Revisiting the phase diagram of hard ellipsoids

In this work the well-known Frenkel-Mulder phase diagram of hard ellipsoids of revolution [Mol. Phys. 55, 1171 (1985)] is revisited by means of replica exchange Monte Carlo simulations. The method provides good sampling of dense systems and so, solid phases can be accessed without the need of imposing a given structure. At high densities, we found plastic solids and fcc-like crystals for semi-spherical ellipsoids (prolates and oblates), and SM2 structures [Phys. Rev. E 75, 020402 (2007)] for x:1-prolates and 1:x-oblates with x>=3. The revised fluid-crystal and isotropic-nematic transitions reasonably agree with those presented in the Frenkel-Mulder diagram. An interesting result is that, for small system sizes (100 particles), we obtained 2:1 and 1.5:1-prolate equations of state without transitions, while some order is developed at large densities. Furthermore, the symmetric oblate cases are also reluctant to form ordered phases.Comment: 8 pages, 6 figure

The Honeycomb Conjecture

This article gives a proof of the classical honeycomb conjecture: any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42423/1/454-25-1-1_10071.pd

Effects of decreased dietary roughage concentration on energy metabolism and nutrient balance in finishing beef cattle

The optimal roughage concentration required in feedlot diets changes continuously for many reasons such as source, availability, price, and interaction with other ingredients in the diet. Wet distillers grains and solubles (WDGS) are common in finishing diets and they contain relatively high amounts of fiber compared with other grains they replace. Therefore, concentration of roughage could be altered when WDGS are included in feedlot diets. There has been very little data published regarding the effects of roughage concentration on energy metabolism and nutrient balance in beef steers. Therefore, the effects of roughage concentration in dryrolled corn (DRC)–based diets containing 25% WDGS were evaluated in 8 steers (BW = 362 ± 3.71 kg) using a replicated Latin square. Data were analyzed with the fixed effects of dietary treatment and period and random effects of square and steer within square were included in the model. Diets consisted of 25% WDGS and the balance being DRC and coarsely ground alfalfa hay (AH) replacing corn at 2% (AH-2), 6% (AH-6), 10% (AH-10), and 14% (AH-14) of dietary dry matter. As a proportion of GE intake, fecal energy loss increased linearly (P = 0.02), and DE decreased linearly (P = 0.02) as dietary level of AH increased. Methane energy loss, as a proportion of GE intake, increased linearly (P \u3c 0.01) and ME decreased linearly (P \u3c 0.01) as dietary concentration of AH increased. Heat production tended (P = 0.10) to decrease reaching a minimum of 10% AH and increased from 10 to 14% AH inclusion. Moreover, as a proportion of GE intake, retained energy (RE) decreased (P \u3c 0.01) as AH level increased in the diet. Reasons for the decrease in RE are 1) the increase in fecal energy loss that is associated with decreased ruminal digestibility of NDF when AH replaced DRC and the shift in ruminal VFA produced, 2) the decreased energy available for animal retention when NDF increased linearly as AH increased in the diet, and 3) the methane and heat energy associated with digestion of the fibrous portion of the AH. Neutral detergent fiber and OM excretion also increased linearly (P \u3c 0.01) with increasing AH in the diet. The increased NDF and OM excretion were likely caused by the difference in digestibility of AH and DRC

Effects of decreased dietary roughage concentration on energy metabolism and nutrient balance in finishing beef cattle

