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35

As a computational physicist working in materials/condensed matter, I'm either highly biased or well-placed to comment on this. Physics, in practice, is divided into three overlapping approaches: experimental, theoretical, and computational. (The highest impact research papers usually include a combined effort from all three.) If you plan to go into ...


35

All of it can be simulated to a certain level of precision - given enough computing power AND correct experimental values for all the parameters. The tricky bit without tests is to get experimental values for eg. the thermal conductivity of Plutonium at TPa of pressure. Experimental tests can also only validate something to a certain level of precision - ...


23

To some extent this answer is echoing things that @Martin said... but from my own point of view. In my experience of (Monte Carlo) simulation, the model you implement captures your knowledge of the physics of the situation; and if your knowledge is "perfect", your calculation, with sufficient compute power at your fingertips, will also be "perfect". ...


18

I think perhaps some of the other answers are taking computer science to be synonymous with computation. I guess that this is perhaps not what you mean, but rather theoretical computer science. There is obviously a huge overlap with quantum information processing of which I think you are already well aware, so I will ignore that. Much of physics (including ...


14

Programming is immensely useful in any branch of physics. I don't know where the notion that programming is not useful at CERN comes from (? Home of the ROOT package, and the internet? Really? TeraGrid, eh? 1 GB/s of data from the detectors at the LHC won't analyze themselves!), but you may wish to revisit your research on that matter. I can say that in ...


13

Starting from 90nm tech processes we've started to see sad signs of stagnation: 1) Most of delay in logic circuits is in interconnect, not transistors 2) Most of energy dissipated is due to quantum tunneling, not transistor switching. By far. 3) As consequence of #2 - transistor gate width scaling has significantly slowed down, as well as dielectric width ...


12

If you really want a general gravitation simulator (i.e. one that will handle more then two bodies), then there are methods for reducing the error involved in the simulation, but there aren't any methods for eliminating the error. Below are a few approaches - none of these approaches are perfect, since there's a balance between physical accuracy, programming ...


11

Crank-Nicholson method is effectively the average of forward (explicit) Euler $\psi(x,t+dt)=\psi(x,t) - i*H \psi(x,t)*dt$ and backward (implicit) Euler method $\psi(x,t+dt)=\psi(x,t) - i*H \psi(x,t+dt)*dt$ The backward component makes Crank-Nicholson method stable. The forward component makes it more accurate, but prone to oscillations. If you want to ...


11

I can't really know why your professor used C++, but there are several reasons why you would: Performance: Scientific computations might require top-notch performance. C++ allows for very low level control over the hardware and has many possibilities for micro-optimization while still providing high-level abstraction. Of course, this is also the reason ...


11

I think anyone who says "there's no need to do experiments, we can simulate everything!" either: Doesn't know what they're talking about Is trying to sell snake oil Is a scientific fraud trying to push pseudoscience as actual science I have never seen a serious, honest scientist claim that simulation is sufficient substitute for empirical evidence, even ...


10

Programming is extremely important in almost every area of physics. Not every physicist has to be an expert programmer, but many are, and virtually all physicists are at least competent programmers. In most experiments, the process of data analysis is complex enough to require some programming. More importantly, in many situations, the best (or only) way of ...


10

EDIT: This answer is specifically from the perspective of very computationally oriented fields like theoretical plasma physics. Most physicists can program, and in fact many are rather good programmers. It would be difficult to work in modern physics without being able to program. Unfortunately, many are also not terribly good programmers (I've read many a ...


10

You are asking two questions. I am only going to address one of them: Can the Church-Turing hypothesis be deduced from other fundamental law of physics? There are two fundamental theories of physics that account for nearly all experiments and observations performed to date: general relativity and the Standard Model. If we could simulate these theories ...


10

this is a broad, complex, somewhat tricky question with many angles that an entire survey or book could be written on but unfortunately it seems one hasnt yet. heres a "grab bag" of some deep parallels noticed over the years that such a book might cover & "research leads" for further inquiry. Modelling and simulation. as computing capability has ...


8

You don't need a really big computer. Peter LePage used to do talks where he'd ask the audience fro a "random" number as the beginning of the talk (but not 7, 17, 42, or 69 'cause he'd already done those) and start a simulation on one screen with that number as a seed. Then he'd give a talk on how to speed up LQCD calculations on the other screen while his ...


