all, but whether such a solution would be "better" in some sense than existing launch methods. Given the expense of the balloons, I can't see how this would reduce the cost of launches. let's look at just one specific aspect: How much would just the gas cost if we were to try this with ...


4

This comes from an approximation of the logarithms. The variance can be written by rearranging the logarithms as $$\left( \ln\left[ \frac{\frac{1}{n_0}\sum_{i=1}^{n_0}f(q_i)e^{-\beta U_1(q_i)}}{\langle f(q)e^{-\beta U_1(q)}\rangle_0} \right] - \ln\left[ \frac{\frac{1}{n_1}\sum_{i=1}^{n_1}f(q_i)e^{-\beta U_0(q_i)}}{\langle f(q)e^{-\beta U_0(q)}\rangle_1} \...


4

So your thought about statistics would be correct if not for one basic fact about atoms and molecules: Molecules are sticky. There's actually a couple of different ways that molecules can be sticky, which is why when you put oil into water the oil sticks to itself and the water sticks to itself, but they don't stick to each other. In fact when things are ...


3

You are confused by a slightly misleading aspect of the usual presentation of the Franck-Condon principle. The FCP does indeed rely on a separation of slow and fast timescales, but now the fast timescale is not that of the electronic motion but that of electronic transitions. The typical setting of single-photon transitions in a weak field is tricky to deal ...


3

A sharp knife is still several molecules thick on the edge; dull blades are even wider. So when you attempt to cut material, it needs to be ripped apart. As explained in other answers, the material either fractures along faults in the lattice, or you separate molecules (as when you cut bread). The only materials where you might split chemical bonds are ...


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