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- Language: English
- Creators: Ira A. Fulton Schools of Engineering
Description
The emerging multimodal mobility as a service (MaaS) and connected and automated mobility (CAM) are expected to improve individual travel experience and entire transportation system performance in various aspects, such as convenience, safety, and reliability. There have been extensive efforts in the literature devoted to enhancing existing and developing new methodologies and tools to investigate the impacts and potentials of CAM systems. Due to the hierarchical nature of CAM systems and associated intrinsic correlated human factors and physical infrastructures from various resolutions, simply considering components across different levels into a single model may be practically infeasible and computationally prohibitive in operation and decision stages. One of the greatest challenges in existing studies is to construct a theoretically sound and computationally efficient architecture such that CAM system modeling can be performed in an inherently consistent cross-resolution manner. This research aims to contribute to the modeling of CAM systems on layered transportation networks, with a special focus on the following three aspects: (1) layered CAM system architecture with a tight network and modeling consistency, in which different levels of tasks can be efficiently performed at dedicated layers; (2) cross-resolution traffic state estimation in CAM systems using heterogeneous observations; and (3) integrated city logistics operation optimization in CAM for improving system performance.
ContributorsLu, Jiawei (Author) / Zhou, Xuesong (Thesis advisor) / Pendyala, Ram (Committee member) / Xue, Guoliang (Committee member) / Mittelmann, Hans (Committee member) / Arizona State University (Publisher)
Created2022
Description
Earth-system models describe the interacting components of the climate system and
technological systems that affect society, such as communication infrastructures. Data
assimilation addresses the challenge of state specification by incorporating system
observations into the model estimates. In this research, a particular data
assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is
applied to the ionosphere, which is a domain of practical interest due to its effects
on infrastructures that depend on satellite communication and remote sensing. This
dissertation consists of three main studies that propose strategies to improve space-
weather specification during ionospheric extreme events, but are generally applicable
to Earth-system models:
Topic I applies the LETKF to estimate ion density with an idealized model of
the ionosphere, given noisy synthetic observations of varying sparsity. Results show
that the LETKF yields accurate estimates of the ion density field and unobserved
components of neutral winds even when the observation density is spatially sparse
(2% of grid points) and there is large levels (40%) of Gaussian observation noise.
Topic II proposes a targeted observing strategy for data assimilation, which uses
the influence matrix diagnostic to target errors in chosen state variables. This
strategy is applied in observing system experiments, in which synthetic electron density
observations are assimilated with the LETKF into the Thermosphere-Ionosphere-
Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm.
Results show that assimilating targeted electron density observations yields on
average about 60%–80% reduction in electron density error within a 600 km radius of
the observed location, compared to 15% reduction obtained with randomly placed
vertical profiles.
Topic III proposes a methodology to account for systematic model bias arising
ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap-
plied with the TIEGCM during a geomagnetic storm, and is used to estimate the
spatiotemporal variations of bias in electron density predictions during the
transitionary phases of the geomagnetic storm. Results show that this strategy reduces
error in 1-hour predictions of electron density by about 35% and 30% in polar regions
during the main and relaxation phases of the geomagnetic storm, respectively.
technological systems that affect society, such as communication infrastructures. Data
assimilation addresses the challenge of state specification by incorporating system
observations into the model estimates. In this research, a particular data
assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is
applied to the ionosphere, which is a domain of practical interest due to its effects
on infrastructures that depend on satellite communication and remote sensing. This
dissertation consists of three main studies that propose strategies to improve space-
weather specification during ionospheric extreme events, but are generally applicable
to Earth-system models:
Topic I applies the LETKF to estimate ion density with an idealized model of
the ionosphere, given noisy synthetic observations of varying sparsity. Results show
that the LETKF yields accurate estimates of the ion density field and unobserved
components of neutral winds even when the observation density is spatially sparse
(2% of grid points) and there is large levels (40%) of Gaussian observation noise.
Topic II proposes a targeted observing strategy for data assimilation, which uses
the influence matrix diagnostic to target errors in chosen state variables. This
strategy is applied in observing system experiments, in which synthetic electron density
observations are assimilated with the LETKF into the Thermosphere-Ionosphere-
Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm.
