178 research outputs found
Mott-glass phase of a one-dimensional quantum fluid with long-range interactions
We investigate the ground-state properties of quantum particles interacting
via a long-range repulsive potential
() or () that interpolates between the Coulomb potential and the
linearly confining potential of the Schwinger model. In the
absence of disorder the ground state is a Wigner crystal when .
Using bosonization and the nonperturbative functional renormalization group we
show that any amount of disorder suppresses the Wigner crystallization when
; the ground state is then a Mott glass, i.e., a state that
has a vanishing compressibility and a gapless optical conductivity. For
the ground state remains a Wigner crystal.Comment: v2) 6+10 pages, 3+1 figure
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 . 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 is larger than and a superconducting one
when -- the FRG predicts the transition line in the plane
to bend in the region but we cannot discard
the possibility of a vertical line at ( and 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 and its conjugate partner, the phase
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 and to remain conjugate variables at
all energy scales, one must dynamically redefine the field 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 from the outset) derived
within the same approximation. Only with the scale-dependent (flowing)
reparametrization of the phase field 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
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