Simulation of Random Growth Processes

Growth and Fractal Structure of Ceramic Precursors

MRS Bulletin ◽

10.1557/s0883769400066914 ◽

1987 ◽

Vol 12 (7) ◽

pp. 29-33 ◽

Cited By ~ 2

Author(s):

Keith D. Keefer

Keyword(s):

Periodic Structures ◽

Dense Body ◽

Chemical Constituents ◽

Ceramic Materials ◽

Growth Processes ◽

Crystalline Materials ◽

Special Cases ◽

Random Structures ◽

Ceramic Precursors ◽

Random Growth

Ceramic precursors are the chemical constituents of ceramic materials in a form in which they can be manipulated and shaped prior to processing to form a dense body. Generally these precursors are finely ground crystalline materials such as oxides or clays. Recently, however, much effort has focused on preparing precursors by chemical rather than mechanical means. The goal is to prepare purer, more homogeneous, and more reactive precursors than mixed crystalline powders. A wide variety of chemical processes have been devised to grow ceramic precursors, including powders formed by precipitation reactions, gels formed by hydrolysis and condensation reactions, and gas phase pyrolysis, to name just a few. Due to the random nature of the growth processes, these precursors often have structures wholly unlike their mechanically derived counterparts on both an atomic and a “macromolecular” scale. Random growth and structure and the effect of these structures on the subsequent processing of ceramics is an area of growing interest.Random structures are inherently more difficult to describe and study than are the ordered, periodic structures of crystals. With the exception of a few special cases, such as random walk polymers, little of a quantitative nature could be said about them until the development of fractal geometry and the accompanying realization that the structures which result from many random growth processes are, in fact, fractal.

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Simulation of random growth processes

The Monte Carlo Method in Condensed Matter Physics - Topics in Applied Physics ◽

10.1007/3-540-60174-0_5 ◽

1992 ◽

pp. 93-120 ◽

Cited By ~ 3

Author(s):

Hans J. Herrmann

Keyword(s):

Growth Processes ◽

Random Growth

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Pattern Learning and the Control of Behaviour by All-Inhibitory Neural Network Hierarchies

Perception ◽

10.1068/p040035 ◽

1975 ◽

Vol 4 (1) ◽

pp. 35-50 ◽

Cited By ~ 8

Author(s):

Vernon Dobson

Keyword(s):

Neural Network ◽

Reaction Times ◽

Input Pattern ◽

Pattern Learning ◽

Growth Processes ◽

Learning Capacity ◽

Inhibitory Network ◽

Complex Sequences ◽

Random Growth

An all-inhibitory network which learns by selective disconnection of synapses is described. This is similar to an ‘associative net'; however, it is simpler in that its neurons do not need to perform arithmetical operations, and the net does not require additional threshold modulating neurons in order to cope with input patterns which are incomplete, or of differing sizes. This fundamental simplicity permits a greater variety and density of connections. These can multiply the capacity of the nets to learn complex sequences of patterns without being saturated. An “all-connected‘’ net is described which has the holograph-like capacity to reconstruct the whole of an input pattern from part patterns without involving delays or threshold devices. All of these inhibitory nets can construct themselves by means of simple random growth processes, without incurring any loss of learning capacity of holographic properties. Similarly, synapses can be allowed to potentiate with use, so that reaction times are progressively reduced by practice, without any reduction in the quality of the performance. Inhibitory connections between arrays can give patterns in one array control over the allocation of channels in which lower arrays store learned information. A description is given of a model, decentralised, inhibitory hierarchy consisting of inter-connected arrays which can learn to execute goal-directed TOTE-type programs of behaviour by means of a simple ‘putting-through’ procedure.

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Random growth in a tessellation

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100077288 ◽

1973 ◽

Vol 74 (3) ◽

pp. 515-528 ◽

Cited By ~ 191

Author(s):

Daniel Richardson

Keyword(s):

Euclidean Space ◽

Growth Process ◽

Dimensional Euclidean Space ◽

Growth Processes ◽

Stochastic Growth ◽

Random Growth

Let S be n dimensional Euclidean space and let T be a division of S into cells. Assume that each cell must be either white or black at any time t. At time 0 the cell at the origin, α0, is black and all other cells are white. Let G be some stochastic growth process which tends to change white cells with black neighbours into black cells. Let C(t) be the black shape at time t. For a family, F, of such growth processes we prove the following theorem.

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