Results show that assimilating targeted electron density observations yields on
average about 60%–80% reduction in electron density error within a 600 km radius of
the observed location, compared to 15% reduction obtained with randomly placed
vertical profiles.
Topic III proposes a methodology to account for systematic model bias arising
ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap-
plied with the TIEGCM during a geomagnetic storm, and is used to estimate the
spatiotemporal variations of bias in electron density predictions during the
transitionary phases of the geomagnetic storm. Results show that this strategy reduces
error in 1-hour predictions of electron density by about 35% and 30% in polar regions
during the main and relaxation phases of the geomagnetic storm, respectively.
ContributorsDurazo, Juan, Ph.D (Author) / Kostelich, Eric J. (Thesis advisor) / Mahalov, Alex (Thesis advisor) / Tang, Wenbo (Committee member) / Moustaoui, Mohamed (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2018
Description
Priced Managed Lanes (MLs) have been increasingly advocated as one of the effective ways to mitigating congestion in recent years. This study explores a new and innovative pricing strategy for MLs called Travel Time Refund (TTR). The proposed TTR provides an additional option to paying drivers that insures their travel time by issuing a refund to the toll cost if they do not reach their destination within specified travel times due to accidents or other unforeseen circumstances. Perceived benefits of TTR include raised public acceptance towards priced MLs, utilization increase of HOV/HOT lanes, overall congestion mitigation, and additional funding for relevant transportation agencies. To gauge travelers’ interests of TTR and to analyse its possible impacts, a stated preference (SP) survey was performed. An exploratory and statistical analysis of the survey responses revealed negative interest towards HOT and TTR option in accordance with common wisdom and previous studies. However, it is found that travelers are less negative about TTR than HOT alone; supporting the idea, that TTR could make HOT facilities more appealing. The impact of travel time reliability and latent variables representing psychological constructs on travelers’ choices in response to this new pricing strategy was also analysed. The results indicate that along with travel time and reliability, the decision maker’s attitudes and the level of comprehension of the concept of HOT and TTR play a significant role in their choice making. While the refund option may be theoretically and analytically feasible, the practical implementation issues cannot be ignored. This study also provides a discussion of the potential implementation considerations that include information provision to connected and non-connected vehicles, distinction between toll-only and refund customers, measurement of actual travel time, refund calculation and processing and safety and human factors issues. As the market availability of Connected and Automated Vehicles (CAVs) is prognosticated by 2020, the potential impact of such technologies on effective demand management, especially on MLs is worth investigating. Simulation analysis was performed to evaluate the system performance of a hypothetical road network at varying market penetration of CAVs. The results indicate that Connected Vehicles (CVs) could potentially encourage and enhance the use of MLs.
ContributorsVadlamani, Sravani (Author) / Lou, Yingyan (Thesis advisor) / Pendyala, Ram (Committee member) / Zhou, Xuesong (Committee member) / Grimm, Kevin (Committee member) / Arizona State University (Publisher)
Created2018
Description
Two urban flows are analyzed, one concerned with pollutant transport in a Phoenix, Arizona neighborhood and the other with windshear detection at the Hong Kong International Airport (HKIA).
Lagrangian measures, identified with finite-time Lyapunov exponents, are first used to characterize transport patterns of inertial pollutant particles. Motivated by actual events the focus is on flows in realistic urban geometry. Both deterministic and stochastic transport patterns are identified, as inertial Lagrangian coherent structures. For the deterministic case, the organizing structures are well defined and are extracted at different hours of a day to reveal the variability of coherent patterns. For the stochastic case, a random displacement model for fluid particles is formulated, and used to derive the governing equations for inertial particles to examine the change in organizing structures due to ``zeroth-order'' random noise. It is found that, (1) the Langevin equation for inertial particles can be reduced to a random displacement model; (2) using random noise based on inhomogeneous turbulence, whose diffusivity is derived from $k$-$\epsilon$ models, major coherent structures survive to organize local flow patterns and weaker structures are smoothed out due to random motion.
