Spatial structures and dynamics of kinetically constrained models for glasses

Kob and Andersen's simple lattice models for the dynamics of structural glasses are analyzed. Although the particles have only hard core interactions, the imposed constraint that they cannot move if surrounded by too many others causes slow dynamics. On Bethe lattices a dynamical transition to a partially frozen phase occurs. In finite dimensions there exist rare mobile elements that destroy the transition. At low vacancy density, $v$, the spacing, $\Xi$, between mobile elements diverges exponentially or faster in $1/v$. Within the mobile elements, the dynamics is intrinsically cooperative and the characteristic time scale diverges faster than any power of $1/v$ (although slower than $\Xi$). The tagged-particle diffusion coefficient vanishes roughly as $\Xi^{-d}$.Comment: 4 pages. Accepted for pub. in Phys. Rev. Let

On QBF Proofs and Preprocessing

QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e.g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.Comment: LPAR 201

Lattice Glass Models

Motivated by the concept of geometrical frustration, we introduce a class of statistical mechanics lattice models for the glass transition. Monte Carlo simulations in three dimensions show that they display a dynamical glass transition which is very similar to that observed in other off-lattice systems and which does not depend on a specific dynamical rule. Whereas their analytic solution within the Bethe approximation shows that they do have a discontinuous glass transition compatible with the numerical observations.Comment: 4 pages, 2 figures; minor change

Cosmological measurements, time and observables in (2+1)-dimensional gravity

We investigate the relation between measurements and the physical observables for vacuum spacetimes with compact spatial surfaces in (2+1)-gravity with vanishing cosmological constant. By considering an observer who emits lightrays that return to him at a later time, we obtain explicit expressions for several measurable quantities as functions on the physical phase space of the theory: the eigentime elapsed between the emission of a lightray and its return to the observer, the angles between the directions into which the light has to be emitted to return to the observer and the relative frequencies of the lightrays at their emission and return. This provides a framework in which conceptual questions about time, observables and measurements can be addressed. We analyse the properties of these measurements and their geometrical interpretation and show how they allow an observer to determine the values of the Wilson loop observables that parametrise the physical phase space of (2+1)-gravity. We discuss the role of time in the theory and demonstrate that the specification of an observer with respect to the spacetime's geometry amounts to a gauge fixing procedure yielding Dirac observables.Comment: 38 pages, 11 eps figures, typos corrected, references update

Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_s$ and walk dimension $d_w$ associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where $d_s = d, d_w = 2$, a semi-classical regime where $d_s = 2d/(2+d), d_w = 2+d$, and the UV-fixed point regime where $d_s = d/2, d_w = 4$. On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.Comment: 26 pages, 6 figure

Compactness for Holomorphic Supercurves

We study the compactness problem for moduli spaces of holomorphic supercurves which, being motivated by supergeometry, are perturbed such as to allow for transversality. We give an explicit construction of limiting objects for sequences of holomorphic supercurves and prove that, in important cases, every such sequence has a convergent subsequence provided that a suitable extension of the classical energy is uniformly bounded. This is a version of Gromov compactness. Finally, we introduce a topology on the moduli spaces enlarged by the limiting objects which makes these spaces compact and metrisable.Comment: 38 page

Relative contributions of lattice distortion and orbital ordering to resonant x-ray scattering in manganites

We investigated the origin of the energy splitting observed in the resonant x-ray scattering (RXS) in manganites. Using thin film samples with controlled lattice parameters and orbital states at a fixed orbital filling, we estimated that the contribution of the interatomic Coulomb interaction relative to the Jahn-Teller mechanism is insignificant and at most 0.27. This indicates that RXS probes mainly Jahn-Teller distortion in manganites.Comment: 8 pages, 4 figure

Cooperative Jahn-Teller transition and resonant x-ray scattering in thin film LaMnO3{\rm LaMnO_3}

Epitaxial thin films of stoichiometric ${\rm LaMnO_3}$ were grown on ${\rm SrTiO_3(110)}$ substrates using the pulsed laser deposition technique. From the high resolution x-ray diffraction measurements, the lattice parameters were determined as a function of temperature and the cooperative Jahn-Teller transition was found to occur at $T_{JT}$=573.0 K. Also measured was resonant x-ray scattering intensity of the orthorhombic (100) peak of ${\rm LaMnO_3}$ near the Mn K edge from low temperatures to above $T_{JT}$. We demonstrate that the integrated intensity of the (100) peak is proportional to the 3/2 power of the orthorhombic strain at all temperatures, and thus provide an experimental evidence that the resonant scattering near the Mn K edge in ${\rm LaMnO_3}$ is largely due to the Jahn-Teller effect.Comment: 13 pages, 4 figure

Protein kinase C and cancer: what we know and what we do not

Since their discovery in the late 1970s, protein kinase C (PKC) isozymes represent one of the most extensively studied signaling kinases. PKCs signal through multiple pathways and control the expression of genes relevant for cell cycle progression, tumorigenesis and metastatic dissemination. Despite the vast amount of information concerning the mechanisms that control PKC activation and function in cellular models, the relevance of individual PKC isozymes in the progression of human cancer is still a matter of controversy. Although the expression of PKC isozymes is altered in multiple cancer types, the causal relationship between such changes and the initiation and progression of the disease remains poorly defined. Animal models developed in the last years helped to better understand the involvement of individual PKCs in various cancer types and in the context of specific oncogenic alterations. Unraveling the enormous complexity in the mechanisms by which PKC isozymes have an impact on tumorigenesis and metastasis is key for reassessing their potential as pharmacological targets for cancer treatment.Centro de Investigaciones Inmunológicas Básicas y Aplicada