Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.

Detection and Isolation of Simultaneous Additive and Parametric Faults in Nonlinear Stochastic Dynamical Systems

This paper presents a new fault detection and isolation scheme for dealing with simultaneous additive and parametric faults. The new design integrates a system for additive fault detection based on Castillo and Zufiria, 2009 and a new parametric fault detection and isolation scheme inspired in Munz and Zufiria, 2008 . It is shown that the so far existing schemes do not behave correctly when both additive and parametric faults occur simultaneously; to solve the problem a new integrated scheme is proposed. Computer simulation results are presented to confirm the theoretical studies.

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

A "Free-Lunch" tour of the Jovian System

An ED-tether mission to Jupiter is presented. A bare tether carrying cathodic devices at both ends but no power supply, and using no propellant, could move 'freely' among Jupiter's 4 great moons. The tour scheme would have current naturally driven throughout by the motional electric field, the Lorentz force switching direction with current around a 'drag' radius of 160,00 kms, where the speed of the jovian ionosphere equals the speed of a spacecraft in circular orbit. With plasma density and magnetic field decreasing rapidly with distance from Jupiter, drag/thrust would only be operated in the inner plasmasphere, current being near shut off conveniently in orbit by disconnecting cathodes or plugging in a very large resistance; the tether could serve as its own power supply by plugging in an electric load where convenient, with just some reduction in thrust or drag. The periapsis of the spacecraft in a heliocentric transfer orbit from Earth would lie inside the drag sphere; with tether deployed and current on around periapsis, magnetic drag allows Jupiter to capture the spacecraft into an elliptic orbit of high eccentricity. Current would be on at succesive perijove passes and off elsewhere, reducing the eccentricity by lowering the apoapsis progressively to allow visits of the giant moons. In a second phase, current is on around apoapsis outside the drag sphere, rising the periapsis until the full orbit lies outside that sphere. In a third phase, current is on at periapsis, increasing the eccentricity until a last push makes the orbit hyperbolic to escape Jupiter. Dynamical issues such as low gravity-gradient at Jupiter and tether orientation in elliptic orbits of high eccentricity are discussed.

Tropical climate and vegetation simulations during the Heinrich event 1 using an Earth System Model of Intermediate Complexity (EMIC) - the University of Victoria Earth System-Climate Model (UVic ESCM)

Abrupt climate changes from 18 to 15 thousand years before present (kyr BP) associated with Heinrich Event 1 (HE1) had a strong impact on vegetation patterns not only at high latitudes of the Northern Hemisphere, but also in the tropical regions around the Atlantic Ocean. To gain a better understanding of the linkage between high and low latitudes, we used the University of Victoria (UVic) Earth System-Climate Model (ESCM) with dynamical vegetation and land surface components to simulate four scenarios of climate-vegetation interaction: the pre-industrial era, the Last Glacial Maximum (LGM), and a Heinrich-like event with two different climate backgrounds (interglacial and glacial). We calculated mega-biomes from the plant-functional types (PFTs) generated by the model to allow for a direct comparison between model results and palynological vegetation reconstructions. Our calculated mega-biomes for the pre-industrial period and the LGM corresponded well with biome reconstructions of the modern and LGM time slices, respectively, except that our pre-industrial simulation predicted the dominance of grassland in southern Europe and our LGM simulation resulted in more forest cover in tropical and sub-tropical South America. The HE1-like simulation with a glacial climate background produced sea-surface temperature patterns and enhanced inter-hemispheric thermal gradients in accordance with the "bipolar seesaw" hypothesis. We found that the cooling of the Northern Hemisphere caused a southward shift of those PFTs that are indicative of an increased desertification and a retreat of broadleaf forests in West Africa and northern South America. The mega-biomes from our HE1 simulation agreed well with paleovegetation data from tropical Africa and northern South America. Thus, according to our model-data comparison, the reconstructed vegetation changes for the tropical regions around the Atlantic Ocean were physically consistent with the remote effects of a Heinrich event under a glacial climate background.

