578 research outputs found
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
-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 where is the
Boltzmann constant, the interface tension and 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 , the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of for which it is close to the primary bifurcation from the normal state. These values of form a curve in the -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]
Regular and quasi black hole solutions for spherically symmetric charged dust distributions in the Einstein-Maxwell theory
Static spherically symmetric distributions of electrically counterpoised dust
(ECD) are used to construct solutions to Einstein-Maxwell equations in
Majumdar--Papapetrou formalism. Unexpected bifurcating behaviour of solutions
with regard to source strength is found for localized, as well as for the
delta-function ECD distributions. Unified treatment of general ECD
distributions is accomplished and it is shown that for certain source strengths
one class of regular solutions approaches Minkowski spacetime, while the other
comes arbitrarily close to black hole solutions.Comment: LaTeX (IOP style) 17 pages, 10 figure
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]
Water Dynamics in Shewanella oneidensis at Ambient and High Pressure using Quasi-Elastic Neutron Scattering
Quasielastic neutron scattering (QENS) is an ideal technique for studying water transport and relaxation dynamics at pico-to nanosecond timescales and at length scales relevant to cellular dimensions. Studies of high pressure dynamic effects in live organisms are needed to understand Earth's deep biosphere and biotechnology applications. Here we applied QENS to study water transport in Shewanella oneidensis at ambient (0.1 MPa) and high (200 MPa) pressure using H/D isotopic contrast experiments for normal and perdeuterated bacteria and buffer solutions to distinguish intracellular and transmembrane processes. The results indicate that intracellular water dynamics are comparable with bulk diffusion rates in aqueous fluids at ambient conditions but a significant reduction occurs in high pressure mobility. We interpret this as due to enhanced interactions with macromolecules in the nanoconfined environment. Overall diffusion rates across the cell envelope also occur at similar rates but unexpected narrowing of the QENS signal appears between momentum transfer values Q = 0.7-1.1 Å-1 corresponding to real space dimensions of 6-9 Å. The relaxation time increase can be explained by correlated dynamics of molecules passing through Aquaporin water transport complexes located within the inner or outer membrane structures
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
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