Insider Trading in Convergent Markets

Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints.     

Deformation behaviour in advanced heat resistant materials during slow strain rate testing at elevated temperature

In this study, slow strain rate tensile testing at elevated temperature is used to evaluate the influence of temperature and strain rate on deformation behaviour in two different austenitic alloys. One austenitic stainless steel (AISI 316L) and one nickel-base alloy (Alloy 617) have been investigated. Scanning electron microscopy related techniques as electron channelling contrast imaging and electron backscattering diffraction have been used to study the damage and fracture micromechanisms. For both alloys the dominante damage micromechanisms are slip bands and planar slip interacting with grain bounderies or precipitates causing strain concentrations. The dominante fracture micromechanism when using a slow strain rate at elevated temperature, is microcracks at grain bounderies due to grain boundery embrittlement caused by precipitates. The decrease in strain rate seems to have a small influence on dynamic strain ageing at 650°C.     

Non-existence of a minimizer to the magnetic Hartree-Fock functional

In the presence of an external magnetic field, we prove absence of a ground state within the Hartree-Fock theory of atoms and molecules. The result is established for a wide class of magnetic fields when the number of electrons is greater than or equal to 2Z + K, where Z is the total charge of K nuclei. Positivity properties are instrumental in the proof of this bound for the maximal ionization.      

Prescribing eigenvalues of the Dirac operator

In this note we show that every compact spin manifold of dimension ≥3 can be given a Riemannian metric for which a finite part of the spectrum of the Dirac operator consists of arbitrarily prescribed eigenvalues with multiplicity 1.     

Dynamics of spin-1/2 quantum plasmas

The fully nonlinear governing equations for spin-1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies of the combined collective and spin dynamics. The linear response of the quantum plasma in an electron-ion system is obtained and analyzed. Applications of the theory to solid state and astrophysical systems as well as dusty plasmas are pointed out.     

Impact of concentration self-quenching on the charge generation yield of fullerene based donor-bridge-acceptor compounds in the solid state

A fullerene based Donor-Bridge-Acceptor (DBA) compound, incorporating a π-extended tetrathiafulvalene electron donor, is investigated with respect to its photophysics in solution versus solid state. Solid films of neat DBA are compared with blend films where the DBA compound is diluted in the inert, low dielectric, polymer poly(styrene). It is found that the moderate intermolecular electronic coupling and donor-acceptor separation (22 ?) in this case leads to the generation of more dissociated, intermolecular charges than a mixture of the donor and acceptor reference compounds. However, the increased intermolecular interactions in the solid state lead to the excited state of the fullerene suffering from concentration self-quenching. This is found to severely affect the charge generation yield in solid films. The impact of competing intra and intermolecular interactions in the solid state upon the film photophysics is analysed in terms of a kinetic model which includes both the effects of concentration self-quenching and the impact of film composition upon the dielectric stabilisation of charge separated states. We conclude that both concentration self-quenching and dielectric stabilisation are critical in determining the photophysics of the blend films, and discuss strategies based upon our observations to enhance the charge photogeneration properties of organic films and photovoltaic devices based upon DBA compounds.     

Creating permanent 3D arrangements of isolated cells using holographic optical tweezers

We report the creation of permanent 3D configurations of cells, at predefined positions, within a gelatin matrix. The technique used holographic optical tweezers to manipulate individual E. coli within a solution comprising monomer precursors. The matrix was then set and after the laser beam was removed, we were able to demonstrate that the structures remained intact for many days. We were also able to demonstrate that, in the presence of appropriate nutrients, the E. coli survived within the gelatin matrix for several days. The technique could have a number of potential future applications, including the arrangement of a variety of different cell types in complex architectures, as motifs for promoting tissue differentiation and growth within the field of cell engineering.     

Surgery and the Spinorial τ-Invariant

We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's σ-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then τ(N) ≥ min{τ(M), Λ _n }, where Λ _n is a positive constant depending only on n = dim M. Various topological conclusions can be drawn, in particular that τ is a spin-bordism invariant below Λ _n . Also, below Λ _n the values of τ cannot accumulate from above when varied over all manifolds of dimension n.