Analysis of chaotic instabilities in a rotating body with internal energy dissipation

Melnikov's method is used to analytically predict the onset of chaotic instability in a rotating body with internal energy dissipation. The model has been found to exhibit chaotic instability when a harmonic disturbance torque is applied to the system for a range of forcing amplitude and frequency. Such a model may be considered to be representative of the dynamical behavior of a number of physical systems such as a spinning spacecraft. In spacecraft, disturbance torques may arise under malfunction of the control system, from an unbalanced rotor, from vibrations in appendages or from orbital variations. Chaotic instabilities arising from such disturbances could introduce uncertainties and irregularities into the motion of the multibody system and consequently could have disastrous effects on its intended operation. A comprehensive stability analysis is performed and regions of nonlinear behavior are identified. Subsequently, the closed form analytical solution for the unperturbed system is obtained in order to identify homoclinic orbits. Melnikov's method is then applied on the system once transformed into Hamiltonian form. The resulting analytical criterion for the onset of chaotic instability is obtained in terms of critical system parameters. The sufficient criterion is shown to be a useful predictor of the phenomenon via comparisons with numerical results. Finally, for the purposes of providing a complete, self-contained investigation of this fundamental system, the control of chaotic instability is demonstated using Lyapunov's method.

Statistical mechanics of distribution networks

This thesis presents an analysis of the stability of complex distribution networks. We present a stability analysis against cascading failures. We propose a spin [binary] model, based on concepts of statistical mechanics. We test macroscopic properties of distribution networks with respect to various topological structures and distributions of microparameters. The equilibrium properties of the systems are obtained in a statistical mechanics framework by application of the replica method. We demonstrate the validity of our approach by comparing it with Monte Carlo simulations. We analyse the network properties in terms of phase diagrams and found both qualitative and quantitative dependence of the network properties on the network structure and macroparameters. The structure of the phase diagrams points at the existence of phase transition and the presence of stable and metastable states in the system. We also present an analysis of robustness against overloading in the distribution networks. We propose a model that describes a distribution process in a network. The model incorporates the currents between any connected hubs in the network, local constraints in the form of Kirchoff's law and a global optimizational criterion. The flow of currents in the system is driven by the consumption. We study two principal types of model: infinite and finite link capacity. The key properties are the distributions of currents in the system. We again use a statistical mechanics framework to describe the currents in the system in terms of macroscopic parameters. In order to obtain observable properties we apply the replica method. We are able to assess the criticality of the level of demand with respect to the available resources and the architecture of the network. Furthermore, the parts of the system, where critical currents may emerge, can be identified. This, in turn, provides us with the characteristic description of the spread of the overloading in the systems.

Travelling waves in a complex Ginzburg-Landau equation with time-delay feedback

One of the simplest ways to create nonlinear oscillations is the Hopf bifurcation. The spatiotemporal dynamics observed in an extended medium with diffusion (e.g., a chemical reaction) undergoing this bifurcation is governed by the complex Ginzburg-Landau equation, one of the best-studied generic models for pattern formation, where besides uniform oscillations, spiral waves, coherent structures and turbulence are found. The presence of time delay terms in this equation changes the pattern formation scenario, and different kind of travelling waves have been reported. In particular, we study the complex Ginzburg-Landau equation that contains local and global time-delay feedback terms. We focus our attention on plane wave solutions in this model. The first novel result is the derivation of the plane wave solution in the presence of time-delay feedback with global and local contributions. The second and more important result of this study consists of a linear stability analysis of plane waves in that model. Evaluation of the eigenvalue equation does not show stabilisation of plane waves for the parameters studied. We discuss these results and compare to results of other models.

Stability of an Optimal Schedule for a Job-Shop Problem with Two Jobs

The usual assumption that the processing times of the operations are known in advance is the strictest one in scheduling theory. This assumption essentially restricts practical aspects of deterministic scheduling theory since it is not valid for the most processes arising in practice. The paper is devoted to a stability analysis of an optimal schedule, which may help to extend the significance of scheduling theory for decision-making in the real-world applications. The term stability is generally used for the phase of an algorithm, at which an optimal solution of a problem has already been found, and additional calculations are performed in order to study how solution optimality depends on variation of the numerical input data.

