Ramification of Some Automorphisms of Local Fields

AbstractLetkbe a perfect field of characteristicpand letγ∈Aut(k((t))). Define the ramification numbers ofγbyim=vt(γpm(t)−t)−1. We give a characterization of the sequences (im) which are the sequences of ramification numbers of infinite order automorphisms of formal power series fields over finite fields. Then, given a perfect field k, we give sufficient conditions on (im) to be the sequence of ramification numbers of an autormorphismγ∈Autk(k((t))) and we investigate these sequences (im) in the case where there existsσ∈Autk(k((t))) such thatσγ=γσwithσ≠γνfor allν∈Zp

Capturing material toughness by molecular simulation: accounting for large yielding effects and limits

The inherent computational cost of molecular simulations limits their use to the study of nanometric systems with potentially strong size effects. In the case of fracture mechanics, size effects due to yielding at the crack tip can affect strongly the mechanical response of small systems. In this paper we consider two examples: a silica crystal for which yielding is limited to a few atoms at the crack tip, and a nanoporous polymer for which the process zone is about one order of magnitude larger. We perform molecular simulations of fracture of those materials and investigate in particular the system and crack size effects. The simulated systems are periodic with an initial crack. Quasi-static loading is achieved by increasing the system size in the direction orthogonal to the crack while maintaining a constant temperature. As expected, the behaviors of the two materials are significantly different. We show that the behavior of the silica crystal is reasonably well described by the classical framework of linear elastic fracture mechanics (LEFM). Therefore, one can easily upscale engineering fracture properties from molecular simulation results. In contrast, LEFM fails capturing the behavior of the polymer and we propose an alternative analysis based on cohesive crack zone models. We show that with a linear decreasing cohesive law, this alternative approach captures well the behavior of the polymer. Using this cohesive law, one can anticipate the mechanical behavior at larger scale and assess engineering fracture properties. Thus, despite the large yielding of the polymer at the scale of the molecular simulation, the cohesive zone analysis offers a proper upscaling methodology.MIT Energy InitiativeShell Oil CompanySchlumberger Limite

Ramification of Automorphisms ofk((t))

AbstractLetkbe a field of characteristicpand letγ∈Autk(k((t))). Form⩾0 defineim=vt(γpmt−t)−1. We show that ifp∤i0is andi1<(p2−p+1)i0then there exists an integerbsuch thatim=i0+bp+bp2+…+bpmfor allm⩾1

Fracture toughness of calcium-silicate-hydrate from molecular dynamics simulations

Concrete is the most widely manufactured material in the world. Its binding phase, calcium-silicate-hydrate (C-S-H), is responsible for its mechanical properties and has an atomic structure fairly similar to that of usual calcium silicate glasses, which makes it appealing to study this material with tools and theories traditionally used for non-crystalline solids. Here, following this idea, we use molecular dynamics simulations to evaluate the fracture toughness of C-S-H, inaccessible experimentally. This allows us to discuss the brittleness of the material at the atomic scale. We show that, at this scale, C-S-H breaks in a ductile way, which prevents one from using methods based on linear elastic fracture mechanics. Knowledge of the fracture properties of C-S-H at the atomic scale opens the way for an upscaling approach to the design of tougher cement paste, which would allow for the design of slender environment-friendly infrastructures, requiring less material