RANI model

The effects of two types of randomness on the behaviour of directed polymers are discussed in this chapter. The first part deals with the effect of randomness in medium so that a directed polymer feels a random external potential. The second part deals with the RANI model of two directed polymers with heterogeneity along the chain such that the interaction is random. The random medium problem is better understood compared to the RANI model. 

Two types of randomness can arise in the context of directed polymers. One type would involve imposition of a random external potential (random medium problem). In the second type, the interaction (between say two chcuns) is random (RANI model). In the random medium problem, the random potential would like to have a realization dependent ground state which may not match with the zero-field state. In the RANI model, the randomness in the interaction may lead to a change in the phase transition behaviour shown by the polymers. These two classes are discussed separately. 

So far we have been considering the problem of random medium. A different situation arises if there is randomness in the interaction of polymers. This is the RANI model [36,37]. Consider the problem of two directed polymers interacting with a short range interaction as in Eq. (51) but take v to be random. Such problems are of interest, especially in the context of DNA where the base sequence provides heterogeneity along the chain. In this DNA context, the randomness can be taken to be dependent only on the z coordinate and not on others like the transverse position r. It can be written as... 

Figure 9. (a) Inter-replica interaction in the RANI model. The dotted wavy line indicates the r -type interaction between the pairs (1,2) and (3,4). (b) indicates a loop formed by the disorder induced interaction. 

Randomness is introduced by allowing the interaction energy to be random on each and every bond. The first model, model A, has independent random energy on all the 2b bonds. The randomness in the second model, model B, is taken only along the longitudinal direction so that equivalent bonds on all directed paths have identical random energy. Model B is a hierarchical lattice version of the continuum RANI model. 

The RANI model remains less understood compared to the random medium problem. Exact renormalization analysis establish the marginal relevance of the disorder at d = 1, indicating a disorder dominated unbinding transition in d > 1. Several features including a generalization of the Harris criterion for this criticality via relevant disorder and aspects of unzipping have been discussed. 

For the disorder problem, u < 0 is not meaningful, but for the interaction problem as in the RANI model, full range of u is allowed. The nontrivial fixed point for d < 2 is a stable fixed point and it describes the phase of repulsive polymers (fermion like). There is a... 

K. Yamuna Rani and S.C. Patwardhan. Data-driven model based control of a multi-product... 

The next group of materials comprises conducting polymers (ICP). Systems with identical polymers have often been reported for polyacetylene. It is known that this ICP forms insertion compounds of the A and D types (see Section 6.4, and No. 5 in Table 12). Cells of this Idnd were successfully cycled [277, 281-283]. However, the current efficiency was only 35% heavy losses were observed due to an overoxidation of the PA [284]. In other cases as for polypyrrole (PPy), the formation of D-PPy was anticipated but did not occur [557, 558]. Entry (6) in Table 12 represents some kind of ideal model. A PPy/PPy cell with alkyl or aryl sulfates or sulfonates rather than perchlorates is claimed in [559]. Similar results were obtained with symmetric polyaniline (PANI) cells [560, 561]. Symmetric PPy and RANI cells yield about 60% current efficiency, much more than with PA. An undoped PPy/A-doped PPy combination yields an anion-concentration cell [562, 563], in analogy to graphite [47], (cf. No. 7). The same principle can be applied with the PPy/PT combination [562, 563] (cf. No. 8). Kaneto et al. [564] have reported in an early paper the combination of two pol54hiophene (PT) thin layers (< 1 pm), but the chargeability was relatively poor (Fig. 40, and No. 9 in Table 12). A pronounced improvement was due to Gottesfeld et al. [342, 343, 562, 563], who employed poly[3-(4-fluoro-phenyl)thiophene], P-3-FPT, in combination with a stable salt electrolyte (but in acetonitrile cf. Fig. 40 and No. 10 in Table 12). In all practical cases, however, Es.th was below 100 Wh/kg. 

These classification methods use different principles and rules for learning and prediction of class membership, but wiU usually produce a comparable result. Some comparisons of the methods have been given (i.e., Kotsiantis, 2007 Rani et al., 2006). Although the modem methods such as SVM have demonstrated very good performance, the drawback is that the model becomes an incomprehensible black-box that removes the explanatory information provided by, for example, a logistic regression model. However, classification performance usually outweighs the need for a comprehensible model. PCA has been used for classification based on bioimpedance measurements. Technically, PCA is not a method for classification but rather a method of data reduction, more suitable as a parameterization step before the classification analysis. 

Useful information can be obtained from models amenable to exact analysis even if they look artificial. Real space renormalization group approach can be handled in an exact fashion for a class of tailor-made lattices called hierarchical lattice. Such lattices are constructed in a recursive fashion as shown in Fig. 1. The problem of a directed polymer in a random medium on hierarchical lattices has been considered in Ref. [44,45]. Here we consider the RANI problem on hierarchical lattices. As already noted, the effective... 

Fig. 24.18 Left cytosine calix[4]pyrrole conjugates with a connection either at the fi- or meso-pyrrolic position (43 and 44) and complex formation of 44 with guanosine monophosphate [52], Right drug delivery vehicle calix[4]pyrrole-/rani -Pt(II) complex (45) and schematic representation of the interaction with adenosine monophosphate as a model compound [53]...

As an initial exploratory experiment dodecafluoro n-pentane was chosen as a model compound for P.T.F.E. to simulate part of the perfluorinated molecular chain and allowed to adsorb at 0.13 pPa pressure and ambient temperature on a freshly prepared iron film produced by an evaporation process in situ from an iron wire wrapped around a tungsten filament. The events inside the vacuum chamber were followed with an MS 10 mass spectrometer and (where appropriate) a Pi rani gauge. These experiments suggest that the clean iron acts as a catalyst for the breakdown of the perf1uorinated alkane producing a variety of transiently reactive fragments, such as CF2, that in turn may react with the borosilicate (Pyrex) glass walls of the reaction chamber. 

Ragsdale SW, Riordan CG (1996) The role of nickel in acetyl-CoA synthesis by the bifunctional enzyme CO dehydrogenase/acetyl-CoA synthase enzymology and model chemistry. J Biol Inorg Chem 1 489-493 Rani KS, Seenayya G (1999) High ethanol tolerance of new isolates of Clostridium thermocellum strains SS21 and SS22. World J Microbiol Biotechnol 15 173-178... 

---