A study of three-dimensional Lagrangian coherent structures (LCS) near HKIA is then presented and related to previous developments of two-dimensional (2D) LCS analyses in detecting windshear experienced by landing aircraft. The LCS are contrasted among three independent models and against 2D coherent Doppler light detection and ranging (LIDAR) data. Addition of the velocity information perpendicular to the lidar scanning cone helps solidify flow structures inferred from previous studies; contrast among models reveals the intramodel variability; and comparison with flight data evaluates the performance among models in terms of Lagrangian analyses. It is found that, while the three models and the LIDAR do recover similar features of the windshear experienced by a landing aircraft (along the landing trajectory), their Lagrangian signatures over the entire domain are quite different - a portion of each numerical model captures certain features resembling those LCS extracted from independent 2D LIDAR analyses based on observations. Overall, it was found that the Weather Research and Forecast (WRF) model provides the best agreement with the LIDAR data.
Finally, the three-dimensional variational (3DVAR) data assimilation scheme in WRF is used to incorporate the LIDAR line of sight velocity observations into the WRF model forecast at HKIA. Using two different days as test cases, it is found that the LIDAR data can be successfully and consistently assimilated into WRF. Using the updated model forecast LCS are extracted along the LIDAR scanning cone and compare to onboard flight data. It is found that the LCS generated from the updated WRF forecasts are generally better correlated with the windshear experienced by landing aircraft as compared to the LIDAR extracted LCS alone, which suggests that such a data assimilation scheme could be used for the prediction of windshear events.
Lagrangian measures, identified with finite-time Lyapunov exponents, are first used to characterize transport patterns of inertial pollutant particles. Motivated by actual events the focus is on flows in realistic urban geometry. Both deterministic and stochastic transport patterns are identified, as inertial Lagrangian coherent structures. For the deterministic case, the organizing structures are well defined and are extracted at different hours of a day to reveal the variability of coherent patterns. For the stochastic case, a random displacement model for fluid particles is formulated, and used to derive the governing equations for inertial particles to examine the change in organizing structures due to ``zeroth-order'' random noise. It is found that, (1) the Langevin equation for inertial particles can be reduced to a random displacement model; (2) using random noise based on inhomogeneous turbulence, whose diffusivity is derived from $k$-$\epsilon$ models, major coherent structures survive to organize local flow patterns and weaker structures are smoothed out due to random motion.
A study of three-dimensional Lagrangian coherent structures (LCS) near HKIA is then presented and related to previous developments of two-dimensional (2D) LCS analyses in detecting windshear experienced by landing aircraft. The LCS are contrasted among three independent models and against 2D coherent Doppler light detection and ranging (LIDAR) data. Addition of the velocity information perpendicular to the lidar scanning cone helps solidify flow structures inferred from previous studies; contrast among models reveals the intramodel variability; and comparison with flight data evaluates the performance among models in terms of Lagrangian analyses. It is found that, while the three models and the LIDAR do recover similar features of the windshear experienced by a landing aircraft (along the landing trajectory), their Lagrangian signatures over the entire domain are quite different - a portion of each numerical model captures certain features resembling those LCS extracted from independent 2D LIDAR analyses based on observations. Overall, it was found that the Weather Research and Forecast (WRF) model provides the best agreement with the LIDAR data.
Finally, the three-dimensional variational (3DVAR) data assimilation scheme in WRF is used to incorporate the LIDAR line of sight velocity observations into the WRF model forecast at HKIA. Using two different days as test cases, it is found that the LIDAR data can be successfully and consistently assimilated into WRF. Using the updated model forecast LCS are extracted along the LIDAR scanning cone and compare to onboard flight data. It is found that the LCS generated from the updated WRF forecasts are generally better correlated with the windshear experienced by landing aircraft as compared to the LIDAR extracted LCS alone, which suggests that such a data assimilation scheme could be used for the prediction of windshear events.
