Shear-induced bifurcations and chaos in models of three coupled lasers

Copyright © 2011 Society for Industrial and Applied MathematicsWe study nonlinear dynamics in a linear array of three coupled laser oscillators with rotational $\mathbb{S}^1$ and reflectional $\mathbb{Z}_2$ symmetry. The focus is on a coupled-laser model with dependence on three parameters: laser coupling strength, $\kappa$, laser frequency detuning, $\Delta$, and degree of coupling between the amplitude and phase of the laser, $\alpha$, also known as shear or nonisochronicity. Numerical bifurcation analysis is used in conjunction with Lyapunov exponent calculations to study the different aspects of the system dynamics. First, the shape and extent of regions with stable phase locking in the $(\kappa,\Delta)$ plane change drastically with $\alpha$. We explain these changes in terms of codimension-two and -three bifurcations of (relative) equilibria. Furthermore, we identify locking-unlocking transitions due to global homoclinic and heteroclinic bifurcations and the associated infinite cascades of local bifurcations. Second, vast regions of deterministic chaos emerge in the $(\kappa,\Delta)$ plane for nonzero $\alpha$. We give an intuitive explanation of this effect in terms of $\alpha$-induced stretch-and-fold action that creates horseshoes and discuss chaotic attractors with different topologies. Similar analysis of a more accurate composite-cavity mode model reveals good agreement with the coupled-laser model on the level of local and global bifurcations as well as chaotic dynamics, provided that coupling between lasers is not too strong. The results give new insight into modeling approaches and methodologies for studying nonlinear behavior of laser arrays

A Journey Through the Dynamical World of Coupled Laser Oscillators

The focus of this thesis is the dynamical behaviour of linear arrays of laser oscillators with nearest-neighbour coupling. In particular, we study how laser dynamics are influenced by laser-coupling strength, $\kappa$, the natural frequencies of the uncoupled lasers, $\tilde{\Omega}_j$, and the coupling between the magnitude and phase of each lasers electric field, $\alpha$. Equivariant bifurcation analysis, combined with Lyapunov exponent calculations, is used to study different aspects of the laser dynamics. Firstly, codimension-one and -two bifurcations of relative equilibria determine the laser coupling conditions required to achieve stable phase locking. Furthermore, we find that global bifurcations and their associated infinite cascades of local bifurcations are responsible for interesting locking-unlocking transitions. Secondly, for large $\alpha$, vast regions of the parameter space are found to support chaotic dynamics. We explain this phenomenon through simulations of $\alpha$-induced stretching-and-folding of the phase space that is responsible for the creation of horseshoes. A comparison between the results of a simple {\it coupled-laser model} and a more accurate {\it composite-cavity mode model} reveals a good agreement, which further supports the use of the simpler model to study coupling-induced instabilities in laser arrays. Finally, synchronisation properties of the laser array are studied. Laser coupling conditions are derived that guarantee the existence of synchronised solutions where all the lasers emit light with the same frequency and intensity. Analytical stability conditions are obtained for two special cases of such laser synchronisation: (i) where all the lasers oscillate in-phase with each other and (ii) where each laser oscillates in anti-phase with its direct neighbours. Transitions from complete synchronisation (where all the lasers synchronise) to optical turbulence (where no lasers synchronise and each laser is chaotic in time) are studied and explained through symmetry breaking bifurcations. Lastly, the effect of increasing the number of lasers in the array is discussed in relation to persistent optical turbulence

A qualitative study of subjective male identities among South African adolescents in rural and urban settings using a photo-narrative method.

Thesis (M.A.)-University of KwaZulu-Natal, Pietermaritzburg, 2005.Masculinity is a relevant and important research priority in South Africa, where problematic constructions of adolescent masculinity are linked with a range of health issues and psychosocial risks. The theoretical basis for this qualitative research study was social constructionism informed by dialogical theory and psychoanalytic accounts of masculinity, including Kristeva's theory of abjection. The overall aim was to explore the lived experience of adolescent boys in order to understand how boys are subjectively positioned in relation to hegemonic standards for 'acceptable' masculinity in social contexts. Following ethical guidelines, boys were purposively sampled for the study from two school settings, a 'multicultural' urban single-sex school and a 'monoracial' rural coeducational secondary. A mixed method approach was used - a photo-narrative visual research method, focus groups and semi-structured interviews within a constructionist paradigm. Visual and verbal data was analysed by means of an integrated quantitative content analysis and qualitative narrative analysis. Findings suggested that hegemonic standards were experienced in different ways by boys in terms of subjective positioning and microcultural context. Peer-groups were identified as having major importance for adolescent boys as a means of validating masculine norms, with sport functioning as an important masculinity marker. A central finding was that peer group norms created the conditions for inclusion and exclusion, which in turn lead to the construction of 'acceptable identities'. Performative 'doing' and symbolic 'having' were identified as two important ways of constructing masculinity - ways that were not always in accord. Another important finding was that boys battled to create even a rough congruence between masculinity norms and an authentic sense of self. There was a convergence around hegemonic norms of toughness, emphasised heterosexuality and displayed risk-taking across contexts; however, these norms were understood in different ways. Non-relational and objectified sex talk was a strong focus of hegemonic masculinity for most boys in the study. Toughness was understood as alternatively verbal, performative or physical, and these differences were linked to racial and cultural differences. Similarly, there were racial and cultural differences in how expressions of masculinity were 'commodified'. Hybridised identities emerged from the multicultural context of School A but not in the monoracial context of School B. Based on the findings that boys occupied several positions simultaneously and experienced contradiction among various identity positions, it was suggested that Connell's masculinity framework provided only a limited macrosociological perspective that neglected the ambiguities of masculine subjectivity. The study identified a range of means by which boys negotiated distances for alternative masculinities outside of hegemonic standards. The collective pressure of meeting an illusory and unattainable standard of masculine acceptability was identified as a source of conflict and anxiety for most of the boys in this study. This anxiety was managed in various ways including finding alternative constructions of masculinity in sub-cultural contexts, religious experience and in traditional cultural practices. These findings have implications for programmes and policies that address issues of masculinity in relation to the challenges and risks facing adolescent boys in South Africa

