Disorders chaotic

Fig. 1.5 The types of pore size distribution (a) monomodal (b) bimodal (c) disordered (chaotic)...

The question of non-classical manifestations is particularly important in view of the chaos that we have seen is present in the classical dynamics of a multimode system, such as a polyatomic molecule, with more than one resonance coupling. Chaotic classical dynamics is expected to introduce its own peculiarities into quantum spectra [29, 77]. In Fl20, we noted that chaotic regions of phase space are readily seen in the classical dynamics corresponding to the spectroscopic Flamiltonian. Flow important are the effects of chaos in the observed spectrum, and in the wavefiinctions of tire molecule In FI2O, there were some states whose wavefiinctions appeared very disordered, in the region of the... 

To melt ice we have to put heat into the system. This increases the system entropy via eqn. (5.20). Physically, entropy represents disorder and eqn. (5.20) tells us that water is more disordered than ice. We would expect this anyway because the atoms in a liquid are arranged much more chaotically than they are in a crystalline solid. When water freezes, of course, heat leaves the system and the entropy decreases. 

We can expect the entropy to increase when a solid melts and its molecules become more disordered. Similarly, we can expect an even greater increase in entropy when a liquid vaporizes, because its molecules then occupy a much greater volume and their motion is highly chaotic. In this section, we develop expressions for the change in entropy at the transition temperature for the prevailing pressure. For instance, if the pressure is 1 atm, then these expressions are applicable only at the normal melting point, Tf (the f stands for fusion), the temperature at which a solid melts when the pressure is 1 atm, or the normal boiling point, Th, the temperature at which a liquid boils when the pressure is 1 atm. 

An ordered arrangement of particles (atoms, ions, or molecules) has lower entropy (smaller disorder) than the same number of particles in random arrangements. Thus, the entropy of a pure substance depends on its state. The entropy of a system increases (becomes more disordered) with temperature, because the motion of particles becomes more chaotic at higher temperatures. See Figure 7.6 on the next page. 

Carbon nanotubes, as graphene and graphite, are highly ordered carbon phases. However, a separate line can be drawn for historical development of disordered carbon phases among them is an amorphous carbon (am-C). In it, strong bonding between carbons did not allow for completely chaotic distribution of carbon atoms in solid-state phase. Instead, amorphous carbon exhibits random distribution of three possible coordinations of carbon atoms in a planar sp, tetrahedral sp and... 

As far as chemistry and life sciences are concerned, there are for me and many others two main reasons for this fascination, summarized in Figure 9.4 firstly, above a certain critical concentration, structural order is achieved starting from the chaotic mixture of disordered surfactant molecules. As discussed earlier, this increase of order is attended by an increase of entropy and a decrease of free energy. 

We can expect entropy to increase when a solid melts to a liquid and its molecules become more disordered. Similarly, we can expect an even greater increase in entropy when a liquid vaporizes, for its molecules then occupy a much greater volume and their motion is highly chaotic. 

Antidepressants modify the long-term course of bipolar disorder as well. When given with lithium or other mood stabilizers, they may reduce depressive episodes. Interestingly, however, antidepressants can flip a depressed bipolar patient into mania, into mixed mania with depression, or into chaotic rapid cycling every few days or hours, especially in the absence of mood stabilizers. Thus, many patients with bipolar disorders require clever mixing of mood stabilizers and antidepressants, or even avoidance of antidepressants, in order to attain the best outcome. 

FIGURE 9—3. One theory about the biological basis of panic disorder is that there is an excess of norepinephrine, causing intermittent and chaotic discharge of noradrenergic neurons from the locus coeruleus. 

To adopt the nice metaphor of Frenking and Krapp [11], aromaticity is a unicorn (a useful mystical animal that everybody is familiar with, although nobody has seen one). It should not be doomed to extinction (as proposed earlier) because if it is tamed, it brings law and order in an otherwise chaotic and disordered world. 

Entropy is often defined as an increase in disorder. A way of understanding entropy is to think in terms of the increase in entropy as an increase in the chaotic state (disorganized, untidy, or hectic state) of the system. Then, the greater the number of arrangements in a system, the greater the entropy. 

