A vector product formulation of special relativity and electromagnetism

The vector product method developed in previous articles for space rotations and Lorentz transformations is extended to the cases of four-vectors, anti-symmetric tensors, and their transformations in Minkowski space. The electromagnetic fields are expressed in six-vector form using the notationH +iE, and this vector form is shown to be relativistically invariant. The wave equations of electromagnetism are derived using these vector products. The following three equations are deduced, which summarize electrodynamics in a compact form: (1) Maxwell's four equations expressed as one, (2) the scalar and vector potential wave equations combined into one relation, and (3) the wave equations for the electric and magnetic fields and the continuity equation combined together. Space inversion, time reversal, and magnetic monopoles are also treated.On leave of absence from the University of Tel Aviv.     

Coupled map lattices as computational systems

The coupled map lattice (CML) as a mathematical model for a computer is considered. Using the theory of synchronous concurrent algorithms, it is shown that the CML is a valid new model for a parallel deterministic analog machine, but that, in principle, such a CML computer does not generate computations that cannot be reproduced by the standard mathematical models for computing on real numbers. The analysis is based on new general mathematical definitions of CMLs, and an axiomatic approach to determining which models of computation can be used to simulate CMLs.     

General refinement strategy for magnetic structures using spherical neutron polarimetry and representation analysis

Spherical neutron polarimetry (SNP) is a powerful technique for the determination of magnetic structures which may otherwise be intractable. The complexity of the neutron scattering process and the large number of different possible trial structures typically leads to refinements based on a simple trial and error generation of possible models and a possible failure to explore valid possible models. The combination of the model symmetry types determined from representational analysis and reverse-Monte Carlo refinement creates a generalized refinement strategy for SNP data that allows refinement in terms of symmetry adapted modes built up from the basis vectors that describe the orientations of the magnetic moments on the different magnetic sites, and those of the different domains that are possible in a sample: spin (S)-domains and K-domains. This methodology typically leads to a large reduction in the number of refined parameters as well as the rigorous inclusion of any symmetry related domains. In combination with reverse-Monte Carlo refinement algorithms a general strategy for refining complex magnetic structures can be created. We present an example of a frustrated magnetic structure that have been determined using this approach Er₂Ti₂O₇.     

Synthesis and characterisation of highly emissive and kinetically stable lanthanide complexes suitable for usage "in cellulo"

The synthesis and photophysical characterisation are reported of a series of cationic, neutral and anionic europium and terbium complexes based on structurally related, nonadentate ligands based on the cyclen macrocycle. Each complex incorporates a tetraazatriphenylene moiety and overall absolute emission quantum yields are in the range 15-40% in aerated aqueous media. Dynamic quenching of the lanthanide excited state occurs with electron-rich donors, e.g. iodide, ascorbate and urate, and a mechanistic interpretation is put forward involving an electron transfer process. The cationic lanthanide complexes are taken up by NlH/3T3 cells and tend to localise inside the cell nucleus.