Cette thèse porte sur la modélisation des piles à combustible à membrane d'échange de protons (PEMFC), en vue de leur surveillance et de leur diagnostic par spectroscopie d'impédance. La première partie du document présente le principe de fonctionnement de ces piles, ainsi que l'état de l'art de la modélisation et des méthodes de surveillance et diagnostic. Le modèle physique multi échelle particulièrement détaillé publié en 2005 par A.A. Franco sert de point de départ. Il est simplifié de façon à aboutir à un système d'équations aux dérivées partielles en une unique dimension spatiale. L'objectif principal de la seconde partie est l'analyse harmonique du fonctionnement de la pile. En s'inspirant de travaux classiques sur l'analyse géométrique de réseaux de réactions électrochimiques, un modèle réduit compatible avec la thermodynamique est obtenu. Cette classe de systèmes dynamiques permet de déterminer, pour un tel réseau, une formule analytique de l'impédance de l'anode et de la cathode d'une pile PEMFC. Un modèle complet de la pile est obtenu en connectant ces éléments à des éléments représentant la membrane, les couches diffuses et les couches de diffusion des gaz. Les modèles précédents supposent la pile représentée par une cellule unique et homogène. Afin de permettre d'en décrire les hétérogénéités spatiales, nous proposons finalement un résultat de modélisation réduite d'un réseau de cellules représentées par leur impédance. Ce modèle approxime l'impédance globale du réseau par une "cellule moyenne", connectée à deux cellules "série" et "parallèle" représentatives d'écart par rapport à la moyenne. / This PhD thesis focuses on reduced modeling of PEM fuel cell for supervision and diagnosis by impedance spectroscopy. The first part of the document presents the principle of the PEM fuel cell, as well as the state of the art of modeling and of the methods for supervision and diagnosis. The multiscale dynamic model published in 2005 by A.A. Franco is particularly detailed and serves as a starting point. It is simplified, in order to obtain a system of partial differential equations in a single spatial dimension. The second part is devoted to harmonic analysis of the PEM Fuel cell. Inspired by classical work on the geometric analysis of electrochemical reactions networks, a model compatible with thermodynamics is obtained. This class of dynamic systems allows establishing, for such a network, an analytical formula of the impedance of the anode and the cathode of the PEM fuel cell. A complete model of the cell is obtained by connecting these elements to the membrane, diffuse layers and gas diffusion layer. The previous models assumed the PEM Fuel cell represented by a single, homogeneous, cell. In order to describe the possible spatial heterogeneities, we finally propose a result of reduced modeling for the impedance of a cell network. This model approximates the overall impedance of the network by a "mean cell", connected to two cells, put in "serial" and "parallel", and representative of the deviations from the average.

Molecular recognition plays an essential role in the self-assembly and self-organisation of biological and chemical systems alike—allowing individual components to form complex interconnected networks. Within these systems, the nature of the recognition and reactive processes determines their functional and structural properties, and even small changes in their identity or orientation can exert a dramatic effect on the observed properties. The rapidly developing field of systems chemistry aims to move away from the established paradigm in which molecules are studied in isolation, towards the study of networks of molecules that interact and react with each other. Taking inspiration from complex natural systems, where recognition processes never operate in isolation, systems chemistry aims to study chemical networks with the view to examining the system-level properties that arise from the interactions and reactions between the components within these systems. The work presented in this thesis aims to advance the nascent field of systems chemistry by bringing together small organic molecules that can react and interact together to form interconnected networks, exhibiting complex behaviour, such as self-replication, as a result. Three simple building blocks are used to construct a network of two structurally similar replicators and their kinetic behaviour is probed through a comprehensive kinetic analysis. The selectivity for one of the recognition-mediated reactive processes over another is examined within the network in isolation as well as in a scenario where the network is embedded within a pool of exchanging components. The interconnected, two-replicator network is examined under far-from-equilibrium reaction-diffusion conditions, showing that chemical replicating networks can exhibit signs of selective replication—a complex phenomenon normally associated with biological systems. Finally, a design of a well-characterised replicator is exploited for the construction of a network integrating self-replication with a another recognition-directed process, leading to the formation of a mechanically-interlocked architecture—a [2]rotaxane.

This thesis is concerned with large-scale systems of Ordinary Differential Equations that model Biomolecular Reaction Networks (BRNs) in Systems and Synthetic Biology. It addresses the strategies of model reduction and decomposition used to overcome the challenges posed by the high dimension and stiffness typical of these models. A number of developments of these strategies are identified, and their implementation on various BRN models is demonstrated. The goal of model reduction is to construct a simplified ODE system to closely approximate a large-scale system. The error estimation problem seeks to quantify the approximation error; this is an example of the trajectory comparison problem. The first part of this thesis applies semi-definite programming (SDP) and dissipativity theory to this problem, producing a single a priori upper bound on the difference between two models in the presence of parameter uncertainty and for a range of initial conditions, for which exhaustive simulation is impractical. The second part of this thesis is concerned with the BRN decomposition problem of expressing a network as an interconnection of subnetworks. A novel framework, called layered decomposition, is introduced and compared with established modular techniques. Fundamental properties of layered decompositions are investigated, providing basic criteria for choosing an appropriate layered decomposition. Further aspects of the layering framework are considered: we illustrate the relationship between decomposition and scale separation by constructing singularly perturbed BRN models using layered decomposition; and we reveal the inter-layer signal propagation structure by decomposing the steady state response to parametric perturbations. Finally, we consider the large-scale SDP problem, where large scale SDP techniques fail to certify a system’s dissipativity. We describe the framework of Structured Storage Functions (SSF), defined where systems admit a cascaded decomposition, and demonstrate a significant resulting speed-up of large-scale dissipativity problems, with applications to the trajectory comparison technique discussed above.

