Biomathématique | EPFL Graph Search

La biomathématique est le domaine d'étude qui réunit la biologie et les mathématiques. De façon précise les biomathématiques sont constituées par l'ensemble des méthodes et techniques mathématiques, numériques et informatiques qui permettent d'étudier et de modéliser les phénomènes et processus biologiques. Il s'agit donc bien d'une science fortement pluridisciplinaire que le mathématicien seul (ou le biologiste seul) est incapable de développer. Pour naître et vivre cette discipline exige des équipes interdisciplinaires mues par le sens du concret. L'abstrait n'est qu'un moyen pour parvenir à une meilleure compréhension des phénomènes biologiques. Les biomathématiques ont des débouchés tant pratiques que théoriques dans de nombreux domaines comme la biologie des populations, la physiologie, la génomique, la pharmacologie Modèle en biomathématiques Un modèle est un système d'équations mathématiques rendant compte de toutes les données expérimentales connues du phénomène b

Exploiting Marginal Stability in Slow-Fast Quasilinear Dynamical Systems

Alessia Ferraro

The accurate investigation of many geophysical phenomena via direct numerical simulations is computationally not possible nowadays due to the huge range of spatial and temporal scales to be resolved. Therefore advances in this field rely on the development of new theoretical tools and numerical algorithms. In this work we investigate a new mathematical formalism that exploits the property of quasi-linear systems to self-tune towards marginally stable states. The inspiration for this study comes from the asymptotic analysis of strongly stratified flows, performed by Chini et al.. The application of multi-scale analysis to this problem, justified by the presence of scale separation, yields to a simplified quasi-linear model. In this reduced description small-scale instabilities evolve linearly about a large-scale hydrostatic field (whose evolution is fully non-linear) and modify it via a feedback term. From the only assumption of scale separation, two extremely interesting features of this model arise. First the presence of the coupling term between the two dynamics and second the quasi-linearity of the dynamics. The first aspect, generally not present in the hydrostatic approximation, can capture the non-local energy transfer between the small and the large scales, which is key for the quantification of the mixing efficiency in the deep ocean. The second aspect, namely the quasi-linearity, is suggestive of the self-organisation of the dynamics about marginally-stable states. This results in a coupled evolution where the fast dynamics adapts (is slaved) to the mean field, maintaining the marginal stability of the latter. The low-dimensional evolution that arises, enables the integration of the reduced system on temporal scales comparable to the characteristic time scale of the slow dynamics, making this novel approach highly suited to the investigation of the stratified flow problem.Building upon the results obtained by Chini et al. in the present work we extend this methodology addressing three different aspects of the reduced model.As a first case we investigate the twofold nature of the fluctuation feedback, which is not sign-definite and might lead to intense bursting events where the fluctuations exhibit positive growth rates on a fast time scale. In this scenario the scale separation is temporarily lost and the two dynamics have to be co-evolved until a new marginally stable manifold can be approached. Here we propose three different co-evolution techniques and test their efficacy on a one-dimensional model problem.The second aspect we address is the presence of a finite scale separation between the two dynamics. We develop an algorithm that carefully identifies the validity regions of the quasi-linear reduction and determines the relevance of the fluctuation feedback w.r.t. the characteristic time scale of the slow dynamics and the growth rate of the fluctuations.As a third case we derive an efficient extension of the original methodology to two-dimensional model problems, deriving an evolution equation for the wavenumber of the fastest growing mode, which then get slaved to the mean dynamics.Eventually the methodologies derived in the context of the two model problems are applied and discussed for the strongly stratified flow problem.

EPFL2022

Enhanced current and voltage regulators for stand-alone applications

Federico De Bosio

State feedback decoupling permits to achieve a better dynamic response for Voltage Source in stand-alone applications. The design of current and voltage regulators is performed in the discrete-time domain since it provides better accuracy and allows direct pole placement. As the attainable bandwidth of the current loop is mainly limited by computational and PWM delays, a lead compensator structure is proposed to overcome this limitation. The design of the voltage regulator is based on the Nyquist criterion, verifying to guarantee a high sensitivity peak. Discrete-time domain implementation issues of an anti-wind up scheme are discussed as well. Laboratory tests in compliance with the standard for UPS systems (IEC 62040-3) are performed to validate the theoretical analysis.

Ieee2016

A theoretical study of disorder and decomposition in multinary nitrides hard coatings materials

Björn Alling

The development of multinary nitrides materials has revolutionised the hard coatings industry over the last 20 years. Especially important materials systems in this matter have been TiAlN and CrAlN which shows higher hardness, better oxidation resistance and can perform at higher temperatures as compared to TiN. When synthesised through physical vapour deposition techniques these system form cubic rock salt structured Ti1-xAlxN and Cr1-xAlxN solid solutions as a metastable phase over a large part of the concentration range. One of the main objectives during the optimisation of the coatings has been to increase the amount of Al in the coating while still keeping the rock salt structure, avoiding phase separation and the formation of hexagonal wurtzite AlN. However, in Al-rich TiAlN coatings it was found that isostructural decomposition within the cubic phase was in fact beneficial for the coatings performance at working temperatures just below 1000 °C. The reason was that the formation of strained coherent c-AlN domains within the grains initiated a age-hardening of the coating. In the CrAlN coatings it is possible to solve a larger amount of Al in the cubic phase. Possibly connected to this fact is that no isostructural decomposition and in principle no age hardening has been observed in rock salt structured Cr1-xAlxN. Although large series of experimental investigations have been performed on these systems, no systematic theoretical study has yet been undertaken. This theoretical work is an attempt by means of first-principles calculations together with thermodynamics considerations within the framework of alloy theory, to close or decrease the knowledge gap between experimental observations of cutting performance of various coatings and the fundamental quantum mechanical and thermodynamics processes that governs it. We first consider the structural properties of the treated mixed nitride systems. The concept of atomic misfit or volume difference, which is well known in the community is studied and the physics that leads to a positive deviation from Vegard's rule is revealed. Then the TiAlN and CrAlN systems are studied in detail. A clear connection between the development of the electronic structure with composition and the mixing enthalpy of the alloys, and thus the tendency for decomposition, is found for TiAlN. The importance of magnetic effects on the thermodynamics of mixing in CrAlN is established leading to a qualitative lower tendency for decomposition. Since the nitrogen composition can deviate substantially from perfect stoichiometry in these systems, a study of the influence of nitrogen vacancies on the decomposition pattern of TiAlN in the cubic phase is performed. The results imply that a presence of nitrogen sub-stoichiometry in Al-rich TiAlN will enhance the tendency for isostructural decomposition. The achieved results including those for the systems ScAlN and HfAlN are compared and discussed especially by considering volume misfit and electronic bandstructure effects as driving forces for coherent and incoherent decomposition.

EPFL2009