Investigating the distribution of polybrominated diphenyl ethers through an Australian wastewater treatment plant

The aim of this study was to quantify the amount of polybrominated diphenyl ethers (PBDEs) released into the environment (biosolids, effluent) from a conventional Australian activated sludge treatment wastewater treatment plant (WWTP). The concentration of PBDE congeners was measured at various treatment stages and included four aqueous samples (raw, primary, secondary and tertiary effluents) and three sludges (primary, secondary and lime stabilized biosolids), collected at three sampling events over the course of the experiment (29 days). Semi-permeable membrane devices (SPMDs) were also installed for the duration of the experiment, the first time that SPMDs have been used to measure PBDEs in a WWTP. Over 99% of the PBDEs entering the WWTP were removed through the treatment processes, principally by sedimentation. The main congeners detected were BDE 47, 99 and 209, which are characteristic of the two major commercial formulations viz penta-BDE and deca-BDE. All the PBDE congeners measured were highly correlated with each other, suggesting a similar origin. In this case, the PBDEs are thought to be from domestic sources since domestic wastewater is the main contribution to the in-flow (approximately 95%). The mean concentration of SigmaPBDEs in chemically stabilized sewage sludge (biosolids) was 300microg kg(-1) dry weight. It is calculated that 2.3+/-0.3kg of PBDEs are disposed of each year with biosolids generated from the WWTP. If all Australian sewage sludge is contaminated to at least this concentration then at least 110kg of PBDEs are associated with Australian sewage sludge annually. Less than 10g are released annually into the environment via ocean outfall and field irrigation; this level of contamination is unlikely to pose risk to humans or the environment. The environmental release of treated effluent and biosolids is not considered a large source of PBDE environmental emissions compared to the quantities used annually in Australia

Dioxin-like compounds in Australian sewage sludge - Review and national survey

An Australian survey of dioxin-like compounds in sewage sludge was conducted in two parts (a) a national survey, and (b) a time-study. All sewage sludge samples analysed as part of these studies had low overall concentrations of dioxin-like compounds. Out of 37 samples, all except one, were within the reported concentration range of soil within the Australian environment. The mean concentration of dioxin-like compounds in the Australian sewage sludge survey of 2006 was found to be 5.6 (s.d. 4.5) ng WHO05 TEQ kg-1 (n = 14) and were within the range of 1.2-15.3 ng WHO05 TEQ kg-1. All the Australian sewage sludge samples cited in these studies were below the Victorian EPA ''investigation limit'' of 50 ng WHO98 TEQ kg-1, and well below the European proposed guidelines of 100 ng I-TEQ kg-1. The burden of dioxin-like compounds in Australian sewage sludge is low and its land application as biosolids is not likely to pose a problem. A general positive relationship was found between population of the town producing the waste and both dioxin-like PCDD/Fs and dioxin-like PCBs. The one exception to this trend was sludge from a town that had a history of smelting and had a relatively high burden of dioxin-like compounds. Sludge from one rural WWTP also had a higher burden of dioxin-like compounds. The treatment plant services a geographically isolated town with a low population and no known emitters of dioxin-like compounds. However, this sample also had a relatively high burden of dioxin-like PCBs, which could be the source of the dioxin-like PCDD/Fs found in this sludge. The time study analyzing sludges from three WWTP from the same city between the years 2002 and 2006 found no apparent difference between WWTPs, but a statistically significant decline of 1.49 ng WHO05 TEQ kg-1 per year. Also, a comprehensive review of the scientific literature, presents typical levels and sources of dioxin-like compounds in international sewage sludges

Polybrominated diphenyl ethers and polybrominated biphenyls in Australian sewage sludge

