On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

Research in parallel computing

This report summarizes work on parallel computations for NASA Grant NAG-1-1529 for the period 1 Jan. - 30 June 1994. Short summaries on highly parallel preconditioners, target-specific parallel reductions, and simulation of delta-cache protocols are provided

Parallel linear equation solvers for finite element computations

The overall objective of this research is to develop efficient methods for the solution of linear and nonlinear systems of equations on parallel and supercomputers, and to apply these methods to the solution of problems in structural analysis. Attention has been given so far only to linear equations. The methods considered for the solution of the stiffness equation Kx=f have been Choleski factorization and the conjugate gradient iteration with SSOR and Incomplete Choleski preconditioning. More detail on these methods will be given on subsequent slides. These methods have been used to solve for the static displacements for the mast and panel focus problems in conjunction with the CSM testbed system based on NICE/SPAR

A new multi-center approach to the exchange-correlation interactions in ab initio tight-binding methods

A new approximate method to calculate exchange-correlation contributions in the framework of first-principles tight-binding molecular dynamics methods has been developed. In the proposed scheme on-site (off-site) exchange-correlation matrix elements are expressed as a one-center (two-center) term plus a {\it correction} due to the rest of the atoms. The one-center (two-center) term is evaluated directly, while the {\it correction} is calculated using a variation of the Sankey-Niklewski \cite{Sankey89} approach generalized for arbitrary atomic-like basis sets. The proposed scheme for exchange-correlation part permits the accurate and computationally efficient calculation of corresponding tight-binding matrices and atomic forces for complex systems. We calculate bulk properties of selected transition (W,Pd), noble (Au) or simple (Al) metals, a semiconductor (Si) and the transition metal oxide Ti$O_2$ with the new method to demonstrate its flexibility and good accuracy.Comment: 17 pages, 5 figure

The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

The nature of magnetoelectric coupling in Pb(Zr,Ti)O3Pb(Fe,Ta)O3

The coupling between magnetization and polarization in a room temperature multiferroic (Pb(Zr,Ti)O3–Pb(Fe,Ta)O3) is explored by monitoring the changes in capacitance that occur when a magnetic field is applied in each of three orthogonal directions. Magnetocapacitance effects, consistent with P2M2 coupling, are strongest when fields are applied in the plane of the single crystal sheet investigated

Using community phylogenetics to assess phylogenetic structure in the fitzcarrald region of Western Amazonia

© 2020 The Authors. Di versity and Distributions Published by SBI. Here we explore the use of community phylogenetics as a tool to document patterns of biodiversity in the Fitzcarrald region, a remote area in Southwestern Amazonia. For these analyses, we subdivide the region into basin-wide assemblages encompassing the headwaters of four Amazonian tributaries (Urubamba, Yuruá, Purús and Las Piedras basins), and habitat types: river channels, terra firme (non-floodplain) streams, and floodplain lakes. We present a robust, well-documented collection of fishes from the region including 272 species collected from 132 field sites over 63 field days and four years, comprising the most extensive collection of fishes from this region to date. We conduct a preliminary community phylogenetic analysis based on this collection and recover results largely statistically indistinguishable from the random expectation, with only a few instances of phylogenetic structure. Based on these results, and of those published in other recent biogeographic studies, we conclude that the Fitzcarrald fish species pool accumulated over a period of several million years, plausibly as a result of dispersal from the larger species pool of Greater Amazonia

Trade-offs between the natural environment and recreational infrastructure:A case study about peatlands under different management scenarios

The importance of peatlands for conservation and provision of public services has been well evidenced in the last years, especially in relation to their contribution to the net zero carbon emission agenda. However, little is known about the importance of recreation relative to conservation and their trade-offs. In this paper we address this knowledge gap by exploring the trade-offs between natural properties of peatlands and recreational infrastructures for different categories of recreationists (walkers, cyclists, anglers, and birdwatchers) of an open heather moors and peatlands landscape. We do so building on a series of management scenarios formulated through participatory methods and applying choice experiment related to an Area of Outstanding Natural Beauty and UNESCO Global Geopark in the UK. Results show a high degree of heterogeneity in landscape preferences across different user groups. Recreationists had a higher appreciation for semi-natural habitats compared to pristine or restored peatland (e.g., land rewetting). Walkers and cyclists were more sensitive to changes in the availability of recreational facilities than to environmental quality, while anglers’ and birdwatchers’ preferences were more aligned with values promoted by restoration policies. Overall, our results point to a potential value conflict between benefits generated by conservation and the benefits valued most by some groups of recreationists. To maximise success conflicts like the one revealed here need to be considered in strategies that provide a central role for peatlands in net zero climate mitigation strategies