Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

Ultralow noise field-effect transistor from multilayer graphene

We present low-frequency electrical resistance fluctuations, or noise, in graphene-based field-effect devices with varying number of layers. In single-layer devices, the noise magnitude decreases with increasing carrier density, which behaved oppositely in the devices with two or larger number of layers accompanied by a suppression in noise magnitude by more than two orders in the latter case. This behavior can be explained from the influence of external electric field on graphene band structure, and provides a simple transport-based route to isolate single-layer graphene devices from those with multiple layers. ©2009 American Institute of Physics

Genetic characterization of field-evolved resistance to phosphine in the rusty grain beetle, Cryptolestes ferrugineus (Laemophloeidae: Coleoptera)

Inheritance of resistance to phosphine fumigant was investigated in three field-collected strains of rusty grain beetle, Cryptolestes ferrugineus, Susceptible (S-strain), Weakly Resistant (Weak-R) and Strongly Resistant (Strong-R). The strains were purified for susceptibility, weak resistance and strong resistance to phosphine, respectively, to ensure homozygosity of resistance genotype. Crosses were established between S-strain × Weak-R, S-strain × Strong-R and Weak-R × Strong-R, and the dose mortality responses to phosphine of these strains and their F1, F2 and F1-backcross progeny were obtained. The fumigations were undertaken at 25 °C and 55% RH for 72 h. Weak-R and Strong-R showed resistance factors of 6.3 × and 505 × compared with S-strain at the LC50. Both weak and strong resistances were expressed as incompletely recessive with degrees of dominance of − 0.48 and − 0.43 at the LC50, respectively. Responses of F2 and F1-backcross progeny indicated the existence of one major gene in Weak-R, and at least two major genes in Strong-R, one of which was allelic with the major factor in Weak-R. Phenotypic variance analyses also estimated that the number of independently segregating genes conferring weak resistance was 1 (nE = 0.89) whereas there were two genes controlling strong resistance (nE = 1.2). The second gene, unique to Strong-R, interacted synergistically with the first gene to confer a very high level of resistance (~ 80 ×). Neither of the two major resistance genes was sex linked. Despite the similarity of the genetics of resistance to that previously observed in other pest species, a significant proportion (~ 15 to 30%) of F1 individuals survived at phosphine concentrations higher than predicted. Thus it is likely that additional dominant heritable factors, present in some individuals in the population, also influenced the resistance phenotype. Our results will help in understanding the process of selection for phosphine resistance in the field which will inform resistance management strategies. In addition, this information will provide a basis for the identification of the resistance genes.

Genetic characterization of field-evolved resistance to phosphine in the rusty grain beetle, Cryptolestes ferrugineus (Laemophloeidae: Coleoptera)

Inheritance of resistance to phosphine fumigant was investigated in three field-collected strains of rusty grain beetle, Cryptolestes ferrugineus, Susceptible (S-strain), Weakly Resistant (Weak-R) and Strongly Resistant (Strong-R). The strains were purified for susceptibility, weak resistance and strong resistance to phosphine, respectively, to ensure homozygosity of resistance genotype. Crosses were established between S-strain × Weak-R, S-strain × Strong-R and Weak-R × Strong-R, and the dose mortality responses to phosphine of these strains and their F1, F2 and F1-backcross progeny were obtained. The fumigations were undertaken at 25 °C and 55% RH for 72 h. Weak-R and Strong-R showed resistance factors of 6.3 × and 505 × compared with S-strain at the LC50. Both weak and strong resistances were expressed as incompletely recessive with degrees of dominance of − 0.48 and − 0.43 at the LC50, respectively. Responses of F2 and F1-backcross progeny indicated the existence of one major gene in Weak-R, and at least two major genes in Strong-R, one of which was allelic with the major factor in Weak-R. Phenotypic variance analyses also estimated that the number of independently segregating genes conferring weak resistance was 1 (nE = 0.89) whereas there were two genes controlling strong resistance (nE = 1.2). The second gene, unique to Strong-R, interacted synergistically with the first gene to confer a very high level of resistance (~ 80 ×). Neither of the two major resistance genes was sex linked. Despite the similarity of the genetics of resistance to that previously observed in other pest species, a significant proportion (~ 15 to 30%) of F1 individuals survived at phosphine concentrations higher than predicted. Thus it is likely that additional dominant heritable factors, present in some individuals in the population, also influenced the resistance phenotype. Our results will help in understanding the process of selection for phosphine resistance in the field which will inform resistance management strategies. In addition, this information will provide a basis for the identification of the resistance genes.

Editorial of "International Journal of Critical Indigenous Studies Volume 1, Number 1, 2008"

We perceive the epistemological boundaries of Critical Indigenous Studies as marked by analyses of contemporary colonising power in its multiple forms in different contexts. This first issue brings together a diverse group of international Indigenous scholars who are politically and intellectually engaged in theorising from their respective standpoints as well as spatial and geographic locations. As such these essays enable dialogue across and within different colonial power contexts addressing epistemological ethical and methodological concerns within the broad field of Indigenous studies. In each essay a connecting theme is the need for intercultural and comparative work and to import Indigenous agency in the writing of history...

