La quantification du risque avalanche à long terme dans un but de zonage et d'optimisation des moyens de protection est fait dans la plupart des pays sur la base de la connaissance des événements de forte intensité. Ces approches fondées sur les périodes de retours, centrées uniquement sur l'aléa, ne considèrent pas explicitement les éléments à risque étudiés (bâtiments, personnes à l'intérieur, etc.) et négligent les possibles contraintes budgétaires. Afin de palier à ces limitations, les méthodes de zonage basés sur le risque et les analyses coût-bénéfice ont récemment émergées. Elles combinent la distribution de l'aléa avec les relations de vulnérabilité des éléments étudiés. Ainsi, l'évaluation systématisée de la vulnérabilité des bâtiments permet de mieux quantifier le risque dans un couloir d'avalanche donné. Cependant, en pratique, les relations de vulnérabilité disponibles restent principalement limitées à de rares estimations empiriques déduites de l'analyse de quelques catastrophes survenues. De plus, les méthodes existantes basées sur le risque font face à des calculs encore lourds, et les hypothèses sur la modélisation de l'aléa sont discutables (choix de quelques scénarios, faible considération des valeurs extrêmes, etc.). Dans cette thèse, ces problèmes sont abordés en construisant grâce à une approche fiabiliste des relations de fragilité de différents configurations de bâtiments en béton armé (BA) sollicités par des avalanches de neige et également des relations de fragilité pour les personnes potentiellement à l'intérieur de ces bâtiments. Ces relations sont ensuite utilisées dans un cadre de quantification du risque et de recherche de structure de défense optimale. L'apport de cette thèse est donc l'enrichissement de la caractérisation de la vulnérabilité et du risque face aux avalanches par des approches de complexités variables utilisables en fonction de la spécificité du cas et du temps imparti pour conduire l'étude. La thèse est composée de quatre volets. D'abord, les courbes de fragilité associées à différents états limites de murs en BA soumis au chargement uniforme d'une avalanche sont obtenues à partir d'approches classiques de dimensionnement du BA. Ensuite, l'approche est étendue à des modèles numériques de bâtis plus riches (modèle masse-ressort) permettant de décrire en particulier l'évolution temporelle de la réponse du système. A partir de ces relations de fragilité, de nouvelles relations pour les personnes à l'intérieur de ces bâtiments sont proposées. Ces relations pour les bâtiments et les personnes sont utilisées dans une analyse complète de sensibilité du risque. Enfin, une formule analytique du risque basée sur la statistique des valeurs extrêmes est proposée pour efficacement quantifier le risque et obtenir une caractéristique optimale de digue paravalanche. / Long term avalanche risk quantification for mapping and the design of defense structures is done in mostcountries on the basis of high magnitude events. Such return period/level approaches, purely hazardoriented,do not consider elements at risk (buildings, people inside, etc.) explicitly, and neglect possiblebudgetary constraints. To overcome these limitations, risk based zoning methods and cost-benefit analyseshave emerged recently. They combine the hazard distribution and vulnerability relations for the elementsat risk. Hence, the systematic vulnerability assessment of buildings can lead to better quantify the riskin avalanche paths. However, in practice, available vulnerability relations remain mostly limited to scarceempirical estimates derived from the analysis of a few catastrophic events. Besides, existing risk-basedmethods remain computationally intensive, and based on discussable assumptions regarding hazard modelling(choice of few scenarios, little consideration of extreme values, etc.). In this thesis, we tackle theseproblems by building reliability-based fragility relations to snow avalanches for several building types andpeople inside them, and incorporating these relations in a risk quantification and defense structure optimaldesign framework. So, we enrich the avalanche vulnerability and risk toolboxes with approaches of variouscomplexity, usable in practice in different conditions, depending on the case study and on the time availableto conduct the study. The developments made are detailed in four papers/chapters.In paper one, we derive fragility curves associated to different limit states for various reinforced