The dynamics of Baroclinic Zonal jets

Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

Paradigm shift to enhanced water supply planning through augmented grids, scarcity pricing and adaptive factory water : a system dynamics approach

This paper details a system dynamics model developed to simulate proposed changes to water governance through the integration of supply, demand and asset management processes. To effectively accomplish this, interconnected feedback loops in tariff structures, demand levels and financing capacity are included in the model design, representing the first comprehensive life-cycle modelling of potable water systems. A number of scenarios were applied to Australia's populated South-east Queensland region, demonstrating that introducing temporary drought pricing (i.e. progressive water prices set inverse with availability), in conjunction with supply augmentation through rain-independent sources, is capable of efficiently providing water security in the future. Modelling demonstrated that this alternative tariff structure reduced demand in scarcity periods thereby preserving supply, whilst revenues are maintained to build new water supply infrastructure. In addition to exploring alternative tariffs, the potential benefits of using adaptive pressure-retarded osmosis desalination plants for both potable water and power generation was explored. This operation of these plants for power production, when they would otherwise be idle, shows promise in reducing their net energy and carbon footprints. Stakeholders in industry, government and academia were engaged in model development and validation. The constructed model displays how water resource systems can be reorganised to cope with systemic change and uncertainty.

Life-history and spatial determinants of somatic growth dynamics in Komodo dragon populations

Somatic growth patterns represent a major component of organismal fitness and may vary among sexes and populations due to genetic and environmental processes leading to profound differences in life-history and demography. This study considered the ontogenic, sex-specific and spatial dynamics of somatic growth patterns in ten populations of the world's largest lizard the Komodo dragon (Varanus komodoensis). The growth of 400 individual Komodo dragons was measured in a capture-mark-recapture study at ten sites on four islands in eastern Indonesia, from 2002 to 2010. Generalized Additive Mixed Models (GAMMs) and information-theoretic methods were used to examine how growth rates varied with size, age and sex, and across and within islands in relation to site-specific prey availability, lizard population density and inbreeding coefficients. Growth trajectories differed significantly with size and between sexes, indicating different energy allocation tactics and overall costs associated with reproduction. This leads to disparities in maximum body sizes and longevity. Spatial variation in growth was strongly supported by a curvilinear density-dependent growth model with highest growth rates occurring at intermediate population densities. Sex-specific trade-offs in growth underpin key differences in Komodo dragon life-history including evidence for high costs of reproduction in females. Further, inverse density-dependent growth may have profound effects on individual and population level processes that influence the demography of this species.

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

Characterization of structure and dynamics of submicrometric systems via fluorescence correlation spectroscopy

The presented thesis revolves around the study of thermally-responsive PNIPAAm-based hydrogels in water/based environments, as studied by Fluorescence Correlation Spectroscopy (FCS).rnThe goal of the project was the engineering of PNIPAAm gels into biosensors. Specifically, a gamma of such gels were both investigated concerning their dynamics and structure at the nanometer scale, and their performance in retaining bound bodies upon thermal collapse (which PNIPAAm undergoes upon heating above 32 ºC).rnFCS’s requirements, as a technique, match the limitations imposed by the system. Namely, the need to intimately probe a system in a solvent, which was also fragile and easy to alter. FCS, on the other hand, both requires a fluid environment to work, and is based on the observation of diffusion of fluorescents at nanomolar concentrations. FCS was applied to probe the hydrogels on the nanometer size with minimal invasivity.rnVariables in the gels were addressed in the project including crosslinking degree; structural changes during thermal collapse; behavior in different buffers; the possibility of decreasing the degree of inhomogeneity; behavior of differently sized probes; and the effectiveness of antibody functionalization upon thermal collapse.rnThe evidenced results included the heightening of structural inhomogeneities during thermal collapse and under different buffer conditions; the use of annealing to decrease the inhomogeneity degree; the use of differently sized probes to address different length scale of the gel; and the successful functionalization before and after collapse.rnThe thesis also addresses two side projects, also carried forward via FCS. One, diffusion in inverse opals, produced a predictive simulation model for diffusion of bodies in confined systems as dependent on the bodies’ size versus the characteristic sizes of the system. The other was the observation of interaction of bodies of opposite charge in a water solution, resulting in a phenomenological theory and an evaluation method for both the average residence time of the different bodies together, and their attachment likelihood.

