We study properties of the fourth rank elasticity tensor C within linear elasticity theory. First C is irreducibly decomposed under the linear group into a Cauchy piece S (with 15 independent components) and a non-Cauchy piece A (with 6 independent c
omponents). Subsequently, we turn to the physically relevant orthogonal group, thereby using the metric. We find the finer decomposition of S into pieces with 9+5+1 and of A into those with 5+1 independent components. Some reducible decompositions, discussed earlier by numerous authors, are shown to be inconsistent. --- Several physical consequences are discussed. The Cauchy relations are shown to correspond to A=0. Longitudinal and transverse sound waves are basically related by S and A, respectively.
The determinization of Buchi automata is a celebrated problem, with applications in synthesis, probabilistic verification, and multi-agent systems. Since the 1960s, there has been a steady progress of constructions: by McNaughton, Safra, Piterman, Sc
hewe, and others. Despite the proliferation of solutions, they are all essentially ad-hoc constructions, with little theory behind them other than proofs of correctness. Since Safra, all optimal constructions employ trees as states of the deterministic automaton, and transitions between states are defined operationally over these trees. The operational nature of these constructions complicates understanding, implementing, and reasoning about them, and should be contrasted with complementation, where a solid theory in terms of automata run DAGs underlies modern constructions. In 2010, we described a profile-based approach to Buchi complementation, where a profile is simply the history of visits to accepting states. We developed a structural theory of profiles and used it to describe a complementation construction that is deterministic in the limit. Here we extend the theory of profiles to prove that every run DAG contains a profile tree with at most a finite number of infinite branches. We then show that this property provides a theoretical grounding for a new determinization construction where macrostates are doubly preordered sets of states. In contrast to extant determinization constructions, transitions in the new construction are described declaratively rather than operationally.
We report on the magnetic behavior of oxygen deficient LaFeAsO1-x (x-0.10) compound, prepared by one-step synthesis, which crystallizes in the tetragonal (S.G. P4/nmm) structure at room temperature. Resistivity measurements show a strong anomaly near
150 K, which is ascribed to the spin density wave (SDW) instability. On the other hand, dc magnetization data shows paramagnetic-like features down to 5 K, with an effective moment of 0.83 mB/Fe. 57Fe Mossbauer studies (MS) have been performed at 95 and 200 K. The spectra at both temperatures are composed of two sub-spectra. At 200 K the major one (88%), is almost a singlet, and corresponds to those Fe nuclei, which have two oxygen ions in their close vicinity. The minor one, with a large quadrupole splitting, corresponds to Fe nuclei, which have vacancies in their immediate neighborhood. The spectrum at 95 K, exhibits a broadened magnetic split major (84%) sub-spectrum and a very small magnetic splitting in the minor subspectrum. The relative intensities of the subspectra facilitate in estimating the actual amount of oxygen vacancies in the compound to be 7.0(5)%, instead of the nominal LaFeAsO0.90. These results, when compared with reported 57Fe MS of non-superconducting LaFeAsO and superconducting LaFeAsO0.9F0.1, confirm that the studied LaFeAsO0.93 is a superconductivity-magnetism crossover compound of the newly discovered Fe based superconducting family.
Magnetization, x-ray diffraction and specific-heat measurements reveal that SmCoAsO undergoes three magnetic phase transitions. A ferromagnetic transition attributed to the Co ions, emerges at TC=57 K with a small saturation moment of 0.15muB/Co. Reo
rientation of the Co moment to an antiferromagnetic state is obtained at TN2=45 K. The relative high paramagnetic effective moment Peff=1.57 MuB/Co indicates an itinerant ferromagnetic state of the Co sublattice. The third magnetic transition at TN1=5 K is observed clearly in the specific-heat study only. Both magnetic and 57Fe Mossbauer studies show that substitution of small quantities of Fe for Co was unsuccessful.
We study the central dark matter (DM) cusp evolution in cosmological galactic halos. Models with and without baryons (baryons+DM, hereafter BDM model, and pure DM, PDM model, respectively) are advanced from identical initial conditions. The DM cusp p
roperties are contrasted by a direct comparison of pure DM and baryonic models. We find a divergent evolution between the PDM and BDM models within the inner ~10 kpc region. The PDM model forms a R^{-1} cusp as expected, while the DM in the BDM model forms a larger isothermal cusp R^{-2} instead. The isothermal cusp is stable until z~1 when it gradually levels off. This leveling proceeds from inside out and the final density slope is shallower than -1 within the central 3 kpc (i.e., expected size of the R^{-1} cusp), tending to a flat core within ~2 kpc. This effect cannot be explained by a finite resolution of our code which produces only a 5% difference between the gravitationally softened force and the exact Newtonian force of point masses at 1 kpc from the center. Neither is it related to the energy feedback from stellar evolution or angular momentum transfer from the bar. Instead it can be associated with the action of DM+baryon subhalos heating up the cusp region via dynamical friction and forcing the DM in the cusp to flow out and to `cool down. The process described here is not limited to low z and can be efficient at intermediate and even high z.