concrete(RC) buildings loaded by an avalanche-like uniform pressure. Numerical methods to describe the RCbehaviour consist in civil engineering abacus and a yield line theory model, to make the computations asfast as possible. Different uncertainty propagation techniques enable to quantify fragility relations linkingpressure to failure probabilities, study the weight of the different parameters and the different assumptionsregarding the probabilistic modelling of the joint input distribution. In paper two, the approach is extendedto more complex numerical building models, namely a mass-spring and a finite elements one. Hence, muchmore realistic descriptions of RC walls are obtained, which are useful for complex case studies for whichdetailed investigations are required. However, the idea is still to derive fragility curves with the simpler,faster to run, but well validated mass-spring model, in a “physically-based meta-modelling” spirit. Inpaper three, we have various fragility relations for RC buildings at hand, thus we propose new relationsrelating death probability of people inside them to avalanche load. Second, these two sets of fragilitycurves for buildings and human are exploited in a comprehensive risk sensitivity analysis. By this way,we highlight the gap that can exist between return period based zoning methods and acceptable riskthresholds. We also show the higher robustness to vulnerability relations of optimal design approaches ona typical dam design case. In paper four, we propose simplified analytical risk formulas based on extremevalue statistics to quantify risk and perform the optimal design of an avalanche dam in an efficient way. Asensitivity study is conducted to assess the influence of the chosen statistical distributions and flow-obstacleinteraction law, highlighting the need for precise risk evaluations to well characterise the tail behaviour ofextreme runouts and the predominant patterns in avalanche - structure interactions.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-03-08T13:00:17Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao_LeonardoDallaPorta.pdf: 4244662 bytes, checksum: 214ab17f2ee3583441af553e0a0a7931 (MD5) / Made available in DSpace on 2017-03-08T13:00:17Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao_LeonardoDallaPorta.pdf: 4244662 bytes, checksum: 214ab17f2ee3583441af553e0a0a7931 (MD5) Previous issue date: 2016-10-06 / FACEPE / Avalanches neuronais, assim como oscilações e sincronização, são padrões de atividade espontânea observados em redes neuronais. O conceito de avalanches neuronais foi concebido na última década. Esse padrão de atividade tem distribuições de tamanhos P(s) e durações P(d) invariantes por escala, i.e., obedecem relações do tipo lei de potência P(s) ∼ s −τ, com expoente τ ≃ 3/2, e P(d) ∼ d−τt, com expoente τt ≃ 2, respectivamente. Essas propriedades são compatíveis com a ideia de que o cérebro opera em um regime crítico. A partir dessas constatações, muitos estudos teóricos e experimentais reportaram os potenciais benefícios de um cérebro operando na criticalidade, como por exemplo a máxima sensibilidade aos estímulos sensoriais, máxima capacidade de informação e transmissão e uma ótima capacidade computacional. Modelos da classe de universalidade de percolação direcionada (DP) têm sido amplamente utilizados para explicar a estatística invariante por escala das avalanches neuronais. Porém estes modelos não levam em consideração a dinâmica dos neurônios inibitórios e, além disso, como apresentam uma transição de fase entre um estado absorvente e uma fase ativa, torna-se difícil conciliar o modelo com correlações temporais de longo alcance que são observadas experimentalmente em diferentes escalas espaciais. Neste contexto, um novo modelo computacional (CROs, do original em inglês Critical Oscillations) surgiu na literatura (Poil et al., J. Neurosci., 32 9817, 2012), incluindo neurônios inibitórios e buscando conciliar correlações temporais com avalanches neuronais. Neste modelo não há uma fase absorvente, e uma suposta transição de fases ocorre entre uma fase ativa e outra com oscilações coletivas. Devido à ausência de uma fase absorvente, avalanches neuronais são definidas comparando-se a atividade instantânea da rede com um limiar que depende da mediana da atividade total. Justamente na linha crítica do espaço de parâmetros, quando há uma balanço entre excitação e inibição neuronal, avalanches neuronais invariantes por escala são observadas