Modelling growth dynamics and toxin production in Ostreopsis cf. ovata

The benthic dinoflagellate O. ovata represents a serious threat for human health and for the ecology of its blooming areas: thanks to its toxicity this microalga has been responsible for several cases of human intoxication and mass mortalities of benthic invertebrates. Although the large number of studies on this dinoflagellate, the mechanisms underpinning O. ovata growth and toxin production are still far to be fully understood. In this work we have enriched the dataset on this species by carrying out a new experiment on an Adriatic O. cf. ovata strain. Data from this experiment (named Beta) and from another comparable experiment previously conducted on the same strain (named Alpha), revealed some interesting aspects of this dinoflagellate: it is able to grow also in a condition of strong intracellular nutrient deficiency (C:P molar ratio > 400; C:N > 25), reaching extremely low values of chlorophyll-a to carbon ratio (0.0004). Was also found a significant inverse relationships (r > -0.7) between cellular toxin to carbon and cellular nutrient to carbon ratios of experiment Alpha. In the light of these result, we hypothesized that in O. cf. ovata nutrient-stress conditions (intended as intracellular nutrient deficiency) can cause: i) an increase in toxin production; ii) a strong decrease in chlorophyll-a synthesis; iii) a lowering of metabolism associated with the formation of a sort of resting stage. We then used a modelling approach to test and critically evaluate these hypotheses in a mechanistic way: newly developed formulation describing toxin production and fate, and ad hoc changes in the already existent formulations describing chlorophyll synthesis, rest respiration, and mortality, have been incorporated in a simplified version of the European Regional Seas Ecosystem Model (ERSEM), together with a new ad hoc parameterization. The adapted model was able to accurately reproduce many of the trends observed in the Alpha experiment, allowing us to support our hypotheses. Instead the simulations of the experiment Beta were not fully satisfying in quantitative terms. We explained this gap with the presumed different physiological behaviors between the algae of the two experiments, due to the different pre-experimental periods of acclimation: the model was not able to reproduce acclimation processes in its simulations of the experiment Beta. Thus we attempt to simulate the acclimation of the algae to nutrient-stress conditions by manual intervention on some parameters of nutrient-stress thresholds, but we received conflicting results. Further studies are required to shed light on this interesting aspect. In this work we also improve the range of applicability of a state of the art marine biogeochemical model (ERSEM) by implementing in it an ecological relevant process such as the production of toxic compounds.

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

A universal description of ultraslow glass dynamics

The dynamics of glass is of importance in materials science but its nature has not yet been fully understood. Here we report that a verification of the temperature dependencies of the primary relaxation time or viscosity in the ultraslowing/ultraviscous domain of glass-forming systems can be carried out via the analysis of the inverse of the Dyre-Olsen temperature index. The subsequent analysis of experimental data indicates the possibility of the self-consistent description of glass-forming low-molecular-weight liquids, polymers, liquid crystals, orientationally disordered crystals and Ising spin-glass-like systems, as well as the prevalence of equations associated with the 'finite temperature divergence'. All these lead to a new formula for the configurational entropy in glass-forming systems. Furthermore, a link to the dominated local symmetry for a given glass former is identified here. Results obtained show a new relationship between the glass transition and critical phenomena.

Symmetric inverse consistent nonlinear registration driven by mutual information.

