High-temperature ferromagnetism of spsp electrons in narrow impurity bands: Application to CaB6_6

Ferromagnetism with high Curie temperature $T_c$, well above room temperature, and very small saturation moment has been reported in various carbon and boron systems. It is argued that the magnetization must be very inhomogeneous with only a small fraction of the sample ferromagnetically ordered. It is shown that a possible source of high $T_c$ within the ferromagnetic regions is itinerant electrons occupying a narrow impurity band. Correlation effects do not reduce the effective interaction which enters the Stoner criterion in the same way as in a bulk band. It is also shown how, in the impurity band case, spin wave excitations may not be effective in lowering $T_c$ below its value given by Stoner theory. These ideas are applied to CaB$_6$ and a thorough review of the experimental situation in this material is given. It is suggested that the intrinsic magnetism of the B$_2$ and O$_2$ dimers might be exploited in suitable structures containing these elements.Comment: 26 pages, 2 figure

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table

Soft systems methodology: a context within a 50-year retrospective of OR/MS

Soft systems methodology (SSM) has been used in the practice of operations research and management science OR/MS) since the early 1970s. In the 1990s, it emerged as a viable academic discipline. Unfortunately, its proponents consider SSM and traditional systems thinking to be mutually exclusive. Despite the differences claimed by SSM proponents between the two, they have been complementary. An extensive sampling of the OR/MS literature over its entire lifetime demonstrates the richness with which the non-SSM literature has been addressing the very same issues as does SSM

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux–Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita–Itoh–Bogoyavlensky, Toda, and Adler–Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new

Foundations of Relational Particle Dynamics

Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as discussion of conceptual issues connected with the problem of time in quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces of shapes are n-spheres and complex projective spaces, from which knowledge I construct natural mechanics on these spaces. I also show that these coincide with Barbour's indirectly-constructed relational dynamics by performing a full reduction on the latter. Then the identification of the configuration spaces as n-spheres and complex projective spaces, for which spaces much mathematics is available, significantly advances the understanding of Barbour's relational theory in spatial dimensions 1 and 2. I also provide the parallel study of a new theory for which positon and scale are purely relative but orientation is absolute. The configuration space for this is an n-sphere regardless of the spatial dimension, which renders this theory a more tractable arena for investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update