juntamente com correlações temporais de longo alcance (ruído 1/ f). No presente trabalho, um estudo mais profundo a respeito dos resultados reportados para o modelo CROs foi realizado. As oscilações neuronais mostraram-se robustas para diferentes tamanhos de rede, e observamos que a dinâmica local reflete a dinâmica oscilatória global da rede. Correlações temporais de longo alcance foram observadas (num intervalo de escalas temporais) através da técnica de Detrended Fluctuation Analysis, sendo robustas perante modificações no tamanho da rede. O resultado foi confirmado pela análise direta do espectro, que apresentou decaimento do tipo 1/ f numa determinada faixa de frequências. O diagrama de fases do modelo mostrou-se robusto em relação ao tamanho da rede, mantendo-se o alcance das interações locais. Entretanto, os resultados mostraram-se fortemente dependentes do limiar utilizado para detecção das avalanches neuronais. Por fim, mostramos que distribuições de durações de avalanches são do tipo lei de potência, com expoente τt ≃ 2. Este resultado é inédito e o valor encontrado coincide com o expoente crítico da classe de universalidade de DP na dimensão crítica superior. Em conjunto, nossos resultados fornecem mais evidências de que o modelo CROs de fato apresenta uma transição de fases. / Neuronal avalanches, as well as waves and synchronization, are types of spontaneous activity experimentally observed in neuronal networks. The concept of neuronal avalanches was conceived in the past decade. This pattern of activity has distributions of size P(s) and duration P(d) which are scale invariant, i.e., follow power-law relations P(s) ∼ s−τ, with exponent τ ≃ 3/2, and P(d) ∼ d−τd, with exponent τt ≃ 2, respectively. These properties are compatible with the idea that the brain operates in a critical regime. From these findings, many theoretical and experimental studies have reported the potential benefits of a brain operating at criticality, such as maximum sensitivity to sensory stimuli, maximum information capacity and transmission and an optimal computational capabilities. Models belonging to the directed percolation universality class (DP) have been widely used to explain the scale invariant statistic of neuronal avalanches. However, these models do not take into account the dynamics of inhibitory neurons and, since as they present a phase transition between an absorbing state and an active phase, it is difficult to reconcile the model with long-range temporal correlations that are observed experimentally at different spatial scales. In this context, a new computational model (CROs, Critical Oscillations) appeared in the literature (Poil et al., J. Neurosci., 32 9817, 2012), including inhibitory neurons and seeking to reconcile temporal correlations with neuronal avalanches. In this model there is no absorbing phase, and a supposed phase transition occurs between an active phase and another with collective oscillations. Due to the lack of an absorbing phase, neuronal avalanches are defined comparing by the instant network activity with a threshold that depends of the total activity median. Precisely at the critical line in parameter space, when a balance between neuronal excitation and inhibition occurs, scale invariant neuronal avalanches are observed with long-range temporal correlations (1/ f-like noise). In the present work, a deeper study about the results reported for the CROs model was performed. Neuronal oscillations have been shown to be robust to increasing network sizes, and it was observed that local dynamic reflects the oscillatory global dynamic of the network. Long-range temporal correlations were observed (in a range of time scales) via Detrended Fluctuation Analysis, being robust against changes in network size. The result was confirmed by direct analysis of the spectrum, which showed a decay like 1/ f in a given frequency band. The phase diagram of the model was robust with respect to the network size, as long as the range of local interactions was kept. However, the results were dependent of the threshold used to detect neuronal avalanches. Finally, we have shown that the distributions of avalanches duration follows a power-law with exponent τt ≃ 2. This result is unprecedented and the value obtained coincides with the critical exponent of the DP universality class in the upper critical dimension. Together, our results provide further evidence that in fact the CROs model presents a phase transition.

