Fitting Effective Diffusion Models to Data Associated with a "Glassy Potential": Estimation, Classical Inference Procedures and Some Heuristics

A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation, goodness-of-fit tests, and confidence interval estimation. The first part of this article uses maximum likelihood estimation to obtain the parameters of a diffusion model from a scalar time series. I address numerical issues associated with attempting to realize asymptotic statistics results with moderate sample sizes in the presence of exact and approximated transition densities. Approximate transition densities are used because the analytic solution of a transition density associated with a parametric diffusion model is often unknown.I am primarily interested in how well the deterministic transition density expansions of Ait-Sahalia capture the curvature of the transition density in (idealized) situations that occur when one carries out simulations in the presence of a "glassy" interaction potential. Accurate approximation of the curvature of the transition density is desirable because it can be used to quantify the goodness-of-fit of the model and to calculate asymptotic confidence intervals of the estimated parameters. The second part of this paper contributes a heuristic estimation technique for approximating a nonlinear diffusion model. A "global" nonlinear model is obtained by taking a batch of time series and applying simple local models to portions of the data. I demonstrate the technique on a diffusion model with a known transition density and on data generated by the Stochastic Simulation Algorithm.Comment: 30 pages 10 figures Submitted to SIAM MMS (typos removed and slightly shortened

Delayed soft X-ray emission lines in the afterglow of GRB 030227

Strong, delayed X-ray line emission is detected in the afterglow of GRB 030227, appearing near the end of the XMM-Newton observation, nearly twenty hours after the burst. The observed flux in the lines, not simply the equivalent width, sharply increases from an undetectable level (<1.7e-14 erg/cm^2/s, 3 sigma) to 4.1e-14 erg/cm^2/s in the final 9.7 ks. The line emission alone has nearly twice as many detected photons as any previous detection of X-ray lines. The lines correspond well to hydrogen and/or helium-like emission from Mg, Si, S, Ar and Ca at a redshift z=1.39. There is no evidence for Fe, Co or Ni--the ultimate iron abundance must be less than a tenth that of the lighter metals. If the supernova and GRB events are nearly simultaneous there must be continuing, sporadic power output after the GRB of a luminosity >~5e46 erg/s, exceeding all but the most powerful quasars.Comment: Submitted to ApJL. 14 pages, 3 figures with AASLaTe

Tur\'an Graphs, Stability Number, and Fibonacci Index

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.Comment: 11 pages, 3 figure

Finite element analysis of stress distribution and the effects of geometry in a laser-generated single-stage ceramic tile grout seal using ANSYS

Optimisation of the geometry (curvature of the vitrified enamel layer) of a laser-generated single-stage ceramic tile grout seal has carried out with a finite element (FE) model. The overall load bearing capacities and load-displacement plots of three selected geometries were determined experimentally by the indentation technique. Simultaneously, a FE model was developed utilising the commercial ANSYS package to simulate the indentation. Although the load-displacement plots generated by the FE model consistently displayed stiffer identities than the experimentally obtained results, there was reasonably close agreement between the two sets of results. Stress distribution profiles of the three FE models at failure loads were analysed and correlated so as to draw an implication on the prediction of a catastrophic failure through an analysis of FE-generated stress distribution profiles. It was observed that although increased curvatures of the vitrified enamel layer do enhance the overall load-bearing capacity of the single-stage ceramic tile grout seal and bring about a lower nominal stress, there is a higher build up in stress concentration at the apex that would inevitably reduce the load-bearing capacity of the enamel glaze. Consequently, the optimum geometry of the vitrified enamel layer was determined to be flat

A repulsive reference potential reproducing the dynamics of a liquid with attractions

A well-known result of liquid state theory is that the structure of dense fluids is mainly determined by repulsive forces. The WCA potential, which cuts intermolecular potentials at their minima, is therefore often used as a reference. However, this reference gives quite wrong results for the viscous dynamics of the Kob-Andersen binary Lennard-Jones liquid [Berthier and Tarjus, Phys. Rev. Lett. 103, 170601 (2009)]. We show that repulsive inverse-power law potentials provide a useful reference for this liquid by reproducing its structure, dynamics, and isochoric heat capacity

Theoretical study of kinks on screw dislocation in silicon

Theoretical calculations of the structure, formation and migration of kinks on a non-dissociated screw dislocation in silicon have been carried out using density functional theory calculations as well as calculations based on interatomic potential functions. The results show that the structure of a single kink is characterized by a narrow core and highly stretched bonds between some of the atoms. The formation energy of a single kink ranges from 0.9 to 1.36 eV, and is of the same order as that for kinks on partial dislocations. However, the kinks migrate almost freely along the line of an undissociated dislocation unlike what is found for partial dislocations. The effect of stress has also been investigated in order to compare with previous silicon deformation experiments which have been carried out at low temperature and high stress. The energy barrier associated with the formation of a stable kink pair becomes as low as 0.65 eV for an applied stress on the order of 1 GPa, indicating that displacements of screw dislocations likely occur via thermally activated formation of kink pairs at room temperature

ISO far-infrared observations of rich galaxy clusters II. Sersic 159-03

The far-infrared emission from rich galaxy clusters is investigated. Maps have been obtained by ISO at 60, 100, 135, and 200 microns using the PHT-C camera. Ground based imaging and spectroscopy were also acquired. Here we present the results for the cooling flow cluster Sersic 159-03. An infrared source coincident with the dominant cD galaxy is found. Some off-center sources are also present, but without any obvious counterparts.Comment: 6 pages, 4 postscript figures, accepted for publication in `Astronomy and Astrophysics

Einstein-Weyl structures and Bianchi metrics

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally K\"ahler ; in the non-exact Einstein-Weyl case with a Bianchi metric of the type $VII_0, VIII$ or $IX$, we show that the distance may be taken in a diagonal form and we obtain its explicit 4-parameters expression. This extends our previous analysis, limited to the diagonal, K\"ahler Bianchi $IX$ case.Comment: Latex file, 12 pages, a minor modification, accepted for publication in Class. Quant. Gra

Anomalous transport in biased ac-driven Josephson junctions: Negative conductances

We investigate classical anomalous electrical transport in a driven, resistively and capacitively shunted Josephson junction device. Novel transport phenomena are identified in chaotic regimes when the junction is subjected to both, a time periodic (ac) and a constant, biasing (dc) current. The dependence of the voltage across the junction on the dc-current exhibits a rich diversity of anomalous transport characteristics: In particular, depending on the chosen parameter regime we can identify so termed absolute negative conductance around zero dc-bias, the occurrence of negative differential conductance and, after crossing a zero conductance, the emergence of a negative nonlinear conductance in the non-equilibrium response regime remote from zero dc-bias.Comment: 7 pages, 5 figure

Strong pressure-energy correlations in van der Waals liquids

Strong correlations between equilibrium fluctuations of the configurational parts of pressure and energy are found in the Lennard-Jones liquid and other simple liquids, but not in hydrogen-bonding liquids like methanol and water. The correlations, that are present also in the crystal and glass phases, reflect an effective inverse power-law repulsive potential dominating fluctuations, even at zero and slightly negative pressure. In experimental data for supercritical Argon, the correlations are found to be approximately 96%. Consequences for viscous liquid dynamics are discussed.Comment: Phys. Rev. Lett., in pres