Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

A numerical algorithm for fully dynamical lubrication problems based on the Elrod-Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark`s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm. [DOI: 10.1115/1.3142903]

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Studies on rainfall variability and the influence of orography and land use on the climate of Peninsular India

The present study helped to understand the trend in rainfall patterns at smaller spatial scales and the large regional differences in the variability of rainfall. The effect of land use and orography on the diurnal variability is also understood. But a better understanding on the long term variation in rainfall is possible by using a longer dataset,which may provide insight into the rainfall variation over country during the past century. The basic mechanism behind the interannual rainfall variability would be possible with numerical studies using coupled Ocean-Atmosphere models. The regional difference in the active-break conditions points to the significance of regional studies than considering India as a single unit. The underlying dynamics of diurnal variability need to be studied by making use of a high resolution model as the present study could not simulate the local onshore circulation. Also the land use modification in this study, selected a region, which is surrounded by crop land. This implies the high possibility for the conversion of the remaining region to agricultural land. Therefore the study is useful than considering idealized conditions, but the adverse effect of irrigated crop is more than non-irrigated crop. Therefore, such studies would help to understand the climate changes occurred in the recent period. The large accumulation of rainfall between 300-600 m height of western Ghats has been found but the reason behind this need to be studied, which is possible by utilizing datasets that would better represent the orography and landuse over the region in high resolution model. Similarly a detailed analysis is needed to clearly identify the causative relations of the predictors identified with the predictant and the physical reasons behind them. New approaches that include nonlinear relationships and dynamical variables from model simulations can be included in the existing statistical models to improve the skill of the models. Also the statistical models for the forecasts of monsoon have to be continually updated.

Assimilation of stratospheric ozone from MIPAS into a global general-circulation model: The September 2002 vortex split

Ozone and temperature profiles from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) have been assimilated, using three-dimensional variational assimilation, into a stratosphere troposphere version of the Met Office numerical weather-prediction system. Analyses are made for the month of September 2002, when there was an unprecedented split in the southern hemisphere polar vortex. The analyses are validated against independent ozone observations from sondes, limb-occultation and total column ozone satellite instruments. Through most of the stratosphere, precision varies from 5 to 15%, and biases are 15% or less of the analysed field. Problems remain in the vortex and below the 60 hPa. level, especially at the tropopause where the analyses have too much ozone and poor agreement with independent data. Analysis problems are largely a result of the model rather than the data, giving confidence in the MIPAS ozone retrievals, though there may be a small high bias in MIPAS ozone in the lower stratosphere. Model issues include an excessive Brewer-Dobson circulation, which results both from known problems with the tracer transport scheme and from the data assimilation of dynamical variables. The extreme conditions of the vortex split reveal large differences between existing linear ozone photochemistry schemes. Despite these issues, the ozone analyses are able to successfully describe the ozone hole split and compare well to other studies of this event. Recommendations are made for the further development of the ozone assimilation system.

Importance of resolution and model configuration when downscaling extreme precipitation

Dynamical downscaling is frequently used to investigate the dynamical variables of extra-tropical cyclones, for example, precipitation, using very high-resolution models nested within coarser resolution models to understand the processes that lead to intense precipitation. It is also used in climate change studies, using long timeseries to investigate trends in precipitation, or to look at the small-scale dynamical processes for specific case studies. This study investigates some of the problems associated with dynamical downscaling and looks at the optimum configuration to obtain the distribution and intensity of a precipitation field to match observations. This study uses the Met Office Unified Model run in limited area mode with grid spacings of 12, 4 and 1.5 km, driven by boundary conditions provided by the ECMWF Operational Analysis to produce high-resolution simulations for the Summer of 2007 UK flooding events. The numerical weather prediction model is initiated at varying times before the peak precipitation is observed to test the importance of the initialisation and boundary conditions, and how long the simulation can be run for. The results are compared to raingauge data as verification and show that the model intensities are most similar to observations when the model is initialised 12 hours before the peak precipitation is observed. It was also shown that using non-gridded datasets makes verification more difficult, with the density of observations also affecting the intensities observed. It is concluded that the simulations are able to produce realistic precipitation intensities when driven by the coarser resolution data.

Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving; the equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure. (C) 2004 Elsevier Ltd. All rights reserved.

THE EFFECT of WEAK DISSIPATION IN TWO-DIMENSIONAL MAPPING

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dissipation and its consequences in the scaling exponents for a family of two-dimensional mappings

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Batch, sequential and hybrid approaches to spacecraft sensor alignment estimation

Two Kalman-filter formulations are presented for the estimation of spacecraft sensor misalignments from inflight data. In the first the sensor misalignments are part of the filter state variable; in the second, which we call HYLIGN, the state vector contains only dynamical variables, but the sensitivities of the filter innovations to the misalignments are calculated within the Kalman filter. This procedure permits the misalignments to be estimated in batch mode as well as a much smaller dimension for the Kalman filter state vector. This results not only in a significantly smaller computational burden but also in a smaller sensitivity of the misalignment estimates to outliers in the data. Numerical simulations of the filter performance are presented.

Initial-condition problem for a chiral Gross-Neveu system

A time-dependent projection technique is used to treat the initial-value problem for self-interacting fermionic fields. On the basis of the general dynamics of the fields, we derive formal equations of kinetic-type for the set of one-body dynamical variables. A nonperturbative mean-field expansion can be written for these equations. We treat this expansion in lowest order, which corresponds to the Gaussian mean-field approximation, for a uniform system described by the chiral Gross-Neveu Hamiltonian. Standard stationary features of the model, such as dynamical mass generation due to chiral symmetry breaking and a phenomenon analogous to dimensional transmutation, are reobtained in this context. The mean-field time evolution of nonequilibrium initial states is discussed.

Batch and filter approaches to spacecraft sensor alignment estimation

Two Kalman-filter formulations are presented for the estimation of spacecraft sensor misalignments from inflight data. In the first the sensor misalignments are part of the filter state variable; in the second the state vector contains only dynamical variables, but the sensitivities of the filter innovations to the misalignments are calculated within the Kalman filter. This procedure permits the misalignments to be estimated in batch mode as well as a much smaller dimension for the Kalman filter state vector. This results not only in a significantly smaller computational burden but also in a smaller sensitivity of the misalignment estimates to outliers in the data. Numerical simulations of the filter performance are presented.

Constraints on space-time manifold in Euclidean supergravity in terms of Dirac eigenvalues

We generalize a previous work on Dirac eigenvalues as dynamical variables of Euclidean supergravity. The most general set of constraints on the curvatures of the tangent bundle and on the spinor bundle of the space-time manifold, under which space-time admits Dirac eigenvalues as observables, are derived.

The Schwinger model on the null-plane

We study the Schwinger Model on the null-plane using the Dirac method for constrained systems. The fermion field is analyzed using the natural null-plane projections coming from the γ-algebra and it is shown that the fermionic sector of the Schwinger Model has only second class constraints. However, the first class constraints are exclusively of the bosonic sector. Finally, we establish the graded Lie algebra between the dynamical variables, via generalized Dirac bracket in the null-plane gauge, which is consistent with every constraint of the theory. © World Scientific Publishing Company.