Dense flows of grains are commonplace throughout natural and industrial environments, from snow-avalanches down the sides of mountains to flows of cereal down chutes as it is transported from one part of a factory to another. A ubiquitous feature in all of these flows is their ability to separate the different grain types when shaken, stirred, sheared or vibrated. Many flows are sheared through gravity and these flows are particularly efficient at segregating particles based on their size, with small particles percolating to the bottom of the flow and large particles collecting at the top. Within this mechanism, an asymmetry between the large and small particles has been observed, with small particles percolating downwards through many large particles at a faster rate than large particles rise upwards through many small particles. This alternative format thesis presents a revised continuum model for segregation of a bidisperse mixture that can account for this asymmetry. A general class of asymmetric segregation flux functions is introduced that gives rise to asymmetric velocities between the large and small grains. Exact solutions for segregation down an inclined chute, with homogenous and normally graded inflow conditions, show that the asymmetry can significantly enhance the distance for complete segregation. Experiments performed using a classical shear-box with refractive index matched scanning are able to quantify the asymmetry between large and small particles on both bulk and particle scales. The dynamics of a single small particle indicate that it not only falls down faster than a single large particle rises, but that it also exhibits a step-like motion compared to the smooth ascent of the large grain. This points towards an underlying asymmetry between the different sized constituents. The relationship between the segregation-time and the volume fraction of small grains is analysed, and solutions presented for the steady-state balance between segregation and diffusive remixing. These help to show the good agreement between the asymmetric model and experimental data. Segregation at the front of natural avalanches produces a recirculation zone, known as a `breaking size-segregation wave', in which large particles are initially segregated upwards, sheared towards the front of the flow, and overrun before being resegregated again. Solutions for the structure of this recirculation zone are derived using the asymmetric flux model, revealing a novel `lens-tail' structure. Critically, it is seen that a few large particles starting close to the bottom of the flow are swept a long way upstream and take a very long time to recirculate. The breaking size-segregation waves highlight the important interplay between segregation and the bulk velocity field. The properties of flowing monodisperse grains are explored through experiments on a cone that produce a beautiful radial fingering pattern. Equations developed in a conical coordinate system reproduce the measured linear relationship between fingering radius and initial flux, whilst also predicting the slowing and thinning dynamics of the flow. Overall, these results illustrate the complex nature of the granular rheology and provide perspectives for future modelling of segregation in dense granular flows.

This dissertation describes efforts to evaluate a recently proposed continuum model for the dense flow of dry granular materials (Jop, Forterre & Pouliquen, 2006, Nature, 441, 167-192). The model, based upon a generalisation of Coulomb sliding friction, is known to perform well when modelling certain simple free surface flows. We extend the application of this model to a wide range of flow configurations, beginning with six simple flows studied in detailed experiments (GDR MiDi, 2004, Eur. Phys. J. E, 14, 341-366). Two-dimensional shearing flows and problems of linear stability are also addressed. These examples are used to underpin a thorough discussion of the strengths and weaknesses of the model. In order to calculate the behaviour of granular material in more complicated configurations, it is necessary to undertake a numerical solution. We discuss several computational techniques appropriate to the model, with careful attention paid to the evolution of any shear-free regions that may arise. In addition, we develop a numerical scheme, based upon a marker-and-cell method, that is capable of modelling two-dimensional granular flow with a moving free surface. A detailed discussion of our unsuccessful attempt to construct a scheme based upon Lagrangian finite elements is presented in an appendix. We apply the marker-and-cell code to the key problem of granular slumping (Balmforth & Kerswell, 2005, J. Fluid Mech., 538, 399-428), which has hitherto resisted explanation by modelling approaches based on various reduced (shallow water) models. With our numerical scheme, we are able to lift the assumptions required for other models, and make predictions in good qualitative agreement with the experimental data. An additional chapter describes the largely unrelated problem of contact between two objects separated by a viscous fluid. Although classical lubrication theory suggests that two locally smooth objects converging under gravity will make contact only after infinite time, we discuss several physical effects that may promote contact in finite time. Detailed calculations are presented to illustrate how the presence of a sharp asperity can modify the approach to contact.