Development and Application of Covalent-Labeling Strategies for the Large-Scale Thermodynamic Analysis of Protein Folding and Ligand Binding

Thermodynamic stability measurements on proteins and protein-ligand complexes can offer insights not only into the fundamental properties of protein folding reactions and protein functions, but also into the development of protein-directed therapeutic agents to combat disease. Conventional calorimetric or spectroscopic approaches for measuring protein stability typically require large amounts of purified protein. This requirement has precluded their use in proteomic applications. Stability of Proteins from Rates of Oxidation (SPROX) is a recently developed mass spectrometry-based approach for proteome-wide thermodynamic stability analysis. Since the proteomic coverage of SPROX is fundamentally limited by the detection of methionine-containing peptides, the use of tryptophan-containing peptides was investigated in this dissertation. A new SPROX-like protocol was developed that measured protein folding free energies using the denaturant dependence of the rate at which globally protected tryptophan and methionine residues are modified with dimethyl (2-hydroxyl-5-nitrobenzyl) sulfonium bromide and hydrogen peroxide, respectively. This so-called Hybrid protocol was applied to proteins in yeast and MCF-7 cell lysates and achieved a ~50% increase in proteomic coverage compared to probing only methionine-containing peptides. Subsequently, the Hybrid protocol was successfully utilized to identify and quantify both known and novel protein-ligand interactions in cell lysates. The ligands under study included the well-known Hsp90 inhibitor geldanamycin and the less well-understood omeprazole sulfide that inhibits liver-stage malaria. In addition to protein-small molecule interactions, protein-protein interactions involving Puf6 were investigated using the SPROX technique in comparative thermodynamic analyses performed on wild-type and Puf6-deletion yeast strains. A total of 39 proteins were detected as Puf6 targets and 36 of these targets were previously unknown to interact with Puf6. Finally, to facilitate the SPROX/Hybrid data analysis process and minimize human errors, a Bayesian algorithm was developed for transition midpoint assignment. In summary, the work in this dissertation expanded the scope of SPROX and evaluated the use of SPROX/Hybrid protocols for characterizing protein-ligand interactions in complex biological mixtures.

Multiphase flow in porous media: meta-modeling techniques for sensitivity analysis and risk assessment

One of the biggest challenges that contaminant hydrogeology is facing, is how to adequately address the uncertainty associated with model predictions. Uncertainty arise from multiple sources, such as: interpretative error, calibration accuracy, parameter sensitivity and variability. This critical issue needs to be properly addressed in order to support environmental decision-making processes. In this study, we perform Global Sensitivity Analysis (GSA) on a contaminant transport model for the assessment of hydrocarbon concentration in groundwater. We provide a quantification of the environmental impact and, given the incomplete knowledge of hydrogeological parameters, we evaluate which are the most influential, requiring greater accuracy in the calibration process. Parameters are treated as random variables and a variance-based GSA is performed in a optimized numerical Monte Carlo framework. The Sobol indices are adopted as sensitivity measures and they are computed by employing meta-models to characterize the migration process, while reducing the computational cost of the analysis. The proposed methodology allows us to: extend the number of Monte Carlo iterations, identify the influence of uncertain parameters and lead to considerable saving computational time obtaining an acceptable accuracy.

Análise experimental e numérica do comportamento de estruturas de solo reforçado com geossintéticos : solo granular versus fino

As estruturas de solo reforçado com geossintéticos são normalmente constituídas por solos granulares com boas propriedades físicas e mecânicas. O uso de apenas este tipo de solos pode proporcionar o aumento, por vezes insustentável, do custo da execução das estruturas e o aumento do seu impacto ambiental. Deste modo, as estruturas de solo reforçado perdem a sua vantagem competitiva em relação a outros tipos de estruturas (muros de betão, muros de gravidade, muros de gabiões, etc.). Para resolver este problema podem ser utilizados outros tipos de solos (solos locais, finos, com propriedades físicas e mecânicas piores mas, no entanto, mais baratos) para a execução deste tipo de estruturas. De forma geral, com este estudo pretendeu-se contribuir para o incremento do conhecimento sobre a utilização de solos finos para a construção de estruturas de solo reforçado (muros e taludes). Para tal avaliaram-se as diferenças no comportamento mecânico dos materiais compósitos (solo granular reforçado versus solo fino reforçado) e das estruturas de solo reforçado constituídas com os dois tipos de solos. Assim, os objetivos deste estudo foram avaliar: a influência de vários parâmetros nas propriedades mecânicas e na capacidade de carga dos solos reforçados com geossintéticos; a influência de vários parâmetros no dimensionamento das estruturas de solo reforçado; e o comportamento das estruturas dimensionadas (incluindo a estabilidade global e a influência do processo construtivo) recorrendo a uma ferramenta numérica (PLAXIS). Para cumprir os objetivos propostos foram realizadas análises experimentais em laboratório (análise do comportamento do solo reforçado através de ensaios triaxiais e de California Bearing Ratio) e análises numéricas (dimensionamento de estruturas de solo reforçado; modelação numérica do comportamento através de uma ferramenta numérica comercial com o método dos elementos finitos). Os resultados dos ensaios experimentais mostraram que o comportamento mecânico e a capacidade de carga do solo foram incrementados com a inclusão das camadas de geossintético. Este efeito variou com os diversos parâmetros analisados mas, de forma geral, foi mais importante no solo fino (solo com propriedades mecânicas piores). As análises numéricas mostraram que as estruturas de solo fino precisaram de maior densidade de reforços para serem estáveis. Além disso, as estruturas de solo fino foram mais deformáveis e o efeito do seu processo construtivo foi mais importante (principalmente para estruturas de solo fino saturado).

