Modelització i estudi de caminadors passius en pendents no constants

Aquest projecte presenta els models matemàtics que generalitzen al cas de pendent no constant els models existents de dos tipus bàsics de caminadors passius en un pendent constant: la rimless wheel i el compass walker. En la memòria s'inclouen la modelització i l'estudi teòric dels models en pendent constant i posteriorment, ambdós models es generalitzen al cas de pendent no constant. En la generalització es descriuen les equacions que governen el moviment del sistema (equació diferencial per la fase de doble pèndol i equació algebraica per la col·lisió del peu) així com la condició de detecció de col·lisió del peu generalitzada. Finalment, en l'estudi dels models es determinen les condicions sota les quals el sistema presenta un cicle límit estable i es completa amb els resultats de les simulacions numèriques de casos representatius de diferents tipologies de camí de baixada per il·lustrar l'existència i estabilitat dels cicles límits d'aquests exemples

Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation

We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can model phenomena described by complex Ginzburg-Landau systems under the added assumption of saturable media. When the saturation parameter is set to zero, we recover a general complex cubic Ginzburg-Landau system with XPM. We first derive conditions for the existence of bounded dynamics, approximating the absorbing set for solutions. We use this to then determine conditions for amplitude death of a single wavefunction. We also construct exact plane wave solutions, and determine conditions for their modulational instability. In a degenerate limit where dispersion and nonlinearity balance, we reduce our system to a saturable nonlinear Schr\"odinger system with XPM parameters, and we demonstrate the existence and behavior of spatially heterogeneous stationary solutions in this limit. Using numerical simulations we verify the aforementioned analytical results, while also demonstrating other interesting emergent features of the dynamics, such as spatiotemporal chaos in the presence of modulational instability. In other regimes, coherent patterns including uniform states or banded structures arise, corresponding to certain stable stationary states. For sufficiently large yet equal XPM parameters, we observe a segregation of wavefunctions into different regions of the spatial domain, while when XPM parameters are large and take different values, one wavefunction may decay to zero in finite time over the spatial domain (in agreement with the amplitude death predicted analytically). While saturation will often regularize the dynamics, such transient dynamics can still be observed - and in some cases even prolonged - as the saturability of the media is increased, as the saturation may act to slow the timescale.Comment: 36 page

Derivation of an effective thermal electrochemical model for porous electrode batteries using asymptotic homogenisation

Thermal electrochemical models for porous electrode batteries (such as lithium ion batteries) are widely used. Due to the multiple scales involved, solving the model accounting for the porous microstructure is computationally expensive, therefore effective models at the macroscale are preferable. However, these effective models are usually postulated ad hoc rather than systematically upscaled from the microscale equations. We present an effective thermal electrochemical model obtained using asymptotic homogenisation, which includes the electrochemical model at the cell level coupled with a thermal model that can be defined either at the cell or the battery level. The main aspects of the model are the consideration of thermal effects, the diffusion effects in the electrode particles, and the anisotropy of the material based on the microstructure, all of them incorporated in a systematic manner. We also compare the homogenised model with the standard electrochemical Doyle, Fuller & Newman model

Systematic derivation and validation of a reduced thermal-electrochemical model for lithium-ion batteries using asymptotic methods

The widely used Doyler-Fuller-Newman (DFN) model for lithium-ion batteries is too computationally expensive for certain applications, which has motivated the appearance of a plethora of simpler models. These models are usually posed in an ad hoc manner, leading to inconsistencies with the DFN model and to multiple formulations of the same model, with the Single Particle Model (SPM) being a very good example of the latter. In this work, we discuss the concept of SPM-type models showing that, despite the multiple formulations found in the literature, these models always follow the same structure, and we extend this discussion to models accounting for thermal effects. Then, we present a Thermal Single Particle Model with electrolyte (TSPMe) derived in a systematic manner using asymptotic techniques. The validation of the TSPMe against a thermal DFN model shows very high accuracy with a computational cost over forty times smaller. The comparison against experimental data shows that the model does a reasonable job predicting the behaviour of a real battery, but a very good parameter set is required to obtain accurate predictions

