7,314 research outputs found
Decidability of quantified propositional intuitionistic logic and S4 on trees
Quantified propositional intuitionistic logic is obtained from propositional
intuitionistic logic by adding quantifiers \forall p, \exists p over
propositions. In the context of Kripke semantics, a proposition is a subset of
the worlds in a model structure which is upward closed. Kremer (1997) has shown
that the quantified propositional intuitionistic logic H\pi+ based on the class
of all partial orders is recursively isomorphic to full second-order logic. He
raised the question of whether the logic resulting from restriction to trees is
axiomatizable. It is shown that it is, in fact, decidable. The methods used can
also be used to establish the decidability of modal S4 with propositional
quantification on similar types of Kripke structures.Comment: v2, 9 pages, corrections and additions; v1 8 page
Normal origamis of Mumford curves
An origami (also known as square-tiled surface) is a Riemann surface covering
a torus with at most one branch point. Lifting two generators of the
fundamental group of the punctured torus decomposes the surface into finitely
many unit squares. By varying the complex structure of the torus one obtains
easily accessible examples of Teichm\"uller curves in the moduli space of
Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves.
A p-adic origami is defined as a covering of Mumford curves with at most one
branch point, where the bottom curve has genus one. A classification of all
normal non-trivial p-adic origamis is presented and used to calculate some
invariants. These can be used to describe p-adic origamis in terms of glueing
squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer
Linking partial and quasi dynamical symmetries in rotational nuclei
Background: Quasi dynamical symmetries (QDS) and partial dynamical symmetries
(PDS) play an important role in the understanding of complex systems. Up to now
these symmetry concepts have been considered to be unrelated. Purpose:
Establish a link between PDS and QDS and find an emperical manifestation.
Methods: Quantum number fluctuations and the intrinsic state formalism are used
within the framework of the interacting boson model of nuclei. Results: A
previously unrecognized region of the parameter space of the interacting boson
model that has both O(6) PDS (purity) and SU(3) QDS (coherence) in the ground
band is established. Many rare-earth nuclei approximately satisfying both
symmetry requirements are identified. Conclusions: PDS are more abundant than
previously recognized and can lead to a QDS of an incompatible symmetry.Comment: 5 pages, 4 figures, 1 tabl
Plastic-crystalline solid-state electrolytes: Ionic conductivity and orientational dynamics in nitrile mixtures
Many plastic crystals, molecular solids with long-range, center-of-mass
crystalline order but dynamic disorder of the molecular orientations, are known
to exhibit exceptionally high ionic conductivity. This makes them promising
candidates for applications as solid-state electrolytes, e.g., in batteries.
Interestingly, it was found that the mixing of two different
plastic-crystalline materials can considerably enhance the ionic dc
conductivity, an important benchmark quantity for electrochemical applications.
An example is the admixture of different nitriles to succinonitrile, the latter
being one of the most prominent plastic-crystalline ionic conductors. However,
until now only few such mixtures were studied. In the present work, we
investigate succinonitrile mixed with malononitrile, adiponitrile, and
pimelonitrile, to which 1 mol% of Li ions were added. Using differential
scanning calorimetry and dielectric spectroscopy, we examine the phase behavior
and the dipolar and ionic dynamics of these systems. We especially address the
mixing-induced enhancement of the ionic conductivity and the coupling of the
translational ionic mobility to the molecular reorientational dynamics,
probably arising via a "revolving-door" mechanism.Comment: 9 pages, 7 figures; revised version as accepted for publication in J.
Chem. Phy
On two intrinsic length scales in polymer physics: topological constraints vs. entanglement length
The interplay of topological constraints, excluded volume interactions,
persistence length and dynamical entanglement length in solutions and melts of
linear chains and ring polymers is investigated by means of kinetic Monte Carlo
simulations of a three dimensional lattice model. In unknotted and
unconcatenated rings, topological constraints manifest themselves in the static
properties above a typical length scale ( being
the volume fraction, the mean bond length).
Although one might expect that the same topological length will play a role
in the dynamics of entangled polymers, we show that this is not the case.
