Single Impurity Anderson Model with Coulomb Repulsion between Conduction Electrons on the Nearest-Neighbour Ligand Orbital

We study how the Kondo effect is affected by the Coulomb interaction between conduction electrons on the basis of a simplified model. The single impurity Anderson model is extended to include the Coulomb interaction on the nearest-neighbour ligand orbital. The excitation spectra are calculated using the numerical renormalization group method. The effective bandwidth on the ligand orbital, $D^{eff}$, is defined to classify the state. This quantity decreases as the Coulomb interaction increases. In the $D^{eff} > \Delta$ region, the low energy properties are described by the Kondo state, where $\Delta$ is the hybridization width. As $D^{eff}$ decreases in this region, the Kondo temperature $T_{K}$ is enhanced, and its magnitude becomes comparable to $\Delta$ for $D^{eff} \sim \Delta$. In the $D^{eff} < \Delta$ region, the local singlet state between the electrons on the $f$ and ligand orbitals is formed.Comment: 5 pages, 3 figures, LaTeX, to be published in J. Phys. Soc. Jpn Vol. 67 No.

Contact-mediated nucleation in melt emulsions investigated by rheo-nuclear magnetic resonance

Increasing the efficiency of disperse phase crystallization is of great interest for melt emulsion production as the fraction of solidified droplets determines product quality and stability. Nucleation events must appear within every single one of the μm-sized droplets for solidification. Therefore, primary crystallization requires high subcooling and is, thus, time and energy consuming. Contact-mediated nucleation is a mechanism for intensifying the crystallization process. It is defined as the successful nucleation of a subcooled liquid droplet induced by contact with an already crystallized droplet. We investigated contact-mediated nucleation under shear flow conditions up to shear rates of 457 s$^{-1}$ for a quantitative assessment of this mechanism. Rheo-nuclear magnetic resonance was successfully used for the time-resolved determination of the solids fraction of the dispersed phase of melt emulsions upon contact-mediated nucleation events. The measurements were carried out in a dedicated Taylor–Couette cell. The efficiency of contact-mediated nucleation $\lambda$$_{sec}$ decreased with increasing shear rate, whereas the effective second order kinetic constant k$_{coll, eff}$ increased approximately linearly at small shear rates and showed a linear decrease for shear rates higher than about 200 s$^{-1}$. These findings are in accordance with coalescence theory. Thus, the nucleation rate is optimal at specific flow conditions. There are limitations for successful inoculation at a low shear rate because of rare contact events and at a high shear rate due to too short contact time

Magnetic impurity coupled to interacting conduction electrons

We consider a magnetic impurity which interacts by hybridization with a system of weakly correlated electrons and determine the energy of the ground state by means of an 1/N_f expansion. The correlations among the conduction electrons are described by a Hubbard Hamiltonian and are treated to lowest order in the interaction strength. We find that their effect on the Kondo temperature, T_K, in the Kondo limit is twofold: First, the position of the impurity level is shifted due to the reduction of charge fluctuations, which reduces T_K. Secondly, the bare Kondo exchange coupling is enhanced as spin fluctuations are enlarged. In total, T_K increases. Both corrections require intermediate states beyond the standard Varma-Yafet ansatz. This shows that the Hubbard interaction does not just provide quasiparticles, which hybridize with the impurity, but also renormalizes the Kondo coupling.Comment: ReVTeX 19 pages, 3 uuenconded postscript figure

The Kondo lattice model with correlated conduction electrons

We investigate a Kondo lattice model with correlated conduction electrons. Within dynamical mean-field theory the model maps onto an impurity model where the host has to be determined self-consistently. This impurity model can be derived from an Anderson-Hubbard model both by equating the low-energy excitations of the impurity and by a canonical transformation. On the level of dynamical mean-field theory this establishes the connection of the two lattice models. The impurity model is studied numerically by an extension of the non-crossing approximation to a two-orbital impurity. We find that with decreasing temperature the conduction electrons first form quasiparticles unaffected by the presence of the lattice of localized spins. Then, reducing the temperature further, the particle-hole symmetric model turns into an insulator. The quasiparticle peak in the one-particle spectral density splits and a gap opens. The size of the gap increases when the correlations of the conduction electrons become stronger. These findings are similar to the behavior of the Anderson-Hubbard model within dynamical mean-field theory and are obtained with much less numerical effort.Comment: 7 pages RevTeX with 3 ps figures, accepted by PR

In‐situ characterization of deposits in ceramic hollow fiber membranes by compressed sensing RARE‐MRI

Ultrafiltration with ceramic hollow fiber membranes was investigated by compressed sensing rapid acquisition relaxation enhancement (CS-RARE) magnetic resonance imaging (MRI) to characterize filtration mechanisms. Sodium alginate was used as a model substance for extracellular polymeric substances. Dependent on the concentration of divalent ions like Ca21 in an aqueous alginate solution, the characteristics of the filtration change from concentration polarization to a gel layer. The fouling inside the membrane lumen could be measured by MRI with a CS-RARE pulse sequence. Contrast agents have been used to get an appropriate contrast between deposit and feed. The lumen was analyzed quantitatively by exploring the membrane’s radial symmetry, and the resulting intensity could be modeled. Thus, different fouling mechanisms could be distinguished. CS-RARE-MRI was proven to be an appropriate in situ tool to quantitatively characterize the deposit formation during in-out filtration processes. The results were underlined by flux interruption experiments and length dependent studies, which make it possible to differentiate between gel layer or cake filtration and concentration polarization filtration processes

Structural characterisation of deposit layer during milk protein microfiltration by means of in-situ mri and compositional analysis

Milk protein fractionation by microfiltration membranes is an established but still growing field in dairy technology. Even under cross-flow conditions, this filtration process is impaired by the formation of a deposit by the retained protein fraction, mainly casein micelles. Due to deposition formation and consequently increased overall filtration resistance, the mass flow of the smaller whey protein fraction declines within the first few minutes of filtration. Currently, there are only a handful of analytical techniques available for the direct observation of deposit formation with opaque feed media and membranes. Here, we report on the ongoing development of a non-invasive and non-destructive method based on magnetic resonance imaging (MRI), and its application to characterise deposit layer formation during milk protein fractionation in ceramic hollow fibre membranes as a function of filtration pressure and temperature, temporally and spatially resolved. In addition, the chemical composition of the deposit was analysed by reversed phase high pressure liquid chromatography (RP-HPLC). We correlate the structural information gained by in-situ MRI with the protein amount and composition of the deposit layer obtained by RP-HPLC. We show that the combination of in-situ MRI and chemical analysis by RP-HPLC has the potential to allow for a better scientific understanding of the pressure and temperature dependence of deposit layer formation

Generalized Heisenberg algebras and k-generalized Fibonacci numbers

It is shown how some of the recent results of de Souza et al. [1] can be generalized to describe Hamiltonians whose eigenvalues are given as k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases considered by de Souza et al. corespond to k=2.Comment: 8 page