Concept

Critical point (mathematics)

Related publications (49)

X-point radiation, its control and an ELM suppressed radiating regime at the ASDEX Upgrade tokamak

Future fusion reactors require a safe, steady state divertor operation. The required detached operation is, in tokamaks with metal walls, usually achieved by seeding of impurities, such as nitrogen. With strong seeding levels, the dominant radiation is emi ...

IOP PUBLISHING LTD2021

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

On the relaxed maximum-likelihood blind MIMO channel estimation for orthogonal space-time block codes

Kamran Kalbasi

This paper concerns the maximum-likelihood channel estimation for MIMO systems with orthogonal space-time block codes when the finite alphabet constraint of the signal constellation is relaxed. We study the channel coefficients estimation subspace generate ...

ELSEVIER2020

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

Florent Gérard Krzakala, Lenka Zdeborová

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we fo ...

Curran Associates, Inc.2020

Buckling of pressurized spherical shells containing a through-thickness defect

Pedro Miguel Nunes Pereira de Almeida Reis, Matteo Pezzulla, Dong Yan

We present a study on the pressure buckling of thin, elastic spherical shells containing a thickness defect. Methodologically, we combine precision model experiments, finite element simulations, and a reduced axisymmetric shell model. We observe qualitativ ...

PERGAMON-ELSEVIER SCIENCE LTD2020

A new mechanism for filament disconnection at the X-point: poloidal shear in radial E × B velocity

Federico Nespoli, Davide Galassi

Plasma filaments generated by turbulence in the scrape-off layer are sometimes observed in experi- ments and simulations to disconnect from the target plate in the vicinity of the X-point, resulting in a “quiescent zone” with reduced fluctuations, possibly ...

2020

Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach

Gérôme Graf

I will try to explain, without going into too much detail, how one can consider a non-linear wave equation as a dynamical system and what it brings to the study of its solutions. We begin by considering our model case, the non-linear Klein-Gordon equation ...

EPFL2019

Simulation of plasma turbulence in the periphery of diverted tokamak by using the GBS code

Paolo Ricci, Paola Paruta, Fabio Riva, Christoph Wersal, Baptiste Jimmy Frei, Carrie Fiona Beadle

We report on the implementation of diverted magnetic equilibria in GBS and on first simulations in this geometry. GBS is a simulation code used to evolve plasma turbulence in the tokamak periphery by solving the drift-reduced Braginskii's equations. The mo ...

2018

Criteria for the existence of a potential well

Charles Stuart

We consider a critical point u(0) of a functional f is an element of C-1 (H, R), where H is a real Hilbert space, and formulate criteria ensuring that u(0) lies in a potential well of f without supposing that f' is Frechet differentiable at u(0). The deriv ...

Pergamon-Elsevier Science Ltd2017

An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the Optimal Power Flow Problem

Colin Neil Jones, Jean-Hubert Hours

A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place of the Cauchy po ...

2017

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