Constitutive modelling of Sandvik 1RK91

A physically based constitutive equation is being developed for the maraging\ud stainless steel Sandvik 1RK91. The steel is used to make precision parts. These parts are formed through multistage forming operations and heat treatments from cold rolled and annealed sheets. The specific alloy is designed to be thermodynamically unstable, so that deformation even at room temperatures can bring about a change in the phase of face centred cubic austenite to either hexagonal closed packed martensite and/or, body centred cubic martensite. This solid state phase change is a function of the strain path, strain, strain rate and temperature. Thus, the fraction of the new phase formed depends on the state of stress at a given location in the part being formed. Therefore a set of experiments is being conducted in order to quantify the stress-strain behavior of this steel under various stress states, strain, strain rate as well as temperature. A magnetic sensor records the fraction of ferromagnetic martensite formed from paramagnetic austenite. A thermocouple as well as an infra red thermometer is used to log the change in temperature of the steel during a mechanical test. The force-displacement data are converted to stress-strain data after correcting for the changes in strain rate and temperature. These data are then cast into a general form of constitutive equation and the transformation equations are derived from Olson-Cohen type functions

The Constitutive Relations and the Magnetoelectric Effect for Moving Media

In this paper the constitutive relations for moving media with homogeneous and isotropic electric and magnetic properties are presented as the connections between the generalized magnetization-polarization bivector $$ and the electromagnetic field F. Using the decompositions of F and $\mathcal{M}$, it is shown how the polarization vector P(x) and the magnetization vector M(x) depend on E, B and two different velocity vectors, u - the bulk velocity vector of the medium, and v - the velocity vector of the observers who measure E and B fields. These constitutive relations with four-dimensional geometric quantities, which correctly transform under the Lorentz transformations (LT), are compared with Minkowski's constitutive relations with the 3-vectors and several essential differences are pointed out. They are caused by the fact that, contrary to the general opinion, the usual transformations of the 3-vectors $$, $\mathbf{B}$, $\mathbf{P}$, $\mathbf{M}$, etc. are not the LT. The physical explanation is presented for the existence of the magnetoelectric effect in moving media that essentially differs from the traditional one.Comment: 18 pages, In Ref. [10] here, which corresponds to Ref. [18] in the published paper in IJMPB, Z. Oziewicz's published paper is added. arXiv admin note: text overlap with arXiv:1101.329

Corrections to Sirlin's Theorem in O(p6)O(p^6) Chiral Perturbation Theory

We present the results of the first two-loop calculation of a form factor in full $SU(3) \times SU(3)$ Chiral Perturbation Theory. We choose a specific linear combination of $\pi^+, K^+, K^0$ and $K\pi$ form factors (the one appearing in Sirlin's theorem) which does not get contributions from order $p^6$ operators with unknown constants. For the charge radii, the correction to the previous one-loop result turns out to be significant, but still there is no agreement with the present data due to large experimental uncertainties in the kaon charge radii.Comment: 6 pages, Latex, 2 LaTeX figure

The Complexity of Reasoning for Fragments of Default Logic

Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified the complexity of the extension existence problem for propositional default logic as \SigmaPtwo-complete, and the complexity of the credulous and skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete. Additionally, he investigated restrictions on the default rules, i.e., semi-normal default rules. Selman made in 1992 a similar approach with disjunction-free and unary default rules. In this paper we systematically restrict the set of allowed propositional connectives. We give a complete complexity classification for all sets of Boolean functions in the meaning of Post's lattice for all three common decision problems for propositional default logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-, P-, NL-complete, trivial) for the extension existence problem, while for the credulous and skeptical reasoning problem we obtain similar classifications without trivial cases.Comment: Corrected versio

Universal distribution of transparencies in highly conductive Nb/AlOx_x/Nb junctions

We report the observation of the universal distribution of transparencies, predicted by Schep and Bauer [Phys. Rev. Lett. {\bf 78}, 3015 (1997)] for dirty sharp interfaces, in uniform Nb/AlO$_x$/Nb junctions with high specific conductance ($10^8$ Ohm$^{-1}$cm$^{-2}$). Experiments used the BCS density of states in superconducting niobium for transparency distribution probing. Experimental results for both the dc $I-V$ curves at magnetic-field-suppressed supercurrent and the Josephson critical current in zero magnetic field coincide remarkably well with calculations based on the multimode theory of multiple Andreev reflections and the Schep-Bauer distribution.Comment: 4 pages, 4 figures, references adde

Subharmonic Shapiro steps and assisted tunneling in superconducting point contacts

We analyze the current in a superconducting point contact of arbitrary transmission in the presence of a microwave radiation. The interplay between the ac Josephson current and the microwave signal gives rise to Shapiro steps at voltages V = (m/n) \hbar \omega_r/2e, where n,m are integer numbers and \omega_r is the radiation frequency. The subharmonic steps (n different from 1) are a consequence of the ocurrence of multiple Andreev reflections (MAR) and provide an unambiguous signature of the peculiar ac Josephson effect at high transmission. Moreover, the dc current exhibits a rich subgap structure due to photon-assisted MARs.Comment: Revtex, 4 pages, 4 figure

Optical activity induced by curvature in a gravitational pp-wave background

We study optical activity induced by curvature. The optical activity model we present has two phenomenological gyration parameters, within which we analyze three model cases, namely, an exactly integrable model, the Landau-Lifshitz model and the Fedorov model, these latter two are solved in the short wavelength approximation. The model background is a gravitational pp-wave. The solutions show that the optical activity induced by curvature leads to Faraday rotation.Comment: 16 pages, late

Two-point function of strangeness-carrying vector-currents in two-loop Chiral Perturbation Theory

We calculate the correlator between two external vector-currents having the quantum-numbers of a charged kaon. We give the renormalized expression to two loops in standard chiral perturbation theory in the isospin limit, which, as a physical result, is finite and scale-independent. Applications include a low energy theorem, valid at two loop order, of a flavor breaking combination of vector current correlators as well as a determination of the phenomenologically relevant finite $O(p^6)$-counterterm combination $Q_V$ by means of inverse moment finite energy sum rules. This determination is less sensitive to isospin-breaking effects than previous attempts.Comment: 24 pages, revtex, 4 figures, 2 tables, revised version, one ref. adde