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Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Related publications (35)

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Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Compact, Spatial-mode-interaction-free, Ultralow-loss, Nonlinear photonic integrated circuits

Tobias Kippenberg, Rui Ning Wang, Xinru Ji, Zheru Qiu, Junqiu Liu, Jijun He

We implement Euler bends to build compact high-Q Si3N4 racetrack microresonators, featuring a small footprint of only 0.21 mm(2) for 19.8 GHz FSR. We demonstrate that these multi-mode microresonators can be operated in the single-mode regime and generate a ...

IEEE2022

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Reaching Paris Agreement Goal through CDR/DAC Development: A Compact OR Model

Marc Vielle, Frédéric Louis François Babonneau, Alain Haurie

A compact operations research (OR) model is proposed to analyse the prospects of meeting the Paris Agreement targets when direct air capture technologies can be used or not. The main features of the model are (i) the representation of the economy and energ ...

2021

Log Barriers for Safe Non-convex Black-box Optimization

Maryam Kamgarpour, Andreas Krause, Ilnura Usmanova

We address the problem of minimizing a smooth function f0(x) over a compact set D defined by smooth functional constraints fi(x)≤0, i=1,…,m given noisy value measurements of fi(x). This problem arises in safety-critical applications, where certain paramete ...

2019

Quantitative estimate on singularities in isoperimetric clusters

Maria Colombo

We prove a quantitative estimate on the number of certain singularities in almost minimizing clusters. In particular, we consider the singular points belonging to the lowest stratum of the Federer-Almgren stratification (namely, where each tangent cone doe ...

2019

Capsule recycling system for domestic coffee machines

Guglielmo Milan, Fernando Castañeda, Luca Massera

The system and method for used capsules (11), such as coffee capsules, with a lid and a capsule body, comprises at least cutting means (17) to cut the lid from the body, capturing means to extract the cut lid from the body, compacting means (12, 14) to com ...

2018

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

, ,

A compact and broadband orthomode transducer (OMT) with two dual linearly polarized ports is reported here for the first time. The component is based on a combination of two ridged Boifot junctions through a series of power dividers that act as an embedded ...

IEEE2018

Introduced 50 years ago by David Kazhdan, Kazhdan's Property (T) has quickly become an active research area in mathematics, with a lot of important results. A few years later, this property has been generalized to discrete group actions by Robert J. Zimmer ...

EPFL2018

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018