The optimal roughage concentration required in feedlot diets changes continuously for many reasons such as source, availability, price, and interaction with other ingredients in the diet. Wet distillers grains and solubles (WDGS) are common in finishing diets and they contain relatively high amounts of fiber compared with other grains they replace. Therefore, concentration of roughage could be altered when WDGS are included in feedlot diets. There has been very little data published regarding the effects of roughage concentration on energy metabolism and nutrient balance in beef steers. Therefore, the effects of roughage concentration in dryrolled corn (DRC)–based diets containing 25% WDGS were evaluated in 8 steers (BW = 362 ± 3.71 kg) using a replicated Latin square. Data were analyzed with the fixed effects of dietary treatment and period and random effects of square and steer within square were included in the model. Diets consisted of 25% WDGS and the balance being DRC and coarsely ground alfalfa hay (AH) replacing corn at 2% (AH-2), 6% (AH-6), 10% (AH-10), and 14% (AH-14) of dietary dry matter. As a proportion of GE intake, fecal energy loss increased linearly (P = 0.02), and DE decreased linearly (P = 0.02) as dietary level of AH increased. Methane energy loss, as a proportion of GE intake, increased linearly (P \u3c 0.01) and ME decreased linearly (P \u3c 0.01) as dietary concentration of AH increased. Heat production tended (P = 0.10) to decrease reaching a minimum of 10% AH and increased from 10 to 14% AH inclusion. Moreover, as a proportion of GE intake, retained energy (RE) decreased (P \u3c 0.01) as AH level increased in the diet. Reasons for the decrease in RE are 1) the increase in fecal energy loss that is associated with decreased ruminal digestibility of NDF when AH replaced DRC and the shift in ruminal VFA produced, 2) the decreased energy available for animal retention when NDF increased linearly as AH increased in the diet, and 3) the methane and heat energy associated with digestion of the fibrous portion of the AH. Neutral detergent fiber and OM excretion also increased linearly (P \u3c 0.01) with increasing AH in the diet. The increased NDF and OM excretion were likely caused by the difference in digestibility of AH and DRC

Helical Tubes in Crowded Environments

When placed in a crowded environment, a semi-flexible tube is forced to fold so as to make a more compact shape. One compact shape that often arises in nature is the tight helix, especially when the tube thickness is of comparable size to the tube length. In this paper we use an excluded volume effect to model the effects of crowding. This gives us a measure of compactness for configurations of the tube, which we use to look at structures of the semi-flexible tube that minimize the excluded volume. We focus most of our attention on the helix and which helical geometries are most compact. We found that helices of specific pitch to radius ratio 2.512 to be optimally compact. This is the same geometry that minimizes the global curvature of the curve defining the tube. We further investigate the effects of adding a bending energy or multiple tubes to begin to explore the more complete space of possible geometries a tube could form.Comment: 10 page

Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex notions are those of boundary and separating edges. When performing proofs about this algorithm, questions of symmetry appear and this exposition attempts to give an account of how these symmetries can be handled. All this work relies on formal developments made with Coq and the mathematical components library

Stacking Characteristics of Close Packed Materials

It is shown that the enthalpy of any close packed structure for a given element can be characterised as a linear expansion in a set of continuous variables $\alpha_n$ which describe the stacking configuration. This enables us to represent the infinite, discrete set of stacking sequences within a finite, continuous space of the expansion parameters $H_n$. These $H_n$ determine the stable structure and vary continuously in the thermodynamic space of pressure, temperature or composition. The continuity of both spaces means that only transformations between stable structures adjacent in the $H_n$ space are possible, giving the model predictive and well as descriptive ability. We calculate the $H_n$ using density functional theory and interatomic potentials for a range of materials. Some striking results are found: e.g. the Lennard-Jones potential model has 11 possible stable structures and over 50 phase transitions as a function of cutoff range. The very different phase diagrams of Sc, Tl, Y and the lanthanides are understood within a single theory. We find that the widely-reported 9R-fcc transition is not allowed in equilibrium thermodynamics, and in cases where it has been reported in experiments (Li, Na), we show that DFT theory is also unable to predict it

Deep observations of the Super-CLASS super-cluster at 325 MHz with the GMRT: the low-frequency source catalogue

