On the nature of the Schmid transition in a resistively shunted Josephson junction

We study the phase diagram of a resistively shunted Josephson junction (RSJJ) in the framework of the boundary sine-Gordon model. Using the non-perturbative functional renormalization group (FRG) we find that the transition is not controlled by a single fixed point but by a line of fixed points, and compute the continuously varying critical exponent $\nu$. We argue that the conductance also varies continuously along the transition line. In contrast to the traditional phase diagram of the RSJJ -- an insulating ground state when the shunt resistance $R$ is larger than $R_q=h/(2e)^2$ and a superconducting one when $R<R_q$ -- the FRG predicts the transition line in the plane $(\alpha,E_J/E_C)$ to bend in the region $\alpha=R_q/R<1$ but we cannot discard the possibility of a vertical line at $\alpha=1$ ($E_J$ and $E_C$ denote the Josephson and charging energies of the junction, respectively). Our results regarding the phase diagram and the nature of the transition are compared with Monte Carlo simulations and numerical renormalization group results.Comment: 15 pages, 15 figure

Flowing bosonization in the nonperturbative functional renormalization-group approach

Bosonization allows one to describe the low-energy physics of one-dimensional quantum fluids within a bosonic effective field theory formulated in terms of two fields: the "density" field $\varphi$ and its conjugate partner, the phase $\vartheta$ of the superfluid order parameter. We discuss the implementation of the nonperturbative functional renormalization group in this formalism, considering a Luttinger liquid in a periodic potential as an example. We show that in order for $\vartheta$ and $\varphi$ to remain conjugate variables at all energy scales, one must dynamically redefine the field $\vartheta$ along the renormalization-group flow. We derive explicit flow equations using a derivative expansion of the scale-dependent effective action to second order and show that they reproduce the flow equations of the sine-Gordon model (obtained by integrating out the field $\vartheta$ from the outset) derived within the same approximation. Only with the scale-dependent (flowing) reparametrization of the phase field $\vartheta$ do we obtain the standard phenomenology of the Luttinger liquid (when the periodic potential is sufficiently weak so as to avoid the Mott-insulating phase) characterized by two low-energy parameters, the velocity of the sound mode and the renormalized Luttinger parameter.Comment: 24 pages, 2 figures; v4) close to published versio

Surrogate Models Coupled with Machine Learning to Approximate Complex Physical Phenomena Involving Aerodynamic and Aerothermal Simulations

Numerical simulations provide a key element in aircraft design process, complementing physical tests and flight tests. They could take advantage of innovative methods, such as artificial intelligence technologies spreading in aviation. Simulating the full flight mission for various disciplines pose important problems due to significant computational cost coupled to varying operating conditions. Moreover, complex physical phenomena can occur. For instance, the aerodynamic field on the wing takes different shapes and can encounter shocks, while aerothermal simulations around nacelle and pylon are sensitive to the interaction between engine flows and external flows. Surrogate models can be used to substitute expensive high-fidelitysimulations by mathematical and statistical approximations in order to reduce overall computation cost and to provide a data-driven approach. In this thesis, we propose two developments: (i) machine learning-based surrogate models capable of approximating aerodynamic experiments and (ii) integrating more classical surrogate models into industrial aerothermal process. The first approach mitigates aerodynamic issues by separating solutions with very different shapes into several subsets using machine learning algorithms. Moreover, a resampling technique takes advantage of the subdomain decomposition by adding extra information in relevant regions. The second development focuses on pylon sizing by building surrogate models substitutingaerothermal simulations. The two approaches are applied to aircraft configurations in order to bridge the gap between academic methods and real-world applications. Significant improvements are highlighted in terms of accuracy and cost gain

Surrogate Modeling of Aerodynamic Simulations for Multiple Operating Conditions Using Machine Learning

International audienceThis paper describes a methodology, called local decomposition method, which aims at building a surrogate model based on steady turbulent aerodynamic fields at multiple operating conditions. The various shapes taken by the aerodynamic fields due to the multiple operation conditions pose real challenges as well as the computational cost of the high-fidelity simulations. The developed strategy mitigates these issues by combining traditional surrogate models and machine learning. The central idea is to separate the solutions with a subsonic behavior from the transonic and high-gradient solutions. First, a shock sensor extracts a feature corresponding to the presence of discontinuities, easing the clustering of the simulations by an unsupervised learning algorithm. Second, a supervised learning algorithm divides the parameter space into subdomains, associated to different flow regimes. Local reduced-order models are built on each subdomain using proper orthogonal decomposition coupled with a multivariate interpolation tool. Finally, an improved resampling technique taking advantage of the subdomain decomposition minimizes the redundancy of sampling. The methodology is assessed on the turbulent two-dimensional flow around the RAE2822 transonic airfoil. It exhibits a significant improvement in terms of prediction accuracy for the developed strategy compared with the classical method of surrogate modeling