8

What you want to do is change the wave equation into a Klein-Gordon equation: $$\frac {1}{c^2} \frac{\partial^2 \psi}{\partial t^2} - \nabla^2 \psi + \alpha^2 \psi = 0,$$ where $\alpha$ is a constant of appropriate dimension and usually (in quantum theory) given by $$\alpha=\frac {m c}{\hbar}.$$ Inserting an ansatz of the form $$\psi=e^{i(kx-\omega ...


8

The sign of a good fit is that the residuals have the same distribution as your model for the errors. Usually the assumption that goes into fitting methods is that the errors are normally distributed. That is, given perfect inputs $x_i$, and an ideal relation $y_i = f(x_i)$, you will measure $y_i + \epsilon_i$, where $\epsilon_i$ are distributed normally. ...


8

But the most glaring is that it is quite clear that the moment you introduce anything less than zero latency (speed of gravity). The entire system falls apart, planets fly off, everything dissipates. Newton himself didn't quite like the instantaneous action at a distance as implied by his law of gravitation. The only saving grace is that it worked. ...


8

Brionus has touched on the key - adaptive time steps. When you start getting large accelerations, reduce the size of your time increments. Also, when you are not accelerating much, increase the size. A fairly standard way to do this is to calculate your position change over one step. Then cut the step in half and, starting from the same starting point, ...


7

While not strictly lattice QCD, Michael Creutz' 30 year old lattice gauge papers have very simple C implementations (!). For example, look at this paper, which gives a very readable explanation of lattice gauge simulations, with source code: http://latticeguy.net/mypubs/pub165.pdf The source code is also available here: http://thy.phy.bnl.gov/~creutz/z2/ ...


7

There exists a variety of options for this task but let me stress first that this is an extremely complicated and difficult issue that is still subject of current research because analytical continuation is an ill posed problem! 1) The 'analytical' analytical continuation can be performed when the function $f(\mathrm i\omega)$ under consideration is a ...


6

The first thing that comes to mind is that the speed of light limits the rate at which different components of a computer, or even a single chip, can communicate with each other. For example, if you have, say, 10 cm of wire running between your motherboard and hard drive, it will necessarily take a minimum of about a third of a nanosecond to fetch data from ...


6

When you think of a physical parameter which is "uncomputable", what precisely do you mean? For us to know that it is uncomputable, it has to arise somehow, on theoretical grounds, from e.g. a compu­tational process which is equivalent to the Halting Problem of theoretical computer science; so that we could not compute it from first principles. ...


6

I'm surprised you haven't found this information online because the equation is one of the most basic in all of physics: $$\mathbf{F} = m\mathbf{a} = m\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}$$ (bold represents a vector). For an application like yours, it will be more useful to rearrange this in the form of an evolution equation ...


6

Some of the SDSS images in JPEG format (for example those served by the SDSS DAS) have sections of the FITS headers of the corresponding data images embedded in them. I expect that other projects have done similar things, but I am not aware of any uniformity in how it is done. For the most part, the image formats you list were really not intended for ...


6

Overlap fermion approach may be the answer (I think for U(1) gauge symmetry only). Ounce a theory is defined on a lattice, it can be simulated by a computer that we already have. Here is a review on overlap fermion approach: Tata lectures on overlap fermions arXiv:1103.4588 R. Narayanan Overlap formalism deals with the construction of chiral gauge ...


6

You are asking quite a few questions, so let me try to go step by step. First, an area law is a very special property among quantum states: If you pick a random state, it will have almost maximal entropy (i.e. a volume rather than an area scaling). So essentially any state would be a counterexample ;-) On the other hand, ground states appearing in nature ...


6

"They" are probably talking about symplectic integrators. Most numerical integrators for (partial) differential equations do not specifically consider the energy of the system; they are generic integrators capable of solving any set of DEs, and not all DE's have a concept like "energy". When these are applied to a classical dynamics problem concerning ...


6

If you look at the Laplacian: $$ \nabla^2=\frac{1}{r}\,\frac{\partial}{\partial r}\left(r\frac{\partial}{\partial r}\right)+\frac1{r^2}\frac{\partial^2}{\partial\phi^2} $$ you can clearly see that this diverges at $r=0$ so discretization of this should also diverge. There are three solutions to remedying the divergent feature that I can think of: Choose a ...



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