This paper presents a brief review of the international scientific literature of polybrominated diphenyl ethers (PBDEs) and polybrominated biphenyls (PBBs) in sewage sludge and a survey of these compounds in sewage sludge from 16 Australian wastewater treatment plants (WWTPs). The ?PBDE mean concentration in the Australian study was 1137 ?g kg-1 dry weight (d.w.) (s.d. 1116) and ranged between 5 and 4 230 ?g kg-1 d.w. The urban mean of 1308 ?g kg-1 (s.d. 1320) and the rural mean of 911 ?g kg-1 (s.d. 831) are not statistically different and are similar to levels in European sludges. Principal components analysis was performed on the data set and revealed that 76% of the data variation could be explained by two components that corresponded to overall concentration of the pentaBDE and the decaBDE commercial formulations. An analysis of variance was performed comparing PBDEs levels at three WWTPs over the years 2005 and 2006, finding differences between treatment plants (BDE-47) but no significant difference in PBDE levels in the years 2005 and 2006. Low levels of BB-153 were detected in all samples of this survey (n = 16); mean 0.6 ?g kg-1 d.w. (s.d. 0.5). This compound has rarely been reported in any other study of sewage sludges undertaken outside Australia. This work highlights the need for a risk assessment of PBDEs in sewage sludge when used for land application, taking into account typical levels found in Australian sludges and soils

A rodent model of HIV protease inhibitor indinavir induced peripheral neuropathy

The research leading to these results is part of the EUROPAIN Collaboration, which has received support from the Innovative Medicines Initiative Joint Undertaking, under grant agreement no 115007, resources of which are composed of financial contribution from the European Union's Seventh Framework Program (FP7/2007‐2013) and EFPIA companies’ in kind contribution. We thank Pfizer for providing indinavir and gabapentin. MC received Conicyt grant (Folio 82130016),to complete this work.Peer reviewedPostprin

Study of 16 Portuguese activated sludge systems based on filamentous bacteria populations and their relationships with environmental parameters

A survey in 16 activated sludge waste water treatment plants (WWTP) was conducted to contribute to the knowledge of the environmental parameters that determine the composition of the filamentous community. A total of 128 samples of mixed liquor from municipal WWTP were collected during 2 years, and 22 filamentous morphotypes were identified. The most frequent and abundant filamentous bacteria were, in both cases and by this order, type 0041/0675, type 0092, Microthrix parvicella and 1851, nocardioforms and Haliscomenobacter hydrossis. Concerning dominance, type 1851 was the most frequently dominant morphotype, followed by M. parvicella and types 0092 and 0041/0675. These were also, and by this order, the dominant morphotypes during bulking occurrences. Significant correlations were obtained between the abundance of filamentous bacteria and environmental parameters, but multivariate statistical analysis only confirmed the correlation between type 0092 and Sludge Volume Index (SVI), emphasizing the association of this filament with bulking. The discussion of the results in light of published works was complicated by the random use of terms such as frequency, abundance, and dominance with different and often unclear meanings. This reinforces the need of clarifying these terms when discussing the causes of filamentous overgrowth in WWTP.Portuguese Foundation for Science and Technology (FCT) and the European Community fund FEDER, through Program COMPETE, in the ambit of the Projects FCOMP-01-0124-FEDER-007025 (PTDC/AMB/68393/2006), PEst-OE/EQB/LA0023/2013, RECI/BBB-EBI/0179/2012 (FCOMP-01-0124-FEDER-027462), and the Project BBioEnv - Biotechnology and Bioengineering for a sustainable world,REF. NORTE-07-0124- FEDER-000048, co-funded by the Programa Operacional Regional do Norte (ON.2 – O Novo Norte), QREN, FEDER. PhD grant SFRH/BD/64848/200

Effectiveness and energy requirements of pasteurisation for the treatment of unfiltered secondary effluent from a municipalwastewater treatment plant

Pasteurisation was investigated as a process to achieve high microbial quality standards in the recycling of water from unfiltered secondary effluents from a wastewater treatment plants in Melbourne, Australia. The relative heat sensitivity of key bacterial, viral, protozoan and helminth wastewater organisms (Escherichia coli, Enterococcus, FRNA bacteriophage, adenovirus, coxsackievirus, Cryptosporidium, and Ascaris) were determined by laboratory scale tests. The FRNA phage were found to be the most heat resistant, followed by enterococci and E. coli. Pilot scale challenge testing of a 2 ML/day pasteurisation pilot plant using unfiltered municipal wastewater and male specific coliphage (MS2) phage showed that temperatures between 69 °C and 75 °C achieved log reductions values between 0.9 ± 0.1 and 5.0 ± 0.5 respectively in the contact chamber. Fouling of the heat exchangers during operation using unfiltered secondary treated effluent was found to increase the energy consumption of the plant from 2.2 kWh/kL to 5.1 kWh/kL. The economic feasibility of pasteurisation for the current municipal application with high heat exchanger fouling potential can be expected to depend largely on the available waste heat from co-generation and on the efforts required to control fouling of the heat exchangers