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We present results of measurements designed to study superconducting I-V scaling in samples of bulk $\rm YBa\sb2Cu\sb3O\sb{7-\delta}$ with varying morphologies, 1$\mu$m $\rm\leq\langle d\sb{g}\rangle\leq20\mu m$ and at selected magnetic fields, $0.5{\rm G}\leq H\leq10\ {\rm T}.$ I-V isotherm measurements performed near the superconducting transition on the samples are consistent with recent predictions of I-V scaling, with critical exponents $\nu\sim1.1-1.75$ and $\rm z\sim2.3-4.3.$ The values for $\nu$ are comparable to those previously reported. The values for z are consistent with those reported by Tieman and Hallock but are somewhat lower than what is predicted by the glassy models. The static exponent does not seem to display any morphology or magnetic field dependence. The dynamic exponent, however, does display some morphology dependance with z higher for the small grain size samples. Furthermore, the data shows some evidence for a crossover between low and high z values in increasing magnetic fields.

We have carried out a series of NMR experiments on $\sp3$He systems filling the pores of silica aerogel with 95% porosity. The systems studied included $\sp3$He-$\sp4$He mixtures in a wide range of concentrations as well as pure $\sp3$He. All experiments were conducted in an 8 Tesla field and for temperatures between 5 and 320 mK. This resulted in strong spin polarization at the lowest temperatures (up to approximately 80%) for the localized layer observed for a pure $\sp3$He sample. For pure $\sp3$He, the magnetic behavior is dominated by the localized spins, which are found to constitute 6% of the sample. The coupled system of localized plus liquid spins displays rapid transverse magnetic relaxation with an anomalous temperature dependence. The longitudinal magnetization is observed to have, at the lowest temperatures, an anomalously long relaxation constant which cannot be readily associated with either the liquid or the localized spins. For mixtures with intermediate concentrations our measurements provide a preliminary indication of the phase diagram of mixtures filling this porous material.

Phase transitions and critical phenomena in several spin models are studied. These models include a two and three dimensional XY model and Ising models in structured and random field. The methods of study are cluster Monte Carlo simulations and network flow optimization algorithms. The XY model and a related soft spin model belonging to the O(2) universality class are studied using a modified version of the Invaded Cluster algorithm. The static critical properties of the models and the dynamic characteristics of the algorithm are studied. The critical exponent η for the O(2) universality class in two and three dimensions is measured. The Invaded Cluster algorithm for the XY model does not show any critical slowing for global variables. Benzene adsorption in a nanoporous solid is modeled with an Ising model with both internal and external magnetic fields. The first order phase transition and the critical properties of the system are studied. The system is simulated using the two replica cluster algorithm. The critical temperature of the system is found to decrease with increasing difference of the values of the internal fields. It is found that the system undergoes a phase transition for a relatively wide, experimentally obtainable, region of values of its parameters. The random field Ising model in three dimensions is studied at zero temperature. The nature of randomness induced phase transition is studied using a numerical network flow optimization method. It is found that the latent heat at the phase transition vanishes in the limit of infinite system size which can be taken as a proof of a second order phase transition.

We carried out experiments on a spin polarized 3He- 4He mixture with 3He concentration x 3 = 6.26 × 10−4, and on pure 3He liquid. Spin polarization affects the transport properties of these Fermi systems. The effect on momentum transport was studied by using a vibrating-wire viscometer to measure viscosity of the 3He-4He mixture over the temperature range 6.09 mK–100 mK in 7.96 T and 1.00 T magnetic fields. A large viscosity increase was observed upon application of the 7.96 T magnetic field for temperature T < TF(TF = 19.5 mK is the Fermi temperature). The observed viscosity is in very good agreement with theoretical calculations for a dilute Fermi gas by Jeon and Mullin [1988, 1989] and Mullin and Jeon [1992]. The polarization effect on spin transport was investigated by measuring the transverse diffusion coefficient D ⊥ in pure 3He liquid at saturated vapor pressure and at 15.85 bar over the temperature range 4.5 mK–159 mK in a 7.96 T magnetic field. We used a pulsed NMR spin echo technique in a field gradient of 16.0 G/cm to do the measurements and fits to the Leggett equations [1970] to obtain D⊥. For T < 20 mK, we found D⊥ is less than measured in earlier experiments at lower magnetic fields. D⊥ does not increase with decreasing temperature as 1/T2, but appears to approach a constant as T → 0 while it is expected that the longitudinal spin diffusion coefficient D∥ ∝ 1/ T2. This is called spin diffusion anisotropy and it was observed for the first time in our 3He liquid experiments. The anisotropy temperature we determined for 3He liquid was Ta = 16.4 ± 2.2 mK at saturated vapor pressure and in a 7.96 T magnetic field. The transverse spin diffusion in 3 He results agree qualitatively with theories proposed by Meyerovich and Musaeflan [1992, 1994]. They also agree qualitatively with theories proposed by Golosov and Ruckenstein [1995, 1998] by extrapolation of the dilute theory to a strongly interacting system.

We report observations of the behavior of superfluid 4He in two porous membranes, Nuclepore and Anopore. Using capacitive measurements, M. P. Lilly had observed hysteresis, return-point memory and avalanche behavior in Nuclepore [49] when superfluid 4He in capillary condensed in its pores. Additionally, he found that the avalanches of draining pores were global on the substrate, and the pore-pore connections as well as the superfluid film enabled the avalanches. We have continued that work to characterize the statistics of the avalanches in Nuclepore. We have seen that the statistics of the avalanches in Nuclepore are dependent on temperature and rate of removal of 4He from the sample cell. We have also observed two distinct regions of avalanche type in Nuclepore, which we propose is due to the pore-pore connections. We have observed power law behavior in the statistics of the avalanche size and measured the correlation of the avalanche events and sizes under various conditions. We have also observed hysteresis, return-point memory and avalanche behavior in Anopore using the same type of capacitive measurement. Anopore differs from Nuclepore in that nominally it has no pore-pore connections. In Anopore, we observed only one type of avalanche draining, and exponential behavior in the statistics of the avalanches instead of power law tendencies. We also measured the correlation of the avalanche events and sizes, and compared our results to those for Nuclepore. We performed simulations of draining on Nuclepore, artificially including and excluding third sound from our “avalanches”. We find that our results are similar to our laboratory measurements. We also performed a simple version of semi-local draining on Anopore, and saw some similarities to our measured results. We conclude that the behavior and statistics of the avalanches in a porous material are good indications of whether one is looking at a substrate that is percolated (Nuclepore) or a substrate that has no internal connections (Anopore).