Scaling dependence on time and distance in nonlinear fractional diffusion equations and possible applications to the water transport in soils

Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different physical systems like: amorphous semicondutors, polymers, composite heterogeneous films and porous media. They have also been used to calculate the heat load intensity change in blast furnace walls, to solve problems of control theory \ and dynamic problems of linear and nonlinear hereditary mechanics of solids. In this work, we investigate the scaling properties related to the nonlinear fractional diffusion equations and indicate the possibilities to the applications of these equations to simulate the water transport in unsaturated soils. Usually, the water transport in soils with anomalous diffusion, the dependence of concentration on time and distance may be expressed in term of a single variable given by $\lambda _{q}=x/t^{q}.$ In particular, for $q=1/2$ the systems obey Fick's law and Richards' equation for water transport. We show that a generalization of Richards' equation via fractional approach can incorporate the above property.Comment: 9 page

Physical properties of single crystalline BaSn5

We present a comprehensive study of the binary intermetallic superconductor, BaSn5. High-quality single crystalline BaSn5 was grown out of Sn flux. Detailed thermodynamic and transport measurements were performed to study BaSn5's normal and superconducting state properties. This material appears to be a strongly coupled, multiband superconductor. Hc2(T)is almost isotropic. De Haas-van Alphen oscillations were observed and two effective masses were estimated from the FFT spectra. Hydrostatic pressure causes a decrease in the superconducting transition temperature at the rate of ~ -0.053 K/kbar.Comment: 8 pages and 9 figure

Spectral index of the H2O-maser emitting planetary nebula IRAS 17347-3139

We present radio continuum observations of the planetary nebula (PN) IRAS 17347-3139 (one of the only two known to harbour water maser emission), made to derive its spectral index and the turnover frequency of the emission. The spectrum of the source rises in the whole frequency range sampled, from 2.4 to 24.9 GHz, although the spectral index seems to decrease at the highest frequencies (0.79+-0.04 between 4.3 and 8.9 GHz, and 0.64+-0.06 between 16.1 and 24.9 GHz). This suggests a turnover frequency around 20 GHz (which is unusual among PNe, whose radio emission usually becomes optically thin at frequencies < 10 GHz), and a relatively high emission measure (1.5 x 10^9 cm^{-6} pc). The radio continuum emission has increased by a factor of ~1.26 at 8.4 GHz in 13 years, which can be explained as expansion of the ionized region by a factor of ~1.12 in radius with a dynamical age of ~120 yr and at an expansion velocity of ~5-40 km/s. These radio continuum characteristics, together with the presence of water maser emission and a strong optical extinction suggest that IRAS 17347-3139 is one of the youngest PNe known, with a relatively massive progenitor star.Comment: Five pages, 2 figures, accepted by MNRA

First-Order Vortex Lattice Melting and Magnetization of YBa2_2Cu3_3O$_{7-\delta}

We present the first non-mean-field calculation of the magnetization $M(T)$ of YBa$_2$Cu$_3$O$_{7-\delta}$ both above and below the flux-lattice melting temperature $T_m(H)$. The results are in good agreement with experiment as a function of transverse applied field $H$. The effects of fluctuations in both order parameter $\psi({\bf r})$ and magnetic induction $B$ are included in the Ginzburg-Landau free energy functional: $\psi({\bf r})$ fluctuates within the lowest Landau level in each layer, while $B$ fluctuates uniformly according to the appropriate Boltzmann factor. The second derivative $(\partial^2 M/\partial T^2)_H$ is predicted to be negative throughout the vortex liquid state and positive in the solid state. The discontinuities in entropy and magnetization at melting are calculated to be $\sim 0.034\, k_B$ per flux line per layer and $\sim 0.0014$~emu~cm$^{-3}$ at a field of 50 kOe.Comment: 11 pages, 4 PostScript figures in one uuencoded fil

Enhanced Eddy Activity in the Beaufort Gyre in Response to Sea Ice Loss

The Beaufort Gyre freshwater content has increased since the 1990s, potentially stabilizing in recent years. The mechanisms proposed to explain the stabilization involve either mesoscale eddy activity that opposes Ekman pumping or the reduction of Ekman pumping due to reduced sea ice?ocean surface stress. However, the relative importance of these mechanisms is unclear. Here, we present observational estimates of the Beaufort Gyre mechanical energy budget and show that energy dissipation and freshwater content stabilization by eddies increased in the late-2000s. The loss of sea ice and acceleration of ocean currents after 2007 resulted in enhanced mechanical energy input but without corresponding increases in potential energy storage. To balance the energy surplus, eddy dissipation and its role in gyre stabilization must have increased after 2007. Our results imply that declining Arctic sea ice will lead to an increasingly energetic Beaufort Gyre with eddies playing a greater role in its stabilization