A natural orbital functional for the many-electron problem

The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the reduced first-order density matrix or equivalently the natural orbitals. In the former approach the unknown part of the functional contains both a kinetic and a potential contribution whereas in the latter approach it contains only a potential energy and consequently has simpler scaling properties. We present an approximate, simple and parameter-free functional of the natural orbitals, based solely on scaling arguments and the near satisfaction of a sum rule. Our tests on atoms show that it yields on average more accurate energies and charge densities than the Hartree Fock method, the local density approximation and the generalized gradient approximations

Molecular dynamics simulations and thermochemistry of reactive ion etching of silicon by chlorine, chlorine dimer, bromine, and bromine dimer cations

Simulations of Cl plasma etch of Si surfaces with MD techniques agree reasonably well with the available experimental information on yields and surface morphologies. This information has been supplied to a Monte Carlo etch profile resulting in substantial agreement with comparable inputs provided through controlled experiments. To the extent that more recent measurements of etch rates are more reliable than older ones, preliminary MD simulations using bond-order corrections to the atomic interactions between neighboring Si atoms on the surface improves agreement with experiment through an increase in etch rate and improved agreement with XPS measurements of surface stoichiometry. Thermochemical and geometric analysis of small Si-Br molecules is consistent with the current notions of the effects of including brominated species in etchant gases

Interaction energy functional for lattice density functional theory: Applications to one-, two- and three-dimensional Hubbard models

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix $\gamma_{ij}$ with respect the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W[\gamma]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of $W$ is obtained throughout the domain of representability of $\gamma_{ij}$, including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for $W$. Goals and limitations of the different approximations are discussed.Comment: 25 pages and 8 figures, submitted to Phys. Rev.

Collective Animal Behavior from Bayesian Estimation and Probability Matching

Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is based on empirical fits to observations and we lack first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching.
In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability given by the Bayesian estimation that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior

Point-detect production and migration in plutonium metal at ambient conditions

Modeling thermodynamics and defect production in plutonium (Pu) metal and its alloys, has proven to be singularly difficult. The multiplicity of phases and the small changes in temperature, pressure, and/or stress that can induce phase changes lie at the heart of this difficulty, In terms of radiation damage, Pu metal represents a unique situation because of the large volume changes that accompany the phase changes. The most workable form of the metal is the fcc (6.) phase, which in practice the 6 phase is stabilized by addition of alloying elements such as Ga or AI. The thermodynamically stable phase at ambient conditions is the between monoclinic (a-) phase, which, however, is approximately 20 % lower in volume than the 6 phase. In stabilized Pu metal, there is an interplay between the natural swelling tendencies of fcc metals and the volume-contraction tendency of the underlying phase transformation to the thermodynamically stable phase. This study explores the point defect production and migration properties that are necessary to eventually model the long-term outcome of this interplay

Thermal Density Functional Theory in Context

This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by illustrating some of its key reformulations. The basics of DFT for thermal ensembles are explained in this context, as are tools useful for analysis and development of approximations. We close by discussing some key ideas relating thermal DFT and the ground state. This review emphasizes thermal DFT's strengths as a consistent and general framework.Comment: Submitted to Spring Verlag as chapter in "Computational Challenges in Warm Dense Matter", F. Graziani et al. ed

Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas

We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real and in reciprocal space, and (iii) accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

Neighbours' Breeding Success and the Sex Ratio of Their Offspring Affect the Mate Preferences of Female Zebra Finches

Several hypotheses on divorce predict that monogamous pairs should split up more frequently after a breeding failure. Yet, deviations from the expected pattern “success-stay, failure-leave” have been reported in several species. One possible explanation for these deviations would be that individuals do not use only their own breeding performance (i.e., private information) but also that of others (i.e., public information) to decide whether or not to divorce. To test this hypothesis, we investigated the relative importance of private and public information for mate choice decisions in female zebra finches (Taeniopygia guttata).We manipulated the reproductive performance of breeding pairs and measured females' preferences for their mate and the neighbouring male first following pair formation and then seven weeks later when all females had laid eggs and the young were independent. Although all females reduced their preference for their mate after a breeding failure, the decrease was significant only when the neighbouring pair had reproduced successfully. Furthermore, there was no evidence that females biased the sex ratio of their offspring according to their mate's attractiveness. On the other hand, after reproduction, both successful and unsuccessful females increased their preferences for males who had produced a larger proportion of sons. Despite the fact that other mechanisms may have also contributed to our findings, we suggest that females changed their mate preferences based on the proportion of sons produced by successful males, because offspring sex ratio reflects the male's testosterone level at the moment of fertilization and hence is an indicator of his immune condition

Schedule-selective biochemical modulation of 5-fluorouracil in advanced colorectal cancer – a phase II study

BACKGROUND: 5-fluorouracil remains the standard therapy for patients with advanced/metastatic colorectal cancer. Pre-clinical studies have demonstrated the biological modulation of 5-fluorouracil by methotrexate and leucovorin. This phase II study was initiated to determine the activity and toxicity of sequential methotrexate – leucovorin and 5-fluorouracil chemotherapy in patients with advanced colorectal cancer. METHODS: Ninety-seven patients with metastatic colorectal cancer were enrolled onto the study. Methotrexate – 30 mg/m(2) was administered every 6 hours for 6 doses followed by a 2 hour infusion of LV – 500 mg/m(2). Midway through the leucovorin infusion, patients received 5-fluorouracil – 600 mg/m(2). This constituted a cycle of therapy and was repeated every 2 weeks until progression. RESULTS: The median age was 64 yrs (34–84) and the Eastern Cooperative Group Oncology performance score was 0 in 37%, 1 in 55% and 2 in 8% of patients. Partial and complete responses were seen in 31% of patients with a median duration of response of 6.4 months. The overall median survival was 13.0 months. The estimated 1-year survival was 53.7%. Grade III and IV toxic effects were modest and included mucositis, nausea and vomiting. CONCLUSIONS: This phase II study supports previously reported data demonstrating the modest clinical benefit of 5-FU modulation utilizing methotrexate and leucovorin in patients with metastatic colorectal cancer. Ongoing studies evaluating 5-fluorouracil modulation with more novel agents (Irinotecan and/or oxaliplatin) are in progress and may prove encouraging

How Group Size Affects Vigilance Dynamics and Time Allocation Patterns: The Key Role of Imitation and Tempo

In the context of social foraging, predator detection has been the subject of numerous studies, which acknowledge the adaptive response of the individual to the trade-off between feeding and vigilance. Typically, animals gain energy by increasing their feeding time and decreasing their vigilance effort with increasing group size, without increasing their risk of predation (‘group size effect’). Research on the biological utility of vigilance has prevailed over considerations of the mechanistic rules that link individual decisions to group behavior. With sheep as a model species, we identified how the behaviors of conspecifics affect the individual decisions to switch activity. We highlight a simple mechanism whereby the group size effect on collective vigilance dynamics is shaped by two key features: the magnitude of social amplification and intrinsic differences between foraging and scanning bout durations. Our results highlight a positive correlation between the duration of scanning and foraging bouts at the level of the group. This finding reveals the existence of groups with high and low rates of transition between activies, suggesting individual variations in the transition rate, or ‘tempo’. We present a mathematical model based on behavioral rules derived from experiments. Our theoretical predictions show that the system is robust in respect to variations in the propensity to imitate scanning and foraging, yet flexible in respect to differences in the duration of activity bouts. The model shows how individual decisions contribute to collective behavior patterns and how the group, in turn, facilitates individual-level adaptive responses