We present the results of 325 MHz GMRT observations of a super-cluster field, known to contain five Abell clusters at redshift $z \sim 0.2$. We achieve a nominal sensitivity of $34\,\mu$Jy beam$^{-1}$ toward the phase centre. We compile a catalogue of 3257 sources with flux densities in the range $183\,\mu\rm{Jy}\,-\,1.5\,\rm{Jy}$ within the entire $\sim 6.5$ square degree field of view. Subsequently, we use available survey data at other frequencies to derive the spectral index distribution for a sub-sample of these sources, recovering two distinct populations -- a dominant population which exhibit spectral index trends typical of steep-spectrum synchrotron emission, and a smaller population of sources with typically flat or rising spectra. We identify a number of sources with ultra-steep spectra or rising spectra for further analysis, finding two candidate high-redshift radio galaxies and three gigahertz-peaked-spectrum radio sources. Finally, we derive the Euclidean-normalised differential source counts using the catalogue compiled in this work, for sources with flux densities in excess of $223 \, \mu$Jy. Our differential source counts are consistent with both previous observations at this frequency and models of the low-frequency source population. These represent the deepest source counts yet derived at 325 MHz. Our source counts exhibit the well-known flattening at mJy flux densities, consistent with an emerging population of star-forming galaxies; we also find marginal evidence of a downturn at flux densities below $308 \, \mu$Jy, a feature so far only seen at 1.4 GHz.Comment: 25 pages, 18 figures, 10 tables. Accepted for publication in MNRA

Ecosystem processes at the watershed scale: Extending optimality theory from plot to catchment

The adjustment of local vegetation conditions to limiting soil water by either maximizing productivity or minimizing water stress has been an area of central interest in ecohydrology since Eagleson's classic study. This work has typically been limited to consider one-dimensional exchange and cycling within patches and has not incorporated the effects of lateral redistribution of soil moisture, coupled ecosystem carbon and nitrogen cycling, and vegetation allocation processes along topographic gradients. We extend this theory to the hillslope and catchment scale, with in situ and downslope feedbacks between water, carbon and nutrient cycling within a fully transient, distributed model. We explore whether ecosystem patches linked along hydrologic flow paths as a catena evolve to form an emergent pattern optimized to local climate and topographic conditions. Lateral hydrologic connectivity of a small catchment is calibrated with streamflow data and further tested with measured soil moisture patterns. Then, the spatial gradient of vegetation density within a small catchment estimated with fine-resolution satellite imagery and field measurements is evaluated with simulated vegetation growth patterns from different root depth and allocation strategies as a function of hillslope position. This is also supported by the correspondence of modeled and field measured spatial patterns of root depths and catchment-level aboveground vegetation productivity. We test whether the simulated spatial pattern of vegetation corresponds to measured canopy patterns and an optimal state relative to a set of ecosystem processes, defined as maximizing ecosystem productivity and water use efficiency at the catchment scale. Optimal carbon uptake ranges show effective compromises between multiple resources (water, light, and nutrients), modulated by vegetation allocation dynamics along hillslope gradient

Ecosystem processes at the watershed scale: extending optimality theory from plot to catchment

[1] The adjustment of local vegetation conditions to limiting soil water by either maximizing productivity or minimizing water stress has been an area of central interest in ecohydrology since Eagleson's classic study. This work has typically been limited to consider one-dimensional exchange and cycling within patches and has not incorporated the effects of lateral redistribution of soil moisture, coupled ecosystem carbon and nitrogen cycling, and vegetation allocation processes along topographic gradients. We extend this theory to the hillslope and catchment scale, with in situ and downslope feedbacks between water, carbon and nutrient cycling within a fully transient, distributed model. We explore whether ecosystem patches linked along hydrologic flow paths as a catena evolve to form an emergent pattern optimized to local climate and topographic conditions. Lateral hydrologic connectivity of a small catchment is calibrated with streamflow data and further tested with measured soil moisture patterns. Then, the spatial gradient of vegetation density within a small catchment estimated with fine-resolution satellite imagery and field measurements is evaluated with simulated vegetation growth patterns from different root depth and allocation strategies as a function of hillslope position. This is also supported by the correspondence of modeled and field measured spatial patterns of root depths and catchmentlevel aboveground vegetation productivity. We test whether the simulated spatial pattern of vegetation corresponds to measured canopy patterns and an optimal state relative to a set of ecosystem processes, defined as maximizing ecosystem productivity and water use efficiency at the catchment scale. Optimal carbon uptake ranges show effective compromises between multiple resources (water, light, and nutrients), modulated by vegetation allocation dynamics along hillslope gradient. Citation: Hwang, T., L. Band, and T. C. Hales (2009), Ecosystem processes at the watershed scale: Extending optimality theory from plot to catchment, Water Resour. Res., 45, W11425