The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

Improved functionalization of oleic acid-coated iron oxide nanoparticles for biomedical applications

Superparamagnetic iron oxide nanoparticles can providemultiple benefits for biomedical applications in aqueous environments such asmagnetic separation or magnetic resonance imaging. To increase the colloidal stability and allow subsequent reactions, the introduction of hydrophilic functional groups onto the particles’ surface is essential. During this process, the original coating is exchanged by preferably covalently bonded ligands such as trialkoxysilanes. The duration of the silane exchange reaction, which commonly takes more than 24 h, is an important drawback for this approach. In this paper, we present a novel method, which introduces ultrasonication as an energy source to dramatically accelerate this process, resulting in high-quality waterdispersible nanoparticles around 10 nmin size. To prove the generic character, different functional groups were introduced on the surface including polyethylene glycol chains, carboxylic acid, amine, and thiol groups. Their colloidal stability in various aqueous buffer solutions as well as human plasma and serum was investigated to allow implementation in biomedical and sensing applications.status: publishe

Palmer LTER: Impact of a Large Diatom Bloom on Macronutrient Distribution in Arthur Harbor During Austral Summer 1991-1992

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation

Grain Refinement in Lightweight Advanced High-Strength Steel Castings

A method has been developed for producing grain refinement in lightweight high manganese and aluminum steels. Many researchers have recently reported that cerium addition produces cerium oxides that serve as heterogeneous nucleation sites for austenite during solidification of Cr-Ni steels. Until now, the use of cerium as a grain refining agent during casting of fully austenitic Fe-Mn-Al-C steels has not been evaluated. In the following study, a Ce-based inoculant in levels of 0, 0.05, and 0.1 wt% Ce was added during the tap and also in-mold to determine the effect of an increasing amount of Ce on reduction in the primary austenite grain size in a Fe-30.5 % Mn-7.55 % Al-0.76 % Si-1.11 % C-0.51 % Mo steel. Addition of 0.05 % Ce during the tap produced only a slight reduction in the grain size. However, in-mold inoculation with 0.1 % Ce produced an order of magnitude reduction in the grain size when compared to the base heat without Ce addition, from 10 to 12 mm to an average of 100 lm. Cerium is very reactive in the melt and readily combines with sulfur and oxygen as well as any residual phosphorus. Inclusion analysis showed that the inclusions in the 0.05 % Ce steel were mainly cerium sulfides while inclusions in the 0.1 % Ce steel were mainly complex cerium oxides, sulfides, and phosphides. Adding cerium greatly increased the nonmetallic inclusion density from 183 to 571 inclusions/mm2 and generally decreased the solution-treated notch toughness from 295 to 141 J. In the as-cast condition and for steels aged for 10 h at 530°C, toughness slightly increased with 0.05 % Ce addition and this is likely the result of the cerium removal of phosphorus from the melt during solidification. Toughness decreased with increasing volume fraction of inclusions and decreasing inclusion spacing regardless of the grain refining effect. It is therefore essential to eliminate sulfur and phosphorus from the melt as much as possible so that cerium will not form sulfides and complex phosphides instead of effective oxide nuclei. This may be achieved with more vigorous calcium addition for desulfurization prior to inoculation with cerium and with the use of nonphosphate bonded refractories to eliminate phosphorus pickup