Heavy rainfall on the evening of January 9 and morning of January 10, 1983 triggered debris avalanches and debris torrents at Smith Creek, western Whatcom County, Washington, USA. Nine debris avalanches are back analyzed in detail. Conclusions are drawn concerning, 1) climatic controls on debris avalanches and debris torrents; 2) debris avalanche characteristics; 3) hillslope hydrology; 4) slope stability. Rainfall data show that the January 9-10, 1983 storm had a 71-year recurrence interval in the 12-hour duration, with less than 6-year recurrence intervals in 1, 2, and 3-hour durations. In contrast, rainfall during a torrent event on January 29-30, 1971 had recurrence intervals of less than 2 years in all durations, but snowmelt was a contributing factor. The types of debris torrents produced by these contrasting storms are discussed. Four distinct failure geometries are defined, based on avalanche descriptions: 1) wedges; 2) drainage depressions; 3) logging roads; 4) discontinuity surfaces. Three scour zones are also distinguished, based on slope segment types observed. To model storm water table levels a one-dimensional, vertical, transient, saturated-unsaturated finite difference infiltration program is linked to a kinematic wave equation. Rainfall duration and intensity, initial conditions, soil hydraulic conductivity, and soil depth are factors controlling vertical soil discharge rates. January, 1983 discharges are clearly distinguishable from comparison storm discharges at all avalanches. Kinematic wave results help differentiate Coulomb shear and washout type failures, and provide pore pressures for stability analyses. The modified Mohr-Coulomb strength equation is used to outline factors controlling debris avalanche initiation. The factors are: 1) slope angle; 2) soil depth; 3) soil density; 4) vegetative cover; 5) bedrock surface characteristics; 6) snow. These factors are quantitatively assessed. Infinite slope analyses show limiting slope angles of 29.7° for Group I vegetation, and 24.6° for Group III vegetation. Vegetative cover and soil depth are the two controlling factors that change significantly over the short term. A root cohesion parameter, Cr, is used to assess the shear strength provided by vegetation. Four vegetative covers are distinguished, three of which were logged between 1918 and 1950: Group I - relatively weak understory vegetation (Cr range: 1.6 -2.0 kPa); Group II - understory plus stunted trees (Cr range: 2.3 - 2.6 kPa); Group III - understory plus mixed, regenerating forest (Cr range: 2.6 - 3.0 kPa); Group IV - old-growth forest of higher root strength. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Neural networks show intrinsic ongoing activity even in the absence of information processing and task-driven activities. This spontaneous activity has been reported to have specific characteristics ranging from scale-free avalanches in microcircuits to the power-law decay of the power spectrum of oscillations in coarse-grained recordings of large populations of neurons. The emergence of scale-free activity and power-law distributions of observables has encouraged researchers to postulate that the neural system is operating near a continuous phase transition. At such a phase transition, changes in control parameters or the strength of the external input lead to a change in the macroscopic behavior of the system. On the other hand, at a critical point due to critical slowing down, the phenomenological mesoscopic modeling of the system becomes realizable. Two distinct types of phase transitions have been suggested as the operating point of the neural system, namely active-inactive and synchronous-asynchronous phase transitions. In contrast to normal phase transitions in which a fine-tuning of the control parameter(s) is required to bring the system to the critical point, neural systems should be supplemented with self-tuning mechanisms that adaptively adjust the system near to the critical point (or critical region) in the phase space. In this work, we introduce a self-organized critical model of the neural network. We consider dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate neurons with conductance-based synapses. Ignoring inhomogeneities and internal fluctuations, we first analyze the mean-field model. We choose the strength of the external excitatory input and the average strength of excitatory to excitatory synapses as control parameters of the model and analyze the bifurcation diagram of the mean-field equations. We focus on bifurcations at the low firing rate regime in which the quiescent state loses stability due to Saddle-node or Hopf bifurcations. In particular, at the Bogdanov-Takens (BT) bifurcation point which is the intersection of the Hopf bifurcation and Saddle-node bifurcation lines of the 2D dynamical system, the network shows avalanche dynamics with power-law avalanche size and duration distributions. This matches the characteristics of low firing spontaneous activity in the cortex. By linearizing gain functions and excitatory and inhibitory nullclines, we can approximate the location of the BT bifurcation point. This point in the control parameter phase space corresponds to the internal balance of excitation and inhibition and a slight excess of external excitatory input to the excitatory population. Due to the tight balance of average excitation and inhibition currents, the firing of the individual cells is fluctuation-driven. Around the BT point, the spiking of neurons is a Poisson process and the population average membrane potential of neurons is approximately at the middle of the operating interval $[V_{Rest}, V_{th}]$. Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes. Next, we consider self-tuning of the system at this critical point. The self-organizing parameter in our network is the balance of opposing forces of inhibitory and excitatory populations' activities and the self-organizing mechanisms are long-term synaptic plasticity and short-term depression of the synapses. The former tunes the overall strength of excitatory and inhibitory pathways to be close to a balanced regime of these currents and the latter which is based on the finite amount of resources in brain areas, act as an adaptive mechanism that tunes micro populations of neurons subjected to fluctuating external inputs to attain the balance in a wider range of external input strengths. Using the Poisson firing assumption, we propose a microscopic Markovian model which captures the internal fluctuations in the network due to the finite size and matches the macroscopic mean-field equation by coarse-graining. Near the critical point, a phenomenological mesoscopic model for excitatory and inhibitory fields of activity is possible due to the time scale separation of slowly changing variables and fast degrees of freedom. We will show that the mesoscopic model corresponding to the neural field model near the local Bogdanov-Takens bifurcation point matches Langevin's description of the directed percolation process. Tuning the system at the critical point can be achieved by coupling fast population dynamics with slow adaptive gain and synaptic weight dynamics, which make the system wander around the phase transition point. Therefore, by introducing short-term and long-term synaptic plasticity, we have proposed a self-organized critical stochastic neural field model.:1. Introduction 1.1. Scale-free Spontaneous Activity 1.1.1. Nested Oscillations in the Macro-scale Collective Activity 1.1.2. Up and Down States Transitions 1.1.3. Avalanches in Local Neuronal Populations 1.2. Criticality and Self-organized Criticality in Systems out of Equilibrium 1.2.1. Sandpile Models 1.2.2. Directed Percolation 1.3. Critical Neural Models 1.3.1. Self-Organizing Neural Automata 1.3.2. Criticality in the Mesoscopic Models of Cortical Activity 1.4. Balance of Inhibition and Excitation 1.5. Functional Benefits of Being in the Critical State 1.6. Arguments Against the Critical State of the Brain 1.7. Organization of the Current Work 2. Single Neuron Model 2.1. Impulse Response of the Neuron 2.2. Response of the Neuron to the Constant Input 2.3. Response of the Neuron to the Poisson Input 2.3.1. Potential Distribution of a Neuron Receiving Poisson Input 2.3.2. Firing Rate and Interspike intervals’ CV Near the Threshold 2.3.3. Linear Poisson Neuron Approximation 3. Interconnected Homogeneous Population of Excitatory and Inhibitory Neurons 3.1. Linearized Nullclines and Different Dynamic Regimes 3.2. Logistic Function Approximation of Gain Functions 3.3. Dynamics Near the BT Bifurcation Point 3.4. Avalanches in the Region Close to the BT Point 3.5. Stability Analysis of the Fixed Points in the Linear Regime 3.6. Characteristics of Avalanches 4. Long Term and Short Term Synaptic Plasticity rules Tune the EI Population Close to the BT Bifurcation Point 4.1. Long Term Synaptic Plasticity by STDP Tunes Synaptic Weights Close to the Balanced State 4.2. Short-term plasticity and Up-Down states transition 5. Interconnected network of EI populations: Wilson-Cowan Neural Field Model 6. Stochastic Neural Field 6.1. Finite size fluctuations in a single EI population 6.2. Stochastic Neural Field with a Tuning Mechanism to the Critical State 7. Conclusion

