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The Global ETD Search service is a free service for researchers
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Stochastic longshore current dynamicsRestrepo, Juan M., Venkataramani, Shankar 12 1900 (has links)
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
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Self-interaction corrected SCAN functional for molecules and solids in the numeric atom-center orbital frameworkBi, Sheng 12 May 2023 (has links)
Das „Strongly Constrained and Appropriately Normed“ (SCAN) Austausch-Korrelations-Funktional gehört zur Familie der meta-GGA (generalized gradient approximation) Funktionale. Es gibt aber auch Nachteile Zum einen leiden SCAN Rechnungen oft unter numerischen Instabilitäten, wodurch sehr viele Iteration zum Erreichen von Selbst-Konsistenz benötigt werden. Zum anderen leidet SCAN unter dem von GGA Methoden bekannten Selbstwechselwirkung-Fehler.
Im ersten Teil der Arbeit habe ich die numerischen Stabilitätsprobleme in SCAN Rechnungen im Rahmen der numerischen Realraum-Integrationsroutinen im Code FHI-aims untersucht. Diese Analyse zeigt, dass die genannte Probleme durch Anwendung von standardisierten Dichte-Mischalgorithmen für die kinetische Energiedichte abgemildert werden können. Dadurch wird auch in SCAN-Rechnungen eine schnelle und stabile Konvergenz zur selbstkonsistenten Lösung ermöglicht.
Im zweiten Teil der Arbeit habe ich untersucht, in welchem Rahmen sich der Selbstwechselwirkung-Fehler in SCAN mittels des von Perdew und Zunger vorgeschlagenen Selbstinteraktionskorrekturalgorithmus (PZ-SIC) verringern lässt. Es wurden aber auch Optimierungen für die PZ-SIC Methode entwickelt. Inspiriert von den ursprünglichen Argumenten in der PZ-SIC-Methode und anderen lokalisierten Methoden, wird in dieser Arbeit eine neuartige Randbedingung (orbital density constraint) vorgeschlagen, die sicherstellt, dass die PZ-SIC Orbitale während des Selbstkonsistenzzyklus lokalisiert bleiben. Dies mildert die Anfangswertabhängigkeit deutlich ab und hilft dabei, in die korrekte selbst-konsistente Lösung mit minimaler Energie zu konvergieren, unabhängig davon ob reelle oder komplexe SIC Orbitale verwendet werden.
Die in dieser Arbeit getägtigen Entwicklungen und Untersuchungen sind Wegbereiter dafür, in Zukunft mit SIC-SCAN Rechnungen deutlich genauere ab initio Rechnungen mit nur gering höherem Rechenaufwand durchführen zu können. / The state-of-the-art “Strongly Constrained and Appropriately Normed” (SCAN) functional pertains to the family of meta-generalized-gradient approximation (meta-GGA) exchange-correlation functionals. Nonetheless, SCAN suffers from some well-documented deficiencies.
In the first part of this thesis, I revisited the known numerical instability problems of the SCAN functional in the context of the numerical, real-space integration framework used in the FHI-aims code. This analysis revealed that applying standard density-mixing algorithms to the kinetic energy density attenuates and largely cures these numerical issues. By this means, SCAN calculations converge towards the self-consistent solution as fast and as efficiently as lower-order GGA calculations.
In the second part of the thesis, I investigated strategies to alleviate the self-interaction error in SCAN calculations by using the self-interaction correction algorithm proposed by Perdew and Zunger (PZ-SIC). Inspired by the original arguments in PZ-SIC and other localized methods, I introduced a mathematical constraint, i.e., the orbital density constraint, that forces the orbitals to retain their localization throughout the self-consistency cycle. In turn, this alleviates the multiple-solutions problem and facilitates the convergence towards the correct, lowest-energy solution both for complex and real SIC orbitals.
The developments and investigations performed in this thesis pave the road towards a more wide-spread use of SIC-SCAN calculations in the future, allowing more accurate predictions within only moderate increases of computational cost.
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Development of high-performance algorithms for a new generation of versatile molecular descriptors. The Pentacle softwareDurán Alcaide, Ángel 04 March 2010 (has links)
The work of this thesis was focused on the development of high-performance algorithms for a new generation of molecular descriptors, with many advantages with respect to its predecessors, suitable for diverse applications in the field of drug design, as well as its implementation in commercial grade scientific software (Pentacle). As a first step, we developed a new algorithm (AMANDA) for discretizing molecular interaction fields which allows extracting from them the most interesting regions in an efficient way. This algorithm was incorporated into a new generation of alignmentindependent molecular descriptors, named GRIND-2. The computing speed and efficiency of the new algorithm allow the application of these descriptors in virtual screening. In addition, we developed a new alignment-independent encoding algorithm (CLACC) producing quantitative structure-activity relationship models which have better predictive ability and are easier to interpret than those obtained with other methods. / El trabajo que se presenta en esta tesis se ha centrado en el desarrollo de algoritmos de altas prestaciones para la obtención de una nueva generación de descriptores moleculares, con numerosas ventajas con respecto a sus predecesores, adecuados para diversas aplicaciones en el área del diseño de fármacos, y en su implementación en un programa científico de calidad comercial (Pentacle). Inicialmente se desarrolló un nuevo algoritmo de discretización de campos de interacción molecular (AMANDA) que permite extraer eficientemente las regiones de máximo interés. Este algoritmo fue incorporado en una nueva generación de descriptores moleculares independientes del alineamiento, denominados GRIND-2. La rapidez y eficiencia del nuevo algoritmo permitieron aplicar estos descriptores en cribados virtuales. Por último, se puso a punto un nuevo algoritmo de codificación independiente de alineamiento (CLACC) que permite obtener modelos cuantitativos de relación estructura-actividad con mejor capacidad predictiva y mucho más fáciles de interpretar que los obtenidos con otros métodos.
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