On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

The TAP approach to intensive and extensive connectivity systems

The Thouless-Anderson-Palmer (TAP) approach was originally developed for analysing the Sherrington-Kirkpatrick model in the study of spin glass models and has been employed since then mainly in the context of extensively connected systems whereby each dynamical variable interacts weakly with the others. Recently, we extended this method for handling general intensively connected systems where each variable has only O(1) connections characterised by strong couplings. However, the new formulation looks quite different with respect to existing analyses and it is only natural to question whether it actually reproduces known results for systems of extensive connectivity. In this chapter, we apply our formulation of the TAP approach to an extensively connected system, the Hopfield associative memory model, showing that it produces identical results to those obtained by the conventional formulation.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

A structural method for the design of fault tolerant distributed control systems

Distributed digital control systems provide alternatives to conventional, centralised digital control systems. Typically, a modern distributed control system will comprise a multi-processor or network of processors, a communications network, an associated set of sensors and actuators, and the systems and applications software. This thesis addresses the problem of how to design robust decentralised control systems, such as those used to control event-driven, real-time processes in time-critical environments. Emphasis is placed on studying the dynamical behaviour of a system and identifying ways of partitioning the system so that it may be controlled in a distributed manner. A structural partitioning technique is adopted which makes use of natural physical sub-processes in the system, which are then mapped into the software processes to control the system. However, communications are required between the processes because of the disjoint nature of the distributed (i.e. partitioned) state of the physical system. The structural partitioning technique, and recent developments in the theory of potential controllability and observability of a system, are the basis for the design of controllers. In particular, the method is used to derive a decentralised estimate of the state vector for a continuous-time system. The work is also extended to derive a distributed estimate for a discrete-time system. Emphasis is also given to the role of communications in the distributed control of processes and to the partitioning technique necessary to design distributed and decentralised systems with resilient structures. A method is presented for the systematic identification of necessary communications for distributed control. It is also shwon that the structural partitions can be used directly in the design of software fault tolerant concurrent controllers. In particular, the structural partition can be used to identify the boundary of the conversation which can be used to protect a specific part of the system. In addition, for certain classes of system, the partitions can be used to identify processes which may be dynamically reconfigured in the event of a fault. These methods should be of use in the design of robust distributed systems.

An advanced real-time predictive maintenance framework for large scale machine systems

This thesis introduces and develops a novel real-time predictive maintenance system to estimate the machine system parameters using the motion current signature. Recently, motion current signature analysis has been addressed as an alternative to the use of sensors for monitoring internal faults of a motor. A maintenance system based upon the analysis of motion current signature avoids the need for the implementation and maintenance of expensive motion sensing technology. By developing nonlinear dynamical analysis for motion current signature, the research described in this thesis implements a novel real-time predictive maintenance system for current and future manufacturing machine systems. A crucial concept underpinning this project is that the motion current signature contains infor­mation relating to the machine system parameters and that this information can be extracted using nonlinear mapping techniques, such as neural networks. Towards this end, a proof of con­cept procedure is performed, which substantiates this concept. A simulation model, TuneLearn, is developed to simulate the large amount of training data required by the neural network ap­proach. Statistical validation and verification of the model is performed to ascertain confidence in the simulated motion current signature. Validation experiment concludes that, although, the simulation model generates a good macro-dynamical mapping of the motion current signature, it fails to accurately map the micro-dynamical structure due to the lack of knowledge regarding performance of higher order and nonlinear factors, such as backlash and compliance. Failure of the simulation model to determine the micro-dynamical structure suggests the pres­ence of nonlinearity in the motion current signature. This motivated us to perform surrogate data testing for nonlinearity in the motion current signature. Results confirm the presence of nonlinearity in the motion current signature, thereby, motivating the use of nonlinear tech­niques for further analysis. Outcomes of the experiment show that nonlinear noise reduction combined with the linear reverse algorithm offers precise machine system parameter estimation using the motion current signature for the implementation of the real-time predictive maintenance system. Finally, a linear reverse algorithm, BJEST, is developed and applied to the motion current signature to estimate the machine system parameters.

Intelligent Model of User Behavior in Distributed Systems

We present a complex neural network model of user behavior in distributed systems. The model reflects both dynamical and statistical features of user behavior and consists of three components: on-line and off-line models and change detection module. On-line model reflects dynamical features by predicting user actions on the basis of previous ones. Off-line model is based on the analysis of statistical parameters of user behavior. In both cases neural networks are used to reveal uncharacteristic activity of users. Change detection module is intended for trends analysis in user behavior. The efficiency of complex model is verified on real data of users of Space Research Institute of NASU-NSAU.

