Critical phenomenaIn physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking.
Critical exponentCritical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on: the dimension of the system the range of the interaction the spin dimension These properties of critical exponents are supported by experimental data.
PetrochemicalPetrochemicals (sometimes abbreviated as petchems) are the chemical products obtained from petroleum by refining. Some chemical compounds made from petroleum are also obtained from other fossil fuels, such as coal or natural gas, or renewable sources such as maize, palm fruit or sugar cane. The two most common petrochemical classes are olefins (including ethylene and propylene) and aromatics (including benzene, toluene and xylene isomers). Oil refineries produce olefins and aromatics by fluid catalytic cracking of petroleum fractions.
Percolation critical exponentsIn the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected to not depend on microscopic details such as the lattice structure, or whether site or bond percolation is considered.
Pulp (paper)Pulp is a lignocellulosic fibrous material prepared by chemically or mechanically separating cellulose fibers from wood, fiber crops, waste paper, or rags. Mixed with water and other chemical or plant-based additives, pulp is the major raw material used in papermaking and the industrial production of other paper products. Before the widely acknowledged invention of papermaking by Cai Lun in China around 105 AD, paper-like writing materials such as papyrus and amate were produced by ancient civilizations using plant materials which were largely unprocessed.
Racemic mixtureIn chemistry, a racemic mixture or racemate (reɪˈsiːmeɪt,_rə-,_ˈræsɪmeɪt), is one that has equal amounts of left- and right-handed enantiomers of a chiral molecule or salt. Racemic mixtures are rare in nature, but many compounds are produced industrially as racemates. The first known racemic mixture was racemic acid, which Louis Pasteur found to be a mixture of the two enantiomeric isomers of tartaric acid. He manually separated the crystals of a mixture by hand, starting from an aqueous solution of the sodium ammonium salt of racemate tartaric acid.
Self-organized criticalitySelf-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality. The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity arises in nature.
PolymerA polymer (ˈpɒlᵻmər; Greek poly-, "many" + -mer, "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function.
ProcyanidinProcyanidins are members of the proanthocyanidin (or condensed tannins) class of flavonoids. They are oligomeric compounds, formed from catechin and epicatechin molecules. They yield cyanidin when depolymerized under oxidative conditions. See the box below entitled "Types of procyanidins" for links to articles on the various types. Procyanidins, including the lesser bioactive / bioavailable polymers (4 or more catechines), represent a group of condensed flavan-3-ols that can be found in many plants, most notably apples, maritime pine bark, cinnamon, aronia fruit, cocoa beans, grape seed, grape skin, and red wines of Vitis vinifera (the common grape).
CatalysisCatalysis (kəˈtæləsɪs) is the process of change in rate of a chemical reaction by adding a substance known as a catalyst (ˈkætəlɪst). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quickly, very small amounts of catalyst often suffice; mixing, surface area, and temperature are important factors in reaction rate. Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process of regenerating the catalyst.
