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Concept

Heat kernel

Related publications (17)

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Raphaël Jean Berthier

Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. T ...

OXFORD UNIV PRESS2022

Fredholm transformation on Laplacian and rapid stabilization for the heat equation

Shengquan Xiang

We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Eva Vidlicková

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

A dependence of the cost of fast controls for the heat equation on the support of initial datum

Hoài-Minh Nguyên

The controllability cost for the heat equation as the control time

T

goes to 0 is well-known of the order

e^{C/T}

for some positive constant

C

, depending on the controlled domain and for all initial datum. In this paper, we prove that the constant $C ...

2021

Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates

Luigi Forcella

We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a Dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State a ...

2021

Generalization of Fourier’s Law into Viscous Heat Equations

Nicola Marzari, Andrea Cepellotti, Michele Simoncelli

Heat conduction in dielectric crystals originates from the dynamics of atomic vibrations, whose evolution is well described by the linearized Boltzmann transport equation for the phonon populations. Recently, it was shown that thermal conductivity can be r ...

American Physical Society2020

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Fabio Nobile, Eva Vidlicková

In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

MATHICSE2019

Thermal conductivity of glassy GeTe4 by first-principles molecular dynamics

Assil Bouzid

A transient thermal regime is achieved in glassy GeTe4 by first-principles molecular dynamics following the recently proposed ''approach-to-equilibrium'' methodology. The temporal and spatial evolution of the temperature do comply with the time-dependent s ...

Royal Soc Chemistry2017

A new method for reducing local heat transfer data in multimicrochannel evaporators

John Richard Thome, Navid Borhani, Nicolas Lamaison, Houxue Huang

Measuring the strong local variation in heat transfer coefficients in multi-microchannel evaporators is related to the inverse heat conduction problem (IHCP). As the local flow heat transfer coefficients change greatly in magnitude from single-phase liquid ...

Elsevier France-Editions Scientifiques Medicales Elsevier2017

Metal artefact reduction in computed tomography images by a fourth-order total variation flow

Alfio Quarteroni, Elena Faggiano

Permanent metallic implants, such as dental fillings and cardiac devices, generate streaks-like artefacts in computed tomography (CT) images. In this article, we propose a strategy to perform metal artefact reduction (MAR) that relies on the total variatio ...

Taylor & Francis Ltd2016

Conservation Schemes For Convection-Diffusion Equations With Robin Boundary Conditions

Jacques Rappaz, Stéphane Flotron

In this article, we present a numerical scheme based on a finite element method in order to solve a time-dependent convection-diffusion equation problem and satisfy some conservation properties. In particular, our scheme is able to conserve the total energ ...

EDP Sciences2013

Thermal diffusivity of seasonal snow determined from temperature profiles

Marc Parlange, Wolf Hendrik Huwald, Chad Higgins, Holly Jayne Oldroyd

Thermal diffusivity of snow is an important thermodynamic property associated with key hydrological phenomena such as snow melt and heat and water vapor exchange with the atmosphere. Direct determination of snow thermal diffusivity requires coupled point m ...

Elsevier2013

Statistical modelling of ground temperature in mountain permafrost

Anthony Christopher Davison, Juliette Ferial Blanchet

Permafrost consists of soil and rocks that remain at 0 degrees C or below for at least two consecutive years. In mountains, permafrost ground ice acts like cement, stabilizing rock walls. Its degradation, following climate warming, may lead to slope instab ...

2012

On Source Coding for Distributed Temperature Sensing with Shift-Invariant Geometries

Robert Konsbruck

We study the source coding problem in sensor networks deployed to monitor the evolution of spatio-temporal temperature distributions. The sensors sample the temperature field, quantize the samples and transmit the encoded samples through digital channels t ...

Institute of Electrical and Electronics Engineers2011

On the truly meshless solution of heat conduction problems in heterogeneous media

Jian Zhao, Aurèle Parriaux, Jiannong Fang, Gaofeng Zhao

A truly meshless method based on the weighted least-squares (WLS) approximation and the method of point collocation is proposed to solve heat conduction problems in heterogeneous media. It is shown that, in the case of strong heterogeneity, accurate and sm ...

2009

An Anisotropic Error Estimator For The Crank-Nicolson Method: Application To A Parabolic Problem

Marco Picasso

In this paper we derive two a posteriori upper bounds for the heat equation. A continuous, piecewise linear finite element discretization in space and the Crank-Nicolson method for the time discretization are used. The error due to the space discretization ...

2009

Simulation numérique des phénomènes thermiques et magnétohydrodynamiques dans une cellule de Hall-Héroult

Yasser Safa

This work is concerned with a numerical simulation of the thermal behaviour of an electrolysis cell for the production of the aluminium. Aluminium is produced by an electrolytic reduction of alumina dissolved in a bath of molten cryolite. In this reduction ...

EPFL2005