DSpace Collection:https://dspace.lboro.ac.uk/2134/902017-10-17T14:48:26Z2017-10-17T14:48:26ZSemiclassical quantization with bifurcating orbitsBartsch, ThomasMain, JorgWunner, Gunterhttps://dspace.lboro.ac.uk/2134/267852017-10-02T10:34:25Z2002-01-01T00:00:00ZTitle: Semiclassical quantization with bifurcating orbits
Authors: Bartsch, Thomas; Main, Jorg; Wunner, Gunter
Abstract: Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra involving uniform approximations. As a prototype example,
the method is shown to yield excellent results for photo-absorption spectra for the hydrogen atom in an electric field in a spectral range where the abundance of bifurcations would render the standard closed-orbit formula without uniform approximations useless. Our method immediately applies to semiclassical trace formulae as well as closed-orbit theory and offers a general technique for the
semiclassical quantization of arbitrary systems.
Description: This paper was accepted for publication in the journal Physical Review A and the definitive published version is available at https://doi.org/10.1103/PhysRevA.66.0334042002-01-01T00:00:00ZMinimum distance estimation of Milky Way model parameters and related inferenceBanerjee, SourabhBasu, AyanendranathBhattacharya, SourabhBose, SmarajitChakrabarty, DaliaMukherjee, Soumendu S.https://dspace.lboro.ac.uk/2134/266662017-09-25T16:00:39Z2015-01-01T00:00:00ZTitle: Minimum distance estimation of Milky Way model parameters and related inference
Authors: Banerjee, Sourabh; Basu, Ayanendranath; Bhattacharya, Sourabh; Bose, Smarajit; Chakrabarty, Dalia; Mukherjee, Soumendu S.
Abstract: We propose a method to estimate the location of the Sun in the disk of the Milky Way using a
method based on the Hellinger distance and construct confidence sets on our estimate of the unknown
location using a bootstrap-based method. Assuming the Galactic disk to be two-dimensional, the
sought solar location then reduces to the radial distance separating the Sun from the Galactic center
and the angular separation of the Galactic center to Sun line, from a pre-fixed line on the disk. On
astronomical scales, the unknown solar location is equivalent to the location of us earthlings who
observe the velocities of a sample of stars in the neighborhood of the Sun. This unknown location
is estimated by undertaking pairwise comparisons of the estimated density of the observed set of
velocities of the sampled stars, with the density estimated using synthetic stellar velocity data
sets generated at chosen locations in the Milky Way disk. The synthetic data sets are generated
at a number of locations that we choose from within a constructed grid, at four different base
astrophysical models of the Galaxy. Thus, we work with one observed stellar velocity data and
four distinct sets of simulated data comprising a number of synthetic velocity data vectors, each
generated at a chosen location. For a given base astrophysical model that gives rise to one such
simulated data set, the chosen location within our constructed grid at which the estimated density
of the generated synthetic data best matches the density of the observed data is used as an estimate
for the location at which the observed data was realized. In other words, the chosen location
corresponding to the highest match offers an estimate of the solar coordinates in the Milky Way
disk. The “match” between the pair of estimated densities is parameterized by the affinity measure
based on the familiar Hellinger distance. We perform a novel cross-validation procedure to establish
a desirable “consistency” property of the proposed method.2015-01-01T00:00:00ZBayesian nonparametric estimation of Milky Way parameters using matrix-variate data in a new Gaussian Process-based methodChakrabarty, DaliaBiswas, MunmunBhattacharya, Sourabhhttps://dspace.lboro.ac.uk/2134/266642017-09-25T15:36:53Z2015-01-01T00:00:00ZTitle: Bayesian nonparametric estimation of Milky Way parameters using matrix-variate data in a new Gaussian Process-based method
Authors: Chakrabarty, Dalia; Biswas, Munmun; Bhattacharya, Sourabh
Abstract: In this paper we develop an inverse Bayesian approach to find the value of the unknown model parameter vector that supports the real (or test) data, where the data comprises measurements of a matrix-variate variable. The method is illustrated via the estimation of the unknown Milky Way feature parameter vector, using available test and simulated (training) stellar velocity data matrices. The data is represented as an unknown function of the model parameters, where this high-dimensional function is modelled using a high-dimensional Gaussian Process (GP). The model for this function is trained using available training data and inverted by Bayesian means, to estimate the sought value of the model parameter vector at which the test data is realised. We achieve a closed-form expression for the posterior of the unknown parameter vector and the parameters of the invoked GP, given test and training data. We perform model fitting by comparing the observed data with predictions made at different summaries of the posterior probability of the model parameter vector. As a supplement, we undertake a leave-one-out cross validation of our method.2015-01-01T00:00:00ZScattering of bulk strain solitary waves in bi-layers with delaminationKhusnutdinova, Karima R.Tranter, Matthew R.https://dspace.lboro.ac.uk/2134/266282017-09-22T12:59:52Z2017-01-01T00:00:00ZTitle: Scattering of bulk strain solitary waves in bi-layers with delamination
Authors: Khusnutdinova, Karima R.; Tranter, Matthew R.
Abstract: We study the scattering of longitudinal bulk strain solitary waves in delaminated bi-layers with different types of bonding. The direct numerical modelling of these problems is challenging and has natural limitations. We develop a semi-analytical approach, based on the use of several matched asymptotic multiple-scale expansions and the Integrability Theory of the Korteweg - de Vries equation by the Inverse Scattering Transform. We show that the semi-analytical approach agrees well with the direct numerical simulations and use it to study the scattering of different types of longitudinal bulk strain solitary waves in a wide range of bi-layers with delamination. In particular, we model the dynamics of a long longitudinal strain solitary wave in a symmetric perfectly bonded bi-layer with delamination. The numerical modelling confirms that delamination causes fission of an incident solitary wave and, thus, can be used to detect the defect. We then extend our approaches to the modelling of the waves in bi-layers with soft (“imperfect”) bonding, described by a system of coupled Boussinesq equations and supporting radiating solitary waves. The results may help us to control the integrity of layered structures.
Description: This paper was presented at the X International Conference on Structural Dynamics, EURODYN 2017, Rome, Italy, 10-13th September. This is an Open Access Article. It is published by Elsevier under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Licence (CC BY-NC-ND). Full details of this licence are available at: http://creativecommons.org/licenses/by-nc-nd/4.0/2017-01-01T00:00:00Z