420 research outputs found
An Intuitionistic Formula Hierarchy Based on High-School Identities
We revisit the notion of intuitionistic equivalence and formal proof
representations by adopting the view of formulas as exponential polynomials.
After observing that most of the invertible proof rules of intuitionistic
(minimal) propositional sequent calculi are formula (i.e. sequent) isomorphisms
corresponding to the high-school identities, we show that one can obtain a more
compact variant of a proof system, consisting of non-invertible proof rules
only, and where the invertible proof rules have been replaced by a formula
normalisation procedure.
Moreover, for certain proof systems such as the G4ip sequent calculus of
Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the
non-invertible proof rules as strict inequalities between exponential
polynomials; a careful combinatorial treatment is given in order to establish
this fact.
Finally, we extend the exponential polynomial analogy to the first-order
quantifiers, showing that it gives rise to an intuitionistic hierarchy of
formulas, resembling the classical arithmetical hierarchy, and the first one
that classifies formulas while preserving isomorphism
Josephson Vortex Bloch Oscillations: Single Pair Tunneling Effect
We consider the Josephson vortex motion in a long one--dimensional Josephson
junction in a thin film. We show that this Josephson vortex is similar to a
mesoscopic capacitor. We demonstrate that a single Cooper pair tunneling
results in nonlinear Bloch--type oscillations of a Josephson vortex in a
current-biased Josephson junction. We find the frequency and the amplitude of
this motion.Comment: 7 pages, 2 figures included as postscript files, LaTe
Properties of superconducting MgB_2 wires: "in-situ" versus "ex-situ" reaction technique
We have fabricated a series of iron-sheathed superconducting wires prepared
by the powder-in-tube technique from (MgB_2)_{1-x}:(Mg+2B)_x initial powder
mixtures taken with different proportions, so that x varies from 0 to 1. It
turned out that "ex-situ" prepared wire (x = 0) has considerable disadvantages
compared to all the other wires in which "in-situ" assisted (0 < x < 1) or pure
"in-situ" (x = 1) preparation was used due to weaker inter-grain connectivity.
As a result, higher critical current densities J_c were measured over the
entire range of applied magnetic fields B_a for all the samples with x > 0.
Pinning of vortices in MgB_2 wires is shown to be due to grain boundaries.
J_c(B_a) behavior is governed by an interplay between the transparency of grain
boundaries and the amount of "pinning" grain boundaries. Differences between
thermo-magnetic flux-jump instabilities in the samples and a possible threat to
practical applications are also discussed.Comment: To be published in Supercond. Sci. Technol. (2003), in pres
Semantics and Proof Theory of the Epsilon Calculus
The epsilon operator is a term-forming operator which replaces quantifiers in
ordinary predicate logic. The application of this undervalued formalism has
been hampered by the absence of well-behaved proof systems on the one hand, and
accessible presentations of its theory on the other. One significant early
result for the original axiomatic proof system for the epsilon-calculus is the
first epsilon theorem, for which a proof is sketched. The system itself is
discussed, also relative to possible semantic interpretations. The problems
facing the development of proof-theoretically well-behaved systems are
outlined.Comment: arXiv admin note: substantial text overlap with arXiv:1411.362
Suppression of surface barrier in superconductors by columnar defects
We investigate the influence of columnar defects in layered superconductors
on the thermally activated penetration of pancake vortices through the surface
barrier. Columnar defects, located near the surface, facilitate penetration of
vortices through the surface barrier, by creating ``weak spots'', through which
pancakes can penetrate into the superconductor. Penetration of a pancake
mediated by an isolated column, located near the surface, is a two-stage
process involving hopping from the surface to the column and the detachment
from the column into the bulk; each stage is controlled by its own activation
barrier. The resulting effective energy is equal to the maximum of those two
barriers. For a given external field there exists an optimum location of the
column for which the barriers for the both processes are equal and the
reduction of the effective penetration barrier is maximal. At high fields the
effective penetration field is approximately two times smaller than in
unirradiated samples. We also estimate the suppression of the effective
penetration field by column clusters. This mechanism provides further reduction
of the penetration field at low temperatures.Comment: 8 pages, 9 figures, submitted to Phys. Rev.
