Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$; hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201

Implementation and evaluation of a new methane model within a dynamic global vegetation model: LPJ-WHyMe v1.3.1

For the first time, a model that simulates methane emissions from northern peatlands is incorporated directly into a dynamic global vegetation model. The model, LPJ-WHyMe (LPJ <B>W</B>etland <B>Hy</B>drology and <B>Me</B>thane), was previously modified in order to simulate peatland hydrology, permafrost dynamics and peatland vegetation. LPJ-WHyMe simulates methane emissions using a mechanistic approach, although the use of some empirical relationships and parameters is unavoidable. The model simulates methane production, three pathways of methane transport (diffusion, plant-mediated transport and ebullition) and methane oxidation. A sensitivity test was conducted to identify the most important factors influencing methane emissions, followed by a parameter fitting exercise to find the best combination of parameter values for individual sites and over all sites. A comparison of model results to observations from seven sites resulted in normalised root mean square errors (NRMSE) of 0.40 to 1.15 when using the best site parameter combinations and 0.68 to 1.42 when using the best overall parameter combination

Statistical interaction modeling of bovine herd behaviors

While there has been interest in modeling the group behavior of herds or flocks, much of this work has focused on simulating their collective spatial motion patterns which have not accounted for individuality in the herd and instead assume a homogenized role for all members or sub-groups of the herd. Animal behavior experts have noted that domestic animals exhibit behaviors that are indicative of social hierarchy: leader/follower type behaviors are present as well as dominance and subordination, aggression and rank order, and specific social affiliations may also exist. Both wild and domestic cattle are social species, and group behaviors are likely to be influenced by the expression of specific social interactions. In this paper, Global Positioning System coordinate fixes gathered from a herd of beef cows tracked in open fields over several days at a time are utilized to learn a model that focuses on the interactions within the herd as well as its overall movement. Using these data in this way explores the validity of existing group behavior models against actual herding behaviors. Domain knowledge, location geography and human observations, are utilized to explain the causes of these deviations from this idealized behavior

X-ray Reflection from Inhomogeneous Accretion Disks: II. Emission Line Variability and Implications for Reverberation Mapping

One of the principal scientific objectives of the upcoming Constellation-X mission is to attempt to map the inner regions of accretion disks around black holes in Seyfert galaxies by reverberation mapping of the Fe K fluorescence line. This area of the disk is likely radiation pressure dominated and subject to various dynamical instabilities. Here, we show that density inhomogeneities in the disk atmosphere resulting from the photon bubble instability (PBI) can cause rapid changes in the X-ray reflection features, even when the illuminating flux is constant. Using a simulation of the development of the PBI, we find that, for the disk parameters chosen, the Fe K and O VIII Ly\alpha lines vary on timescales as short as a few hundredths of an orbital time. In response to the changes in accretion disk structure, the Fe K equivalent width (EW) shows variations as large as ~100 eV. The magnitude and direction (positive or negative) of the changes depends on the ionization state of the atmosphere. The largest changes are found when the disk is moderately ionized. The O VIII EW varies by tens of eV, as well as exhibiting plenty of rapid, low-amplitude changes. This effect provides a natural explanation for some observed instances of short timescale Fe K variability which was uncorrelated with the continuum (e.g., Mrk 841). New predictions for Fe K reverberation mapping should be made which include the effects of this accretion disk driven line variability and a variable ionization state. Reflection spectra averaged over the evolution of the instability are well fit by constant density models in the 2-10 keV region.Comment: 20 pages, 3 figures. Accepted by Ap

The interaction of Trypanosoma congolense with endothelial cells

Factors which affect adhesion of cultured Trypanosoma congolense bloodstream forms to mammalian feeder cells have been examined. Using an in vitro binding assay, the initial events following interaction of trypanosomes with bovine aorta endothelial (BAE) cells were monitored by both light- and electron microscopy. Metabolic inhibitors and other biochemicals were incubated with either cells or parasites, to test whether any inhibited the process. Our findings suggest that adhesion of the parasites is an active process requiring metabolic energy from the trypanosomes, but not from endothelial cells. We also provide data suggesting that T. congolense bloodstream forms possess a lectin-like domain, localized at distinct sites on their flagellar surface, which interacts with specific carbohydrate receptors, most likely sialic acid residues, on the endothelial cell plasma membrane. We also suggest that the cytoskeletal protein actin is probably involved in this interactio

Transform of Riccati equation of constant coefficients through fractional procedure