Development of experimental techniques for parameterization of multi-scale lithium-ion battery models

Presented here, is an extensive 35 parameter experimental data set of a cylindrical 21700 commercial cell (LGM50), for an electrochemical pseudo-two-dimensional (P2D) model. The experimental methodologies for tear-down and subsequent chemical, physical, electrochemical kinetics and thermodynamic analysis, and their accuracy and validity are discussed. Chemical analysis of the LGM50 cell shows that it is comprised of a NMC 811 positive electrode and bi-component Graphite-SiOx negative electrode. The thermodynamic open circuit voltages (OCV) and lithium stoichiometry in the electrode are obtained using galvanostatic intermittent titration technique (GITT) in half cell and three-electrode full cell configurations. The activation energy and exchange current coefficient through electrochemical impedance spectroscopy (EIS) measurements. Apparent diffusion coefficients are estimated using the Sand equation on the voltage transient during the current pulse; an expansion factor was applied to the bi-component negative electrode data to reflect the average change in effective surface area during lithiation. The 35 parameters are applied within a P2D model to show the fit to experimental validation LGM50 cell discharge and relaxation voltage profiles at room temperature. The accuracy and validity of the processes and the techniques in the determination of these parameters are discussed, including opportunities for further modelling and data analysis improvements

Extended Stefan problem for the solidification of binary alloys in a sphere

We study the extended Stefan problem which includes constitutional supercooling for the solidification of a binary alloy in a finite spherical domain. We perform an asymptotic analysis in the limits of large Lewis number and small Stefan number which allows us to identify a number of spatio-temporal regimes signifying distinct behaviours in the solidification process, resulting in an intricate boundary layer structure. Our results generalise those present in the literature by considering all time regimes for the Stefan problem while also accounting for impurities and constitutional supercooling. These results also generalise recent work on the extended Stefan problem for finite planar domains to spherical domains, and we shall highlight key differences in the asymptotic solutions and the underlying boundary layer structure which result from this change in geometry. We compare our asymptotic solutions with both numerical simulations and real experimental data arising from the casting of molten metallurgical grade silicon through the water granulation process, with our analysis highlighting the role played by supercooling in the solidification of binary alloys appearing in such applications

Investigating changes in transport, kinetics and heat generation over NCA/Gr-SiOx battery lifetime

We present a study of battery ageing, comparing pristine, calendar-aged, and cycle-aged lithium-ion cells. Insight into degradation was obtained via differential voltage analysis and by estimating and tracking changes in a subset of electrochemical model parameters of the single particle model through inverse modelling. We show that both diffusion time and kinetic overpotential increase in cycle-aged cells, while calendar-aged cells experienced no diffusion time changes but some kinetic overpotential increase. The latter is also evident in 50% higher irreversible heat generation in cycle-aged cells. This study highlights the importance of updating battery model parameters during ageing

Segmentation and Scene Content in Moving Images

The problem of scene content in moving images was brought by Aralia. The goal in this study group was to consider two problems. The first was image segmentation and the second is the context of the scene. These problems were explored in different areas, namely the Bayesian approach to image segmentation, shadow detection, shape recognition and background separation

"Knees" in lithium-ion battery aging trajectories

Lithium-ion batteries can last many years but sometimes exhibit rapid, nonlinear degradation that severely limits battery lifetime. In this work, we review prior work on "knees" in lithium-ion battery aging trajectories. We first review definitions for knees and three classes of "internal state trajectories" (termed snowball, hidden, and threshold trajectories) that can cause a knee. We then discuss six knee "pathways", including lithium plating, electrode saturation, resistance growth, electrolyte and additive depletion, percolation-limited connectivity, and mechanical deformation -- some of which have internal state trajectories with signals that are electrochemically undetectable. We also identify key design and usage sensitivities for knees. Finally, we discuss challenges and opportunities for knee modeling and prediction. Our findings illustrate the complexity and subtlety of lithium-ion battery degradation and can aid both academic and industrial efforts to improve battery lifetime.Comment: Submitted to the Journal of the Electrochemical Societ