Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/ . Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under la

Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians

In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians. We introduce the notion of an input-Koopman operator, and show how input-Koopman operators can be used to cast a nonlinear system into the classical state-space form, and identify conditions under which input and state observable functions are well separated. We then extend an existing method of dynamic mode decomposition for learning Koopman operators from data known as deep dynamic mode decomposition to systems with controls or disturbances. We illustrate the accuracy of the method in learning an input-state separable Koopman operator for an example system, even when the underlying system exhibits mixed state-input terms. We next introduce a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes internal subsystem observability and disturbance rejection from unwanted noise from other subsystems. We derive a relaxation based on Koopman Gramians and multi-way partitioning for the resulting NP-hard decomposition problem. We lastly illustrate the proposed algorithm with the swing dynamics for an IEEE 39-bus system.Comment: 8 pages, submitted to IEEE 2018 AC

Research and Technology

Langley Research Center is engaged in the basic an applied research necessary for the advancement of aeronautics and space flight, generating advanced concepts for the accomplishment of related national goals, and provding research advice, technological support, and assistance to other NASA installations, other government agencies, and industry. Highlights of major accomplishments and applications are presented

Aeronautical engineering: A continuing bibliography with indexes (supplement 216)

This bibliography lists 505 reports, articles and other documents introduced into the NASA scientific and technical information system in July, 1987

Role of Surface Gravity Waves in Aquaplanet Ocean Climates

We present a set of idealised numerical experiments of a solstitial aquaplanet ocean and examine the thermodynamic and dynamic implications of surface gravity waves (SGWs) upon its mean state. The aquaplanet's oceanic circulation is dominated by an equatorial zonal jet and four Ekman driven meridional overturning circulation (MOC) cells aligned with the westerly atmospheric jet streams and easterly trade winds in both hemispheres. Including SGW parameterization (representing modulations of air-sea momentum fluxes, Langmuir circulation and Stokes-Coriolis force) increases mixed layer vertical momentum diffusivity by approx. 40% and dampens surface momentum fluxes by approx. 4%. The correspondingly dampened MOC impacts the oceanic density structure to 1 km depth by lessening the large-scale advective transports of heat and salt, freshening the equatorial latitudes (where evaporation minus precipitation [E-P] is negative) and increasing salinity in the subtropics (where E-P is positive) by approx. 1%. The midlatitude pycnocline in both hemispheres is deepened by the inclusion of SGWs. Including SGWs into the aquaplanet ocean model acts to increase mixed layer depth by approx. 10% (up to 20% in the wintertime in midlatitudes), decrease vertical shear in the upper 200 m and alter local midlatitude buoyancy frequency. Generally, the impacts of SGWs upon the aquaplanet ocean are found to be consistent across cooler and warmer climates. We suggest that the implications of these simulations could be relevant to understanding future projections of SGW climate, exoplanetary oceans, and the dynamics of the Southern Ocean mixed layer

Methodological and empirical challenges in modelling residential location choices

The modelling of residential locations is a key element in land use and transport planning. There are significant empirical and methodological challenges inherent in such modelling, however, despite recent advances both in the availability of spatial datasets and in computational and choice modelling techniques. One of the most important of these challenges concerns spatial aggregation. The housing market is characterised by the fact that it offers spatially and functionally heterogeneous products; as a result, if residential alternatives are represented as aggregated spatial units (as in conventional residential location models), the variability of dwelling attributes is lost, which may limit the predictive ability and policy sensitivity of the model. This thesis presents a modelling framework for residential location choice that addresses three key challenges: (i) the development of models at the dwelling-unit level, (ii) the treatment of spatial structure effects in such dwelling-unit level models, and (iii) problems associated with estimation in such modelling frameworks in the absence of disaggregated dwelling unit supply data. The proposed framework is applied to the residential location choice context in London. Another important challenge in the modelling of residential locations is the choice set formation problem. Most models of residential location choices have been developed based on the assumption that households consider all available alternatives when they are making location choices. Due the high search costs associated with the housing market, however, and the limited capacity of households to process information, the validity of this assumption has been an on-going debate among researchers. There have been some attempts in the literature to incorporate the cognitive capacities of households within discrete choice models of residential location: for instance, by modelling households’ choice sets exogenously based on simplifying assumptions regarding their spatial search behaviour (e.g., an anchor-based search strategy) and their characteristics. By undertaking an empirical comparison of alternative models within the context of residential location choice in the Greater London area this thesis investigates the feasibility and practicality of applying deterministic choice set formation approaches to capture the underlying search process of households. The thesis also investigates the uncertainty of choice sets in residential location choice modelling and proposes a simplified probabilistic choice set formation approach to model choice sets and choices simultaneously. The dwelling-level modelling framework proposed in this research is practice-ready and can be used to estimate residential location choice models at the level of dwelling units without requiring independent and disaggregated dwelling supply data. The empirical comparison of alternative exogenous choice set formation approaches provides a guideline for modellers and land use planners to avoid inappropriate choice set formation approaches in practice. Finally, the proposed simplified choice set formation model can be applied to model the behaviour of households in online real estate environments.Open Acces