Cone penetration testing to assess slope stability in the 1979 Nice landslide area (Ligurian Margin, SE France)

In the landslide-prone area near the Nice international airport, southeastern France, an interdisciplinary approach is applied to develop realistic lithological/geometrical profiles and geotechnical/strength sub-seafloor models. Such models are indispensable for slope stability assessments using limit equilibrium or finite element methods. Regression analyses, based on the undrained shear strength (su) of intact gassy sediments are used to generate a sub-seafloor strength model based on 37 short dynamic and eight long static piezocone penetration tests, and laboratory experiments on one Calypso piston and 10 gravity cores. Significant strength variations were detected when comparing measurements from the shelf and the shelf break, with a significant drop in su to 5.5 kPa being interpreted as a weak zone at a depth between 6.5 and 8.5 m below seafloor (mbsf). Here, a 10% reduction of the in situ total unit weight compared to the surrounding sediments is found to coincide with coarse-grained layers that turn into a weak zone and detachment plane for former and present-day gravitational, retrogressive slide events, as seen in 2D chirp profiles. The combination of high-resolution chirp profiles and comprehensive geotechnical information allows us to compute enhanced 2D finite element slope stability analysis with undrained sediment response compared to previous 2D numerical and 3D limit equilibrium assessments. Those models suggest that significant portions (detachment planes at 20 m or even 55 mbsf) of the Quaternary delta and slope apron deposits may be mobilized. Given that factors of safety are equal or less than 1 when further considering the effect of free gas, a high risk for a landslide event of considerable size off Nice international airport is identified

In-situ based reanalysis of the global ocean temperature and salinity with ISAS: variability of the heat content and steric height

The In Situ Analysis System (ISAS) was developed to produce gridded fields of temperature and salinity that preserve as much as possible the time and space sampling capabilities of the Argo network of profiling floats. Since the first global re-analysis performed in 2009, the system has evolved and a careful delayed mode processing of the 2002-2012 dataset has been carried out using version 6 of ISAS and updating the statistics to produce the ISAS13 analysis. This last version is now implemented as the operational analysis tool at the Coriolis data centre. The robustness of the results with respect to the system evolution is explored through global quantities of climatological interest: the Ocean Heat Content and the Steric Height. Estimates of errors consistent with the methodology are computed. This study shows that building reliable statistics on the fields is fundamental to improve the monthly estimates and to determine the absolute error bars. The new mean fields and variances deduced from the ISAS13 re-analysis and dataset show significant changes relative to the previous ISAS estimates, in particular in the southern ocean, justifying the iterative procedure. During the decade covered by Argo, the intermediate waters appear warmer and saltier in the North Atlantic and fresher in the Southern Ocean than in WOA05 long term mean. At inter-annual scale, the impact of ENSO on the Ocean Heat Content and Steric Height is observed during the 2006-2007 and 2009-2010 events captured by the network.

How essential are Argo observations to constrain a global ocean data assimilation system?

Observing system experiments (OSEs) are carried out over a 1-year period to quantify the impact of Argo observations on the Mercator Ocean 0.25° global ocean analysis and forecasting system. The reference simulation assimilates sea surface temperature (SST), SSALTO/DUACS (Segment Sol multi-missions dALTimetrie, d'orbitographie et de localisation précise/Data unification and Altimeter combination system) altimeter data and Argo and other in situ observations from the Coriolis data center. Two other simulations are carried out where all Argo and half of the Argo data are withheld. Assimilating Argo observations has a significant impact on analyzed and forecast temperature and salinity fields at different depths. Without Argo data assimilation, large errors occur in analyzed fields as estimated from the differences when compared with in situ observations. For example, in the 0–300 m layer RMS (root mean square) differences between analyzed fields and observations reach 0.25 psu and 1.25 °C in the western boundary currents and 0.1 psu and 0.75 °C in the open ocean. The impact of the Argo data in reducing observation–model forecast differences is also significant from the surface down to a depth of 2000 m. Differences between in situ observations and forecast fields are thus reduced by 20 % in the upper layers and by up to 40 % at a depth of 2000 m when Argo data are assimilated. At depth, the most impacted regions in the global ocean are the Mediterranean outflow, the Gulf Stream region and the Labrador Sea. A significant degradation can be observed when only half of the data are assimilated. Therefore, Argo observations matter to constrain the model solution, even for an eddy-permitting model configuration. The impact of the Argo floats' data assimilation on other model variables is briefly assessed: the improvement of the fit to Argo profiles do not lead globally to unphysical corrections on the sea surface temperature and sea surface height. The main conclusion is that the performance of the Mercator Ocean 0.25° global data assimilation system is heavily dependent on the availability of Argo data.

