Exotic pairing

According to Figure 5.2 and to chemical experience, the selection of other pairs of non-miscible organic liquids is difficult and yields mainly unusual (not to say, exotic) solvents or pairs of solvents [68] such as fluorous liquids (cf. Chapter 6). This is the reason why no other organic-organic biphasic catalytic processes have yet been commercialised. 

Neutron stars (NSs) are perhaps the most interesting astronomical objects from the physical point of view. They are associated with a variety of extreme phenomena and matter states for example, magnetic fields beyond the QED vacuum pair-creation limit, supranuclear densities, superfluidity, superconductivity, exotic condensates and deconfined quark matter, etc. 

It is quite likely to find dense quark matter inside compact stars like neutron stars. However, when we study the quark matter in compact stars, we need to take into account not only the charge and color neutrality of compact stars and but also the mass of the strange quark, which is not negligible at the intermediate density. By the neutrality condition and the strange quark mass, the quarks with different quantum numbers in general have different chemical potentials and different Fermi momenta. When the difference in the chemical potential becomes too large the Cooper-pairs breaks or other exotic phases like kaon condensation or crystalline phase is more preferred to the BCS phase. 

The next section makes use of the much more recent observation19 that there is a nearly constant difference of the enthalpies of formation of corresponding vinyl and phenyl derivatives. If vinyl relates to cyclopropyl, and vinyl also relates to phenyl, then how do corresponding cyclopropyl and phenyl derivatives relate Conceptually, vinylcyclopropane (10), also identified as 1, X = Cypr and 2, X = Vi) and styrene (11, X = Vi, also identified as 1, X = Ph) are thus relatable. Likewise, relatable are cyclopropylamine (2, X = NH2) and aniline (11, X = NH2)18. This thermochemical comparison of benzene and cyclopropane derivatives is not merely a check of two purported identities in terms of a third, arithmetically derivable, identity. Benzene is the archetypical 7i-delocalized aromatic species from which understanding of this widespread phenomenon evolves. Cyclopropane is the paradigm of cr-aromatic species from which understanding of this more exotic phenomenon evolves20. Benzene and cyclopropane are thus naturally paired as conceptual models for delocalization and aromaticity. Section III discusses these and related issues. 

Positronium, being a readily available purely leptonic system and also a particle-antiparticle pair, has attracted considerable experimental interest over the years as a testing ground for the existence of exotic particles or couplings. The latter may perhaps manifest themselves in the decay properties of positronium, so that attempts have been made to observe forbidden modes. In particular, the longstanding discrepancy between the Michigan experimental value for oAo-ps and the results from QED calculations, described in subsection 7.1.1, has acted as a spur to such investigations. 

A variational theory which includes all these different contributions was recently proposed and applied for completely stretched polyelectrolyte stars (so-called porcupines ) [203, 204]. As a result, the effective interaction V(r) was very soft, mainly dominated by the entropy of the counterions inside the coronae of the stars supporting on old idea of Pincus [205]. If this pair potential is used as an input in a calculation of a solution of many stars, a freezing transition was found with a variety of different stable crystal lattices including exotic open lattices [206]. The method of effective interactions has the advantage to be generalizable to more complicated complexes which are discussed in this contribution-such as oppositely charged polyelectrolytes and polyelectrolyte-surfactant complexes-but this has still to be worked out in detail. 

The author and A. Robatino have pointed out that the sharp positron spectrum resembles electron spectra found in atomic collisions by Niehaus and coworkers. [21),25] The quantum mechanics in both cases is analogous. In our point of view, the sharpness of the spectra arises from interferences arising at avoided crossings of potential curves of the molecules formed by the collision partners. In particular, such a model is consistent in a natural way with the multiple summed energies found by the G. S. I. experimenters. [15,16,19] The molecular model predicts very different angular distributions than those of the particle model. [26] The more recent discovery of electron positron pairs is equally consistent with the molecular model, as with more exotic explanations. [26]... 

The elementary excitations of a conjugated polymer chain can be described within the mono-electronic approach as electron and hole quasiparticles [74] in a one-dimensional band structure, possibly weakly bound into extended Wannier-type excitons [71,75]. Within this framework, electron-phonon interactions lead to a peculiar family of exotic excitations including solitons, polarons, polaron pairs and bipolarons. In many cases, however, disorder is so significant that the polymer films are better described as an ensemble of relatively short conjugated segments [76], essentially behaving... 

In the meantime some new routes towards high temperature and possibly exotic superconductivity have been investigated. This is the case for the heavy fermion compounds in which the close interplay between local magnetic moments and the spin of delocalized electrons has led to the possibility of a nonphonon mediated mechanism for electron pairing [4]. A very successful route towards high-T, s has been followed with conducting layered cuprates after the discovery of superconductivity in (La, Sr)2Cu04 [5]. 

More exotic has been the proposal made by Little for the possibility of an excitonic pairing mechanism in some organic conductors leading to a supposedly tremendously large increase of [6]. Little s mechanism relies on the possibility to obtain an attractive interaction between the mates of a Cooper pair in an energy... 

The five-coordination compounds show some more exotic possibilities. PF5 has a trigonal bipyramidal shape with inequivalent axial and equatorial positions. The lone pair in SF4 chooses an equatorial position since it can do less damage there— it make a 90° angle with two F atoms, whereas an axial position would make 90° angles with three F atoms. This leaves SF4 with a shape resembling a distorted. seesaw. The two lone pairs in CIF3 are most stable when located in two equatorial positions, separated by 120". This leaves Cll 3 in a distorted tee shape. The eomplex that forms between 1 and l> in iK iieous solution is a linear ion. 

The MCS of a set of N compounds, however, may be very small or may not even exist if an exotic structure is contained in the set. TTierefore, the common structural characteristics of a set of structures are better described by a set of MCS, each of them being the MCS of a pair of structures. Such a set is obtained by determining the MCS for all the N(N-l)/2 pairs of compounds then the number N, of occurrences of each different MCS is counted in the set. Finally, an ordered set of MCS is obtained by a ranking function which consideres both frequency and size of the MCS ... 

Secondary antiprotons have a kinematic feature analogous to that in 7r°-decay gamma rays but at a higher energy related to the nucleon mass. In this case the feature is related to the high threshold for production of a nucleon-antinucleon pair in a proton-proton collision. This kinematic feature is observed in the data (Orito et al., 2000), and suggests that an exotic component of antiprotons is not required. Antiproton fluxes are consistent with the basic model of cosmic-ray propagation described in the Introduction. 

So far we have concentrated on the particular parameter values <7 = 10, b =, r = 28, as in Lorenz (1963). What happens if we change the parameters It s like a walk through the jungle—one can find exotic limit cycles tied in knots, pairs of limit cycles linked through each other, intermittent chaos, noisy periodicity, as well as strange attractors (Sparrow 1982, Jackson 1990). You should do some exploring on your own, perhaps starting with some of the exercises. 

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