35

One example that appears in many areas of physics, and in particular classical mechanics and quantum physics, is the two-body problem. The two-body problem here means the task of calculating the dynamics of two interacting particles which, for example, interact by gravitational or Coulomb forces. The solution to this problem can often be found in closed form ...


27

A famous example is the boolean satisfiability problem (SAT). 2-SAT is not complicated to solve in polynomial time, but 3-SAT is NP-complete.


27

In one and two dimensions, all roads lead to Rome, but not in three dimensions. Specifically, given a random walk (equally likely to move in any direction) on the integers in one or two dimensions, then no matter the starting point, with probability one (a.k.a. almost surely), the random walk will eventually get to a specific designated point ("Rome"). ...


21

Here's one close to the hearts of the contributors at SciComp.SE: The Navier–Stokes existence and smoothness problem The three-dimensional version is of course a famous open problem and the subject of a million-dollar Clay Millenium Prize. But the two-dimensional version has already been resolved a long time ago, with an affirmative answer. Terry Tao notes ...


20

In social choice theory, designing an election scheme with two candidates is easy (majority rules), but designing an election scheme with three or more candidates necessarily involves making trade-offs between various reasonable-sounding conditions. (Arrow's impossibility theorem).


14

I personally have come the way from Gnuplot to Matplotlib with PGFPlots as an intermediate step. I will try to name all aspects of Matplotlib that I like. It is very versatile. You are not limited to line or scatter plots, you can easily do bar plots, images (matrix visualization!), basic 3D plotting and even some animation. You can use Matplotlib as a GUI ...


14

The link Godric pointed out under the question is exactly right. It gives a good overview of the many talents a computational scientist has to have. In general, the difference between being a Computational X (X=mathematician, civil engineer, materials scientist) and being a Theoretical X or Experimental X is that the former tackle problems with computers ...


11

For such a small simulation, I would strongly suggest looking into GPU-based solutions. This is probably what will get you the most ns/day/Euro. In my opinion, the fastest fully-featured GPU-based Molecular Dynamics (MD) software out there is ACEMD (see here for timings). The software, however, is commercial, but has a single-GPU free version that can be ...


11

Simultaneous diagonalization of two matrices $A_1$ and $A_2$: $$ U_1^T A_1 V = \Sigma_1,\quad U_2^TA_2V=\Sigma_2 $$ is covered by existing generalized singular value decomposition. However, when the simultaneous reduction of three matrices to a canonical form (weaker condition compared to the above) is required: $$ Q^T A_1 Z = \tilde{A_1},\quad Q^T A_2 Z = ...


9

Your goal has a lot of challenges. I'll break them down into parts. SMILES is not a trivial language to parse, and the rules for aromaticity perception are not well defined. The detailed grammar definition from the OpenSMILES project should help some. SMILES defines the topology, but does not give 2D or 3D information. Making either is hard. (That is, if ...


9

There are plenty of examples in quantum computing, although I've been out of this for a while and so don't remember many. One major one is that bipartite entanglement (entanglement between two systems) is relatively easy whereas entanglement among three or more systems is an unsolved mess with probably a hundred papers written on the topic. The root of ...


8

The most popular molecular dynamics codes are namd and gromacs, and maybe also desmond. These packages are freely available and "open source" in the sense that the source code is made available for free. Wikipedia hosts a list of software for molecular modeling which may contain other good links. These codes, however, are also quite complex and therefore if ...


8

Aesin already answered part of your question. I can provide you with some more information on GAMESS(US). It is possible to make GAMESS(US) use the same 'type' of B3LYP as Gaussian 03. For this, you need to specify "DFT=B3LYP1" as you already mentioned in your question. This selects B3LYP with VWN formula 1 RPA local correlation which, to the best of my ...


8

Some of the algorithms are available from the source code for the different packages. PyMol is one such, and VMD's source is also accessible. I implemented VMD's ribbon algorithm in the 1990s. The first step is the structure determination - where are the amino acids? which are connected into a chain? where are the C-alpha atoms? Next, as Kyle said, is the ...


8

Many of us in scientific computing simply have well-equipped laptops for regular software development tasks, some multicore workstations for smaller-scale testing, and access to clusters for larger runs. To give you an idea: My laptop is a Dell M3800 (4-core Intel i7, hyperthreading, 16GB of RAM). This is good enough to regularly compile my software and do ...


