An algebraic extension of Dirac quantization: Examples

An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of non-linear, diffeomorphism invariant theories such as general relativity. Recently, an extension of the required type was proposed by one of us using algebraic quantization methods. In this paper, the key conceptual and technical aspects of the algebraic program are illustrated through a number of finite dimensional examples. The choice of examples and some of the analysis is motivated by certain peculiar problems endemic to quantum gravity. However, prior knowledge of general relativity is not assumed in the main discussion. Indeed, the methods introduced and conclusions arrived at are applicable to any system with first class constraints. In particular, they resolve certain technical issues which are present also in the reduced phase space approach to quantization of these systems.Comment: 43 pages, Latex, CGPG-94/6-1. (References added; particularly to earlier work by C.J.Isham using group theoretic ideas, in the introduction.

Minisuperspaces: Observables and Quantization

A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or, Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit expressions of Dirac observables, i.e.\ phase space functions which commute weakly with the constraint. This, in turn, enables us to carry out a general quantization program to completion. We are also able to address the issue of time through ``deparametrization'' and discuss physical questions such as the fate of initial singularities in the quantum theory. We find that they persist in the quantum theory {\it inspite of the fact that the evolution is implemented by a 1-parameter family of unitary transformations}. Finally, certain of these models admit conditional symmetries which are explicit already prior to the canonical transformation. These can be used to pass to quantum theory following an independent avenue. The two quantum theories --based, respectively, on Dirac observables in the new canonical variables and conditional symmetries in the original ADM variables-- are compared and shown to be equivalent.Comment: 34 page

An algebraic approach to the quantization of cosntrained systems: finite dimensional examples

From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate non-canonical variables. In this dissertation I consider an algebraic formulation of the Dirac approach to the quantization of constrained systems, due to A. Ashtekar. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. I also clarify the role in quantum theory of possible algebraic identities between the elementary variables. I use this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to \gr, and may give some insight into the pitfalls lurking in \qg. In (spatially compact) general relativity, the Hamiltonian is constrained to vanish. I present various approaches one can take to obtain an interpretation of the quantum theory of such ``dynamically constrained'' systems. I apply some of these ideas to the Bianchi I cosmology, and analyze the issue of the initial singularity in quantum theory.Comment: 124 pages, LaTeX (run twice before printing), SU-GP-92/8-1. (Minor corruption (extra blank line at line 2994) hopefully fixed.

Time-of-arrival in quantum mechanics

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.Comment: Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev.

Trace gas/aerosol boundary concentrations and their impacts on continental-scale AQMEII modeling domains

Copyright 2011 Elsevier B.V., All rights reserved.Over twenty modeling groups are participating in the Air Quality Model Evaluation International Initiative (AQMEII) in which a variety of mesoscale photochemical and aerosol air quality modeling systems are being applied to continental-scale domains in North America and Europe for 2006 full-year simulations for model inter-comparisons and evaluations. To better understand the reasons for differences in model results among these participating groups, each group was asked to use the same source of emissions and boundary concentration data for their simulations. This paper describes the development and application of the boundary concentration data for this AQMEII modeling exercise. The European project known as GEMS (Global and regional Earth-system Monitoring using Satellite and in-situ data) has produced global-scale re-analyses of air quality for several years, including 2006 (http://gems.ecmwf.int). The GEMS trace gas and aerosol data were made available at 3-hourly intervals on a regular latitude/longitude grid of approximately 1.9° resolution within 2 "cut-outs" from the global model domain. One cut-out was centered over North America and the other over Europe, covering sufficient spatial domain for each modeling group to extract the necessary time- and space-varying (horizontal and vertical) concentrations for their mesoscale model boundaries. Examples of the impact of these boundary concentrations on the AQMEII continental simulations are presented to quantify the sensitivity of the simulations to boundary concentrations. In addition, some participating groups were not able to use the GEMS data and instead relied upon other sources for their boundary concentration specifications. These are noted, and the contrasting impacts of other data sources for boundary data are presented. How one specifies four-dimensional boundary concentrations for mesoscale air quality simulations can have a profound impact on the model results, and hence, this aspect of data preparation must be performed with considerable care.Peer reviewedFinal Accepted Versio

Numerical modelling of advanced modulation formats and WDM transmission

This thesis presents a theoretical investigation of the application of advanced modelling formats in high-speed fibre lightwave systems. The first part of this work focuses on numerical optimisation of dense wavelength division multiplexing (DWDM) system design. We employ advanced spectral domain filtering techniques and carrier pulse reshaping. We then apply these optimisation methods to investigate spectral and temporal domain characteristics of advanced modulation formats in fibre optic telecommunication systems. Next we investigate numerical methods used in detecting and measuring the system performance of advanced modulation formats. We then numerically study the combination of return-to-zero differential phase-shift keying (RZ-DPSK) with advanced photonic devices. Finally we analyse the dispersion management of Nx40 Gbit/s RZ-DPSK transmission applied to a commercial terrestrial lightwave system

Model evaluation and ensemble modelling of surface-level ozone in Europe and North America in the context of AQMEII

