The superconducting motors and generators are a particularly interesting solution for electric propulsion and power generation. These superconducting devices are used to obtain power and torque and mass volume very high. Moreover, the high efficiency of these machines, making them attractive in terms of saving energy. One goal is to find new structures of superconducting machines or optimizing existing ones. One of technical challenges that are superconducting windings must be cooled to a few tens of Kelvin and connected to transmit torque to the outside environment at room temperature with minimal heat loss. Among all the achievements we may distinguish several major areas of power. Firstly, there are small machines with a capacity below 10 kilowatts. It is essentially built laboratory prototypes in academia to study all topologies engines imaginable and validate the principles of operation. In addition, there are machines whose power is between 10 and 100 kilowatts. These machines are intermediate between machines laboratory and industrial demonstrations. Their power, relatively large, validates technical solutions and explore topologies machine outside the box. Then there motors or alternators superconducting high power. These projects cover all industrial demonstrations to check the feasibility of such large-scale machinery and possibly locate a site of use. It is possible to replace the copper windings of an inductor by son superconductors. But another solution exists: to manufacture superconducting magnets. In the first case, we have high capacity power transmission son of superconductors, in the second case, we use the capacity of superconducting materials massive trap magnetic fields. It is necessary to compare the performance of these two types of inducers. Among the problems, there is the need to magnetize the superconducting materials in situ. The behavior of the superconducting magnet when subjected to a magnetizing field is one of the crucial points. One issue for the project we propose is to check if it is possible to induce a superconductor with superconducting magnets and compare it with an inductor designed with superconducting son. This industrial research project is divided into two parts: a very practical approach aimed at integrating conductive elements according to precise specifications in an electric motor sized target pre purposes of demonstration and validation, then a forward-looking approach aimed at use these results on devices larger machines or rotating at high speed. These efforts also aim to assess the potential of materials and their impacts on topology machines and associated cryogenic systems.

The motivation for the work planned in this project is to develop fondamental concepts and tools to reason about resource-related properties of software and computational systems. The approach followed is that of implicit computational complexity (ICC), which studies calculi and programming languages for complexity-bounded computation, for instance languages in which all programs are by construction of complexity Ptime (polynomial time w.r.t. the size of the input). ICC has been developed since the early 90s, starting from approaches in logic, recursion theory and functional programming. Various disciplines have been given in these calculi, based for instance on restrictions of recursion schemes or logical rules, and which allow to characterize complexity classes like Ptime, Pspace (e.g. work by Leivant, Jones, Girard, Marion) Typical techniques used are linear logic, type systems, interpretations, termination orderings... This project will investigate several directions of ICC. On the one hand it will deepen the semantical and logical foundations of ICC, in particular in linear logic. It will study how to certify the complexity of functional programs and will improve the criteria available in this area (in particular based on quasi-interpretations). Moreover it will explore the extension of ICC to two new areas: extraction from formal proofs of complexity-bounded programs on the one hand, and design of ICC criteria for concurrent systems in the setting of process calculi (like the Pi-calculus), on the other. In the first area, the idea is to define proof-systems such that after constructing a proof establishing the totality of a function defined by a specification, one can extract from the proof a program implementing the specification and certified of Ptime complexity. In the second area, concurrent systems, we would like to define techniques similar to those of the functional setting, allowing to certify statically for a system some bounds on the usage of resources,, like its running time or its number of processes and their sizes. Finally the project will also study the usage of ICC for characterizing parallel complexity classes like NC, the class of efficiently parallelizable algorithms.