Spectral functions and time evolution from the Chebyshev recursion

We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor $\sim\frac{1}{6}$. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time evolution algorithm that instead of the group operator $e^{-iHt}$ only involves the action of the generator $H$. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from $H$ than time evolution algorithms when fixing a given amount of created entanglement.Comment: 12 pages + 6 pages appendix, 11 figure

Averting biodiversity collapse in tropical forest protected areas

The rapid disruption of tropical forests probably imperils global biodiversity more than any other contemporary phenomenon¹⁻³. With deforestation advancing quickly, protected areas are increasingly becoming final refuges for threatened species and natural ecosystem processes. However, many protected areas in the tropics are themselves vulnerable to human encroachment and other environmental stresses⁴⁻⁹. As pressures mount, it is vital to know whether existing reserves can sustain their biodiversity. A critical constraint in addressing this question has been that data describing a broad array of biodiversity groups have been unavailable for a sufficiently large and representative sample of reserves. Here we present a uniquely comprehensive data set on changes over the past 20 to 30 years in 31 functional groups of species and 21 potential drivers of environmental change, for 60 protected areas stratified across the world’s major tropical regions. Our analysis reveals great variation in reserve ‘health’: about half of all reserves have been effective or performed passably, but the rest are experiencing an erosion of biodiversity that is often alarmingly widespread taxonomically and functionally. Habitat disruption, hunting and forest-product exploitation were the strongest predictors of declining reserve health. Crucially, environmental changes immediately outside reserves seemed nearly as important as those inside in determining their ecological fate, with changes inside reserves strongly mirroring those occurring around them. These findings suggest that tropical protected areas are often intimately linked ecologically to their surrounding habitats, and that a failure to stem broad-scale loss and degradation of such habitats could sharply increase the likelihood of serious biodiversity declines.Keywords: Ecology, Environmental scienc

Studies of flow redistribution of external parallel coolant or moderator flow through tube bundles

The problem of transverse flow redistribution for geometries of interest to nuclear reactor technology are investigated from a macroscopic point of view by studying methods of solving the pertinent equations, their finite difference representation, convergence criteria, the choice of boundary conditions and the selection of the "control volume" within the matrix of fuel rods. The arrays selected consist of a fixed number of fuel rods surrounded by the coolant or moderator inside a square, rectangular, or cylindrical structural member. The driving function is the set of initial mass velocities which are assumed to be constant and known at the flow channel entrances. Because the number of degrees of freedom for the flow redistribution in these geometries exceeds the number of flow equations, special techniques have been used to achieve convergence of not only the axial pressure drop, but which will also yield a symmetrical flow redistribution when symmetrical problems are solved. A Fortran program has been devised which will solve the continuity equation for the outlet velocity and transverse velocities for given input values. The momentum equation is then solved to obtain the pressure drop in each control volume which results from dividing the flow channel length in equal axial increments. An average pressure drop is estimated toward which all channel pressure drops are corrected by correcting the transverse mass velocities. Thus, having corrected the transverse mass velocities, the above steps are repeated until the pressure dropper control volume is the same in the axial interval selected, within a convergence criteria. The outlet enthalpy are then evaluated assuming the inlet enthalpy at each control volume and the heat source per fuel rod. The results of this axial calculation are used as input to the next set of calculations for the next axial interval and the procedure is repeated until the whole length of the flow channel is transversed. Results of sample calculations for a square (3x3 rods) and a cylindrical (19 rod bundle) array are presented. In the former system, results for both cases, symmetrical and unsymmetrical, are reported. The computer programs used in the calculations are also included

Studies of flow redistribution of external parallel coolant or moderator flow through tube bundles

The problem of transverse flow redistribution for geometries of interest to nuclear reactor technology are investigated from a macroscopic point of view by studying methods of solving the pertinent equations, their finite difference representation, convergence criteria, the choice of boundary conditions and the selection of the "control volume" within the matrix of fuel rods. The arrays selected consist of a fixed number of fuel rods surrounded by the coolant or moderator inside a square, rectangular, or cylindrical structural member. The driving function is the set of initial mass velocities which are assumed to be constant and known at the flow channel entrances. Because the number of degrees of freedom for the flow redistribution in these geometries exceeds the number of flow equations, special techniques have been used to achieve convergence of not only the axial pressure drop, but which will also yield a symmetrical flow redistribution when symmetrical problems are solved. A Fortran program has been devised which will solve the continuity equation for the outlet velocity and transverse velocities for given input values. The momentum equation is then solved to obtain the pressure drop in each control volume which results from dividing the flow channel length in equal axial increments. An average pressure drop is estimated toward which all channel pressure drops are corrected by correcting the transverse mass velocities. Thus, having corrected the transverse mass velocities, the above steps are repeated until the pressure dropper control volume is the same in the axial interval selected, within a convergence criteria. The outlet enthalpy are then evaluated assuming the inlet enthalpy at each control volume and the heat source per fuel rod. The results of this axial calculation are used as input to the next set of calculations for the next axial interval and the procedure is repeated until the whole length of the flow channel is transversed. Results of sample calculations for a square (3x3 rods) and a cylindrical (19 rod bundle) array are presented. In the former system, results for both cases, symmetrical and unsymmetrical, are reported. The computer programs used in the calculations are also included