Instead, a different intrinsic length de, which scales like excluded volume
blob size , governs the scaling of the dynamical properties of both linear
chains and rings.Comment: 7 pages. 4 figure
3D gravity and non-linear cosmology
By the inclusion of an additional term, non-linear in the scalar curvature
, it is tested if dark energy could rise as a geometrical effect in 3D
gravitational formulations. We investigate a cosmological fluid obeying a
non-polytropic equation of state (the van der Waals equation) that is used to
construct the energy-momentum tensor of the sources, representing the
hypothetical inflaton in gravitational interaction with a matter contribution.
Following the evolution in time of the scale factor, its acceleration, and
the energy densities of constituents it is possible to construct the
description of an inflationary 3D universe, followed by a matter dominated era.
For later times it is verified that, under certain conditions, the non-linear
term in can generate the old 3D universe in accelerated expansion, where
the ordinary matter is represented by the barotropic limit of the van der Waals
constituent.Comment: 7 pages, to appear in Mod. Phys. Let
Effect of Pressure on Superconducting Ca-intercalated Graphite CaC
The pressure effect on the superconducting transition temperature () of
the newly-discovered Ca-intercalated graphite compound CaC has been
investigated up to 16 kbar. is found to increase under pressure
with a large relative ratio / of +0.4 %/kbar. Using
first-principles calculations, we show that the large and positive effect of
pressure on can be explained in the scope of electron-phonon theory due
to the presence of a soft phonon branch associated to in-plane vibrations of Ca
atoms. Implications of the present findings on the current debate about the
superconducting mechanism in graphite intercalation compounds are discussed.Comment: 6 pages, 5 figs, final PRB versio
Self-avoiding walks on scale-free networks
Several kinds of walks on complex networks are currently used to analyze
search and navigation in different systems. Many analytical and computational
results are known for random walks on such networks. Self-avoiding walks (SAWs)
are expected to be more suitable than unrestricted random walks to explore
various kinds of real-life networks. Here we study long-range properties of
random SAWs on scale-free networks, characterized by a degree distribution
. In the limit of large networks (system size ), the average number of SAWs starting from a generic site
increases as , with . For finite ,
is reduced due to the presence of loops in the network, which causes the
emergence of attrition of the paths. For kinetic growth walks, the average
maximum length, , increases as a power of the system size: , with an exponent increasing as the parameter is
raised. We discuss the dependence of on the minimum allowed degree in
the network. A similar power-law dependence is found for the mean
self-intersection length of non-reversal random walks. Simulation results
support our approximate analytical calculations.Comment: 9 pages, 7 figure
Cooperative motion and growing length scales in supercooled confined liquids
Using molecular dynamics simulations we investigate the relaxation dynamics
of a supercooled liquid close to a rough as well as close to a smooth wall. For
the former situation the relaxation times increase strongly with decreasing
distance from the wall whereas in the second case they strongly decrease. We
use this dependence to extract various dynamical length scales and show that
they grow with decreasing temperature. By calculating the frequency dependent
average susceptibility of such confined systems we show that the experimental
interpretation of such data is very difficult.Comment: 7 pages of Latex, 3 figure
Non-linear terms in 2D cosmology
In this work we investigate the behavior of two-dimensional (2D) cosmological
models, starting with the Jackiw-Teitelboim (JT) theory of gravitation. A
geometrical term, non-linear in the scalar curvature , is added to the JT
dynamics to test if it could play the role of dark energy in a 2D expanding
universe. This formulation makes possible, first, the description of an early
(inflationary) 2D universe, when the van der Waals (vdW) equation of state is
used to construct the energy-momentum tensor of the gravitational sources.
Second, it is found that for later times the non-linear term in can
generate an old 2D universe in accelerated expansion, where an ordinary matter
dominated era evolves into a decelerated/accelerated transition, giving to the
dark energy effects a geometrical origin. The results emerge through numerical
analysis, following the evolution in time of the scale factor, its
acceleration, and the energy densities of constituents.Comment: tex file plus figures in two zipped files. To appear in Europhys.
Let
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