Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Realization of first order optical systems using thin lensest

A first order optical system is investigated in full generality within the context of wave optics. The problem is reduced to a study of the ray transfer matrices. The simplest such systems correspond to axially symmetric propagation. Realization of such systems by centrally located lenses separated by finite distances is studied. It is shown that, contrary to the commonly held view, the set of first order systems that can be realized using axially symmetric thin lenses exhausts the entire SL(2, R) group; at most three lenses are needed to realize any element of this group. In particular, the inverse of free propagation can be so realized. Among anisotropic systems it is again shown that every element of the lens group Sp(4, R) can be realized using a finite number of thin lenses.

An investigation of first-order transition across charge ordered and ferromagnetic phases in Gd0.5Sr0.5MnO3 single crystals by magnetic and magnetotransport studies

Gadolinium strontium manganite single crystals of the composition Gd0.5Sr0.5MnO3 were grown using the optical float zone method. We report here the magnetic and magnetotransport properties of these crystals. A large magnetoresistance similar to 10(9)% was observed at 45 K under the application of a 110 kOe field. We have observed notable thermomagnetic anomalies such as open hysteresis loops across the broadened first-order transition between the charge order insulator and the ferromagnetic metallic phase while traversing the magnetic field-temperature (H-T) plane isothermally or isomagnetically. In order to discern the cause of these observed anomalies, the H-T phase diagram for Gd0.5Sr0.5MnO3 is formulated using the magnetization-field (M-H), magnetization-temperature (M-T) and resistance-temperature (R-T) measurements. The temperature dependence of the critical field (i.e. H-up, the field required for transformation to the ferromagnetic metallic phase) is non-monotonic. We note that the non-monotonic variation of the supercooling limit is anomalous according to the classical concepts of the first-order phase transition. Accordingly, H-up values below similar to 20 K are unsuitable to represent the supercooling limit. It is possible that the nature of the metastable states responsible for the observed open hysteresis loops is different from that of the supercooled ones.

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of 'sensorless' control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.

Post-seizure EEG fractal dimension of first ECT predicts antidepressant response at two weeks

Background: Duration of seizure by itself is an insufficient criterion for a therapeutically adequate seizure in ECT. Therefore, measures of seizure EEG other than its duration need to be explored as indices of seizure adequacy and predictors of treatment response. We measured the EEG seizure using a geometrical method-fractal dimension (FD) and examined if this measure predicted remission. Methods: Data from an efficacy study on melancholic depressives (n = 40) is used for the present exploration. They received thrice or once weekly ECTs, each schedule at two energy levels - high or low energy level. FD was computed for early-, mid- and post-seizure phases of the ictal EEG. Average of the two channels was used for analysis. Results: Two-thirds of the patients (n = 25) were remitted at the end of 2 weeks. As expected, a significantly higher proportion of patients receiving thrice weekly ECT remitted than in patients receiving once weekly ECT. Smaller post-seizure FD at first ECT is the only variable which predicted remission status after six ECTs. within the once weekly ECT group too, smaller post-seizure FD was associated with remission status. Conclusions: Post-seizure FD is proposed as a novel measure of seizure adequacy and predictor of treatment response. Clinical implications: Seizure measures at first ECT may guide selection of ECT schedule to optimize ECT. Limitations: The study examined short term antidepressant effects only. The results may not be generalized to medication-resistant depressives. (C) 1999 Elsevier Science B.V. All rights reserved.

Base Triggered Enhancement of First Hyperpolarizability of a Keto-Enol Tautomer

This work describes the base triggered enhancement of first hyperpolarizability of a tautomeric organic molecule, namely, benzoylacetanilide (BA). We have used the hyper-Rayleigh scattering technique to measure the first hyperpolarizability (beta) of BA which exists in the pure keto form in water and as a keto-enol tautomer in ethanol. Its anion exists in equilibrium with the keto and enol forms at pH 11 in aqueous solution. The beta value of the anion form is 709 X 10(-30) esu, whereas that of the enol is 232 x 10(-3) esu and of the keto is 88 X 10(-30) esu. There is an enhancement of beta by similar to 8 times for the anion and similar to 3 times for the enol compared to the keto form. All these are achieved by altering the equilibrium between the three forms of BA by simple means. MP2 calculations reproduce the experimental trend, but the computed beta values are much lower than the measured values. DFT calculations with the standard B3LYP functional could not predict the right order in the beta values. The difference between experimental and calculated values is, perhaps, due to the fact that electron correlation effects are important in computing optical nonlinearities of large organic molecules and MP2 and B3LYP calculations done here for different forms of BA could not account for such effects adequately.