Although most processes governing the surface mass balance on mountain glaciers are well understood, the causes and extent of spatial variability in accumulation remain poorly constrained. In the present study, the EBFM distributed mass balance model is newly coupled to terrain based modelling routines estimating mass redistribution by snowdrift, preferential deposition, and avalanching (ST-EBFM) in order to model winter balance on Storglaciären, Sweden. STEBFM improves the spatial accuracy of winter balance simulations and proves to be a versatile and computationally inexpensive model. Accumulation on Storglaciären is primarily driven by direct precipitation, which seems locally increased due to small scale orographic effects. Wind driven snow transport leads to significant deposition in the accumulation zone and slight erosion in the ablation zone. The pattern is generally consistent from year to year. Avalanching is the smallest contributor to winter balance, but cannot be neglected. The physical complexity of avalanches and high year to year variability render simulations of the process somewhat uncertain, but observations seem to confirm the large impact that the process can have on the glacier at very localised scales. The role of mass transporting processes in maintaining the current mass equilibrium on Storglaciären highlights the necessity to understand the links between climatic predictors and accumulation in order to accurately assess climate sensitivity.

La croissance démographique récente au Nunavik a amené l'expansion de certains villages nordiques près de zones de relief propice au déclenchement d'avalanches de neige tant à l'hiver qu'au printemps. Dans l'optique de développer une méthode de prévision précoce des avalanches au Nunavik, la surveillance des versants en contexte périglaciaire est primordiale. Les objectifs principaux de cette recherche sont donc de caractériser les événements avalancheux survenus de 2017 à 2020 sur le versant sud-ouest de la vallée Tasiapik (Umiujaq, Nunavik) et d'identifier les conditions météorologiques favorables à leur déclenchement. Pour ce faire, nous avons utilisé des appareils photographiques automatisés qui affichent une valeur de température sur chaque image capturée. Les données de température extraites sur près de 39 500 photographies ont été comparées aux données de température de deux stations météorologiques à proximité. Les résultats ont démontré que les appareils photographiques sont précis pour la mesure de la température à la fin de l'automne et à l'hiver. Au printemps et en été, ils ont une grande propension à surestimer la température. Les erreurs de mesure de température des appareils photographiques ont été statistiquement liées à la couverture nuageuse et à la radiation solaire incidente moyenne journalière. Par ailleurs, les photographies ont permis de caractériser 130 dépôts avalancheux. Deux principaux régimes d'avalanches ont été décrits : un régime hivernal, et un régime printanier. Des analyses de régression progressive ont permis d'établir que les conditions météorologiques propices au déclenchement des avalanches hivernales sont l'augmentation de la température minimale quotidienne et les chutes de neige ≥ à 10 cm à court terme (2 à 4 jours). Au printemps, ces conditions consistent en l'accumulation de degrés-jours de fonte, l'augmentation de la température minimale quotidienne, et la hauteur du couvert nival. Deux modèles de régression logistique ont été testés. Ensemble, ces modèles ont maintenu un taux de bonne classification global de 70.21% et ont correctement identifié 45 des 79 journées avalancheuses observées dans la vallée Tasiapik de 2017 à 2020. / Recent population growth in Nunavik has led to the expansion of northern villages some of which are located near mountainous areas prone to snow avalanches releases in winter and in spring. To develop an early avalanche forecasting method in Nunavik, monitoring of slopes in a periglacial context is essential. The main objectives of this research were to characterize avalanche events that occurred from 2017 to 2020 on the southwestern slope of the Tasiapik Valley (Umiujaq, Nunavik) and to identify the meteorological conditions that were favorable to their triggering. To do so, we used automated time-lapse cameras which displayed a temperature value on each captured image. Temperature data extracted from nearly 39,500 photographs were compared to temperature data from two nearby weather stations. The results showed that the cameras were accurate in measuring temperature in the late fall and winter. In spring and summer, they have a high propensity to overestimate temperature. The temperature measurement errors of the cameras were statistically related to the observable cloud coverage and the daily average incident solar radiation. In addition, the photographs were used to characterize 130 snow avalanche deposits. Two main avalanche regimes were described: winter and spring. Stepwise regression analyses established that the meteorological conditions conducive to winter snow avalanche initiation are the increasing daily minimum air temperature and short term (2-4 days) snowfall episodes ≥ 10 cm. In spring, these conditions are the accumulation of melting degree days, the increase in daily minimum air temperature, and snow cover height. Two logistic regression models were tested. Together, the models maintained a global correct classification rate of 70.21% correctly identifying 45 of 79 avalanche days observed within Tasiapik Valley from 2017 to 2020.