Using the Simulation Modeling Methods for the Designing Real-Time Integrated Expert Systems

Certain theoretical and methodological problems of designing real-time dynamical expert systems, which belong to the class of the most complex integrated expert systems, are discussed. Primary attention is given to the problems of designing subsystems for modeling the external environment in the case where the environment is represented by complex engineering systems. A specific approach to designing simulation models for complex engineering systems is proposed and examples of the application of this approach based on the G2 (Gensym Corp.) tool system are described.

Improving the predictability of time series by chaotic parameter estimation

Limited literature regarding parameter estimation of dynamic systems has been identified as the central-most reason for not having parametric bounds in chaotic time series. However, literature suggests that a chaotic system displays a sensitive dependence on initial conditions, and our study reveals that the behavior of chaotic system: is also sensitive to changes in parameter values. Therefore, parameter estimation technique could make it possible to establish parametric bounds on a nonlinear dynamic system underlying a given time series, which in turn can improve predictability. By extracting the relationship between parametric bounds and predictability, we implemented chaos-based models for improving prediction in time series. ^ This study describes work done to establish bounds on a set of unknown parameters. Our research results reveal that by establishing parametric bounds, it is possible to improve the predictability of any time series, although the dynamics or the mathematical model of that series is not known apriori. In our attempt to improve the predictability of various time series, we have established the bounds for a set of unknown parameters. These are: (i) the embedding dimension to unfold a set of observation in the phase space, (ii) the time delay to use for a series, (iii) the number of neighborhood points to use for avoiding detection of false neighborhood and, (iv) the local polynomial to build numerical interpolation functions from one region to another. Using these bounds, we are able to get better predictability in chaotic time series than previously reported. In addition, the developments of this dissertation can establish a theoretical framework to investigate predictability in time series from the system-dynamics point of view. ^ In closing, our procedure significantly reduces the computer resource usage, as the search method is refined and efficient. Finally, the uniqueness of our method lies in its ability to extract chaotic dynamics inherent in non-linear time series by observing its values. ^

Parameter space of experimental chaotic circuits with high-precision control parameters

The authors thank Professor Iber^e Luiz Caldas for the suggestions and encouragement. The authors F.F.G.d.S., R.M.R., J.C.S., and H.A.A. acknowledge the Brazilian agency CNPq and state agencies FAPEMIG, FAPESP, and FAPESC, and M.S.B. also acknowledges the EPSRC Grant Ref. No. EP/I032606/1.

Dynamical Heterogeneity and Nonlinear Susceptibility in Short-Ranged Attractive Supercooled Liquids

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here, we study in detail the behavior of non-linear, higher-order correlation functions that measure the growth of length scales associated with dynamical heterogeneity in both types of systems. We find that this measure is qualitatively different in the repulsive and attractive cases with regards to the wave vector dependence as well as the time dependence of the standard non-linear four-point dynamical susceptibility. We discuss the implications of these results for the general understanding of dynamical heterogeneity in glass-forming liquids.

Stratigraphic Architecture of Deep Sea Depositional Systems in the Southern Tyrrhenian Sea: Some Examples in the Ischia and Stromboli Volcanic Islands (Southern Italy)

The stratigraphic architecture of deep sea depositional systems has been discussed in detail. Some examples in Ischia and Stromboli volcanic islands (Southern Tyrrhenian sea, Italy) are here shown and discussed. The submarine slope and base of slope depositional systems represent a major component of marine and lacustrine basin fills, constituting primary targets for hydrocarbon exploration and development. The slope systems are characterized by seven seismic facies building blocks, including the turbiditic channel fills, the turbidite lobes, the sheet turbidites, the slide, slump and debris flow sheets, lobes and tongues, the fine-grained turbidite fills and sheets, the contourite drifts and finally, the hemipelagic drapes and fills. Sparker profiles offshore Ischia are presented. New seismo-stratigraphic evidence on buried volcanic structures and overlying Quaternary deposits of the eastern offshore of the Ischia Island are here discussed to highlight the implications on marine geophysics and volcanology. Regional seismic sections in the Ischia offshore across buried volcanic structures and debris avalanche and debris flow deposits are here presented and discussed. Deep sea depositional systems in the Ischia Island are well developed in correspondence to the Southern Ischia canyon system. The canyon system engraves a narrow continental shelf from Punta Imperatore to Punta San Pancrazio, being limited southwestwards from the relict volcanic edifice of the Ischia bank. While the eastern boundary of the canyon system is controlled by extensional tectonics, being limited from a NE-SW trending (counter-Apenninic) normal fault, its western boundary is controlled by volcanism, due to the growth of the Ischia volcanic bank. Submarine gravitational instabilities also acted in relationships to the canyon system, allowing for the individuation of large scale creeping at the sea bottom and hummocky deposits already interpreted as debris avalanche deposits. High resolution seismic data (Subbottom Chirp) coupled to high resolution Multibeam bathymetry collected in the frame of the Stromboli geophysical experiment aimed at recording seismic active data and tomography of the Stromboli Island are here presented. A new detailed swath bathymetry of Stromboli Island is here shown and discussed to reconstruct an up-to-date morpho-bathymetry and marine geology of the area, compared to volcanologic setting of the Aeolian volcanic complex. The Stromboli DEM gives information about the submerged structure of the volcano, particularly about the volcano-tectonic and gravitational processes involving the submarine flanks of the edifice. Several seismic units have been identified around the volcanic edifice and interpreted as volcanic acoustic basement pertaining to the volcano and overlying slide chaotic bodies emplaced during its complex volcano-tectonic evolution. They are related to the eruptive activity of Stromboli, mainly poliphasic and to regional geological processes involving the geology of the Aeolian Arc.

