Finite-size scaling and universality of the thermal resistivity of liquid 4He near Tlambda

Surface-Dominated Finite-Size Effects in Nanoconfined Superfluid Helium

Superfluid ^{4}He (He II) is a widely studied model system for exploring finite-size effects in strongly confined geometries. Here, we study He II confined in millimeter-scale channels of 25 and 50 nm height at high pressures using a nanofluidic Helmholtz resonator. We find that the superfluid density is measurably suppressed in the confined geometry from the transition temperature down to 0.6 K. Importantly, this suppression can be accounted for by rotonlike thermal excitations with an energy gap of 5 K. We show that the surface-bound excitations lead to the previously unexplained lack of finite-size scaling of suppression of the superfluid density.

Diminution of the ordering in plastic and liquid crystalline phases by confinement

In a compound exhibiting plastic (crystal B) and liquid crystalline (smectic A) phases, we report calorimetric and X-ray features that are drastically affected by confinement and orientation in Anopore membranes. Data on the untreated membranes in which the molecules aligned parallel to the pore axes, show a significant diminution in the correlation length corresponding to the positional order of the plastic phase suggesting that finite size effects can perhaps transform the plastic phase to a hexatic one. In the orthogonal case, having the molecules in the plane of the membrane, a new phase is induced, whose structural possibilities are discussed. Calorimetric measurements corroborate these results and also bring out the different thermal behaviors, not only between the bulk and the confined cases, but also between the situations wherein the orientations of the molecules are different. These findings are expected to open up a new path to understand the melting phenomenon, especially that which occurs in lower dimensions.

Increase of universality in human brain during mental imagery from visual perception

Background

Different complex systems behave in a similar way near their critical points of phase transitions which leads to an emergence of a universal scaling behaviour. Universality indirectly implies a long-range correlation between constituent subsystems. As the distributed correlated processing is a hallmark of higher complex cognition, I investigated a measure of universality in human brain during perception and mental imagery of complex real-life visual object like visual art.

Methodology/Principal Findings

A new method was presented to estimate the strength of hidden universal structure in a multivariate data set. In this study, I investigated this method in the electrical activities (electroencephalogram signals) of human brain during complex cognition. Two broad groups - artists and non-artists - were studied during the encoding (perception) and retrieval (mental imagery) phases of actual paintings. Universal structure was found to be stronger in visual imagery than in visual perception, and this difference was stronger in artists than in non-artists. Further, this effect was found to be largest in the theta band oscillations and over the prefrontal regions bilaterally.

Conclusions/Significance

Phase transition like dynamics was observed in the electrical activities of human brain during complex cognitive processing, and closeness to phase transition was higher in mental imagery than in real perception. Further, the effect of long-term training on the universal scaling was also demonstrated.

Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions

We calculate finite-size effects of the Gaussian model in a Lx(d-1) box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 2<d<4. We also consider film geometry (L--> infinity ). Finite-size scaling is found to be valid for d<3 and d>3 but logarithmic deviations from finite-size scaling are found for the free energy and energy density at the Gaussian upper borderline dimension d*=3. The logarithms are related to the vanishing critical exponent 1-alpha-nu=(d-3)/2 of the Gaussian surface energy density. The latter has a cusplike singularity in d>3 dimensions. We show that these properties are the origin of nonscaling finite-size effects in the mean spherical model with free boundary conditions in d > or =3 dimensions. At bulk T(c), in d=3 dimensions we find an unexpected nonlogarithmic violation of finite-size scaling for the susceptibility chi approximately L3 of the mean spherical model in film geometry, whereas only a logarithmic deviation chi approximately L2 ln L exists for box geometry. The result for film geometry is explained by the existence of the lower borderline dimension d(l)=3, as implied by the Mermin-Wagner theorem, that coincides with the Gaussian upper borderline dimension d*=3. For 3<d<4 we find a power-law violation of scaling chi approximately L(d-1) at bulk T(c) for box geometry and a nonscaling temperature dependence chi(surface) approximately xi(d) of the surface susceptibility above T(c). For 2<d<3 dimensions we show the validity of universal finite-size scaling for the susceptibility of the mean spherical model with free boundary conditions for both box and film geometry and calculate the corresponding universal scaling functions for T > or =T(c).