Dans. les régions montagneuses, les avalanches de neige exercent une influence majeure sur la structure et la composition du couvert végétal résultant en une fragmentation de l'espace forestier. En France, la dendrochronologie est encore peu utilisée pour la reconstitution du régime passé des avalanches, la plupart des études s'appuyant sur des données .cl' archive. Cette étude présente une chronologie des avalanches sur un versant forestier d'un vallon du Massif des Écrins (Alpes françaises) depuis 1880. Cette reconstitution repose sur l'étude de cinq couloirs d'avalanche. Elle -montre que 27 avalanches de grande amplitude ont affecté le versant depuis 1880, dont 23 entre 1950 et 2006. L'activité des avalanches a été la plus forte lors des hivers 1951, 1991 et 2001. Les arbres (mélèze d'Europe (Larix decidua Mill.)) ont colonisé l'ensemble du versant au cours de la seconde moitié du XIXe siècle, autant dans les zones forestières que dans les couloirs actuels. L'analyse des conditions météorologiques locales met en évidence le rôle des précipitations de neige des mois de décembre et janvier dans l'activité des avalanches. Les avalanches ont contribué à la fragmentation de la forêt le long de trajectoires préférentielles. Le mélèze d'Europe se caractérise par une grande plasticité lui permettant de se maintenir dans les trajectoires d'avalanche. Les dommages répétés, comme le basculement ou la cassure de la tige, l'abrasion locale de la tige causant la destruction locale du cambium ou encore le déracinement des arbres, résultent en une diversité de formes de croissance . . Une classification a été développée dans le but d'illustrer la relation existant entre ces formes et le nombre d'avalanches ayant endommagé les arbres.

Dans cette thèse, on étudie des processus stochastiques issus de la physique statistique. Le mouvement Brownien fractionnaire, objet central des premiers chapitres, généralise le mouvement Brownien aux cas où la mémoire est importante pour la dynamique. Ces effets de mémoire apparaissent par exemple dans les systèmes complexes et la diffusion anormale. L’absence de la propriété de Markov rend difficile l’étude probabiliste du processus. On développe une approche perturbative autour du mouvement Brownien pour obtenir de nouveaux résultats, sur des observables liées aux statistiques des extrêmes. En plus de leurs applications physiques, on explore les liens de ces résultats avec des objets mathématiques, comme les lois de Lévy et la constante de Pickands. / In this thesis, we study stochastic processes appearing in different areas of statistical physics: Firstly, fractional Brownian motion is a generalization of the well-known Brownian motion to include memory. Memory effects appear for example in complex systems and anomalous diffusion, and are difficult to treat analytically, due to the absence of the Markov property. We develop a perturbative expansion around standard Brownian motion to obtain new results for this case. We focus on observables related to extreme-value statistics, with links to mathematical objects: Levy’s arcsine laws and Pickands’ constant. Secondly, the model of elastic interfaces in disordered media is investigated. We consider the case of a Brownian random disorder force. We study avalanches, i.e. the response of the system to a kick, for which several distributions of observables are calculated analytically. To do so, the initial stochastic equation is solved using a deterministic non-linear instanton equation. Avalanche observables are characterized by power-law distributions at small-scale with universal exponents, for which we give new results.