Stochastic Structural Stability Theory applied to roll/streak formation in boundary layer shear flow

Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this work SSST is applied to the problem of understanding the formation of the roll/streak structures that arise from free-stream turbulence (FST) and are associated with bypass transition in boundary layers. Roll structures in the cross-stream/spanwise plane and associated streamwise streaks are shown to arise as a linear instability of interaction between the FST and the mean flow. In this interaction incoherent Reynolds stresses arising from FST are organized by perturbation streamwise streaks to coherently force perturbation rolls giving rise to an amplification of the streamwise streak perturbation and through this feedback to an instability of the combined roll/streak/turbulence complex. The dominant turbulent perturbation structures involved in supporting the roll/streak/turbulence complex instability are non-normal optimal perturbations with the form of oblique waves. The cooperative linear instability giving rise to the roll/streak structure arises at a bifurcation in the parameter of STM excitation parameter. This structural instability eventually equilibrates nonlinearly at finite amplitude and although the resulting statistical equilibrium streamwise streaks are inflectional the associated flows are stable. Formation and equilibration of the roll/streak structure by this mechanism can be traced to the non-normality which underlies interaction between perturbations and mean flows in modally stable systems.Comment: 16 pages, 24 figures, has been submitted for publication to Physics of Fluid

Phenotypic Variation and Bistable Switching in Bacteria

Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.

Nonlinear Dimensionality Reduction Methods in Climate Data Analysis

Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mapping algorithm, and Hessian locally linear embedding. I use these three methods to examine El Nino variability in the different data sets and assess the suitability of these nonlinear dimensionality reduction approaches for climate data analysis. I conclude that although, for the application presented here, analysis using NLPCA, Isomap and Hessian locally linear embedding does not provide additional information beyond that already provided by principal component analysis, these methods are effective tools for exploratory data analysis.Comment: 273 pages, 76 figures; University of Bristol Ph.D. thesis; version with high-resolution figures available from http://www.skybluetrades.net/thesis/ian-ross-thesis.pdf (52Mb download

On the Empty Miles of Ride-Sourcing Services: Theory, Observation and Countermeasures

The proliferation of smartphones in recent years has catalyzed the rapid growth of ride-sourcing services such as Uber, Lyft, and Didi Chuxing. Such on-demand e-hailing services significantly reduce the meeting frictions between drivers and riders and provide the platform with unprecedented flexibility and challenges in system management. A big issue that arises with service expansion is the empty miles produced by ride-sourcing vehicles. To overcome the physical and temporal frictions that separate drivers from customers and effectively reposition themselves towards desired destinations, ride-sourcing vehicles generate a significant number of vacant trips. These empty miles traveled result in inefficient use of the available fleet and increase traffic demand, posing substantial impacts on system operations. To tackle the issues, my dissertation is dedicated to deepening our understanding of the formation and the externalities of empty miles, and then proposing countermeasures to bolster system performance. There are two essential and interdependent contributors to empty miles generated by ride-sourcing vehicles: cruising in search of customers and deadheading to pick them up, which are markedly dictated by forces from riders, drivers, the platform, and policies imposed by regulators. In this dissertation, we structure our study of this complex process along three primary axes, respectively centered on the strategies of a platform, the behaviors of drivers, and the concerns of government agencies. In each axis, theoretical models are established to help understand the underlying physics and identify the trade-offs and potential issues that drive behind the empty miles. Massive data from Didi Chuxing, a dominant ride-sourcing company in China, are leveraged to evidence the presence of matters discussed in reality. Countermeasures are then investigated to strengthen management upon the empty miles, balance the interests of different stakeholders, and improve the system performance. Although this dissertation scopes out ride-sourcing services, the models, analyses, and solutions can be readily adapted to address related issues in other types of shared-use mobility services.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163209/1/xzt_1.pd