Some Remarks on the Model Theory of Epistemic Plausibility Models

Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic plausibility models have been introduced. Because these are much richer structures than Kripke models, they do not straightforwardly inherit the model-theoretical results of modal logic. Therefore, while epistemic plausibility structures are well-suited for modeling purposes, an extensive investigation of their model theory has been lacking so far. The aim of the present paper is to fill exactly this gap, by initiating a systematic exploration of the model theory of epistemic plausibility models. Like in 'ordinary' modal logic, the focus will be on the notion of bisimulation. We define various notions of bisimulations (parametrized by a language L) and show that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type result, and also two undefinability results. However, our main point is a negative one, viz. that bisimulations cannot straightforwardly be generalized to epistemic plausibility models if conditional belief is taken into account. We present two ways of coping with this issue: (i) adding a modality to the language, and (ii) putting extra constraints on the models. Finally, we make some remarks about the interaction between bisimulation and dynamic model changes.Comment: 19 pages, 3 figure

Resistivity and Hall effect of LiFeAs: Evidence for electron-electron scattering

LiFeAs is unique among the broad family of FeAs-based superconductors, because it is superconducting with a rather large $T_c\simeq 18$ K under ambient conditions although it is a stoichiometric compound. We studied the electrical transport on a high-quality single crystal. The resistivity shows quadratic temperature dependence at low temperature giving evidence for strong electron-electron scattering and a tendency towards saturation around room temperature. The Hall constant is negative and changes with temperature, what most probably arises from a van Hove singularity close to the Fermi energy in one of the hole-like bands. Using band structure calculations based on angular resolved photoemission spectra we are able to reproduce all the basic features of both the resistivity as well as the Hall effect data.Comment: 6 pages, 3 figures included; V2 has been considerably revised and contain a more detailed analysis of the Hall effect dat

Magnetoelectricity and Magnetostriction due to the Rare Earth Moment in TmAl3_3(BO3_3)4_4

The magnetic properties, the magnetostriction, and the magnetoelectric effect in the d-electron free rare-earth aluminum borate TmAl$_3$(BO$_3$)$_4$ are investigated between room temperature and 2 K. The magnetic susceptibility reveals a strong anisotropy with the hexagonal c-axis as the hard magnetic axis. Magnetostriction measurements show a large effect of an in-plane field reducing both, the a- and c-axis lattice parameters. The magnetoelectric polarization change in a- and c-directions reaches up to 300 $\mu$C/m$^2$ at 70 kOe with the field applied along the a-axis. The magnetoelectric polarization is proportional to the lattice contraction in magnetic field. The results of this investigation prove the existence of a significant coupling between the rare earth magnetic moment and the lattice in $R$Al$_3$(BO$_3$)$_4$ compounds ($R$ = rare earth). They further show that the rare earth moment itself will generate a large magnetoelectric effect which makes it easier to study and to understand the origin of the magnetoelectric interaction in this class of materials.Comment: 4 pages, 5 figure

Zeeman splittings of the 5D0–7F2 transitions of Eu3+ ions implanted into GaN

We report the magnetic field splittings of emission lines assigned to the 5D0–7F2 transitions of Eu3+ centres in GaN. The application of a magnetic field in the c-axis direction (B||c) leads to a splitting of the major lines at 621 nm, 622 nm and 622.8 nm into two components. The Zeeman splitting is linear with magnetic field up to 5 Tesla for each line. In contrast, a magnetic field applied in the growth plane (B┴c) does not influence the photoluminescence spectra. The estimated g-factors vary slightly from sample to sample with mean values of g|| ~2.8, ~1.5 and ~2.0 for the emission lines at 621 nm, 622 nm and 622.8 nm respectively

Dynamic interference of photoelectrons produced by high-frequency laser pulses

The ionization of an atom by a high-frequency intense laser pulse, where the energy of a single-photon is sufficient to ionize the system, is investigated from first principles. It is shown that as a consequence of an AC Stark effect in the continuum, the energy of the photoelectron follows the envelope of the laser pulse. This is demonstrated to result in strong dynamic interference of the photoelectrons of the same kinetic energy emitted at different times. Numerically exact computations on the hydrogen atom demonstrate that the dynamic interference spectacularly modifies the photoionization process and is prominently manifested in the photoelectron spectrum by the appearance of a distinct multi-peak pattern. The general theory is shown to be well approximated by explicit analytical expressions which allow for a transparent understanding of the discovered phenomena and for making predictions on the dependence of the measured spectrum on the properties of the pulse.Comment: 5 figure

The Kaidun Breccia Material Variety: New Clasts and Updated Hypothesis on a Space Trawl Origin

The Kaidun meteorite is a breccia containing a wide variety of different material types [1-5]. It contains lithologies of CI, CM1 and CM2, CR chondrites [6], CAIs of Types A and B [7, 8], enstatite chondrite materials (EH and EL) [3, 4], including altered enstatite clasts [9], ordinary chondrites [10], and possible R chondrite material [11] as well as glass fragments and altered shock melt veins [4]. It also contains different achondritic clasts (including alkaline rocks) with unusual oxygen isotopic compositions representing unknown differentiated parent bodies [2, 12]. Based on Fe/Mn and Fe/Mg ratios these clasts correspond to the SNC and HED meteorites and confirm their origin from differentiated parent bodies that experienced impact events and aqueous alteration, and not represented by known meteorites. We continue studying Kaidun and report results on investigation of newly discovered objects and discuss processes of their formation, and the origin of the Kaidun microbreccia as a whole. Results and Discussion: Clast #d7.2-68 was found in Kaidun section #7.2d. It consists of pyroxene and SiO_(2-)phases. Pyroxene is pigeonite (Fs_(63-67), Wo_(10-14), Fe/Mn – 40.1) with augite lamellae (Fs_(44-57), Wo_(20-34), Fe/Mn – 40.4) (up to 10 µm width). Equilibrium temperature of coexisting pyroxenes is close to 900°C at 5 Kbar [13]. The observed smooth shape of the CaO profile across the pyroxene lamellae could correspond to mild metamorphism after exsolution. On a plot of Fe/Mn vs. Fe/Mg, the clast falls at the far Fe-rich end of the HED pyroxenes cluster. The SiO_(2)-phase is enriched in Al_2O_3 and FeO and possibly is tridymite. The exsolution textures of pyroxenes require annealing for a long period of time and are typical features of achondrites, especially eucrites. This clast could represent a fragment of differentiated material of a body size of which is similar to the HED parent body

Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators

Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at $(mN_c+1)$-th oscillators in the ring, where $m$ is an integer and $N_c$ is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength $\epsilon_c$ with a scaling exponent $\gamma$. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents (CLEs) of the coupled systems. We find that the same scaling relation exists for $m$ couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength $\epsilon$. In addition, we have found that $\epsilon_c$ shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of R\"ossler and Lorenz oscillators.Comment: Accepted for Publication in Physical Review