Evaluating and improving the cluster variation method entropy functional for Ising alloys

The success of the "Cluster Variation Method" (CVM) in reproducing quite accurately the free energies of Monte Carlo (MC) calculations on Ising models is explained in terms of identifying a cancellation of errors: We show that the CVM produces correlation functions that are too close to zero, which leads to an overestimation of the exact energy, E, and at the same time, to an underestimation of -TS, so the free energy F=E-TS is more accurate than either of its parts. This insight explains a problem with "hybrid methods" using MC correlation functions in the CVM entropy expression: They give exact energies E and do not give significantly improved -TS relative to CVM, so they do not benefit from the above noted cancellation of errors. Additionally, "hybrid methods" suffer from the difficulty of adequately accounting for both ordered and disordered phases in a consistent way. A different technique, the "Entropic Monte Carlo" (EMC), is shown here to provide a means for critically evaluating the CVM entropy. Inspired by EMC results, we find a universal and simple correction to the CVM entropy which produces individual components of the free energy with MC accuracy, but is computationally much less expensive than either MC thermodynamic integration or EMC.Comment: 7 pages, ReVTeX galley format, 4 eps figures embedded using epsf, to be published in J. Chem. Phy

Protein Supplementation Is Vital for Beef Cattle Fed with Tropical Pasture

The production of beef on pasture is one of the potentials of Brazilian agriculture, mainly due to the territorial extension and climatic conditions. Therefore, the production of beef on tropical pastures mainly consists of the use of tropical forages; when correctly handled, forage plants show good productivity and improvement in the nutritive value. Among main factors that affect the performance of beef cattle fed on pastures, the availability and quality of the pasture stand first. In tropical regions, during the dry period of the year, the production of forage as well as its nutritive value is diminished. Hence, it is necessary to use protein supplements as a feed strategy to promote increased intake and improved nutrient utilization efficiency by animals. In view of this, by-products of biodiesel from oilseeds, such as peanuts, cottonseed and sunflower seeds, with high nutritional values can be used as an animal feed alternative to the protein sources commonly used for the formulation of supplements. Protein supplementation contributes to an increase in live weight gain as well as improvement in ruminal microbiota activity and, consequently, potentiates nutrient utilization efficiency in beef cattle fed with tropical pasture

Cation- and vacancy-ordering in Li_xCoO_2

Using a combination of first-principles total energies, a cluster expansion technique, and Monte Carlo simulations, we have studied the Li/Co ordering in LiCoO_2 and Li-vacancy/Co ordering in CoO_2. We find: (i) A ground state search of the space of substitutional cation configurations yields the (layered) CuPt structure as the lowest-energy state in the octahedral system LiCoO_2 (and CoO_2), in agreement with the experimentally observed phase. (ii) Finite temperature calculations predict that the solid-state order- disorder transitions for LiCoO_2 and CoO_2 occur at temperatures (~5100 K and ~4400 K, respectively) much higher than melting, thus making these transitions experimentally inaccessible. (iii) The energy of the reaction E(LiCoO_2) - E(CoO_2) - E(Li) gives the average battery voltage V of a Li_xCoO_2/Li cell. Searching the space of configurations for large average voltages, we find that CuPt (a monolayer superlattice) has a high voltage (V=3.78 V), but that this could be increased by cation randomization (V=3.99 V), partial disordering (V=3.86 V), or by forming a 2-layer Li_2Co_2O_4 superlattice along (V=4.90 V).Comment: 12 Pages, RevTeX galley format, 5 figures embedded using epsf Phys. Rev. B (in press, 1998

Robust Expansion of Uncertain Volterra Kernels into Orthonormal Series

Abstract-This paper is concerned with the computation of uncertainty bounds for the expansion of uncertain Volterra models into an orthonormal basis of functions, such as the Laguerre or Kautz bases. This problem has already been addressed in the context of linear systems by means of an approach in which the uncertainty bounds of the expansion coefficients have been estimated from a structured set of impulse responses describing a linear uncertain process. This approach is extended here towards nonlinear Volterra models through the computation of the uncertainty bounds of the expansion coefficients from a structured set of uncertain Volterra kernels. The proposed formulation assures that the resulting model is able to represent all the original uncertainties with minimum intervals for the expansion coefficients. An example is presented to illustrate the effectiveness of the proposed formulation

Point-charge electrostatics in disordered alloys

A simple analytic model of point-ion electrostatics has been previously proposed in which the magnitude of the net charge q_i on each atom in an ordered or random alloy depends linearly on the number N_i^(1) of unlike neighbors in its first coordination shell. Point charges extracted from recent large supercell (256-432 atom) local density approximation (LDA) calculations of Cu-Zn random alloys now enable an assessment of the physical validity and accuracy of the simple model. We find that this model accurately describes (i) the trends in q_i vs. N_i^(1), particularly for fcc alloys, (ii) the magnitudes of total electrostatic energies in random alloys, (iii) the relationships between constant-occupation-averaged charges and Coulomb shifts (i.e., the average over all sites occupied by either $A$ or $B$ atoms) in the random alloy, and (iv) the linear relation between the site charge q_i and the constant- charge-averaged Coulomb shift (i.e., the average over all sites with the same charge) for fcc alloys. However, for bcc alloys the fluctuations predicted by the model in the q_i vs. V_i relation exceed those found in the LDA supercell calculations. We find that (a) the fluctuations present in the model have a vanishing contribution to the electrostatic energy. (b) Generalizing the model to include a dependence of the charge on the atoms in the first three (two) shells in bcc (fcc) - rather than the first shell only - removes the fluctuations, in complete agreement with the LDA data. We also demonstrate an efficient way to extract charge transfer parameters of the generalized model from LDA calculations on small unit cells.Comment: 15 pages, ReVTeX galley format, 7 eps figures embedded using psfig, to be published in Phys. Rev.

Cosmology with exponential potentials

We examine in the context of general relativity the dynamics of a spatially flat Robertson-Walker universe filled with a classical minimally coupled scalar field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic matter. This system is reduced to a first-order ordinary differential equation, providing direct evidence on the acceleration/deceleration properties of the system. As a consequence, for positive potentials, passage into acceleration not at late times is generically a feature of the system, even when the late-times attractors are decelerating. Furthermore, the structure formation bound, together with the constraints on the present values of \Omega_{m}, w_{\phi} provide, independently of initial conditions and other parameters, necessary conditions on \mu. Special solutions are found to possess intervals of acceleration. For the almost cosmological constant case w_{\phi} ~ -1, as well as, for the generic late-times evolution, the general relation \Omega_{\phi}(w_{\phi}) is obtained.Comment: RevTex4, 9 pages, 2 figures, References adde

Inflation and Dark Energy from spectroscopy at z > 2

The expansion of the Universe is understood to have accelerated during two epochs: in its very first moments during a period of Inflation and much more recently, at z < 1, when Dark Energy is hypothesized to drive cosmic acceleration. The undiscovered mechanisms behind these two epochs represent some of the most important open problems in fundamental physics. The large cosmological volume at 2 < z < 5, together with the ability to efficiently target high-$z$ galaxies with known techniques, enables large gains in the study of Inflation and Dark Energy. A future spectroscopic survey can test the Gaussianity of the initial conditions up to a factor of ~50 better than our current bounds, crossing the crucial theoretical threshold of $\sigma(f_{NL}^{\rm local})$ of order unity that separates single field and multi-field models. Simultaneously, it can measure the fraction of Dark Energy at the percent level up to $z = 5$, thus serving as an unprecedented test of the standard model and opening up a tremendous discovery space