ContributorsKnutson, Brent (Author) / Tang, Wenbo (Thesis advisor) / Calhoun, Ronald (Committee member) / Huang, Huei-Ping (Committee member) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2018
Description
This dissertation research is concerned with the study of two important traffic phenomena; merging and lane-specific traffic behavior. First, this research investigates merging traffic behavior through empirical analysis and evaluation of freeway merge ratios. Merges are important components of freeways and traffic behavior around them have a significant impact in the evolution and stability of congested traffic. At merges, drivers from conflicting traffic branches take turns to merge into a single stream at a rate referred to as the “merge ratio”. In this research, data from several freeway merges was used to evaluate existing macroscopic merge models and theoretical principles of merging behavior. Findings suggest that current merge ratio estimation methods can be insufficient to represent site-specific merge ratios, due to observed within-site variations and unaccounted effects of downstream merge geometry. To overcome these limitations, merge ratios were formulated based on their site-specific lane flow distribution (LFD), the proportion of flow in each freeway lane, for two types of merge geometries. Results demonstrate that the proposed methods are able to improve merge ratio estimates, reproduce within-site variations of merge ratio, and represent more effectively disproportionate redistribution of merging flow for merges where vehicles compete directly to merge due a downstream lane reduction.
Second, this research investigates lane-specific traffic behavior through empirical analysis and statistical modeling of lane flow distribution. Lane-specific traffic behavior is also an important component in evaluating freeway performance and has a significant impact in the mechanism of queue evolution, particularly around merges, and bottleneck discharge rate. In this research, site-specific linear LFD trends of three-lane congested freeways were investigated and modeled. A large-scale data collection process was implemented to systematically characterize the effects of several traffic and geometric features of freeways in the occurrence of between-site LFD variations. Also, an innovative three-stage modeling framework was used to model LFD behavior using multiple logistic regression to describe between-site LFD variations and Dirichlet regression to model recurrent combinations of linear LFD trends. This novel approach is able to represent both between and within site variations of LFD trends better, while accounting for the unit-sum constraint and distribution assumptions inherent of proportions data. Results revealed that proximity to freeway merges, a site’s level of congestion, and the presence of HOV lanes are significant factors that influence site-specific recurrent LFD behavior.
Findings from this work significantly improve the state-of-the-art knowledge on merging and lane-specific traffic behavior, which can help to improve traffic operations and reduce traffic congestion in freeways.
Second, this research investigates lane-specific traffic behavior through empirical analysis and statistical modeling of lane flow distribution. Lane-specific traffic behavior is also an important component in evaluating freeway performance and has a significant impact in the mechanism of queue evolution, particularly around merges, and bottleneck discharge rate. In this research, site-specific linear LFD trends of three-lane congested freeways were investigated and modeled. A large-scale data collection process was implemented to systematically characterize the effects of several traffic and geometric features of freeways in the occurrence of between-site LFD variations. Also, an innovative three-stage modeling framework was used to model LFD behavior using multiple logistic regression to describe between-site LFD variations and Dirichlet regression to model recurrent combinations of linear LFD trends. This novel approach is able to represent both between and within site variations of LFD trends better, while accounting for the unit-sum constraint and distribution assumptions inherent of proportions data. Results revealed that proximity to freeway merges, a site’s level of congestion, and the presence of HOV lanes are significant factors that influence site-specific recurrent LFD behavior.
Findings from this work significantly improve the state-of-the-art knowledge on merging and lane-specific traffic behavior, which can help to improve traffic operations and reduce traffic congestion in freeways.
