Search results for " Geometry"

Nature of O2, CO, and CN binding to hemoprotein models

2004

Parametrization of a molecular-mechanics program to include terms specific for five- and six-coordinate transition metal complexes results in computer-simulated structures of hemo complexes. The principal new feature peculiar to five- and six-coordination is a term that measures the effect of electron-pair repulsion modified by the ligand electronegativity and takes into account the different structural possibilities. The work consists in the modification of program molecular mechanics for penta and hexacoordination. The model system takes into account the structural differences of the fixing center in the hemoglobin subunits. The customary proximal histidine is added. The macrocycle hemo I…

Nature of FeIII–O2, FeII–CO and FeIII–CN complexes of hemoprotein models

2003

Abstract Parametrization of a molecular-mechanics program to include terms specific for 5- and 6-coordinate transition metal complexes results in computer-simulated structures of hemo complexes. The principal new feature peculiar to 5- and 6-coordination is a term that measures the effect of electron-pair repulsion modified by the ligand electronegativity and takes into account the different structural possibilities. The work consists in the modification of program molecular mechanics for 5- and 6-coordination. The model system takes into account the structural differences of the fixing centre in the haemoglobin (Hb) subunits. The customary proximal histidine is added. The macrocycle hemo I…

Geodesics on spaces of almost hermitian structures

1994

A natural metric on the space of all almost hermitian structures on a given manifold is investigated.

Hermitian natural differential operators

1986

A note on Sobolev isometric immersions below W2,2 regularity

2017

Abstract This paper aims to investigate the Hessian of second order Sobolev isometric immersions below the natural W 2 , 2 setting. We show that the Hessian of each coordinate function of a W 2 , p , p 2 , isometric immersion satisfies a low rank property in the almost everywhere sense, in particular, its Gaussian curvature vanishes almost everywhere. Meanwhile, we provide an example of a W 2 , p , p 2 , isometric immersion from a bounded domain of R 2 into R 3 that has multiple singularities.

Magnetised Polish doughnuts revisited

2017

We discuss a procedure to build new sequences of magnetised, equilibrium tori around Kerr black holes which combines two approaches previously considered in the literature. For simplicity we assume that the test-fluid approximation holds, and hence we neglect the self-gravity of the fluid. The models are built assuming a particular form of the angular momentum distribution from which the location and morphology of equipotential surfaces can be computed. This ansatz includes, in particular, the constant angular momentum case originally employed in the construction of thick tori - or Polish doughnuts - and it has already been used to build equilibrium sequences of purely hydrodynamical models…

A variational method for spectral functions

2016

The Generalized Eigenvalue Problem (GEVP) has been used extensively in the past in order to reliably extract energy levels from time-dependent Euclidean correlators calculated in Lattice QCD. We propose a formulation of the GEVP in frequency space. Our approach consists of applying the model-independent Backus-Gilbert method to a set of Euclidean two-point functions with common quantum numbers. A GEVP analysis in frequency space is then applied to a matrix of estimators that allows us, among other things, to obtain particular linear combinations of the initial set of operators that optimally overlap to different local regions in frequency. We apply this method to lattice data from NRQCD. Th…

N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant

1991

We discuss gauge theory with a topological N=2 symmetry. This theory captures the de Rham complex and Riemannian geometry of some underlying moduli space $\cal M$ and the partition function equals the Euler number of $\cal M$. We explicitly deal with moduli spaces of instantons and of flat connections in two and three dimensions. To motivate our constructions we explain the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics and introduce a new kind of supersymmetric quantum mechanics based on the Gauss-Codazzi equations. We interpret the gauge theory actions from the Atiyah-Jeffrey point of view and relate them to supersymmetric quantum mechanics on spaces of…

The dyon charge in noncommutative gauge theories

2007

We present an explicit classical dyon solution for the noncommutative version of the Yang-Mills-Higgs model (in the Prasad-Sommerfield limit) with a tehta term. We show that the relation between classical electric and magnetic charges also holds in noncommutative space. Extending the Noether approach to the case of a noncommutative gauge theory, we analyze the effect of CP violation at the quantum level, induced both by the theta term and by noncommutativity and we prove that the Witten effect formula for the dyon charge remains the same as in ordinary space.

Lines on the Dwork pencil of quintic threefolds

2012

We present an explicit parametrization of the families of lines of the Dwork pencil of quintic threefolds. This gives rise to isomorphic curves which parametrize the lines. These curves are 125:1 covers of certain genus six curves. These genus six curves are first presented as curves in P^1*P^1 that have three nodes. It is natural to blow up P^1*P^1 in the three points corresponding to the nodes in order to produce smooth curves. The result of blowing up P^1*P^1 in three points is the quintic del Pezzo surface dP_5, whose automorphism group is the permutation group S_5, which is also a symmetry of the pair of genus six curves. The subgroup A_5, of even permutations, is an automorphism of ea…