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Long and winding central paths
No full textPreprint arXiv:1405.4161We disprove a continuous analog of the Hirsch conjecture proposed by Deza, Terlaky and Zinchenko, by constructing a family of linear programs with 3r+4 inequalities in dimension 2r+2 where the central path has a total curvature in Ω(2r/r). Our method is to tropicalize the central path in linear programming. The tropical central path is the piecewise-linear limit of the central paths of parameterized families of classical linear programs viewed through logarithmic glasses. We show in particular that the tropical analogue of the analytic center is nothing but the tropical barycenter, i.e., the maximum of a tropical polyhedron. It follows that unlike in the classical case, the tropical central path may lie on the boundary of the tropicalization of the feasible set, and may even coincide with a path of the tropical simplex method. Finally, our counter-example is obtained as a deformation of a family of tropical linear programs introduced by Bezem, Nieuwenhuis and Rodríguez-Carbonell
Méthodes numériques pour la spatialisation sonore, de la simulation à la synthèse binaurale: Thèse pour l'obtention du titre de Docteur de l’École Polytechnique
No full textResearch conducted during this PhD were initiated by an industrial need identified by Digital Media Solutions, namely the creation of a tool for spatial sound rendering on headphones for blind people. Despite the many existing devices, technical 3D sound on headphones face since their appearance the major obstacle that prevents the achievement of high quality products. Indeed, to make the illusion of a perceptible sound space, it is necessary to individualize listening to each listener. Measurements in the laboratory provide with convincing results, but the process is not yet applicable to the public. Mathematical modeling of this experiment allows to consider replacing the measure by a numerical simulation. This thesis proposes both an efficient calculation engine adapted to the problem, and a 3D audio rendering engine in order to validate the approach.Les recherches effectuées lors de ce doctorat furent initiées par un besoin industriel identifié par la société Digital Media Solutions, à savoir la réalisation d'un outil de spatialisation sonore au casque destiné aux non-voyants. Malgré les nombreux dispositifs déjà existants, les techniques de son 3D sur casque butent, depuis leur apparition, sur un obstacle majeur, qui empêche la réalisation de produits de haute qualité. En effet, pour rendre l'illusion d'un espace sonore perceptible, il est nécessaire d'individualiser l'écoute pour chaque auditeur. Des mesures en laboratoire offrent des résultats convaincants, mais le processus n'est pas encore applicable au grand public. La modélisation mathématique de cette expérience permet d'envisager de remplacer la mesure par une simulation numérique. Cette thèse propose à la fois un moteur de calcul numérique efficace et adapté au problème posé, ainsi qu'un moteur de rendu audio 3D pour valider cette approch
Effect of Electron Irradiation on Superconductivity in Single Crystals of Ba(Fe1−xRux)2As2 (x = 0.24)
No full textInternational audienceA single crystal of isovalently substituted BaðFe1−xRuxÞ2As2 (x = 0.24) is sequentially irradiated with2.5 MeV electrons up to a maximum dose of 2.1 × 10^19 e−=cm2. The electrical resistivity is measuredin situ at T =22 K during the irradiation and ex situ as a function of temperature between subsequentirradiation runs. Upon irradiation, the superconducting transition temperature Tc decreases and the residualresistivity ρ0 increases. We find that electron irradiation leads to the fastest suppression of Tc comparedto other types of artificially introduced disorder, probably due to the strong short-range potential of thepointlike irradiation defects. A more detailed analysis within a multiband scenario with variable scatteringpotential strength shows that the observed Tc versus ρ0 is fully compatible with s+/-pairing, in contrast to earlier claims that this model leads to a too rapid suppression of Tc with scattering
On the steady flow of reactive gaseous mixture
No full textWe present the study of systems of equations governing a steady flow of poly-atomic, heat-conducting reactive gas mixture. It is shown that the corresponding system of PDEs admits a weak solution and renormalized solution to the continuity equation, provided the adiabatic exponent for the mixture γ is greater than 5 3
An incremental method for building and evaluating agent-based models of systems of cities