We use a particular fractional generalization of the ordinary differential equations that we apply to the Riccati equation of constant coefficients. By this means the latter is transformed into a modified Riccati equation with the free term expressed as a power of the independent variable which is of the same order as the order of the applied fractional derivative. We provide the solutions of the modified equation and employ the results for the case of the cosmological Riccati equation of FRW barotropic cosmologies that has been recently introduced by FaraoniComment: 7 pages, 2 figure

Quantum Entanglement in the Two Impurity Kondo Model

In order to quantify quantum entanglement in two impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, $I$. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created (and quantum information processing (QIP) be possible) if the RKKY interaction exchange energy, $I$, is at least several times larger than the Kondo temperature, $T_K$. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.Comment: 7 pages, 3 figures, 1 tabl

Electronic spectra of polyatomic molecules with resolved individual rotational transitions

The density of rotational transitions for a polyatomic molecule is so large that in general many such transitions are hidden under the Doppler profile, this being a fundamental limit of conventional high resolution electronic spectroscopy. We present here the first Doppler-free cw two-photon spectrum of a polyatomic molecule. In the case of benzene, 400 lines are observed of which 300 are due to single rotational transitions, their spacing being weil below the Doppler profile. The resolution so achieved is 1.5 X 10'. Benzene is a prototype planar molecule taken to have D •• symmetry in the ground as weil as in the first excited state. From our ultra-high resolution results it is found that benzene in the excited SI state i8 a symmetrical rotor to a high degree. A negative inertial defect is found for the excited state. The origin of this inertial defect is discused

Effect of quantum nuclear motion on hydrogen bonding

This work considers how the properties of hydrogen bonded complexes, D-H....A, are modified by the quantum motion of the shared proton. Using a simple two-diabatic state model Hamiltonian, the analysis of the symmetric case, where the donor (D) and acceptor (A) have the same proton affinity, is carried out. For quantitative comparisons, a parametrization specific to the O-H....O complexes is used. The vibrational energy levels of the one-dimensional ground state adiabatic potential of the model are used to make quantitative comparisons with a vast body of condensed phase data, spanning a donor-acceptor separation (R) range of about 2.4-3.0 A, i.e., from strong to weak bonds. The position of the proton and its longitudinal vibrational frequency, along with the isotope effects in both are discussed. An analysis of the secondary geometric isotope effects, using a simple extension of the two-state model, yields an improved agreement of the predicted variation with R of frequency isotope effects. The role of the bending modes in also considered: their quantum effects compete with those of the stretching mode for certain ranges of H-bond strengths. In spite of the economy in the parametrization of the model used, it offers key insights into the defining features of H-bonds, and semi-quantitatively captures several experimental trends.Comment: 12 pages, 8 figures. Notation clarified. Revised figure including the effect of bending vibrations on secondary geometric isotope effect. Final version, accepted for publication in Journal of Chemical Physic

Rapid Evolution of BRCA1 and BRCA2 in Humans and Other Primates

The maintenance of chromosomal integrity is an essential task of every living organism and cellular repair mechanisms exist to guard against insults to DNA. Given the importance of this process, it is expected that DNA repair proteins would be evolutionarily conserved, exhibiting very minimal sequence change over time. However, BRCA1, an essential gene involved in DNA repair, has been reported to be evolving rapidly despite the fact that many protein-altering mutations within this gene convey a significantly elevated risk for breast and ovarian cancers. Results: To obtain a deeper understanding of the evolutionary trajectory of BRCA1, we analyzed complete BRCA1 gene sequences from 23 primate species. We show that specific amino acid sites have experienced repeated selection for amino acid replacement over primate evolution. This selection has been focused specifically on humans and our closest living relatives, chimpanzees (Pan troglodytes) and bonobos (Pan paniscus). After examining BRCA1 polymorphisms in 7 bonobo, 44 chimpanzee, and 44 rhesus macaque (Macaca mulatta) individuals, we find considerable variation within each of these species and evidence for recent selection in chimpanzee populations. Finally, we also sequenced and analyzed BRCA2 from 24 primate species and find that this gene has also evolved under positive selection. Conclusions: While mutations leading to truncated forms of BRCA1 are clearly linked to cancer phenotypes in humans, there is also an underlying selective pressure in favor of amino acid-altering substitutions in this gene. A hypothesis where viruses are the drivers of this natural selection is discussed.National Institutes of Health R01-GM-093086, 8U42OD011197-13National Science Foundation BCS-07115972Burroughs Wellcome FundMolecular Bioscience