Proof of phase separation in the binary-alloy problem: the one-dimensional spinless Falicov-Kimball model

The ground states of the one-dimensional Falicov-Kimball model are investigated in the small-coupling limit, using nearly degenerate perturbation theory. For rational electron and ion densities, respectively equal to $\frac{p}{q}$, $\frac{p_i}{q}$, with $p$ relatively prime to $q$ and $\frac{p_i}{q}$ close enough to $\frac{1}{2}$, we find that in the ground state the ion configuration has period $q$. The situation is analogous to the Peierls instability where the usual arguments predict a period-$q$ state that produces a gap at the Fermi level and is insulating. However for $\frac{p_i}{q}$ far enough from $\frac{1}{2}$, this phase becomes unstable against phase separation. The ground state is a mixture of a period-$q$ ionic configuration and an empty (or full) configuration, where both configurations have the same electron density to leading order. Combining these new results with those previously obtained for strong coupling, it follows that a phase transition occurs in the ground state, as a function of the coupling, for ion densities far enough from $\frac{1}{2}$.Comment: 22 pages, typeset in ReVTeX and one encapsulated postscript file embedded in the text with eps

Dynamical mean-field theory for light fermion--heavy boson mixtures on optical lattices

We theoretically analyze Fermi-Bose mixtures consisting of light fermions and heavy bosons that are loaded into optical lattices (ignoring the trapping potential). To describe such mixtures, we consider the Fermi-Bose version of the Falicov-Kimball model on a periodic lattice. This model can be exactly mapped onto the spinless Fermi-Fermi Falicov-Kimball model at zero temperature for all parameter space as long as the mixture is thermodynamically stable. We employ dynamical mean-field theory to investigate the evolution of the Fermi-Bose Falicov-Kimball model at higher temperatures. We calculate spectral moment sum rules for the retarded Green's function and self-energy, and use them to benchmark the accuracy of our numerical calculations, as well as to reduce the computational cost by exactly including the tails of infinite summations or products. We show how the occupancy of the bosons, single-particle many-body density of states for the fermions, momentum distribution, and the average kinetic energy evolve with temperature. We end by briefly discussing how to experimentally realize the Fermi-Bose Falicov-Kimball model in ultracold atomic systems.Comment: 10 pages with 4 figure

Regulation of Wages and Hours Prior to 1938

Direct numerical simulations are performed to investigate the transient upstream propagation (flashback) of premixed hydrogen–air flames in the boundary layer of a fully developed turbulent channel flow. Results show that the well-known near-wall velocity fluctuations pattern found in turbulent boundary layers triggers wrinkling of the initially flat flame sheet as it starts propagating against the main flow direction, and that the structure of the characteristic streaks of the turbulent boundary layer ultimately has an important impact on the resulting flame shape and on its propagation mechanism. It is observed that the leading edges of the upstream-propagating premixed flame are always located in the near-wall region of the channel and assume the shape of several smooth, curved bulges propagating upstream side by side in the spanwise direction and convex towards the reactant side of the flame. These leading-edge flame bulges are separated by thin regions of spiky flame cusps pointing towards the product side at the trailing edges of the flame. Analysis of the instantaneous velocity fields clearly reveals the existence, on the reactant side of the flame sheet, of backflow pockets that extend well above the wall-quenching distance. There is a strong correspondence between each of the backflow pockets and a leading edge convex flame bulge. Likewise, high-speed streaks of fast flowing fluid are found to be always colocated with the spiky flame cusps pointing towards the product side of the flame. It is suggested that the origin of the formation of the backflow pockets, along with the subsequent mutual feedback mechanism, is due to the interaction of the approaching streaky turbulent flow pattern with the Darrieus–Landau hydrodynamic instability and pressure fluctuations triggered by the flame sheet. Moreover, the presence of the backflow pockets, coupled with the associated hydrodynamic instability and pressure–flow field interaction, greatly facilitate flame propagation in turbulent boundary layers and ultimately results in high flashback velocities that increase proportionately with pressure

Time resolution below 100 ps for the SciTil detector of PANDA employing SiPM

The barrel time-of-flight (TOF) detector for the PANDA experiment at FAIR in Darmstadt is planned as a scintillator tile hodoscope (SciTil) using 8000 small scintillator tiles. It will provide fast event timing for a software trigger in the otherwise trigger-less data acquisition scheme of PANDA, relative timing in a multiple track event topology as well as additional particle identification in the low momentum region. The goal is to achieve a time resolution of sigma ~ 100 ps. We have conducted measurements using organic scintillators coupled to Silicon Photomultipliers (SiPM). The results are encouraging such that we are confident to reach the required time resolution.Comment: 10 pages, 7 figure

Elementary steps of the catalytic NO_x reduction with NH₃: Cluster studies on reaction paths and energetics at vanadium oxide substrate

We consider different reaction scenarios of the selective catalytic reduction (SCR) of NO in the presence of ammonia at perfect as well as reduced vanadium oxide surfaces modeled by V2O5(010) without and with oxygen vacancies. Geometric and energetic details as well as reaction paths are evaluated using extended cluster models together with density-functional theory. Based on earlier work of adsorption, diffusion, and reaction of the different surface species participating in the SCR we confirm that at Brønsted acid sites (i.e., OH groups) of the perfect oxide surface nitrosamide, NH2NO, forms a stable intermediate. Here adsorption of NH3 results in NH4 surface species which reacts with gas phase NO to produce the intermediate. Nitrosamide is also found as intermediate of the SCR near Lewis acid sites of the reduced oxide surface (i.e., near oxygen vacancies). However, here the adsorbed NH3 species is dehydrogenated to surface NH2 before it reacts with gas phase NO to produce the intermediate. The calculations suggest that reaction barriers for the SCR are overall higher near Brønsted acid sites of the perfect surface compared with Lewis acid sites of the reduced surface, examined for the first time in this work. The theoretical results are consistent with experimental findings and confirm the importance of surface reduction for the SCR proces

Lower bound for the segregation energy in the Falicov-Kimball model

In this work, a lower bound for the ground state energy of the Falicov-Kimball model for intermediate densities is derived. The explicit derivation is important in the proof of the conjecture of segregation of the two kinds of fermions in the Falicov-Kimball model, for sufficiently large interactions. This bound is given by a bulk term, plus a term proportional to the boundary of the region devoid of classical particles. A detailed proof is presented for density n=1/2, where the coefficient 10^(-13) is obtained for the boundary term, in two dimensions. With suitable modifications the method can also be used to obtain a coefficient for all densities.Comment: 8 pages, 2 figure

Two-stage Optimization for Building Energy Management

AbstractContinuous increase of energy demand on one hand and integration of large number of renewable energy sources on the other require advanced control strategies to provide an uninterrupted service and guarantee high energy efficiency. Utilities and transmission system operators permanently supervise production facilities and grids to compensate any mismatch between production and consumption. With the gradual change from a centralized system with a few large power plants to a decentralized and distributed generation based on many renewable energy sources, local energy management systems can contribute to grid balancing. This paper presents a building energy management which determines the optimal scheduling of the different components of the local energy system. The two-stage optimization is based on the minimization of an economic function subject to the physical system constraints and uses a receding horizon approach. The proposed building energy management is implemented using mixed integer linear programming and applied in simulation to a hotel with photovoltaic installation and battery system

A discrete methodology for controlling the sign of curvature and torsion for NURBS

This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration