Non-archimedean tame topology and stably dominated types

Let $V$ be a quasi-projective algebraic variety over a non-archimedean valued field. We introduce topological methods into the model theory of valued fields, define an analogue $\hat {V}$ of the Berkovich analytification $V^{an}$ of $V$, and deduce several new results on Berkovich spaces from it. In particular we show that $V^{an}$ retracts to a finite simplicial complex and is locally contractible, without any smoothness assumption on $V$. When $V$ varies in an algebraic family, we show that the homotopy type of $V^{an}$ takes only a finite number of values. The space $\hat {V}$ is obtained by defining a topology on the pro-definable set of stably dominated types on $V$. The key result is the construction of a pro-definable strong retraction of $\hat {V}$ to an o-minimal subspace, the skeleton, definably homeomorphic to a space definable over the value group with its piecewise linear structure.Comment: Final versio

Energy Balance in the Solar Transition Region. IV. Hydrogen and Helium Mass Flows With Diffusion

In this paper we have extended our previous modeling of energy balance in the chromosphere-corona transition region to cases with particle and mass flows. The cases considered here are quasi-steady, and satisfy the momentum and energy balance equations in the transition region. We include in all equations the flow velocity terms and neglect the partial derivatives with respect to time. We present a complete and physically consistent formulation and method for solving the non-LTE and energy balance equations in these situations, including both particle diffusion and flows of H and He. Our results show quantitatively how mass flows affect the ionization and radiative losses of H and He, thereby affecting the structure and extent of the transition region. Also, our computations show that the H and He line profiles are greatly affected by flows. We find that line shifts are much less important than the changes in line intensity and central reversal due to the effects of flows. In this paper we use fixed conditions at the base of the transition region and in the chromosphere because our intent is to show the physical effects of flows and not to match any particular observations. However, we note that the profiles we compute can explain the range of observed high spectral and spatial resolution Lyman alpha profiles from the quiet Sun. We suggest that dedicated modeling of specific sequences of observations based on physically consistent methods like those presented here will substantially improve our understanding of the energy balance in the chromosphere and corona.Comment: 50 pages + 20 figures; submitted to ApJ 9/10/01; a version with higher resolution figures is available at http://cfa-www.harvard.edu/~avrett

Pressure Distribution Tests on PW-9 Wing Models from -18 Degree Through 90 Degree Angle of Attack

At the request of the Army Air Corps, an investigation of the pressure distribution over PW-9 wing models was conducted in the atmospheric wind tunnel of the National Advisory Committee for Aeronautics. The primary purpose of these tests was to obtain wind-tunnel data on the load distribution on the cellule to be correlated with similar information obtained in flight tests, both to be used for design purposes. Because of the importance of the conditions beyond the stall as affecting the control and stability, this investigation was extended through 90 degree angle of attack. The results for the range of normal flight have been given in NACA Technical Report No. 271. The present paper presents the same results in a different form and includes, in addition, those over the greater range of angle of attack, -18 degrees through 90 degrees. The results show that: (1) at angles of attack above maximum lift, the biplane upper wing pressures are decreased by the shielding action of the lower wing. (2) the burble of the biplane lower wing, with respect to the angle of attack, is delayed, due to the shielding action of the lower wing. (3) the center of pressure of the biplane upper wing (semispan) is, in general, displaced forward and outward with reference to that of the wing as a monoplane, while for the lower wing there is but slight difference for both conditions. (4) the overhanging portion of the upper wing is little affected by the presence of the lower wing

Magnetic anomalies in single crystalline ErPd2Si2

Considering certain interesting features in the previously reported 166Er Moessbauer effect and neutron diffraction data on the polycrystalline form of ErPd2Si2 crystallizing in ThCr2Si2-type tetragonal structure, we have carried out magnetic measurements (1.8 to 300 K) on the single crystalline form of this compound. We observe significant anisotropy in the absolute values of magnetization (indicating that the easy axis is c-axis) as well as in the features due to magnetic ordering in the plot of magnetic susceptibility (chi) versus temperature (T) at low temperatures. The chi(T) data reveal that there is a pseudo-low dimensional magnetic order setting in at 4.8 K, with a three-dimensional antiferromagnetic ordering setting in at a lower temperature (3.8 K). A new finding in the chi(T) data is that, for H//, but not for H//, there is a broad shoulder in the range 8-20 K, indicative of the existence of magnetic correlations above 5 K as well, which could be related to the previously reported slow-relaxation-dominated Moessbauer spectra. Interestingly, the temperature coefficient of electrical resistivity is found to be isotropic; no feature due to magnetic ordering could be detected in the electrical resistivity data at low temperatures, which is attributed to magnetic Brillioun-zone boundary gap effects. The results reveal complex nature of the magnetism of this compound

Plant community responses to livestock grazing: an assessment of alternative management practices in a semi-arid grassland

One of the most prevalent land-use practices in the American Southwest, and one of the most contentious issues among land-use policymakers, is the grazing of domestic livestock. In an effort to contribute scientific understanding to this debate, we have designed experiments comparing the effects of alternative grazing regimes on plant communities. In a semiarid grassland of northern Arizona, we have implemented a replicated study of four treatments: (1) low-intensity, long-duration grazing rotations; (2) highintensity, short-duration rotations (Holistic Resource Management-style grazing); (3) very high intensity, short duration grazing (to simulate herd impact); and (4) livestock exclosure. Beginning in 1997, we conducted annual surveys of the plant communities with Modified-Whittaker plots. Preliminary results suggest that interannual variability affecting all study plots is high, and that these alternative management strategies do not have dramatic short-term effects on the plant community. Comparisons of native and exotic species richness, as well as ground cover of grasses and forbs, showed no consistent pattern due to treatment over a 3-year period. Our results suggest that the effects of alternative livestock management styles in the semiarid grasslands studied are modest, at least in the short-term, and that future plant monitoring programs would greatly benefit from a multiscale sampling design

Non-archimedean integrals as limits of complex integrals

We explain how non-archimedean integrals considered by Chambert-Loir and Ducros naturally arise in asymptotics of families of complex integrals. To perform this analysis we work over a non-standard model of the field of complex numbers, which is endowed at the same time with an archimedean and a non-archimedean norm. Our main result states the existence of a natural morphism between bicomplexes of archimedean and non-archimedean forms which is compatible with integration.Comment: 55 page

Reframing the grazing debate: Evaluating ecological sustainability and bioregional food production

The semi-arid grasslands of the Colorado Plateau are productive, diverse, and extensive ecosystems. The majority of these ecosystems have been altered by human land use, primarily through the grazing of domestic livestock, yielding a plethora of environmental and social consequences that are tightly interconnected. From an agroecological perspective, untangling these issues requires both an understanding of the role of livestock grazing in bioregional food production and the effect of that grazing on ecological sustainability. To address the former, we discuss the importance of cattle ranching as a bioregional food source, including estimates of meat production and water use in Arizona. To address the latter, we present data from a long-term project addressing changes in native plant community composition, under a range of alternative livestock management strategies. Our study site near Flagstaff, AZ includes four different management treatments: (1) conventional low-intensity, long-duration grazing rotations; (2) high-intensity, short-duration rotations; (3) very high-impact, very short-duration grazing (to simulate herd impact); and, (4) livestock exclosure. Preliminary results suggest belowground properties are responding more quickly to grazing treatments than aboveground properties. Particular response variables, such as cyanobacteria and diatoms, show a marked short-term response to very high-impact, short-duration grazing, but long-term implications are as yet unknown

Pseudogap and photoemission spectra in the attractive Hubbard model

Angle-resolved photoemission spectra are calculated microscopically for the two-dimensional attractive Hubbard model. A system of self-consistent T-matrix equations are solved numerically in the real-time domain. The single-particle spectral function has a two-peak structure resulting from the presense of bound states. The spectral function is suppressed at the chemical potential, leading to a pseudogap-like behavior. At high temperatures and densities the pseudogap diminishes and finally disappears; these findings are similar to experimental observations for the cuprates.Comment: 5 pages, 4 figures, published versio