Stability of membrane bound reactions

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space e.g. by binding to a membrane. The non-diffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length of the diffusing partner. The activated fraction of the fixed species determines the size of an active sub-region of the cluster. Linear stability analysis reveals that diffusion is one of the ma jor determinants of the stability of the dynamics. We illustrate the model concept with Ca²⁺ dynamics in living cells, which has release channels as fixed reaction partners. Our results suggest that spatial and temporal structures in intracellular Ca²⁺ dynamics are caused by fluctuations due to the small number of channels per cluster.

Mode locking in a spatially extended neuron model: active soma and compartmental tree

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a code conveying information about spatial location. Thus it is important to explore the role of neuronal dendrites in generating the response to periodic current injection. In this paper we pursue this using a compartmental model, with linear dynamics for each compartment, coupled to an active soma model that generates action potentials. By working with the piece-wise linear McKean model for the soma we show how the response of the whole neuron model (soma and dendrites) can be written in closed form. We exploit this to construct a stroboscopic map describing the response of the spatially extended model to periodic forcing. A linear stability analysis of this map, together with a careful treatment of the non-differentiability of the soma model, allows us to construct the Arnol'd tongue structure for 1:q states (one action potential for q cycles of forcing). Importantly we show how the presence of quasi-active membrane in the dendrites can influence the shape of tongues. Direct numerical simulations confirm our theory and further indicate that resonant dendritic membrane can enlarge the windows in parameter space for chaotic behavior. These simulations also show that the spatially extended neuron model responds differently to global as opposed to point forcing. In the former case spatio-temporal patterns of activity within an Arnol'd tongue are standing waves, whilst in the latter they are traveling waves.

Towards a predictive model of Ca²⁺ puffs

We investigate key characteristics of Ca²⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca²⁺ liberation in a three dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca²⁺ concentrations at a releasing cluster range from 80 µM to 170 µM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca²⁺ concentrations eliminate Ca²⁺ oscillations in a deterministic model of an IP[subscript]3R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP[subscript]3R gating dynamics, so that only fluctuations can restore experimentally observed Ca²⁺ oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca²⁺ puffs and hence the stochastic time scale of intracellular Ca²⁺ dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca²⁺ oscillations.

Investigation of seismic effects on disturbed rock slope stability assessments

For general stability analysis of rock slopes, rock mass strength and rock mass disturbance are definitely should be considered. In addition, the impact of earthquakes must be taken into account. In fact, the rock mass strength is very difficult to be assessed which causes the difficulty of analysing rock slope stability. Therefore, an empirical failure criterion, the Hoek-Brown failure criterion, has been proposed. It is one of the most widely accepted approaches to estimate rock mass strength. The rock mass disturbance is important and was found having significant influence on evaluating rock slope stability, especially for rock slope with poor quality rock mass. In the Hoek-Brown failure criterion, the disturbance factor can represent the level of the rock mass disturbance which would provide a reasonable basis for estimating rock mass strength. This research will not only discuss the slope factor of safety, but also consider the influence of the seismic force on rock slope stability assessment using pseudo-static method. In practice, only horizontal seismic coefficient is used. Various magnitudes of the disturbance factor and recommended blasting damage zone thickness are also taken into account. The blasting damage zone thickness considered ranges from 0.5 to 2.5 times of slope height. The research results have potential to be extended and then sets of comprehensive stability charts can be provided for the rock slope stability evaluations. They will be convenient tools for practising engineers. In this study, finite element upper bound and lower bound limit analysis methods are employed. Their applicability has been investigated in some previous studies. The differences between upper bound and lower bound solutions are less than ±10% which would provide reasonable and acceptable range for rock slope stability safety factor estimation.

Analysis of texture and R value variations in asymmetric rolling of if steel

Asymmetric rolling (ASR) is a potential process to reach better grain refinement than in conventional rolling, thus, can lead to better mechanical properties. It is not known, however, how the introduction of a shear component will change the ideal orientations of the textures, and consequently, the evolution of plastic anisotropy. To understand the effect of the added shear on texture evolution in ASR, a stability analysis is carried out in orientation space and the variations in the position and strength of the ideal orientations are analysed as a function of the shear component. Then, modelling of R values is presented for various cases. On that basis, it is shown that there is an upper limit for the shear component in asymmetric rolling that still retains the 〈1 1 1〉 ND fibre (ND: direction normal to the sheet) which is good for formability. It is also found that better persistence of the ND fibre can be obtained by cyclically alternating the shear component. The theoretical results are well supported by comparison to experimental evidences. © 2011 Elsevier B.V. All rights reserved.