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

Charge mobility of discotic mesophases: A multiscale quantum/classical study

A correlation is established between the molecular structure and charge mobility of discotic mesophases of hexabenzocoronene derivatives by combining electronic structure calculations, Molecular Dynamics, and kinetic Monte Carlo simulations. It is demonstrated that this multiscale approach can provide an accurate ab-initio description of charge transport in organic materials

Irreversible Processes in a Universe modelled as a mixture of a Chaplygin gas and radiation

The evolution of a Universe modelled as a mixture of a Chaplygin gas and radiation is determined by taking into account irreversible processes. This mixture could interpolate periods of a radiation dominated, a matter dominated and a cosmological constant dominated Universe. The results of a Universe modelled by this mixture are compared with the results of a mixture whose constituents are radiation and quintessence. Among other results it is shown that: (a) for both models there exists a period of a past deceleration with a present acceleration; (b) the slope of the acceleration of the Universe modelled as a mixture of a Chaplygin gas with radiation is more pronounced than that modelled as a mixture of quintessence and radiation; (c) the energy density of the Chaplygin gas tends to a constant value at earlier times than the energy density of quintessence does; (d) the energy density of radiation for both mixtures coincide and decay more rapidly than the energy densities of the Chaplygin gas and of quintessence.Comment: 8 pages, 1 figure, to be published in GR

Lattice and polarizability mediated spin activity in EuTiO_3

EuTiO_3 is shown to exhibit novel strong spin-charge-lattice coupling deep in the paramagnetic phase. Its existence is evidenced by an, until now, unknown response of the paramagnetic susceptibility at temperatures exceeding the structural phase transition temperature T_S = 282K. The "extra" features in the susceptibility follow the rotational soft zone boundary mode temperature dependence above and below T_S. The theoretical modeling consistently reproduces this behavior and provides reasoning for the stabilization of the soft optic mode other than quantum fluctuations.Comment: 8 pages, 4 figure

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

Revealing the pure confinement effect in glass-forming liquids by dynamic mechanical analysis

Many molecular glass forming liquids show a shift of the glass transition Tg to lower temperatures when the liquid is confined into mesoporous host matrices. Two contrary explanations for this effect are given in literature: First, confinement induced acceleration of the dynamics of the molecules leads to an effective downshift of Tg increasing with decreasing pore size. Secondly, due to thermal mismatch between the liquid and the surrounding host matrix, negative pressure develops inside the pores with decreasing temperature, which also shifts Tg to lower temperatures. Here we present novel dynamic mechanical analysis measurements of the glass forming liquid salol in Vycor and Gelsil with pore sizes of d = 2.6, 5.0 and 7.5 nm. The dynamic complex elastic susceptibility data can be consistently described with the assumption of two relaxation processes inside the pores: A surface induced slowed down relaxation due to interaction with rough pore interfaces and a second relaxation within the core of the pores. This core relaxation time is reduced with decreasing pore size d, leading to a downshift of Tg in perfect agreement with recent DSC measurements

Evidence of a bond-nematic phase in LiCuVO4

Polarized and unpolarized neutron scattering experiments on the frustrated ferromagnetic spin-1/2 chain LiCuVO4 show that the phase transition at HQ of 8 Tesla is driven by quadrupolar fluctuations and that dipolar correlations are short-range with moments parallel to the applied magnetic field in the high-field phase. Heat-capacity measurements evidence a phase transition into this high-field phase, with an anomaly clearly different from that at low magnetic fields. Our experimental data are consistent with a picture where the ground state above HQ has a next-nearest neighbour bond-nematic order along the chains with a fluid-like coherence between weakly coupled chains.Comment: 5 pages, 4 figures. To appear in Phys. Rev. Let

Polymers near Metal Surfaces: Selective Adsorption and Global Conformations

We study the properties of a polycarbonate melt near a nickel surface as a model system for the interaction of polymers with metal surfaces by employing a multiscale modeling approach. For bulk properties a suitably coarse grained bead spring model is simulated by molecular dynamics (MD) methods with model parameters directly derived from quantum chemical calculations. The surface interactions are parameterized and incorporated by extensive quantum mechanical density functional calculations using the Car-Parrinello method. We find strong chemisorption of chain ends, resulting in significant modifications of the melt composition when compared to an inert wall.Comment: 8 pages, 3 figures (2 color), 1 tabl