Propiedades estructuralesy magnéticas de aleaciones cristalinas desordenadas Fe50Mn25+xSn25-x con x: -1.25, 0.0, 2.5, 5.0, 7.5

Disordered crystalline Fe50Mn25+xSn25-x alloys, with x = -1.25, 0.0, 2.5, 5.0, 7.5 (close to the full-Heusler alloys), were arc-melted in a high purity argon atmosphere and the molten pellets were individually sealed in quartz tubes also under argon atmosphere. Subsequently, they were annealed at 1173 K for 4 days, being finally quenched in a bath with cold water. Structural and magnetic properties have systematically been studied using X-ray diffraction, 57Fe, and 119Sn Mössbauer spectroscopies, and magnetization measurements recorded at room temperature. Rietveld refinement of the X-ray diffraction patterns of the annealed samples with x = -1.25 and 0 has revealed the presence of two hexagonal crystallographic phases: (i) a chemically disordered solid solution identified as  e-(Fe/Mn)3Sn (majority fraction) and (ii) the e-Fe5Sn3 intermetallic compound (minority fraction). For samples with x = 2.5, 5.0, and 7.5, the Rietveld analysis has only indicated the presence of a chemically disordered solid solution identified as e-(Fe/Mn)3(Sn/Fe/Mn). Although compositions of the Fe50Mn25+xSn25-x alloys are close to that of full-Heusler alloys, none of them has the expected L21 structure. The average crystallite sizes, estimated from the Williamson-Hall method, are in the range of 256-62 nm. The average sizes has gradually decreased as the x-content is increased. Mössbauer results have shown localized-type magnetism from Fe non-equivalent sites, and itinerant-like magnetism on 119Sn-probes. Magnetic hysteresis loops, recorded at 300 K for a maximum field of 2200 Oe, have indicated that the remanent and coercive fields have systematically decreased as the x-parameter has increased. Coercive fields are in the range for soft magnets (1-20 Oe).Aleaciones cristalinas desordenadas Fe50Mn25+xSn25-x, con x = -1.25, 0.0, 2.5, 5.0, 7.5, cercanas a las composiciones de Heusler-211, fueron preparadas por fusión en atmósfera inerte, subsecuentemente, sometidas a recocido térmico durante 4 días a 1173 K y, finalmente, enfriadas en agua helada. Todas las aleaciones han sido sistemáticamente analizadas mediante difracción de rayos X, espectroscopias Mössbauer de 57Fe y 119Sn, y medidas de magnetización a temperatura ambiente. Los análisis Rietveld de los difractogramas de las muestras con x = -1.25 y 0.0 muestran la presencia de dos fases cristalográficas hexagonales: (i) la solución sólida químicamente desordenada e-(Fe/Mn)3Sn (mayoritaria), y (ii) el intermetálico e-Fe5Sn3 (minoritaria); mientras que, las aleaciones con x = 2.5, 5.0 y 7.5, presentan solo la solución sólida desordenada, e-(Fe/Mn)3(Sn/Fe/Mn). Si bien, las composiciones de las aleaciones Fe50Mn25+xSn25-x son cercanas a las de Heusler-211, ninguna tiene la estructura cúbica L21 característica de estas. Los tamaños medios de los cristalitos, calculados por el método de Williamson-Hall, están dentro del rango 256-62 nm y disminuyen cuando x aumenta. Los resultados Mössbauer de todas las aleaciones muestran la característica de magnetismo localizado a través de la distribución de campos magnéticos hiperfinos en los sitios de Fe, y de magnetismo itinerante a través de los campos transferidos desde los átomos de Fe en los núcleos de 119Sn. Los campos coercitivos y remanentes, obtenidos por medidas de magnetización bajo campo magnético aplicado entre -2200 y +2200 Oe, disminuyen cuando x aumenta. Los valores de los campos coercitivos están en el rango de los magnetos blandos (1-20 Oe)