On 4 July 2005, many observatories around the world and in space observed the collision of Deep Impact with comet 9P/Tempel 1 or its aftermath. This was an unprecedented coordinated observational campaign. These data show that (i) there was new material after impact that was compositionally different from that seen before impact; (ii) the ratio of dust mass to gas mass in the ejecta was much larger than before impact; (iii) the new activity did not last more than a few days, and by 9 July the comet's behavior was indistinguishable from its pre-impact behavior; and (iv) there were interesting transient phenomena that may be correlated with cratering physics.

The results of 2D Finite Element thermal simulations of Direct Energy Deposition of a High Speed Steel thick deposit explain the observed microstructural heterogeneities over the whole height of a 36layer deposit. The Finite Element model is validated by the recorded substrate temperature and the melt pool depth of the last clad layer experimentally measured. The correlation between the computed thermal fields and the microstructures of three points of interest located at different depths within the deposit is carried out. The effect of both the melt superheating temperature and the thermal cyclic history on the carbides type, shape and size is discussed.

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The microstructure directly influences the subsequent mechanical properties of materials. In the manufactured parts, the elaboration processes set the microstructure features such as phase types or the characteristics of defects and grains. In this light, this article aims to understand the evolution of the microstructure during the directed energy deposition (DED) manufacturing process of Ti6Al4V alloy. It sets out a new concept of time-phase transformation-block (TTB). This innovative segmentation of the temperature history in different blocks allows us to correlate the thermal histories computed by a 3D finite element (FE) thermal model and the final microstructure of a multilayered Ti6Al4V alloy obtained from the DED process. As a first step, a review of the state of the art on mechanisms that trigger solid-phase transformations of Ti6Al4V alloy is carried out. This shows the inadequacy of the current kinetic models to predict microstructure evolution during DED as multiple values are reported for transformation start temperatures. Secondly, a 3D finite element (FE) thermal simulation is developed and its results are validated against a Ti6Al4V part representative of repair technique using a DED process. The building strategy promotes the heat accumulation and the part exhibits heterogeneity of hardness and of the nature and the number of phases. Within the generated thermal field history, three points of interest (POI) representative of different microstructures are selected. An in-depth analysis of the thermal curves enables distinguishing solid-phase transformations according to their diffusive or displacive mechanisms. Coupled with the state of the art, this analysis highlights both the variable character of the critical points of transformations, and the different phase transformation mechanisms activated depending on the temperature value and on the heating or cooling rate. The validation of this approach is achieved by means of a thorough qualitative description of the evolution of the microstructure at each of the POI during DED process. The new TTB concept is thus shown to provide a flowchart basis to predict the final microstructure based on FE temperature fields.

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The aim of this work is to present an efficient procedure for growing large metallic single crystals that associates a classical growth technique (namely, the critical strain-annealing—CSA—method) with advanced methods of accurate full-field strain measurements based on digital image correlation (DIC) technique and of sample geometry design using finite element analysis. Measuring the critical plastic strains with an accuracy better than 0.1% resulted in a significantly improved construction of the recrystallization diagram. Applying this “DIC-assisted CSA method” to an A1050 commercially pure aluminum allowed obtaining in less than two days (26 h to 30 h) large multi-crystal samples with a half dozen of large grains. Their length between 35 mm and 100 mm was in full agreement with the obtained recrystallization diagram.

The classical Marcinkiewicz theorem states that if an entire characteristic function Ψ X (u) := E[e iuX ] of a non-degenerate real-valued random variable X is of the form exp(P (u)) for some polynomial P , then X has to be a Gaussian. In this work, we obtain a broad, quantitative extension of this framework in several directions, establish central limit theorems (CLTs) with explicit rates of convergence, and demonstrate Gaussian fluctuations in continuous spin systems and general classes of point processes. Our work complements classical work of Ostrovskii, Linnik, Zimogljad and others, as well as recent advances by Michelen and Sahasrabudhe, and Eremenko and Fryntov. In particular, we obtain quantitative decay estimates on the Kolmogorov-Smirnov distance between X and a Gaussian under the condition that Ψ does not vanish only on a bounded disk. This leads to quantitative CLTs applicable to very general and possibly strongly dependent random systems. In spite of the general applicability, our rates for the CLT match the classic Berry-Esseen bounds for independent sums up to a log factor. We implement this programme for two important classes of models in probability and statistical physics. First, we extend to the setting of continuous spins a popular paradigm for obtaining CLTs for discrete spin systems that is based on the theory of Lee-Yang zeros, focussing in particular on the XY model, Heisenberg ferromagnets and generalised Ising models. Secondly, we establish Gaussian fluctuations for linear statistics of so-called α-determinantal processes for α ∈ R (including the usual determinantal, Poisson and permanental processes) under very general conditions, including in particular higher dimensional settings where structural alternatives such as random matrix techniques are not available. Our applications demonstrate the significance of having to control the characteristic function only on a (small) disk, and lead to CLTs which, to the best of our knowledge, are not known in generality. CONTENTS 4.5. Variance growth of Λ(ϕ L ) for α < 0 30 4.6. Proof of Theorem 1.6 35 References 36