Role of Interfaces in the Proximity Effect in Anisotropic Superconductors
We report measurements of the critical temperature of YBCO-Co doped YBCO
Superconductor-Normal bilayer films. Depending on the morphology of the S-N
interface, the coupling between S and N layers can be turned on to depress the
critical temperature of S by tens of degrees, or turned down so the layers
appear almost totally decoupled. This novel effect can be explained by the
mechanism of quasiparticle transmission into an anisotropic superconductor.Comment: 13 pages, 3 figure
From Display to Labelled Proofs for Tense Logics
We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt
Thermal suppression of surface barrier in ultrasmall superconducting structures
In the recent experiment by Cren \textit{et al.} [Phys. Rev. Lett.
\textbf{102}, 127005 (2009)], no hysteresis for vortex penetration and
expulsion from the nano-island of Pb was observed. In the present paper, we
argue that this effect can be associated with the thermoactivated surmounting
of the surface barrier by a vortex. The typical entrance (exit) time is found
analytically from the Fokker-Planck equation, written in the form suitable for
the extreme vortex confinement. We show that this time is several orders of
magnitude smaller than 1 second under the conditions of the experiment
considered. Our results thus demonstrate a possibility for the thermal
suppression of the surface barrier in nanosized low- superconductors. We
also briefly discuss other recent experiments on vortices in related
structures.Comment: 12 pages, 2 figure
Predictions of Astrometric Jitter for Sun-like Stars. II. Dependence on Inclination, Metallicity, and Active-Region Nesting
Ultra-precise astrometry from the Gaia mission is expected to lead to
astrometric detections of more than 20,000 exoplanets in our Galaxy. One of the
factors that could hamper such detections is the astrometric jitter caused by
the magnetic activity of the planet host stars. In our previous study, we
modeled astrometric jitter for the Sun observed equator-on. In this work, we
generalize our model and calculate the photocenter jitter as it would be
measured by the Gaia and Small-JASMINE missions for stars with solar rotation
rate and effective temperature, but with various values of the inclination
angle of the stellar rotation axis. In addition, we consider the effect of
metallicity and of nesting of active regions (i.e. the tendency of active
regions to emerge in the vicinity of each other). We find that, while the
jitter of stars observed equator-on does not have any long-term trends and can
be easily filtered out, the photocenters of stars observed out of their
equatorial planes experience systematic shifts over the course of the activity
cycle. Such trends allow the jitter to be detected with continuous
measurements, in which case it can interfere with planet detectability. An
increase in the metallicity is found to increase the jitter caused by stellar
activity. Active-region nesting can further enhance the peak-to-peak amplitude
of the photocenter jitter to a level that could be detected by Gaia.Comment: 24 pages, 20 figures in the main body and 4 in the appendix, accepted
for publication in Ap
Magnetic flux jumps in textured Bi2Sr2CaCu2O(8+d)
Magnetic flux jumps in textured Bi2Sr2CaCu2O(8+d) have been studied by means
of magnetization measurements in the temperature range between 1.95 K and Tc,
in an external magnetic field up to 9 T. Flux jumps were found in the
temperature range 1.95 K - 6 K, with the external magnetic field parallel to
the c axis of the investigated sample. The effect of sample history on magnetic
flux jumping was studied and it was found to be well accounted for by the
available theoretical models. The magnetic field sweep rate strongly influences
the flux jumping and this effect was interpreted in terms of the influence of
both flux creep and the thermal environment of the sample. Strong flux creep
was found in the temperature and magnetic field range where flux jumps occur
suggesting a relationship between the two. The heat exchange conditions between
the sample and the experimental environment also influence the flux jumping
behavior. Both these effects stabilize the sample against flux instabilities,
and this stabilizing effect increases with decreasing magnetic field sweep
rate. Demagnetizing effects are also shown to have a significant influence on
flux jumping.Comment: 10 pages, 6 figures, RevTeX4, submitted to Phys. Rev.
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