CACR Entrance Examination: Advanced Computing Techniques (Level I)

(Two Hours)

Candidates may attempt as many questions as time permits. The use of calculators is permitted. Candidates who conceal about their person, and then attempt to use, any type of supercomputer, will be disqualified.

(1) A next-generation hypercube supercomputer is installed in CACR, and begins running a large N-body problem. Nodes in the machine are allocated a fraction 1/M of the computational elements, where M is the problem size. During execution of the application, each node displays its CPU load via a set of bright LEDs on the front panel of the machine. Describe the appearance of the machine:

1. Under rotational transformation of each node

2. Under rotational transformation of the observer

3. Under water

4. In the plane of observer

5. In the train or automobile of the observer

(2) The Beowulf system, an ensemble of 32 PCs, is re-programmed to run a multi-player death-match frag-fest in Quake II. If the only weapon available to the game proponents is the Nine-Inch Nailgun, evaluate the network load on the Ethernet switch for each inter-node nail.

(3) A Computational Fluid Dynamics (CFD) code has been developed which allows Monte Carlo simulation of the motion of liquid down a human throat. Develop a set of simulation boundary conditions in the case of gas-filled beverages, and evaluate an approximate condition beyond which chaotic behaviour of the liquid occurs in the region of the throat.

(4) A region of the night sky is digitised using a telescope situated in Pasadena, and a similar instrument situated in Hawaii. Show that the images are equivalently detailed only after a ten-year traffic ban in the Los Angeles basin. Using the formula you derived, make arguments justifying an extended stay in Hawaii to examine the instrument located there.

(5) Add a term to the equation governing the gravitational attraction between two bodies, to arrive at a formula predicting anti-gravity at large inter-body distances. Use a hand-held calculator if necessary. Propose a method of simulating how the Crab Nebula would appear under the influence of this new law, and sketch its probable shape.

(6) The largest SMP machine in the CACR computer center is an air-cooled, eight-cabinet, 256 CPU turbo charged device running off a 110 volt overhead power line, backed up by an Uninterruptible Power Supply (UPS) consisting of three thousand 12 volt car batteries wired in series and parallel. Describe the effect of shorting the switching fabric to a conveniently located 12 foot square copper plate sunk in the ground.

(7) Scientists have searched for many years for the solution to everlasting Youth. Evaluate the impact of a discovery in this area when applied to supercomputing research, and elaborate it with your own interpretations of Einstein’s general theory of Relativity. You may use a slide-rule.

ÓJ.J.Bunn, 2000