Editorial of "International Journal of Critical Indigenous Studies Volume 4, Number 1, 2011"

This special edition of the International Journal of Critical Indigenous Studies highlights the work of emerging scholars in the field of Indigenous Studies. The five featured authors were all finalists for the prize awarded by the Native American and Indigenous Studies Association (NAISA) to the best post-graduate student paper at the NAISA meeting held in 2010 in Tucson, Arizona. While the breadth of scholarship encompassed by the term ‘Indigenous Studies’ and the global representation of Indigenous peoples at NAISA mean that the topics and approaches vary widely, a common thematic of fraught post-colonial relations can be discerned within all five articles.

A conditional random field-based downscaling method for assessment of climate change impact on multisite daily precipitation in the Mahanadi basin

Downscaling to station-scale hydrologic variables from large-scale atmospheric variables simulated by general circulation models (GCMs) is usually necessary to assess the hydrologic impact of climate change. This work presents CRF-downscaling, a new probabilistic downscaling method that represents the daily precipitation sequence as a conditional random field (CRF). The conditional distribution of the precipitation sequence at a site, given the daily atmospheric (large-scale) variable sequence, is modeled as a linear chain CRF. CRFs do not make assumptions on independence of observations, which gives them flexibility in using high-dimensional feature vectors. Maximum likelihood parameter estimation for the model is performed using limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. Maximum a posteriori estimation is used to determine the most likely precipitation sequence for a given set of atmospheric input variables using the Viterbi algorithm. Direct classification of dry/wet days as well as precipitation amount is achieved within a single modeling framework. The model is used to project the future cumulative distribution function of precipitation. Uncertainty in precipitation prediction is addressed through a modified Viterbi algorithm that predicts the n most likely sequences. The model is applied for downscaling monsoon (June-September) daily precipitation at eight sites in the Mahanadi basin in Orissa, India, using the MIROC3.2 medium-resolution GCM. The predicted distributions at all sites show an increase in the number of wet days, and also an increase in wet day precipitation amounts. A comparison of current and future predicted probability density functions for daily precipitation shows a change in shape of the density function with decreasing probability of lower precipitation and increasing probability of higher precipitation.

Entanglement production due to quench dynamics of an anisotropic XY chain in a transverse field

We compute concurrence and negativity as measures of two-spin entanglement generated by a power-law quench (characterized by a rate tau(-1) and an exponent alpha) which takes an anisotropic XY chain in a transverse field through a quantum critical point (QCP). We show that only spins separated by an even number of lattice spacings get entangled in such a process. Moreover, there is a critical rate of quench, tau(-1)(c), above which no two-spin entanglement is generated; the entire entanglement is multipartite. The ratio of the entanglements between consecutive even neighbors can be tuned by changing the quench rate. We also show that for large tau, the concurrence (negativity) scales as root alpha/tau(alpha/tau), and we relate this scaling behavior to defect production by the quench through a QCP.

The dielectric coated conducting sphere - modal and near field characteristics.

A modal analysis and near-field study for a dielectric-coated conducting sphere excited by a delta function electric field source has been made. The structure can support an infinite number of modes theoretically. For equatorial excitation only odd order modes are excited, whereas for non-equatorial excitation both even and odd order modes are excited. The variation of the amplitude coefficients both internal and external exhibit a different nature of variation with respect to the various structure parameters for different modes. The field distributions both in the r and theta directions for non-equatorial excitation show good agreement between theory and experiment for the strongest mode.

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion. induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.

The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Algebraic distributed space-time codes with low ML decoding complexity

"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic constructions of full diversity Distributed Space-Time Codes (DSTCs) are provided for any power of two number of relays. The left regular matrix representation has been shown to naturally result in space-time codes meeting the additional constraints required for DSTCs. The DSTCs so constructed have the salient feature of reduced Maximum Likelihood (ML) decoding complexity. In particular, the ML decoding of these codes can be performed by applying the lattice decoder algorithm on a lattice of four times lesser dimension than what is required in general. Moreover these codes have a uniform distribution of power among the relays and in time, thus leading to a low Peak to Average Power Ratio at the relays.

Multiple excitation nano-spot generation and confocal detection for far-field microscopy

An imaging technique is developed for the controlled generation of multiple excitation nano-spots for far-field microscopy. The system point spread function (PSF) is obtained by interfering two counter-propagating extended depth-of-focus PSF (DoF-PSF), resulting in highly localized multiple excitation spots along the optical axis. The technique permits (1) simultaneous excitation of multiple planes in the specimen; (2) control of the number of spots by confocal detection; and (3) overcoming the point-by-point based excitation. Fluorescence detection from the excitation spots can be efficiently achieved by Z-scanning the detector/pinhole assembly. The technique complements most of the bioimaging techniques and may find potential application in high resolution fluorescence microscopy and nanoscale imaging.

Field performance of in-service cast iron gas reticulation pipe buried in reactive clay

Field instrumentation of an in-service cast iron gas pipe buried in a residential area is detailed in this paper. The aim of the study was to monitor the long-term pipe behavior to understand the mechanisms of pipe bending in relation to ground movement as a result of seasonal fluctuation of soil moisture content. Field data showed that variation of soil temperature, suction, and moisture content are closely related to the prevailing climate. Change of soil temperature is generally related to the ambient air temperature, with a variation of approximately −3°C −3°C per meter depth from the ground surface in summer (decrease with depth) and winter (increase with depth). Seasonal cyclic variation in moisture content was observed with maxima in February and March, and a minimum around September. The pipe top was under tensile strain during summer and subsequently subjected to compressive strain as soil swelling occurred as a result of increase in moisture content. The study suggests that downward pipe bending occurs in summer because of soil shrinkage, while upward pipe bending occurs in winter when the soil swells.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.