A consistent Mathematical Framework for linear feedback systems using distributions.

In this thesis, when the signals are either discrete time or continuous time signals, three different Mathematical Formalisms for feedback systems are investigated. The first one, the Standard Formalism, uses mathematical elements that are adopted from the conventional analysis for feedback systems (conventional analysis as in [1]). It is shown how consistency can be regained, but with the effect of severely restricting the class of signals. Moreover, it is shown under which conditions the Standard Formalism becomes a consistent Framework. The second one, the Generalised Formalism, extends the class of systems but lacks of a transform domain analysis. The third one, a Framework using Distributions, is shown to be consistent. Moreover, the class of signals does not need any restriction and a transform domain analysis can be performed. The class of signals is the space of distributions, or generalised functions. Being those an extension of the concept of ”classical” function, the traditional class of signals is largely increased. The class of systems on the distributions are, in time domain the convolutes on the distributions, and in transform domain the multipliers on the Fourier transforms of distributions. Convolutes and multipliers are a broader class of systems than the traditional class of convolutions and algebraic functions, in time and transform domain, respectively. Since this is a consistent Framework, paradoxes and inconsistencies, such as the Georgiou Smith paradox, do not occur. Hence, it is proved that the Framework using Distributions is suitable for the analysis and design of feedback systems

Deploying and optimizing performance of a 3D hydrodynamic model on cloud

This papers presents details on deploying the Environmental Fluid Dynamics Code (EFDC) on a container-based cloud environment. Results are compared to a bare metal deployment. Application-specific benchmarking tests are complemented by detailed network tests that evaluate isolated MPI communication protocols both at intra-node and inter-node level with varying degrees of self-contention. Cloud-based simulations report significant performance loss in mean run-times. A containerised environment increases simulation time by up to 50%. More detailed analysis demonstrates that much of this performance penalty is a result of large variance in MPI communciation times. This manifests as simulation runtime variance on container cloud that hinders both simulation run-time and collection of well-defined quality-of-service metrics

Parameterization Of Turbulence Models Using 3DVAR Data Assimilation

In this research the 3DVAR data assimilation scheme is implemented in the numerical model DIVAST in order to optimize the performance of the numerical model by selecting an appropriate turbulence scheme and tuning its parameters. Two turbulence closure schemes: the Prandtl mixing length model and the two-equation k-ε model were incorporated into DIVAST and examined with respect to their universality of application, complexity of solutions, computational efficiency and numerical stability. A square harbour with one symmetrical entrance subject to tide-induced flows was selected to investigate the structure of turbulent flows. The experimental part of the research was conducted in a tidal basin. A significant advantage of such laboratory experiment is a fully controlled environment where domain setup and forcing are user-defined. The research shows that the Prandtl mixing length model and the two-equation k-ε model, with default parameterization predefined according to literature recommendations, overestimate eddy viscosity which in turn results in a significant underestimation of velocity magnitudes in the harbour. The data assimilation of the model-predicted velocity and laboratory observations significantly improves model predictions for both turbulence models by adjusting modelled flows in the harbour to match de-errored observations. 3DVAR allows also to identify and quantify shortcomings of the numerical model. Such comprehensive analysis gives an optimal solution based on which numerical model parameters can be estimated. The process of turbulence model optimization by reparameterization and tuning towards optimal state led to new constants that may be potentially applied to complex turbulent flows, such as rapidly developing flows or recirculating flows

Thermoclinic Assessment Of A Preliminary Circulation Model For Lake George In The Jefferson Project

The Jefferson Project is a collaboration between the Rensselaer Polytechnic Institute, IBM, and the FUND for Lake George aimed at understanding and managing complex factors (road salt, storm water runoff, invasive species) threatening Lake George, New York. Lake George is located about 80 km north of Albany in upstate New York and is known internationally for its water clarity. Understanding the hydrodynamics of the lake is fundamental for creation and maintenance of a research and monitoring program for the early detection of and response to adverse environmental and biological change. In this work a 3D circulation model of the lake is developed to better understand the hydro-environmental conditions of the lake; forcing is by a combination of local public survey data for the water budget and atmospheric data from the NWS (NOAA National Weather Service). The model is validated by a combination of water chemistry data collected by Darrin Fresh Water Institute (DFWI) over the last three decades, and known empirical relationships of the lake\u27s structural profile. Numerical simulations run over several years to capture the seasonal progression of thermocline depth throughout the lake, the south to north salt and surface thermal gradients and the timing of the spring and fall overturn events. Validation is by comparison with physical and chemical measurements collected over the last three decades. The study presents a novel combination of observational data, numerical modelling and empirical relationships to better understand and predict the lake circulation, and consequently the natural ecosystem

A consistent Mathematical Framework for linear feedback systems using distributions.

In this thesis, when the signals are either discrete time or continuous time signals, three different Mathematical Formalisms for feedback systems are investigated. The first one, the Standard Formalism, uses mathematical elements that are adopted from the conventional analysis for feedback systems (conventional analysis as in [1]). It is shown how consistency can be regained, but with the effect of severely restricting the class of signals. Moreover, it is shown under which conditions the Standard Formalism becomes a consistent Framework. The second one, the Generalised Formalism, extends the class of systems but lacks of a transform domain analysis. The third one, a Framework using Distributions, is shown to be consistent. Moreover, the class of signals does not need any restriction and a transform domain analysis can be performed. The class of signals is the space of distributions, or generalised functions. Being those an extension of the concept of ”classical” function, the traditional class of signals is largely increased. The class of systems on the distributions are, in time domain the convolutes on the distributions, and in transform domain the multipliers on the Fourier transforms of distributions. Convolutes and multipliers are a broader class of systems than the traditional class of convolutions and algebraic functions, in time and transform domain, respectively. Since this is a consistent Framework, paradoxes and inconsistencies, such as the Georgiou Smith paradox, do not occur. Hence, it is proved that the Framework using Distributions is suitable for the analysis and design of feedback systems

A consistent Mathematical Framework for linear feedback systems using distributions.

In this thesis, when the signals are either discrete time or continuous time signals, three different Mathematical Formalisms for feedback systems are investigated. The first one, the Standard Formalism, uses mathematical elements that are adopted from the conventional analysis for feedback systems (conventional analysis as in [1]). It is shown how consistency can be regained, but with the effect of severely restricting the class of signals. Moreover, it is shown under which conditions the Standard Formalism becomes a consistent Framework. The second one, the Generalised Formalism, extends the class of systems but lacks of a transform domain analysis. The third one, a Framework using Distributions, is shown to be consistent. Moreover, the class of signals does not need any restriction and a transform domain analysis can be performed. The class of signals is the space of distributions, or generalised functions. Being those an extension of the concept of ”classical” function, the traditional class of signals is largely increased. The class of systems on the distributions are, in time domain the convolutes on the distributions, and in transform domain the multipliers on the Fourier transforms of distributions. Convolutes and multipliers are a broader class of systems than the traditional class of convolutions and algebraic functions, in time and transform domain, respectively. Since this is a consistent Framework, paradoxes and inconsistencies, such as the Georgiou Smith paradox, do not occur. Hence, it is proved that the Framework using Distributions is suitable for the analysis and design of feedback systems