No full textThis paper offers a feedback on a modeling experience with the MARIUS model. It aims at exposing a method of parsimonious modeling using intensive quantitative evaluation. By confronting simple mechanisms of interurban exchanges with Soviet data of urban evolution, we explore the capacity of two models (the most parsimonious and a complexified one) to satisfy the macro-goal of reproducing the system's structure as well as a realistic simulation of micro-dynamics. This confrontation relies on a historical database and is evaluated through a calibration process and a sensitivity analysis using distributed computation. We show that the most simple model of spatial interactions we could think of was unable to reproduce the actual evolution of Soviet urbanisation between 1959 and 1989. However, by complexifying the model's structure by only two mechanisms, we were able to find results in accordance with our evaluation goals
Etude de la matière dense et tiède à l'aide de diagnostics X - Applications aux intérieurs planétaires
No full textWith the recent discovery of many exoplanets, modelling the interior of these celestial bodies is becoming a fascinating scientific challenge. In this context, it is crucial to accurately know the equations of state and the macroscopic and microscopic physical properties of their constituent materials in the Warm Dense Matter regime (WDM). Moreover, planetary models rely almost exclusively on physical properties obtained using first principles simulations based on density functional theory (DFT) predictions. It is thus of paramount importance to validate the basic underlying mechanisms occurring for key planetary constituents (metallization, dissociation, structural modifications, phase transitions, etc…) as pressure and temperature both increase. In this thesis, we were interested in two materials that can be mainly found in the Earth-like planets: silica, or SiO2, as a model compound of the silicates that constitute the major part of their mantles, and iron, which is found in abundance in their cores. These two materials were compressed and brought to the WDM regime by using strong shock created by laser pulses during various experiments performed on the LULI2000, JLF, GEKKO XII and LCLS laser facilities. In order to penetrate this dense matter and to have access to its both ionic and electronic structures, we have probed silica and iron with X-ray diagnostics, such as time-resolved X-ray Absorption Near Edge Structure (XANES) and time-resolved X-ray diffraction. In parallel with these experiments, we performed quantum molecular dynamics simulations based on DFT at conditions representative of the region investigated experimentally so as to extract the interesting physical processes and comprehend the limits of the implemented models. In particular, these works allowed us to highlight the metallization processes of silica in temperature and the structural changes of its liquid in density, as well as to more constrain the melting curve of iron at very high pressures.La découverte récente d’un grand nombre d’exoplanètes et en particulier de super-Terres fascine, entrainant avec elle des interrogations toutes aussi nombreuses. Comment modéliser la dynamique de ces objets célestes ? Comment interpréter leurs relations masse/volume ? Qu’en est-il de leur champ magnétique ? Pour aborder ces questions, il est primordial de connaître précisément les équations d’état et les propriétés physiques, autant macroscopiques que microscopiques, des matériaux qui les composent et qui sont soumis à des conditions extrêmes relevant du domaine de la matière dense et tiède (WDM). En outre, les propriétés physiques de ces matériaux, sur lesquels reposent presque exclusivement les modèles planétaires, sont obtenues grâce à des calculs de premier principe basés sur la théorie de la fonctionnelle de la densité (DFT). Il est par conséquent crucial de valider les processus fondamentaux intrinsèques à ces matériaux lorsque leur pression et leur température augmentent afin de confirmer et/ou corriger ces modèles : modifications de leur structure ionique et électronique, métallisation, dissociation, changements de phase, etc. Les travaux réalisés au cours de cette thèse se sont concentrés sur deux matériaux que l’on retrouve principalement dans les planètes de type tellurique : la silice, ou SiO2, comme composé modèle des silicates constituant essentiellement leur manteau, et le fer, élément présent en abondance en leur cœur. Ces matériaux ont été portés dans le régime de la WDM à l’aide de chocs créés par laser au cours de différentes campagnes expérimentales réalisées sur les grandes installations laser LULI2000, JLF (LLNL-USA), GEKKO XII (Japon) et LCLS (Stanford-USA). Afin de pénétrer et sonder cette matière dense et de collecter des renseignements précieux tant sur sa structure ionique