Phase Transitions in Engineered Ultracold Quantum Systems

The study of quantum degenerate gases has many applications in topics such as condensed matter dynamics, precision measurements and quantum phase transitions. We built an apparatus to create 87Rb Bose-Einstein condensates (BECs) and generated, via optical and magnetic interactions, novel quantum systems in which we studied the contained phase transitions. For our first experiment we quenched multi-spin component BECs from a miscible to dynamically unstable immiscible state. The transition rapidly drives any spin fluctuations with a coherent growth process driving the formation of numerous spin polarized domains. At much longer times these domains coarsen as the system approaches equilibrium. For our second experiment we explored the magnetic phases present in a spin-1 spin-orbit coupled BEC and the contained quantum phase transitions. We observed ferromagnetic and unpolarized phases which are stabilized by the spin-orbit coupling’s explicit locking between spin and motion. These two phases are separated by a critical curve containing both first-order and second-order transitions joined at a critical point. The narrow first-order transition gives rise to long-lived metastable states. For our third experiment we prepared independent BECs in a double-well potential, with an artificial magnetic field between the BECs. We transitioned to a single BEC by lowering the barrier while expanding the region of artificial field to cover the resulting single BEC. We compared the vortex distribution nucleated via conventional dynamics to those produced by our procedure, showing our dynamical process populates vortices much more rapidly and in larger number than conventional nucleation.

Close-in planets around giant stars: lack of hot-Jupiters and prevalence of multiplanetary systems

Extrasolar planets abound in almost any possible configuration. However, until five years ago, there was a lack of planets orbiting closer than 0.5 au to giant or subgiant stars. Since then, recent detections have started to populated this regime by confirming 13 planetary systems. We discuss the properties of these systems in terms of their formation and evolution off the main sequence. Interestingly, we find that 70.0 ± 6.6% of the planets in this regime are inner components of multiplanetary systems. This value is 4.2σ higher than for main-sequence hosts, which we find to be 42.4 ± 0.1%. The properties of the known planets seem to indicate that the closest-in planets (a< 0.06 au) to main-sequence stars are massive (i.e., hot Jupiters) and isolated and that they are subsequently engulfed by their host as it evolves to the red giant branch, leaving only the predominant population of multiplanetary systems in orbits 0.06

Seasonal changes of heat and moisture fluxes from the Caspian Sea surface and its effect on synoptic systems with heavy rainfalls in southern shores of the sea during 2005-2010

Caspian Sea with its unique characteristics is a significant source to supply required heat and moisture for passing weather systems over the north of Iran. Investigation of heat and moisture fluxes in the region and their effects on these systems that could lead to floods and major financial and human losses is essential in weather forecasting. Nowadays by improvement of numerical weather and climate prediction models and the increasing need to more accurate forecasting of heavy rainfall, the evaluation and verification of these models has been become much more important. In this study we have used the WRF model as a research-practical one with many valuable characteristics and flexibilities. In this research, the effects of heat and moisture fluxes of Caspian Sea on the synoptic and dynamical structure of 20 selective systems associated with heavy rainfall in the southern shores of Caspian Sea are investigated. These systems are selected based on the rainfall data gathered by three local stations named: Rasht, Babolsar and Gorgan in different seasons during a five-year period (2005-2010) with maximum amount of rainfall through the 24 hours of a day. In addition to synoptic analyses of these systems, the WRF model with and without surface flues was run using the two nested grids with the horizontal resolutions of 12 and 36 km. The results show that there are good consistencies between the predicted distribution of rainfall field, time of beginning and end of rainfall by the model and the observations. But the model underestimates the amounts of rainfall and the maximum difference with the observation is about 69%. Also, no significant changes in the results are seen when the domain and the resolution of computations are changed. The other noticeable point is that the systems are severely weakened by removing heat and moisture fluxes and thereby the amounts of large scale rainfall are decreased up to 77% and the convective rainfalls tend to zero.

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin–orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star–planet–satellite systems and triple stellar systems.