Molecular Dynamics in grafted layers of poly(dimethylsiloxane) (PDMS)

Dielectric relaxation spectroscopy 10^-1 Hz to 10^6 Hz) is employed to study the molecular dynamics of poly(dimethylsiloxane) (PDMS, Mw=1.7 10^5 g/mol and Mw=9.6 10^4 g/mol as grafted films with thicknesses d below and above the radius of gyration Rg. For d smaller than Rg the molecular dynamics becomes faster by up to three orders of magnitude with respect to the bulk resulting in a pronounced decrease of the Vogel temperature T0 and hence the calorimetric glass transition temperature Tg. For d larger than Rg the molecular dynamics is comparable to that of the bulk melt. The results are interpreted in terms of a chain confinement effect and compared with the findings for low molecular eight glass forming liquids contained in nanoporous glasses and zeolites. Crystallization effects - well known for PDMS - are observed for films of thicknesses above and below Rg.Comment: 20 pages, 4 figure

Adaptive Resolution Molecular Dynamics Simulation: Changing the Degrees of Freedom on the Fly

We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially localized domains whereas a lower mesoscopic level of detail is sufficient for the rest of the system. Our method allows an on-the-fly interchange between a given molecule's atomic and coarse-grained level of description, enabling us to reach large length and time scales while spatially retaining atomistic details of the system. The new approach is tested on a model system of a liquid of tetrahedral molecules. The simulation box is divided into two regions: one containing only atomistically resolved tetrahedral molecules, the other containing only one particle coarse-grained spherical molecules. The molecules can freely move between the two regions while changing their level of resolution accordingly. The coarse-grained and the atomistically resolved systems have the same statistical properties at the same physical conditions.Comment: 17 pages, 11 figures, 5 table

Accelerated expansion in bosonic and fermionic 2D cosmologies with quantum effects

In this work we analyze the effects produced by bosonic and fermionic constituents, including quantum corrections, in two-dimensional (2D) cosmological models. We focus on a gravitational theory related to the Callan-Giddings-Harvey-Strominger model, to simulate the dynamics of a young, spatially-lineal, universe. The cosmic substratum is formed by an {\it inflaton} field plus a matter component, sources of the 2D gravitational field; the degrees of freedom also include the presence of a dilaton field. We show that this combination permits, among other scenarios, the simulation of a period of inflation, that would be followed by a (bosonic/fermionic) matter dominated era. We also analyse how quantum effects contribute to the destiny of the expansion, given the fact that in 2D we have a consistent (renormalizable) quantum theory of gravity. The dynamical behavior of the system follows from the solution of the gravitational field equations, the (Klein-Gordon and Dirac) equations for the sources and the dilaton field equation. Consistent (accelerated) regimes are present among the solutions of the 2D equations; the results depend strongly on the initial conditions used for the dilaton field. In the particular case where fermions are included as matter fields a transition to a decelerated expansion is possible, something that does not happen in the exclusively bosonic case.Comment: 6 pages, 5 figures, to appear in EP

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

On big rip singularities

In this comment we discuss big rip singularities occurring in typical phantom models by violation of the weak energy condition. After that, we compare them with future late-time singularities arising in models where the scale factor ends in a constant value and there is no violation of the strong energy condition. In phantom models the equation of state is well defined along the whole evolution, even at the big rip. However, both the pressure and the energy density of the phantom field diverge. In contrast, in the second kind of model the equation of state is not defined at the big rip because the pressure bursts at a finite value of the energy density.Comment: 8 page

Surface micro-discharges on spacecraft dielectrics

Extensive measurements on Teflon and Kapton in a scanning electron microscope indicate the existence of a well-defined family of surface micro-discharges characteristic of the dielectric material. For a given small region exposed to the 16-20 kV electron beam, the strongest discharge pulses are similar in shape and amplitude. For Teflon, typical pulse durations are 2-3 ns, rise and fall times are sometimes as low as 0.2 ns, current amplitudes are approximately 100 mA flowing down to the pedestal and the pulses are unidirectional with no ringing. The use of a rapid-scan electron microscope with a secondary-electron imaging system reveals complex charge distributions resembling Lichtenberg figures on a supposedly flat homogeneous dielectric surface. These patterns undergo extensive alteration at each micro-discharge pulse and indicate that both the charging and discharging processes are highly nonuniform over the dielectric surface. The use of floodbeam causes the occurrence of a large-scale macro-discharges, in which a typical peak current is 40 A with a duration of 120 ns

Inflationary and dark energy regimes in 2+1 dimensions

In this work we investigate the behavior of three-dimensional (3D) cosmological models. The simulation of inflationary and dark-energy-dominated eras are among the possible results in these 3D formulations; taking as starting point the results obtained by Cornish and Frankel. Motivated by those results, we investigate, first, the inflationary case where we consider a two-constituent cosmological fluid: the scalar field represents the hypothetical inflaton which is in gravitational interaction with a matter/radiation contribution. For the description of an old universe, it is possible to simulate its evolution starting with a matter dominated universe that faces a decelerated/accelerated transition due to the presence of the additional constituent (simulated by the scalar field or ruled by an exotic equation of state) that plays the role of dark energy. We obtain, through numerical analysis, the evolution in time of the scale factor, the acceleration, the energy densities, and the hydrostatic pressure of the constituents. The alternative scalar cosmology proposed by Cornish and Frankel is also under investigation in this work. In this case an inflationary model can be constructed when another non-polytropic equation of state (the van der Waals equation) is used to simulate the behavior of an early 3D universe.Comment: Latex file, plus 9 figures. To appear in General Relativity and Gravitatio