Exactly Conservative Integrators

Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.Comment: 30 pages, postscript (1.3MB). Submitted to SIAM J. Sci. Comput

Reference gene selection and RNA preservation protocol in the cat flea, Ctenocephalides felis, for gene expression studies

This work was supported by a Knowledge Transfer Network BBSRC Industrial Case (#414 BB/L502467/1) studentship in association Zoetis Inc.Peer reviewedPostprin

Hydrogenation of Magnesium Nickel Boride for Reversible Hydrogen Storage

We report that a ternary magnesium nickel boride (MgNi_(2.5)B_2) mixed with LiH and MgH_2 can be hydrogenated reversibly forming LiBH_4 and Mg_2NiH_4 at temperatures below 300 °C. The ternary boride was prepared by sintering a mechanically milled mixture of MgB_2 and Ni precursors at 975 °C under inert atmosphere. Hydrogenation of the ternary, milled with LiH and MgH_2, was performed under 100 to 160 bar H_2 at temperatures up to 350 °C. Analysis using X-ray diffraction, Fourier transform infrared, and ^(11)B magic angle spinning NMR confirmed that the ternary boride was hydrogenated forming borohydride anions. The reaction was reversible with hydrogenation kinetics that improved over three cycles. This work suggests that there may be other ternary or higher order boride phases useful for reversible hydrogen storage

An Exactly Conservative Integrator for the n-Body Problem

The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem, and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and center of mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators.Comment: 17 pages, 3 figures; to appear in J. Phys. A.: Math. Ge

ABERRANT TESTA SHAPE encodes a KANADI family member, linking polarity determination to separation and growth of Arabidopsis ovule integuments

The Arabidopsis aberrant testa shape (ats) mutant produces a single integument instead of the two integuments seen in wild-type ovules. Cellular anatomy and patterns of marker gene expression indicate that the single integument results from congenital fusion of the two integuments of the wild type. Isolation of the ATS locus showed it to encode a member of the KANADI (KAN) family of putative transcription factors, previously referred to as KAN4. ATS was expressed at the border between the two integuments at the time of their initiation, with expression later confined to the abaxial layer of the inner integument. In an inner no outer (ino) mutant background, where an outer integument does not form, the ats mutation led to amorphous inner integument growth. The kan1 kan2 double mutant exhibits a similar amorphous growth of the outer integument without affecting inner integument growth. We hypothesize that ATS and KAN1/KAN2 play similar roles in the specification of polarity in the inner and outer integuments, respectively, that parallel the known roles of KAN proteins in promoting abaxial identity during leaf development. INO and other members of the YABBY gene family have been hypothesized to have similar parallel roles in outer integument and leaf development. Together, these two hypotheses lead us to propose a model for normal integument growth that also explains the described mutant phenotypes

Neutron Vibrational Spectroscopy and First-Principles Calculations of the Ternary Hydrides Li\u3csub\u3e4\u3c/sub\u3eSi\u3csub\u3e2\u3c/sub\u3eH(D) and Li\u3csub\u3e4\u3c/sub\u3eGe\u3csub\u3e2\u3c/sub\u3eH(D): Electronic Structure and Lattice Dynamics

Using combined neutron spectroscopy and first-principles calculations, we investigated the electronic structure and vibrational dynamics of the recently discovered class of ternary hydrides Li4Tt2H (Tt=Si and Ge). In these compounds, all hydrogen atoms are located in a single type of Li6-defined octahedral site. The Tt atoms form long-range Tt-Tt chains sandwiched between each Li6-octahedra layer. The Li-H interactions are strongly ionic, with bond lengths comparable to those in LiH. Our density functional theory calculations indicate that Li atoms transfer their electrons to both H and Tt atoms. Tt atoms within the Tt-Tt chain are bonded covalently. The electronic density of states reveals that both hydrides exhibit metallic behavior. The observed vibrational spectra of these hydrides are in good overall agreement with the calculated phonon modes. There is evidence of dispersion induced splitting in the optical phonon peaks that can be ascribed to the coupling of H vibrations within the Li6-octahedra layers