Computing singularities of perturbation series

Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the perturbed Hamiltonian on a vector, and does not rely on the terms in the perturbation series. Some illustrative model problems are studied, including a Helium-like model with $\delta$-function interactions for which M{\o}ller--Plesset perturbation theory is considered and the radius of convergence found.Comment: 11 figures, submitte

Frozen capillary waves on glass surfaces: an AFM study

Using atomic force microscopy on silica and float glass surfaces, we give evidence that the roughness of melted glass surfaces can be quantitatively accounted for by frozen capillary waves. In this framework the height spatial correlations are shown to obey a logarithmic scaling law; the identification of this behaviour allows to estimate the ratio $kT\_F/\pi\gamma$ where $k$ is the Boltzmann constant, $\gamma$ the interface tension and $T\_F$ the temperature corresponding to the ``freezing'' of the capillary waves. Variations of interface tension and (to a lesser extent) temperatures of annealing treatments are shown to be directly measurable from a statistical analysis of the roughness spectrum of the glass surfaces

Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity

The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]

Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Optimization of Ultrasonic Defect Reconstruction with Multi-Saft

Ultrasonic nondestructive inspection (NDI) is widely applied in order to evaluate the structural integrity of steel components. The main reason for this success is that ultrasonic NDI is an excellent means for detecting inhomogeneities. Ultrasonic characterization of inhomogeneities, however, is less successful, as ultrasonic measurements do not directly provide the information, such as size and shape, needed to apply the rules of fracture mechanics. Although the location and orientation of an inhomogeneity may sometimes be estimated quite accurately from ultrasonic measurements, its size and shape are often very hard to determine. Cross-sectional images of the region containing the inhomogeneity would be particularly suitable for extracting these characteristic features. It is possible to reconstruct an image of a possible defect from ultrasonic B-scan data using the well-known Synthetic Aperture Focusing Technique (SAFT) [1]

Coarse Bifurcation Diagrams via Microscopic Simulators: A State-Feedback Control-Based Approach

The arc-length continuation framework is used for the design of state feedback control laws that enable a microscopic simulator trace its own open-loop coarse bifurcation diagram. The steering of the system along solution branches is achieved through the manipulation of the bifurcation parameter, which becomes our actuator. The design approach is based on the assumption that the eigenvalues of the linearized system can be decomposed into two well separated clusters: one containing eigenvalues with large negative real parts and one containing (possibly unstable) eigenvalues close to the origin

How mobile are protons in the structure of dental glass ionomer cements?

The development of dental materials with improved properties and increased longevity can save costs and minimize discomfort for patients. Due to their good biocompatibility, glass ionomer cements are an interesting restorative option. However, these cements have limited mechanical strength to survive in the challenging oral environment. Therefore, a better understanding of the structure and hydration process of these cements can bring the necessary understanding to further developments. Neutrons and X-rays have been used to investigate the highly complex pore structure, as well as to assess the hydrogen mobility within these cements. Our findings suggest that the lower mechanical strength in glass ionomer cements results not only from the presence of pores, but also from the increased hydrogen mobility within the material. The relationship between microstructure, hydrogen mobility and strength brings insights into the material's durability, also demonstrating the need and opening the possibility for further research in these dental cements