Dirac delta function

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Effect of collisions on non-adiabatic electron dynamics in ITG-driven microturbulence

Stephan Brunner, Justin Richard Ball

Non-adiabatic electron response leads to significant changes in ion temperature gradient (ITG) eigenmodes, leading, in particular, to fine-structures that are significantly extended along the magnetic field lines at corresponding mode rational surfaces (MR ...

2021

Fractional extreme distributions

Thomas Simon, Lotfi Boudabsa

We consider three classes of linear differential equations on distribution functions, with a fractional order alpha is an element of [0; 1]. The integer case alpha = 1 corresponds to the three classical extreme families. In general, we show that there is a ...

2020

Explicit dynamic approach for unbounded domains in frictional contact with Rate and State laws

Jean-François Molinari, Roozbeh Rezakhani

The paper explores the ability of an explicit time integration procedure to simulate the dynamics of shear rupture between unbounded elastic blocks on frictional interface, modeled with the finite element method. The behaviour of the interface is governed ...

ELSEVIER2020

TV-based reconstruction of periodic functions

Matthieu Martin Jean-André Simeoni, Julien René Pierre Fageot

We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is formulated as a penalized convex optimization problem, taking the form of a sum ...

IOP PUBLISHING LTD2020

Discrete Helmholtz charge distribution at liquid-liquid interfaces: Electrocapillarity, capacitance and non-linear spectroscopy studies

Hubert Girault, Grégoire Clément Gschwend

The structure of the polarised interface between two immiscible electrolyte solutions (ITIES) has usually been deduced from electrocapillarity and capacitance measurements. However, these two methods only offer an indirect access to the surface change dens ...

ELSEVIER SCIENCE SA2020

Single shot acquisition of spatially resolved spin wave dispersion relations using X-ray microscopy

Dirk Grundler

For understanding magnonic materials the fundamental characterization of their frequency response is essential. However, determining full dispersion relations and real space wavelength measurements are challenging and time-consuming tasks. We present an ap ...

Nature Research2020

Strong convergence of multivariate maxima

Simone Padoan, Stefano Rizzelli

It is well known and readily seen that the maximum of n independent and uniformly on [0, 1] distributed random variables, suitably standardised, converges in total variation distance, as n increases, to the standard negative exponential distribution. We ex ...

CAMBRIDGE UNIV PRESS2020

A Note on BIBO Stability

Michaël Unser

The statements on the BIBO stability of continuoustime convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identi ...

2020

Efficient learning of smooth probability functions from Bernoulli tests with guarantees

Volkan Cevher, Paul Thierry Yves Rolland, Ali Kavis

We study the fundamental problem of learning an unknown, smooth probability function via pointwise Bernoulli tests. We provide a scalable algorithm for efficiently solving this problem with rigorous guarantees. In particular, we prove the convergence rate ...

2019

Optimal Spline Generators for Derivative Sampling

Michaël Unser, Shayan Aziznejad, Alireza Naderi

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

IEEE2019

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Discrete Helmholtz charge distribution at liquid-liquid interfaces: Electrocapillarity, capacitance and non-linear spectroscopy studies

Hubert Girault, Grégoire Clément Gschwend

ELSEVIER SCIENCE SA2020