Smeared criticality

In this section, the nature of the PN-N phase transition in LCEs will be presented, as revealed by H-NMR and supported by ac calorimetry. It will be demonstrated that the smooth phase transition in LCEs is a manifestation of both the field conjugate to the local order parameter (which in LCEs takes up close-to critical values) and the pronounced heterogeneity of LCEs, in the sense of distributed random fields. Particular attention will be paid to the description of a simple model based on the LdG approach, which considers these two features of LCEs. This model predicts the temperature profiles of the first and the second moment of the H-NMR spectral lines. The accordance of this model with the experimental results will be discussed. Finally, the idea of a smeared criticality in LCEs will be presented. 

One should thus not regard LCEs as entirely below-critical or above-critical systems, but rather as systems in which both types of phase-transition behaviours may be found, the extent of which is determined by the values of (G) and Gg- We shall introduce the term smeared criticality for such behaviour. In Fig. 16a, the graphical representation illustrates the extent of each type of phase transition behaviour in two LCEs, one prevalently below critical and the other prevalently above critical. A straightforward manifestation of the smeared criticality is the presence of latent heat in many LCE systems that exhibit a supercritical, effective thermodynamic response (see Sect. 5). This latent heat is released by the below-critical component of the LCE whose extent is given by the surface of the shaded area in Fig. 16. 

We shall see in Sect. 5 that LCEs can be tailored to exhibit a thermodynamic response spanning from subcritical to supercritical. However, the classification in terms of subcritical, critical or supercritical is, in the presented picture of smeared criticality, applicable only for describing the average (effective) response of LCEs. 

In the previous sections, the basic principles of the PN-N transition in LCEs and the experimental techniques were introduced to the reader. The issue of a smeared criticality observed in LCEs was introduced in Sect. 4. In this section, the experimental results providing an insight for the understanding of the PN-N transition are presented. These data were obtained by deuteron NMR and ac calorimetry on side-chain and main-chain LCEs. The distinct role of each parameter that affects the critical behaviour of the PN-N phase transition of LCEs will be demonstrated in different subsections. These parameters influence the relative strength of the locked-in mechanical field G and, as demonstrated in the previous sections, they may alter the order of the PN-N transition. 

Contribution of pairing fluctuations to the specific heat in the hadron shell is minor for the case of the neutron pairing due to a small value of Tc < IMeV compared to the value of the neutron chemical potential f//, > 50 MeV). Therefore in the neutron channel fluctuations of the gap are relevant only in a very narrow vicinity of the critical point. However this effect might be not so small for protons, for which the chemical potential is of the order of several MeV, whereas the gap is of the order of one MeV. Therefore it seems that fluctuations may smear the phase transition in a rather broad vicinity of the critical point of the proton superconductivity. 

Fig presented here is a copy of Fig 1 of Ref 16, p 840. It is a sketch of a photo-. graphic record (made by means of a highspeed smear camera from the butt end of the tube) of a detonation passing from a narrow tube to a wider one. The diams of tubes are larger than critical. Dark zones correspond... 

Another characteristic property of the electron density of 1 is its relatively high value at the centre e of the ring (more than 80% of that at the CC bond critical point). Density is smeared out over the ring surface and concentrated at its centre because of the occupation of the w0 -orbital (MO 8, 3a(, Figure 6), which has the character of a surface orbital . Cremer and Kraka9, n 13 have termed this phenomenon surface delocalization of electrons, to be distinguished from ribbon delocalization and volume delocalization of electrons (Figure 12)12. 

Figure 13. Schematic phase diagram of water s metastable states. Line (1) indicates the upstroke transition LDA —>HDA —>VHDA discussed in Refs. [173, 174], Line (2) indicates the standard preparation procedure of VHDA (annealing of uHDA to 160 K at 1.1 GPa) as discussed in Ref. [152]. Line (3) indicates the reverse downstroke transition VHDA—>HDA LDA as discussed in Ref. [155]. The thick gray line marked Tx represents the crystallization temperature above which rapid crystallization is observed (adapted from Mishima [153]). The metastability fields for LDA and HDA are delineated by a sharp line, which is the possible extension of a first-order liquid-liquid transition ending in a hypothesized second critical point. The metastability fields for HDA and VHDA are delineated by a broad area, which may either become broader (according to the singularity free scenario [202, 203]) or alternatively become more narrow (in case the transition is limited by kinetics) as the temperature is increased. The question marks indicate that the extrapolation of the abrupt LDA<- HDA and the smeared HDA <-> VHDA transitions at 140 K to higher temperatures are speculative. For simplicity, we average out the hysteresis effect observed during upstroke and downstroke transitions as previously done by Mishima [153], which results in a HDA <-> VHDA transition at T=140K and P 0.70 GPa, which is 0.25 GPa broad and a LDA <-> HDA transition at T = 140 K and P 0.20 GPa, which is at most 0.01 GPa broad (i.e., discontinuous) within the experimental resolution.

The question of whether there is a tme glassy nature of amorphous ices is of interest when speculating about possible liquid-liquid transitions in (deeply) supercooled water. For true glasses, the amorphous-amorphous transitions described here can be viewed as the low-temperature extension of liquid-liquid transitions among LDL, HDL, and possibly VHDL. That is, the first-order like LDA <-> HDA transition may map into a first-order LDL HDL transition, and the continuous HDA <-> VHDA transition may map into a smeared HDL VHDL transition. Many possible scenarios are used how to explain water s anomalies [40], which share the feature of a liquid-liquid transition [202, 207-212]. They differ, however, in the details of the nature of the liquid-liquid transition Is it continuous or discontinuous Does it end in a liquid-liquid critical point or at the reentrant gas-liquid spinodal ... 

A clinical suspicion of an Acanthamoeba infection is the critical first therapeutic step. Acanthamoeba can be diagnosed by eye smears, culture, tissue biopsy, polymerase chain reaction, and confocal microscopy. 

As is known, the polypeptide a-helix molecules are rod-shaped if the helical internal structures are smeared out. Therefore, we may expect a phase separation in their solutions also. Indeed, Robinson (27) found in 1956 a phase separation in several solutions of the a-helix, poly-y-benzyl-L-glutamate, in which the second phase, separated out as small droplets, showed an optical birefringence. ITie critical concentration is of course a function of the molecular length. 

If the barrier energy is lower than this critical value, rotational motion will be fast at 6 K and the STM image will be smeared out and STM simulations will need to include time averaging. If the barrier is larger, then the image may have threefold or sixfold symmetry depending on the energies of the local minima. 

This paper has highlighted that a number of components, important to fault seal analysis, are often either not included or not quantified in sufficient detail to allow a low risk seal evaluation. The main components which are not always considered in detail are (i) the errors in throw patterns which arise from seismic resolution and fault damage zone structures (ii) the assumption that juxtaposition of reservoir against low permeability units and shale smear are the only sealing mechanisms and (iii) that fault seal data from anywhere is directly applicable to any other sealing problem, i.e., that the geohistory is not critical... 

Clay smearing is the critical sealing mechanism in only -35% of cases. 

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