ContributorsReina, Paulina (Author) / Ahn, Soyoung (Thesis advisor) / Pendyala, Ram (Committee member) / Kaloush, Kamil (Committee member) / Arizona State University (Publisher)
Created2015
Description
Alternative fuel vehicles (AFVs) have seen increased attention as a way to reduce reliance on petroleum for transportation, but adoption rates lag behind conventional vehicles. One crucial barrier to their proliferation is the lack of a convenient refueling infrastructure, and there is not a consensus on how to locate initial stations. Some approaches recommend placing stations near where early adopters live. An alternate group of methods places stations along busy travel routes that drivers from across the metropolitan area traverse each day. To assess which theoretical approach is most appropriate, drivers of compressed natural gas (CNG) vehicles in Southern California were surveyed at stations while they refueled. Through GIS analysis, results demonstrate that respondents refueled on the way between their origins and destinations ten times more often than they refueled near their home, when no station satisfied both criteria. Freeway interchanges, which carry high daily passing traffic volumes in metropolitan areas, can be appropriate locations for initial stations based on these results. Stations cannot actually be built directly at these interchange sites, so suitable locations on nearby street networks must be chosen. A network GIS method is developed to assess street network locations' ability to capture all traffic passing through 72 interchanges in greater Los Angeles, using deviation from a driver's shortest path as the metric to assess a candidate site's suitability. There is variation in the ability of these locations to capture passing traffic both within and across interchanges, but only 7% of sites near interchanges can conveniently capture all travel directions passing through the interchange, indicating that an ad hoc station location strategy is unlikely to succeed. Surveys were then conducted at CNG stations near freeway interchanges to assess how drivers perceive and access refueling stations in these environments. Through comparative analysis of drivers' perceptions of stations, consideration of their choice sets, and the observed frequency of the use of a freeway to both access and leave these stations, results indicate that initial AFV stations near freeway interchanges can play an important role in regional AFV infrastructure.
ContributorsKelley, Scott (Author) / Kuby, Michael (Thesis advisor) / Wentz, Elizabeth (Committee member) / Pendyala, Ram (Committee member) / Arizona State University (Publisher)
Created2015
Description
The role of environmental factors that influence atmospheric propagation of sound originating from freeway noise sources is studied with a combination of field experiments and numerical simulations. Acoustic propagation models are developed and adapted for refractive index depending upon meteorological conditions. A high-resolution multi-nested environmental forecasting model forced by coarse global analysis is applied to predict real meteorological profiles at fine scales. These profiles are then used as input for the acoustic models. Numerical methods for producing higher resolution acoustic refractive index fields are proposed. These include spatial and temporal nested meteorological simulations with vertical grid refinement. It is shown that vertical nesting can improve the prediction of finer structures in near-ground temperature and velocity profiles, such as morning temperature inversions and low level jet-like features. Accurate representation of these features is shown to be important for modeling sound refraction phenomena and for enabling accurate noise assessment. Comparisons are made using the acoustic model for predictions with profiles derived from meteorological simulations and from field experiment observations in Phoenix, Arizona. The challenges faced in simulating accurate meteorological profiles at high resolution for sound propagation applications are highlighted and areas for possible improvement are discussed.
A detailed evaluation of the environmental forecast is conducted by investigating the Surface Energy Balance (SEB) obtained from observations made with an eddy-covariance flux tower compared with SEB from simulations using several physical parameterizations of urban effects and planetary boundary layer schemes. Diurnal variation in SEB constituent fluxes are examined in relation to surface layer stability and modeled diagnostic variables. Improvement is found when adapting parameterizations for Phoenix with reduced errors in the SEB components. Finer model resolution (to 333 m) is seen to have insignificant ($<1\sigma$) influence on mean absolute percent difference of 30-minute diurnal mean SEB terms. A new method of representing inhomogeneous urban development density derived from observations of impervious surfaces with sub-grid scale resolution is then proposed for mesoscale applications. This method was implemented and evaluated within the environmental modeling framework. Finally, a new semi-implicit scheme based on Leapfrog and a fourth-order implicit time-filter is developed.
A detailed evaluation of the environmental forecast is conducted by investigating the Surface Energy Balance (SEB) obtained from observations made with an eddy-covariance flux tower compared with SEB from simulations using several physical parameterizations of urban effects and planetary boundary layer schemes. Diurnal variation in SEB constituent fluxes are examined in relation to surface layer stability and modeled diagnostic variables. Improvement is found when adapting parameterizations for Phoenix with reduced errors in the SEB components. Finer model resolution (to 333 m) is seen to have insignificant ($<1\sigma$) influence on mean absolute percent difference of 30-minute diurnal mean SEB terms. A new method of representing inhomogeneous urban development density derived from observations of impervious surfaces with sub-grid scale resolution is then proposed for mesoscale applications. This method was implemented and evaluated within the environmental modeling framework. Finally, a new semi-implicit scheme based on Leapfrog and a fourth-order implicit time-filter is developed.