The Second Law is sometimes stated as the Entropy Law. Entropy is a measure of randomness or disorder in a system. Systems that are more randomized, chaotic, or evenly mixed have more entropy. The Second Law states the entropy of the universe is constantly increasing. One clear implication of the Second Law is that the universe never, and a system almost never, spontaneously becomes more organized. So, hot molecules will not spontaneously separate themselves from cold molecules. Mixtures of oxygen and nitrous oxide will not spontaneously separate and send the oxygen to the patient separately from the nitrous oxide. IV fluids will mix evenly throughout the circulatory system, and not congregate in just the left arm. 

For synthesis of composite films with M/SC nanoparticles distributed in the volume of a dielectric matrix, method PVD is used as co-deposition of M/ SC and dielectric material vapors. A comparison of films produced by codeposition and layer-by-layer deposition PVD methods has been made on the example of BN-Fe nanocomposite films [57]. Unlike the above considered film from alternating layers of Fe and BN, which has ordered structure, co-deposited BN-Fe nanocomposite films consist of amorphous completely disorder matrix BN containing a chaotic system of immobilized Fe nanoparticles. At the same time, these particles in contrast to those of layered film have much smaller size (d — 2.3 nm) since in this case the metal atoms are inside a matrix which slowdowns the diffusion process of atoms aggregation. 

The Time Course of Recurrent Mood Disorders Periodic, Noisy and Chaotic Disease Patterns... 

Fig. 7.2 (a) The prototypical time course of disease episodes in affective disorders (modified after [18]). Disease episodes are initially related to external stressors with increasing strength of the episodes (kindling) which then leads to autonomous progression (episode sensitization) with periodically occurring disease episode of increasing frequency up to ultra-rapid, chaotic mood fluctuations, (b) Analogous activity pattern of... 

Gottschalk, A., Bauer, M.S., and Whybrow, P.C. Evidence of chaotic mood variation in bipolar disorder. Arch Gen Psychiatry 1995, 52 947-959. 

In this theory, the dynamics of the intrinsic-surface-confined excitons account surprisingly well—in a natural way, without introducing ad hoc parameters—for the surface emissive properties, and they allow, a contrario, a very sensitive probing of various types of surface disorders, whether residual, accidental, or induced. The disorder may be thermal, substitutional, chaotic owing to surface chemistry, or mechanical owing to interface compression. It may be analyzed as a specific perturbation of the surface exciton s coherence and of its enhanced emissive properties. 

When all the rotations are possible in the solid state the symmetry increases to hexagonal. This form corresponds to the close packing of spheres or cylinders and the molecule is in a rotational crystalline state, characterized by rigorous order in the arrangement of the center (axes) of the molecules and by disordered azimuthal rotations [118]. If the chain molecules are azimuthally chaotic (they rotate freely around their axes), their average cross sections are circular and, for this reason, they choose hexagonal packing. The ease of rotation of molecules in the crystal depends merely on the molecular shape, as in molecules of an almost spherical shape like methane and ethane derivatives with small substituents, or molecules of a shape close to that of a cylinder (e.g., paraffin-like molecules). 

Liquids are neither characterised by the random chaotic motion of molecules, which one find in gases, nor by the perfect order of moleculars arrangement in solids. They occupy an intermediary position where molecules are more disorderly than those of a solid, but much less disorderly than those of gases. Because of this fact the enthalpy change when a crystal melts is always positive and the corresponding entropy change is also positive. This implies that there is less of order when a crystal melts. The liquid is thus intermediate between the complete order of the crystalline state and the complete disorder of the gaseous state. Because of this fact, the development of a molecular theory for liquids has posed formidable difficulties. 

Percolation theory is a statistical theory that studies disordered or chaotic systems where the components are randomly distributed in a lattice. A cluster is defined as a group of neighboring occupied sites in the lattice, being considered an infinite or percolating cluster when it extends from one side to the rest of the sides of the lattice, that is, percolates the whole system [38],... 

There is a loud noise. Bits and pieces of balloon get scattered all around. The hydrogen gas inside the balloon, which was clearly separated from the air around, gets mixed with air. There probably was a sudden drop in temperature of hydrogen molecules as the pressure on it was released. All this presents a totally chaotic and disorderly picture. No wonder that scientists have associated increased entropy with increased disorder. 

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