7

ChemSpider (http://www.chemspider.com/) provides structures in mol format, which is simple enough to convert to XYZ, e.g. using OpenBabel (http://openbabel.org/wiki/Main_Page).


7

The Hartree-Fock equations are the result of performing constrained Newton-Raphson minimization of the energy with respect to the parameter space of Slater determinants (I don't have my copy of Szabo-Ostlund at hand, but I believe this is pointed out in the derivation). Hence, HF-SCF will converge if your starting guess is in a convex region around a minimum....


7

I oftem use Matlab and then save the result as an eps file via print -depsc2 -f1 fig. This saves figure 1 as an eps file named fig.eps. There is also the Plot2Svg from matlab file exchange that can save as svg. This is really nice since you can then open the files in Inkscape or other vector graphics software and edit them. If you are willing to learn new ...


7

If you're willing to overcome the learning curve of Gnuplot, you can generate top-quality figures with it (as exemplified in http://www.gnuplotting.org/). In particular, I'd recommend using the epslatex terminal as it allows you to use LaTeX to render all the text in the figure (including any mathematical notation that you may wish to input). If you want ...


6

I'll take a stab at it. The protein cartoon (also known as ribbon) representation consist of three parts corresponding to the three types of protein secondary structure. Random Coil (shown in green) - A B-spline, usually of order 2 or 3, passing through the alpha-carbons of each amino acid residue. Occasionally the spline will also pass through the amino-...


6

To put it crudely, you will not be a good professional if you claim to do 'computational science' but do not know programming. To do computation, you need a tool. And computer is such a tool. Programming is the only way to teach computer how to do a thing. Therefore programming is an essential part of computational science. This is not to say that it is ...


6

You could install BOINC on those machines. When the computers become idle, the BOINC screensaver/client requests tasks from a server and computes them. See more information about it here. This is the software used by a number of projects such as SETI@Home. You can create your own project with BOINC and then put your desktop machines to work.


5

Would Pymol or VMD be a suitable tool for your video needs? (VMD at least includes Tk/Tcl scripting features.) You would need a PDB-like description of your geometry in order to use VMD; this would probably be sufficient for Pymol as well (but I haven't used Pymol, so perhaps someone else can comment on that).


5

The way I'd do it would probably be: Put the molecular geometry into Avogadro Set up the view to be exactly the way I want it Export to POVRay, not rendering but keeping the input file Work out which atom is which in the POVRay file Add vectors using cylinders and cones (probably using a macro to define a vector to make it easier and visually consistent) ...


5

Frozen core approximations use explicit orbitals for each core electron, which leads to explicit Coulombic potential terms: $$ \langle v|V_{val,core}|w\rangle = \sum_{i\in core} \int \frac{v^\ast(r)w(r)|\phi_i(r_1)|^2}{\|r-r_1\|}-\frac{v^\ast(r)\phi_i(r)\phi_i^\ast(r_1)w(r_1)}{\|r-r_1\|}d^3r_1d^3r$$ Effective core potentials model the potential directly ...


5

Besides Pedro's suggestions, you could also look at Quantum Espresso, which among other things allows for Car-Parrinello computations. It is (or at least, it was) written in Fortran 90.


5

writing software is an iterative process - write code -> see how far you can get then plan next steps -> write code -> repeat. At this stage in learning the art I'd suggest you jump in soon just to test the waters. No need to plan the entire system up front. Yes python would be a good first language. For visualization try out MatPlotLib, also NumPy and ...


5

You can use HTCondor that is designed exactly to "steal" cpu cycles from remote machines. It may be a little difficult to setup but I think this may be the best approach.


5

Your intuition is right, for example in 3D Orbitals (German Wikipedia) the caption explicitly states that 90% iso-surfaces are used. I have however seen different percentages before where the results look similar. Did you check the Mayavi Example Atomic Orbital? If you remove the phase-coloring and find the additional parameter to contour that sets the ...


5

You could either fit a logistic function (possibly composing it with a linear function), use segmented regression, or classification and regression trees, among other options. The original data, shown in the figure below, was fitted in Gnuplot using the following commands: h(x) = k * 0.5 * (1.0 - tanh(0.5 * (a * x + b))) + c * x + d fit h(x) 'plot-EV.txt' ...


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