ContributorsShaffer, Stephen R. (Author) / Moustaoui, Mohamed (Thesis advisor) / Mahalov, Alex (Committee member) / Fernando, Harindra J.S. (Committee member) / Ovenden, Nicholas C. (Committee member) / Huang, Huei-Ping (Committee member) / Calhoun, Ronald (Committee member) / Arizona State University (Publisher)
Created2014
Description
Traffic congestion is a major externality in modern transportation systems with negative economic, environmental and social impacts. Freeway bottlenecks are one of the key elements besides the demand for travel by automobiles that determine the extent of congestion. The primary objective of this research is to provide a better understanding of factors for variations in bottleneck discharge rates. Specifically this research seeks to (i) develop a methodology comparable to the rigorous methods to identify bottlenecks and measure capacity drop and its temporal (day to day) variations in a region, (ii) understand the variations in discharge rate of a freeway weaving bottleneck with a HOV lane and (iii) understand the relationship between lane flow distribution and discharge rate on a weaving bottleneck resulted from a lane drop and a busy off-ramp. In this research, a methodology has been developed to de-noise raw data using Discrete Wavelet Transforms (DWT). The de-noised data is then used to precisely identify bottleneck activation and deactivation times, and measure pre-congestion and congestion flows using Continuous Wavelet Transforms (CWT). To this end a methodology which could be used efficiently to identify and analyze freeway bottlenecks in a region in a consistent, reproducible manner was developed. Using this methodology, 23 bottlenecks have been identified in the Phoenix metropolitan region, some of which result in long queues and large delays during rush-hour periods. A study of variations in discharge rate of a freeway weaving bottleneck with a HOV lane showed that the bottleneck discharge rate diminished by 3-25% upon queue formations, however, the discharge rate recovered shortly thereafter upon high-occupancy-vehicle (HOV) lane activation and HOV lane flow distribution (LFD) has a significant effect on the bottleneck discharge rate: the higher the HOV LFD, the lower the bottleneck discharge rate. The effect of lane flow distribution and its relationship with bottleneck discharge rate on a weaving bottleneck formed by a lane drop and a busy off-ramp was studied. The results showed that the bottleneck discharge rate and lane flow distribution are linearly related and higher utilization of the median lane results in higher bottleneck discharge rate.
ContributorsKandala, Srinivasa Srivatsav (Author) / Ahn, Soyoung (Thesis advisor) / Pendyala, Ram (Committee member) / Kaloush, Kamil (Committee member) / Arizona State University (Publisher)
Created2014
Description
The environmental and economic assessment of neighborhood-scale transit-oriented urban form changes should include initial construction impacts through long-term use to fully understand the benefits and costs of smart growth policies. The long-term impacts of moving people closer to transit require the coupling of behavioral forecasting with environmental assessment. Using new light rail and bus rapid transit in Los Angeles, California as a case study, a life-cycle environmental and economic assessment is developed to assess the potential range of impacts resulting from mixed-use infill development. An integrated transportation and land use life-cycle assessment framework is developed to estimate energy consumption, air emissions, and economic (public, developer, and user) costs. Residential and commercial buildings, automobile travel, and transit operation changes are included and a 60-year forecast is developed that compares transit-oriented growth against growth in areas without close access to high-capacity transit service. The results show that commercial developments create the greatest potential for impact reductions followed by residential commute shifts to transit, both of which may be effected by access to high-capacity transit, reduced parking requirements, and developer incentives. Greenhouse gas emission reductions up to 470 Gg CO2-equivalents per year can be achieved with potential costs savings for TOD users. The potential for respiratory impacts (PM10-equivalents) and smog formation can be reduced by 28-35%. The shift from business-as-usual growth to transit-oriented development can decrease user costs by $3,100 per household per year over the building lifetime, despite higher rental costs within the mixed-use development.
ContributorsNahlik, Matthew (Author) / Chester, Mikhail V (Thesis advisor) / Pendyala, Ram (Committee member) / Fraser, Matthew (Committee member) / Arizona State University (Publisher)
Created2014
Description
The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions.
For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained.
This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.
For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained.
This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.
ContributorsWalker, Phillip (Author) / Tang, Wenbo (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Moustaoui, Mohamed (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2018