More than ten state-of-the-art regional air quality models have been applied as part of the Air Quality Model Evaluation International Initiative (AQMEII). These models were run by twenty independent groups in Europe and North America. Standardised modelling outputs over a full year (2006) from each group have been shared on the web-distributed ENSEMBLE system, which allows for statistical and ensemble analyses to be performed by each group. The estimated ground-level ozone mixing ratios from the models are collectively examined in an ensemble fashion and evaluated against a large set of observations from both continents. The scale of the exercise is unprecedented and offers a unique opportunity to investigate methodologies for generating skilful ensembles of regional air quality models outputs. Despite the remarkable progress of ensemble air quality modelling over the past decade, there are still outstanding questions regarding this technique. Among them, what is the best and most beneficial way to build an ensemble of members? And how should the optimum size of the ensemble be determined in order to capture data variability as well as keeping the error low? These questions are addressed here by looking at optimal ensemble size and quality of the members. The analysis carried out is based on systematic minimization of the model error and is important for performing diagnostic/probabilistic model evaluation. It is shown that the most commonly used multi-model approach, namely the average over all available members, can be outperformed by subsets of members optimally selected in terms of bias, error, and correlation. More importantly, this result does not strictly depend on the skill of the individual members, but may require the inclusion of low-ranking skill-score members. A clustering methodology is applied to discern among members and to build a skilful ensemble based on model association and data clustering, which makes no use of priori knowledge of model skill. Results show that, while the methodology needs further refinement, by optimally selecting the cluster distance and association criteria, this approach can be useful for model applications beyond those strictly related to model evaluation, such as air quality forecasting. (C) 2012 Elsevier Ltd. All rights reserved.Peer reviewe

Analysis of meteorology-chemistry interactions during air pollution episodes using online coupled models within AQMEII Phase-2

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).This study reviews the top ranked meteorology and chemistry interactions in online coupled models recommended by an experts’ survey conducted in COST Action EuMetChem and examines the sensitivity of those interactions during two pollution episodes: the Russian forest fires 25 Jul -15 Aug 2010 and a Saharan dust transport event from 1 Oct -31 Oct 2010 as a part of the AQMEII phase-2 exercise. Three WRF-Chem model simulations were performed for the forest fire case for a baseline without any aerosol feedback on meteorology, a simulation with aerosol direct effects only and a simulation including both direct and indirect effects. For the dust case study, eight WRF-Chem and one WRF-CMAQ simulations were selected from the set of simulations conducted in the framework of AQMEII. Of these two simulations considered no feedbacks, two included direct effects only and five simulations included both direct and indirect effects. The results from both episodes demonstrate that it is important to include the meteorology and chemistry interactions in online-coupled models. Model evaluations using routine observations collected in AQMEII phase-2 and observations from a station in Moscow show that for the fire case the simulation including only aerosol direct effects has better performance than the simulations with no aerosol feedbacks or including both direct and indirect effects. The normalized mean biases are significantly reduced by 10-20% for PM10 when including aerosol direct effects. The analysis for the dust case confirms that models perform better when including aerosol direct effects, but worse when including both aerosol direct and indirect effects, which suggests that the representation of aerosol indirect effects needs to be improved in the model.Peer reviewedFinal Published versio

Fumigant toxicity of essential oils and their combinations on population buildup of three stored product coleoptera in stored wheat and effect on quality of wheat: Poster

Experiments carried out to find the fumigant toxicity of three essential oils and their combinations from Murraya koenigii, Citrus reticulata, Curcuma longa on population buildup of Sitophilus oryzae, Rhyzopertha dominica, Tribolium castaneum in stored wheat at different days of infestation. The oil of M. koenigii, C. reticulata at 0.2% and M. koenigii+C. reticulata, M. koenigii+C. longa at 0.1% each were found highly effective against S. oryzae fumigated after 5, 10, 15 and 20 days. The oil of M. koenigii and C. reticulata at 0.2% M. koenigii+C. reticulata, M. koenigii+C. longa, C. reticulata+C. longa at 0.1% each and M. koenigii+C. reticulata+C. longa at 0.07% each were found highly effective against R. dominica fumigated after 5, 10, 15 and 20 days. Only M. koenigii at 0.2% was found highly effective against T. castaneum fumigated after 5, 10, 15 and 20 day. The fumigation of grain with M. koenigii at 0.2% completely suppress the infestation and weight loss when it was fumigated after 5, 10, 15 and 20 days while very low infestation and weight loss was observed in grain treated with M. koenigii +C. reticulata at 0.1% each and not affect the organoleptic properties and germination of wheat.Experiments carried out to find the fumigant toxicity of three essential oils and their combinations from Murraya koenigii, Citrus reticulata, Curcuma longa on population buildup of Sitophilus oryzae, Rhyzopertha dominica, Tribolium castaneum in stored wheat at different days of infestation. The oil of M. koenigii, C. reticulata at 0.2% and M. koenigii+C. reticulata, M. koenigii+C. longa at 0.1% each were found highly effective against S. oryzae fumigated after 5, 10, 15 and 20 days. The oil of M. koenigii and C. reticulata at 0.2% M. koenigii+C. reticulata, M. koenigii+C. longa, C. reticulata+C. longa at 0.1% each and M. koenigii+C. reticulata+C. longa at 0.07% each were found highly effective against R. dominica fumigated after 5, 10, 15 and 20 days. Only M. koenigii at 0.2% was found highly effective against T. castaneum fumigated after 5, 10, 15 and 20 day. The fumigation of grain with M. koenigii at 0.2% completely suppress the infestation and weight loss when it was fumigated after 5, 10, 15 and 20 days while very low infestation and weight loss was observed in grain treated with M. koenigii +C. reticulata at 0.1% each and not affect the organoleptic properties and germination of wheat