A nonlinear viscoelastic image registration algorithm based on the demons paradigm and incorporating inverse consistent constraint (ICC) is implemented. An inverse consistent and symmetric cost function using mutual information (MI) as a similarity measure is employed. The cost function also includes regularization of transformation and inverse consistent error (ICE). The uncertainties in balancing various terms in the cost function are avoided by alternatively minimizing the similarity measure, the regularization of the transformation, and the ICE terms. The diffeomorphism of registration for preventing folding and/or tearing in the deformation is achieved by the composition scheme. The quality of image registration is first demonstrated by constructing brain atlas from 20 adult brains (age range 30-60). It is shown that with this registration technique: (1) the Jacobian determinant is positive for all voxels and (2) the average ICE is around 0.004 voxels with a maximum value below 0.1 voxels. Further, the deformation-based segmentation on Internet Brain Segmentation Repository, a publicly available dataset, has yielded high Dice similarity index (DSI) of 94.7% for the cerebellum and 74.7% for the hippocampus, attesting to the quality of our registration method.

Coronal fluid-dynamics in laser fusion

The fluid-dynamics of the corona ejected by laser-fusion targets in the direct-drive approach (thermal radiation and atomic physics unimportant) is discussed. A two-fluid model involves inverse bremsstrahlung absorption, refraction, different ion and electron temperatures with energy exchange, different ion and electron velocities and magnetic field generation, and their effect on ion-electron friction and heat flux. Four dimensionless parameters determine coronal regimes for one-dimensional flows under uniform irradiation. One additional parameter is involved in two-dimensional problems,including the stability of one-dimensional flows, and the smoothing of nonuniform driving.

Preliminary results of the relation between ice viscosity and water content using an inverse method

One of the outstanding problems of the modelling of temperate ice dynamics is the limited knowledge on the rheology of temperate ice and, in particular, on how the rate factor depends on the liquid water content. Though it is well known that the rate factor depends strongly on the water content, in practice the only available experimentally-based relationship is that by Duval (1977), which is only valid for water contents up to 1%. However, actual water contents found in temperate and polythermal glaciers are sometimes substantially larger.

Initializing the DSSAT-Century model: inverse calibration of carbon pools from apparent soil N mineralization

The CENTURY soil organic matter model was adapted for the DSSAT (Decision Support System for Agrotechnology Transfer), modular format in order to better simulate the dynamics of soil organic nutrient processes (Gijsman et al., 2002). The CENTURY model divides the soil organic carbon (SOC) into three hypothetical pools: microbial or active material (SOC1), intermediate (SOC2) and the largely inert and stable material (SOC3) (Jones et al., 2003). At the beginning of the simulation, CENTURY model needs a value of SOC3 per soil layer which can be estimated by the model (based on soil texture and management history) or given as an input. Then, the model assigns about 5% and 95% of the remaining SOC to SOC1 and SOC2, respectively. The model performance when simulating SOC and nitrogen (N) dynamics strongly depends on the initialization process. The common methods (e.g. Basso et al., 2011) to initialize SOC pools deal mostly with carbon (C) mineralization processes and less with N. Dynamics of SOM, SOC, and soil organic N are linked in the CENTURY-DSSAT model through the C/N ratio of decomposing material that determines either mineralization or immobilization of N (Gijsman et al., 2002). The aim of this study was to evaluate an alternative method to initialize the SOC pools in the DSSAT-CENTURY model from apparent soil N mineralization (Napmin) field measurements by using automatic inverse calibration (simulated annealing). The results were compared with the ones obtained by the iterative initialization procedure developed by Basso et al., 2011.

Studies to develop and investigate an inverse formulation for numerically solving three-dimensional free surface potential fluid flows,

Research carried out under Naval Ship Systems Command, General Hydromechanics Research Program, subproject SR 009 01 01, administered by the Naval Ship Research and Development Center, contract no. N00014-67-A-0220-0003.

Tyre-force estimation by Kalman inverse filtering: applications to off-highway mining trucks

Kalman inverse filtering is used to develop a methodology for real-time estimation of forces acting at the interface between tyre and road on large off-highway mining trucks. The system model formulated is capable of estimating the three components of tyre-force at each wheel of the truck using a practical set of measurements and inputs. Good tracking is obtained by the estimated tyre-forces when compared with those simulated by an ADAMS virtual-truck model. A sensitivity analysis determines the susceptibility of the tyre-force estimates to uncertainties in the truck's parameters.