qu’électronique, des diagnostics principalement basés sur l'emploi de rayonnement X - à savoir spectroscopie d'absorption près du flanc K (XANES) et diffraction résolues temporellement – ont été utilisés. Parallèlement à ces expériences, des calculs de dynamique moléculaire ab initio basés sur la théorie de la DFT ont été réalisés dans les mêmes conditions que celles atteintes expérimentalement afin d'en extraire les processus physiques intéressants et d'appréhender les limites de la modélisation mise en œuvre. L’ensemble de ces travaux a notamment permis de comprendre le mécanisme de fermeture du gap lors du processus de métallisation de la silice en température et les changements de structure de son liquide en densité, ainsi que de contraindre davantage la courbe de fusion du fer aux très hautes pressions
MODELING REAL ESTATE INVESTMENT DECISIONS IN HOUSEHOLDS
No full textThere is substantial literature on modelling individual residential location choices. We restrict here our attention to some key aspects discussed below, which remain overlooked in the litterature. First, the set of decisions related to residential location in a multiperiod setting typically involve a very large number of alternatives. At a given date, a choice entails several dimensions: where to locate, which dwelling types and which tenure status. A fine tuned demand analysis of housing choices, would consider dozens of small geographical units for potential locations, at least two tenure types (own or rent) and at least two dwelling types (apartment or house). Another aspect is: who makes residential location related decisions. Recent litterature (see Picard & Chiappori (2011), de Palma et al. (2013)) shows that accounting for intra-household negotiation processes provide a new understanding about how residential location choices may result from consensus reached by household members. Most of research work is yet based on unitary household approaches that consider there is a single decision maker in the family
Variations of oxygen-18 in West Siberian precipitation during the last 50 years
No full textInternational audienceGlobal warming is associated with large increases in surface air temperature in Siberia. Here, we apply the isotope-enabled atmospheric general circulation model ECHAM5-wiso to explore the potential of water isotope measurements at a recently opened monitoring station in Kourovka (57.04° N, 59.55° E) in order to successfully trace climate change in western Siberia. Our model is constrained to atmospheric reanalysis fields for the period 1957-2013 to facilitate the comparison with observations of dD in total column water vapour from the GOSAT satellite, and with precipitation d18O measurements from 15 Russian stations of the Global Network of Isotopes in Precipitation. The model captures the observed Russian climate within reasonable error margins, and displays the observed isotopic gradients associated with increasing continentality and decreasing meridional temperatures. The model also reproduces the observed seasonal cycle of d18O, which parallels the seasonal cycle of temperature and ranges from -25 &permil; in winter to 5 &permil; in summer. Investigating West Siberian climate and precipitation d18O variability during the last 50 years, we find long-term increasing trends in temperature and d18O, while precipitation trends are uncertain. During the last 50 years, winter temperatures have increased by 1.7 °C. The simulated long-term increase of precipitation d18O is at the detection limit (<1 &permil; per 50 years) but significant. West Siberian climate is characterized by strong interannual variability, which in winter is strongly related to the North Atlantic Oscillation. In winter, regional temperature is the predominant factor controlling d18O variations on interannual to decadal timescales with a slope of about 0.5 ‰ °C-1. In summer, the interannual variability of d18O can be attributed to short-term, regional-scale processes such as evaporation and convective precipitation. This finding suggests that precipitation d18O has the potential to reveal hydrometeorological regime shifts in western Siberia which are otherwise difficult to identify. Focusing on Kourovka, the simulated evolution of temperature, d18O and, to a smaller extent, precipitation during the last 50 years is synchronous with model results averaged over all of western Siberia, suggesting that this site will be representative to monitor future isotopic changes in the entire region. © 2014 Author(s)
The diurnal cycle of marine cloud feedback in climate models
