A Computation in a Cellular Automaton Collider Rule 110

A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.Comment: 39 pages, 32 figures, 3 table

Cellular automaton supercolliders

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems

Development of a collision table for three dimensional lattice gases

Bibliography: pages 92-95.A lattice gas is a species of cellular automaton used for numerically simulating fluid flows. TransGas [9], the lattice gas code currently in use at the CSIR, is based on the FHP-I model [5], and is used to perform various two-dimensional flow simulations. In order to broaden the scope of the applications in which lattice gases can be used locally, the development of a three-dimensional lattice gas capability is required. The first major task in setting up a three dimensional-lattice gas is the construction of an efficient collision rule generator which will determine collision outcomes. For suitability to local applications, the collision rules should be chosen in such a way as to maximise the Reynolds coefficient of the flow, while conserving quantities such as mass and momentum. Part of the task thus becomes an optimisation problem. When expanding from two to three dimensions, the number of possible collision rules increases from 64 to 16777216. If a complete collision rule table is used for determining collision outcomes, storage problems are encountered on the available hardware. Selection and optimisation of collision rules cannot be done by hand when there are so many rules to choose from. Selection of rules is thus non-trivial. The work outlined in this thesis provides the CSIR with a 3-D lattice gas collision table which is well suited to the available hardware capabilities. The necessary theoretical background is considered, and a survey of the literature is presented. Based on the findings of this literature study, various methods of collision outcome determination are implemented which are considered to be suitable to the local needs, while remaining within the constraints set by hardware availability. An isometric collision algorithm, and a reduced collision table are generated and tested. A measure of the overall efficiency of a lattice gas model is determined by two factors, namely the computational efficiency and the implementation efficiency. In testing a collision table, the first is characterised by the rate at which post-collision states can be determined, and depends on the hardware and programming techniques. The second factor can be expressed by means of a number called the Reynolds coefficient, which is defined and discussed in the following chapters. The higher the Reynolds coefficient of a model, the greater the scope of flow regimes which may be simulated using it. Another advantage of having a high Reynolds coefficient is that the simulation time required for a given flow regime decreases as the Reynolds coefficient of the model increases. The overall efficiency of the isometric model is too low to be of practical use, but a significant improvement is obtained by using the method of reduced tables. In the isometric case, the number of collision outcomes that can be determined per second is similar to that of the reduced table, but the Reynolds coefficient is very much lower. Simulation of a flow regime with a Reynolds number of about 100, on a lattice of size 128³, over 20 thousand timesteps, making use of the isometric model, would take of the order of a few years to complete on the currently available hardware. Since the simulation parameters mentioned above are typical of the local requirements for lattice gas simulations, this method is obviously unsatisfactory. The isometric method does however serve as a useful introduction to three-dimensional lattice gas collision rule methods. The reduced collision table has been constructed so that it maintains semi-detailed balance, and the Boltzmann Reynolds coefficient has been calculated. In the reduced collision table model, the efficiency is higher than the isometric case in respect of both the rate at which collision outcomes can be determined, and in terms of the Reynolds coefficient. As a result of these improvements, the simulation time for the exact case mentioned above would reduce to the order of days, on the same hardware. This simulation time is sufficiently low for immediate practical application in the local environment

Pattern Recognition, Tracking and Vertex Reconstruction in Particle Detectors

The book describes methods of track and vertex resonstruction in particle detectors. The main topics are pattern recognition and statistical estimation of geometrical and physical properties of charged particles and of interaction and decay vertices