High-resolution dynamical downscaling products for the North Slope of Alaska and surrounding areas, links to model result files

Climatic changes are most pronounced in northern high latitude regions. Yet, there is a paucity of observational data, both spatially and temporally, such that regional-scale dynamics are not fully captured, limiting our ability to make reliable projections. In this study, a group of dynamical downscaling products were created for the period 1950 to 2100 to better understand climate change and its impacts on hydrology, permafrost, and ecosystems at a resolution suitable for northern Alaska. An ERA-interim reanalysis dataset and the Community Earth System Model (CESM) served as the forcing mechanisms in this dynamical downscaling framework, and the Weather Research & Forecast (WRF) model, embedded with an optimization for the Arctic (Polar WRF), served as the Regional Climate Model (RCM). This downscaled output consists of multiple climatic variables (precipitation, temperature, wind speed, dew point temperature, and surface air pressure) for a 10 km grid spacing at three-hour intervals. The modeling products were evaluated and calibrated using a bias-correction approach. The ERA-interim forced WRF (ERA-WRF) produced reasonable climatic variables as a result, yielding a more closely correlated temperature field than precipitation field when long-term monthly climatology was compared with its forcing and observational data. A linear scaling method then further corrected the bias, based on ERA-interim monthly climatology, and bias-corrected ERA-WRF fields were applied as a reference for calibration of both the historical and the projected CESM forced WRF (CESM-WRF) products. Biases, such as, a cold temperature bias during summer and a warm temperature bias during winter as well as a wet bias for annual precipitation that CESM holds over northern Alaska persisted in CESM-WRF runs. The linear scaling of CESM-WRF eventually produced high-resolution downscaling products for the Alaskan North Slope for hydrological and ecological research, together with the calibrated ERA-WRF run, and its capability extends far beyond that. Other climatic research has been proposed, including exploration of historical and projected climatic extreme events and their possible connections to low-frequency sea-atmospheric oscillations, as well as near-surface permafrost degradation and ice regime shifts of lakes. These dynamically downscaled, bias corrected climatic datasets provide improved spatial and temporal resolution data necessary for ongoing modeling efforts in northern Alaska focused on reconstructing and projecting hydrologic changes, ecosystem processes and responses, and permafrost thermal regimes. The dynamical downscaling methods presented in this study can also be used to create more suitable model input datasets for other sub-regions of the Arctic.

Ice-atmosphere interactions and sea ice predictability at multiple resolutions in the Community Earth System Model

Thesis (Master's)--University of Washington, 2016-06

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.

Charge transport in a quantum electromechanical system

We describe a quantum electromechanical system comprising a single quantum dot harmonically bound between two electrodes and facilitating a tunneling current between them. An example of such a system is a fullerene molecule between two metal electrodes [Park et al., Nature 407, 57 (2000)]. The description is based on a quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise. This dynamical description is related to observable features of the system including the stationary current as a function of bias voltage

Analysis of dynamical tunneling experiments with a Bose-Einstein condensate

Dynamical tunneling is a quantum phenomenon where a classically forbidden process occurs that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunneling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three-dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunneling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.

Dynamical creation of entanglement by homodyne-mediated feedback

For two two-level atoms coupled to a single Bosonic mode that is driven and heavily damped, the steady state can be entangled by resonantly driving the system [S. Schneider and G. J. Milburn, Phys. Rev. A 65, 042107 (2002)]. We present a scheme to significantly increase the steady-state entanglement by using homodyne-mediated feedback, in which the Bosonic mode is that of an electromagnetic cavity, the output of which is measured and the resulting homodyne photocurrent is used to modulate the field driving the qubits. Such feedback can increase the nonlinear response to both the decoherence process of the two-qubit system and the coherent evolution of individual qubits. We present the properties of the entangled states using the SO(3) Q function.

Dynamical frustration of protein's environment at the nanoseconds time scale

A 21-residue peptide in explicit water has been simulated using classical molecular dynamics. The system's trajectory has been analysed with a novel approach that quantifies the process of how atom's environment trajectories are explored. The approach is based on the measure of Statistical Complexity that extracts complete dynamical information from the signal. The introduced characteristic quantifies the system's dynamics at the nanoseconds time scale. It has been found that the peptide exhibits nanoseconds long periods that significantly differ in the rates of the exploration of the dynamically allowed configurations of the environment. During these periods the rates remain the same but different from other periods and from the rate for water. Periods of dynamical frustration are detected when only limited routes in the space of possible trajectories of the surrounding atoms are realised.

Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.