Critical threshold

Critical threshold, a notion derived from the percolation theory, refers to a threshold, that summons up to a critical mass. Under the threshold the phenomenon tends to abort, above the threshold, it tends to grow exponentially.

In cases where the phenomenon is not sudden and takes time to operate, in the form of a transition phase or phase transition, we talk about a critical phase more than a critical point that would mark a clear threshold.

Examples

This process is common in physics (nuclear chain reaction), chemistry, biology, ecology, but also in economics. Many economic processes, from product life cycles or economic development to stock-market bubbles follows also such a succession of phases, first building up pressure, then breaking through.

Percolation Phenomena in Polymer Compounding

An interesting manifestation of percolation is in polymer compounding. Polymer compounding is the science of modifying and manipulating the material properties of polymer materials through the addition of additives. In general, composite materials are materials that consist of at least two different phases at the macroscopic level, and recently with growing interest, also at the nanoscopic level. A phase is a part in a material that is distinct in properties from the material around it. A phase must have a distinct boundary that separates it from the other materials or material phases surrounding it. Example, an open glass of iced water is a two-phase system, in which liquid water is one phase, and the ice is the other: the two phases are separated by the ice-water boundary, across which one finds solid H2O on one side, and liquid H2O on the other. In a composite, a phase that is dispersed in a larger material is usually termed the dispersed phase, while the larger phase is the matrix. A polymer composite usually consist of a polymer matrix in which is embedded the dispersed "additive" phase which can be substances such as lime, talc, glass fibre, carbon fibre, beads, metallic particles, etc. The presence and quantity of the dispersed phase in a composite usually has a very significant effect on the mechanical properties of the overall composite, mechanical properties such as tensite strength, toughness, hardness, as well as physical properties such as bulk / surface electrical conductivity, thermal conductivity, glass transition temperature, flammability, viscosity in processing, moldability, etc. This effect is not always linear. Very often, an additive (for instance, carbon fibres) on a physical property such as electrical conductivity, shows little effect at low added percentages. At a certain threshold (the percolation threshold), the electrical conductivity of a polymer composite suddenly and dramatically increases. This is what is meant by percolation, as far as polymer compounding is concerned.

A specific example in economic geography / spatial economics

In some locations, resources and competences amass and develop a science and high tech oriented cluster like the Silicon Valley, or recently Bangalore software center and AMD´s chip-plants, FAB's, in Dresden, F.R. Germany.

See also

* Michael Porter
* Business cluster
* Techno cluster
* self-organized criticality
* Ilya Prigogine
* percolation thresholds