The behavior of the Deoxyribonucleic Acid (DNA) molecule can be exploited to perform useful computation. It can also be ”programmed” using the language of Chemical Reaction Networks (CRNs). One specialized CRN construct is the Surface Chemical Reaction Network (SCRN). The SCRN construct can implement asynchronous cellular automata, which can in turn be used to implement digital logic circuits. SCRN based digital logic circuits are thought to have several advantages over regular CRN circuits. One of these proposed advantages is their scalability. This thesis investigates the scalability of SCRN based adder circuits, how does an increase in the number of bits affect the time required for the circuit to produce a correct result? Additionally, how is the throughput of the circuit affected when multiple additions are performed in a pipelined fashion? These questions are studied through experiments where the execution of optimized SCRN adder circuits is simulated. Due to the stochastic nature of SCRNs each such execution is all but guaranteed to be unique, requiring the simulation of the circuits to be repeated until a sufficiently large statistical sample has been collected. The results show these samples to follow a Gaussian distribution, regardless of the number of bits or the number of pipelined operations. The experiments show the simulated latency of the studied SCRN adder circuits to scale linearly with the number of input bits. The results also show that the throughput can be greatly improved through the pipelining of multiple operations. However, the results are inconclusive as to the maximum possible throughput of SCRN adder circuits. A conclusion of the project is that SCRN digital logic circuit design could conceivably benefit from the implementation of specialized components beyond the standard logic gates. / DNA-molekylen kan utnyttjas för att genomföra användbara beräkningar. Den kan också ”programmeras” via abstraktionen kemiska reaktionsnätverk. Ytbundna Kemiska Reaktionsnätverk (YKR) är i sin tur en vidare specialisering av sådana reaktionsnätverk. Ett YKR kan implementera en asynkrona cellulära automat, som i sin tur kan implementera kretsar för digital logik. Kretsar för digital logik byggda med YKR anses ha flera fördelar gentemot motsvarande kretsar byggda från vanliga kemiska reaktionsnätverk. En av dessa tilltänkta fördelar ligger i deras skalbarhet. Detta examensarbete undersöker skalbarheten hos YKR-baserade additions-kretsar, hur påverkar ett ökat antal bitar tiden som krävs för att kretsen ska producera ett korrekt resultat? Vidare, hur påverkas genomströmningen när flera operationer matas in direkt och genomför efter varandra i en pipeline? Dessa frågor studeras genom experiment där körningar av optimerande YKR-baserade additionskretsar simuleras. På grund av de stokastiska egenskaperna hos YKR är varje sådan körning i princip garanterad att vara unik, vilket kräver upprepade simuleringar av varje krets tills ett tillräckligt stort statistiskt urval har insamlats. Dessa resultat visar sig följa en normalfördelningskurva, oavsett antalet bitar eller antalet operationer som matats in i en pipeline. Experimenten visar att den simulerade latensen skalar linjärt med antalet indata-bitar för de studerade additionskretsarna. Resultaten visar även att genomströmningen förbättras avsevärt när flera operationer körs direkt efter varandra i en pipeline. Resultaten är dock ofullständiga när det gäller uppmätandet av additionskretsarna högsta möjliga genomströmning. En slutsats av projektet är att YKR-baserade kretsar för digital logik möjligen skulle kunna gagnas av implementerandet av specialiserade komponenter utöver de vanliga logikgrindarna.

Dynamical structure functions were developed as a partial structure representation of linear time-invariant systems to be used in the reconstruction of biological networks. Dynamical structure functions contain more information about structure than a system's transfer function, while requiring less a priori information for reconstruction than the complete computational structure associated with the state space realization. Early sufficient conditions for network reconstruction with dynamical structure functions severely restricted the possible applications of the reconstruction process to networks where each input independently controls a measured state. The first contribution of this thesis is to extend the previously established sufficient conditions to incorporate both necessary and sufficient conditions for reconstruction. These new conditions allow for the reconstruction of a larger number of networks, even networks where independent control of measured states is not possible. The second contribution of this thesis is to extend the robust reconstruction algorithm to all reconstructible networks. This extension is important because it allows for the reconstruction of networks from real data, where noise is present in the measurements of the system. The third contribution of this thesis is a Matlab toolbox that implements the robust reconstruction algorithm discussed above. The Matlab toolbox takes in input-output data from simulations or real-life perturbation experiments and returns the proposed Boolean structure of the network. The final contribution of this thesis is to increase the applicability of dynamical structure functions to more than just biological networks by applying our reconstruction method to wireless communication networks. The reconstruction of wireless networks produces a dynamic interference map that can be used to improve network performance or interpret changes of link rates in terms of changes in network structure, enabling novel anomaly detection and security schemes.