No full textInternational audienceWe examine the diurnal cycle of marine cloud feedback using high frequency outputs in CFMIP-2 idealised uniform +4 K SST perturbation experiments from seven CMIP5 models. Most of the inter-model spread in the diurnal mean marine shortwave cloud feedback can be explained by low cloud responses, although these do not explain the model responses at the neutral/weakly negative end of the feedback range, where changes in mid and high level cloud properties are more important. All of the models show reductions in marine low cloud fraction in the warmer climate, and these are in almost all cases largest in the mornings when more cloud is present in the control simulations. This results in shortwave cloud feedbacks being slightly stronger and having the largest inter-model spread at this time of day. The diurnal amplitudes of the responses of marine cloud properties to the warming climate are however small compared to the inter-model differences in their diurnally meaned responses. This indicates that the diurnal cycle of cloud feedback is not strongly relevant to understanding inter-model spread in overall cloud feedback and climate sensitivity. A number of unusual behaviours in individual models are highlighted for future investigation. © 2014 Crown Copyright
Amélioration des accélérateurs laser-plasma : vers un laser à électrons libres compact
No full textWhen an intense and short laser pulse propagates through an underdensegas, it can accelerate a fraction of the electrons of the gas, andthereby generate an electron bunch with an energy of a few hundreds ofMeV. This phenomenon, which is referred to as laser-wakefield acceleration, has many potential applications, including the design of ultra-bright X-ray sources known as freeelectron lasers (FEL). However, these applications require the electronbunch to have an excellent quality (low divergence, emittance andenergy spread). In this thesis, different solutions to improve thequality of the electron bunch are developed, both analytically and through the use of Particle-In-Cell (PIC) simulations. It is first shown however that PIC simulations tend to erroneously overestimate the emittance of the bunch, due to the numerical Cherenkov effect. Thus, in order to correctly estimate the emittance, a modified PICalgorithm is proposed, which is not subject to this unphysical Cherenkov effect. Using this algorithm, we observed and studied a new mechanism togenerate the electron bunch: optical transverse injection. This mechanism can produce bunches with ahigh charge, a low emittance and a low energy spread. In addition, wealso proposed an experimental setup - the laser-plasma lens- which can strongly reduce the final divergence of the bunch.Finally, these results are put into context by discussing the propertiesrequired for the design of a compact FEL. It is shown in particularthat laser-wakefield accelerator could be advantageously combinedwith innovative laser-plasma undulators, in order to produce brightX-rays sources.Lorsque l'on focalise une impulsion laser courte et intense dans un gazsous-dense, celle-ci peut accélérer une fraction des électrons du gaz,et ainsi générer un faisceau d'électrons ayant une énergie de quelquescentaines de MeV. Ce phénomène, connu sous le nom d'accélérationlaser-plasma, pourrait avoir de nombreuses applications,notamment pour la réalisation de sources de rayons Xultra-intenses appelées lasers à électrons libres (LEL). Cependant,ces applications nécessitent que le faisceau d'électrons ait uneexcellente qualité (faible divergence, faible émittance et faible dispersion en énergie).Au cours de cette thèse, différentes solutions ont été développéesafin d'améliorer la qualité des faisceaux d'électrons issus del'accélération laser-plasma. Ce travail est effectué à travers desmodèles analytiques ainsi que dessimulations Particle-In-Cell (PIC). Nous commençons cependant par montrer que les simulations PIC onttendance à surestimer l'émittance du faisceau, en raison de l'effetCherenkov numérique. Afin d'estimer correctement l'émittance ici, nousproposons un algorithme PIC modifié qui n'est pas sujet à l'effetCherenkov numérique.A l'aide de cet algorithme, un nouveau mécanisme permettant de générerle faisceau est observé puis étudié : il s'agit de l'injection optique transverse. Les faisceaux produits par ce mécanisme sontcaractérisés par une forte charge, une faible divergence et une faibleémittance. Par ailleurs, nous proposons un dispositif - la lentille laser-plasma - qui permet defortement réduire la divergence finale des faisceaux. Cesrésultats sont placés dans leur contexte, à travers une discussion despropriétés nécessaires pour un laser à électrons libres compact. Nousmontrons en particulier que les accélérateurs laser-plasma pourraientêtre avantageusement combinés avec des onduleurs laser-plasmainnovants, afin de produire des sources de rayons X intenses