Complexity hierarchy

In the case of liquid crystals in particular, vibrational properties reflect very directly the complex hierarchy of the structure and bonding problem in these materials. For example, in a single mesogenic molecule vibrational frequencies range from about 10 cm to over 3000 cm which arise from the very wide range of force constants present [79]. 

The complex hierarchy of native protein structure may be disrupted by multiple possible destabilizing mechanisms. As has been described in the foregoing, these processes may disrupt noncovalent forces of interaction or may involve covalent bond breakage or formation. A summary of the processes involved in the irreversible inactivation of proteins is illustrated in Fig. 3 and described briefly in the following section. Detailed discussions of mechanisms of protein desta-... 

Farre, L. and Oksala, T., eds. (1998). Emergency, complexity, hierarchy, organisation. Selected papers from the ECFIO III Conference (ESPOO, Finland), Acta Polytechnica ScandL, 91. 

Escherichia coli carries about 3,000 genes. Only a small fraction of the genome is actively transcribed at any given time. But all of the genes are in a state where they can be readily turned on or turned off in a reversible fashion. The level of transcription is regulated by a complex hierarchy of control elements. 

It seems likely that the pivotal events in the evolution of a differentiated cell reflect changes in gene expression that result from a complex hierarchy of controls. The key to understanding differentiation, therefore, is to identify the regulatory factors responsible for the controls involved in differentiation and to explain how they act. 

All components constituting the pool from which the catalysts should be composed, and optionally the division of all those components into an arbitrarily complex hierarchy of component types (such as support, active components, dopants), component subtypes, subsubtypes, etc. 

Detailed structures of many crystalline materials can be determined by diffraction methods. However, because of the complex hierarchy of the cotton fiber and its very small crystallites, diffraction experiments on cotton fibers cannot provide fine details of molecular structure. Instead, the best data on cellulose structure comes from other sources. One of the major points of interest is the finding that cellulose has many different crystalline forms, or polymorphs, depending on the sources and subsequent treatments. Historically, there are four polymorphs or allomorphs, I to IV, and subclasses have been identified for all but cellulose II. 

UHMWPE comes from a family of polymers with a deceptively simple chemical composition, consisting of only hydrogen and carbon. However, the simplicity inherent in its chemical composition belies a more complex hierarchy of organizational structures at the molecular and supermolecular length scales. At a molecular level, the carbon backbone of polyethylene can twist, rotate, and fold into ordered crystalline regions. At a supermolecular level, the UHMWPE consists of powder (also known as resin or flake) that must be consolidated at elevated temperatures and pressures to form a bulk material. Further layers of complexity are introduced by chemical changes that arise in UHMWPE due to radiation sterilization and processing. 

Based on Dalton s atomic theory, an atom is the basic unit of an element that can enter into chemical combination. Dalton imagined an atom that was both extremely small and indivisible. However, a series of investigations that began in the 1850s and extended into the twentieth century clearly demonstrated that atoms actually possess internal structure that is, they are made up of even smaller subatomic particles. Particle physicists have discovered a complex hierarchy (or zoo ) of such particles, but only electrons, protons, and neutrons are of primary importance in chemical reactions. 

The special form of the invariant submanifold li(k) in Eq. (2.3) is due to the explicit existence of fast-reacting radical species. Well known (Maas and Pope [1], Lam [2]) is the existence of invariant manifolds also in reactions systems without simple separation of radical (fast) and nonradical (slow) chemical species, but with a complex hierarchy of reactions at very different time scales. In this situation we can at least suppose the existence of an invariant submanifold U C in concentration space representing the slow... 

These biomimetic strategies have prompted new collaborations between biologists and chemists, often under the umbrella of a new interdisciplinary field called materials science and engineering. Biomaterials have taught chemists many lessons first, most of these materials are multi-functional and represent a good if not maximal compromise between the various functions they fulfil. Second, unlike artificial chemical products, biomaterials do not exclude or even avoid the presence of impurities, flaws, mixtures and composites. Third, the examination of their fine structure reveals that biomaterials present a complex hierarchy of structures with difierent structural features appearing at different levels of magnification. 

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