Localization errors of the stochastic heat equation

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We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...

We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key fea ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the

C^1

requirement of Kirchhoff-Love-based discretizations. Weak enforcement of coupling conditions is achiev ...

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

In the attempt to reduce fuel consumption, a new generation of Ultra-High-By-Pass-Ratio (UHBR) turbofans have been introduced in the aeronautic industry which are structurally noisier especially at lower frequencies, because of their larger diameter, lower ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, ...

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...

We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily paralle ...

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

A luminescent solar concentrator (LSC) offers a viable solution to spectrally convert and concentrate both direct and diffuse sunlight without the need for tracking. Its potential for commercialization is currently limited by the optical performance. A det ...

Plasmas with negative triangularity (NT) shape have been recently shown to be able to achieve H-mode levels of confinement in L-mode, avoiding detrimental edge localised modes. Therefore, this plasma geometry is now studied as a possible viable option for ...

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...

Rubble stone masonry is a common construction typology of historical city centres and vernacular architecture. While past earthquakes have shown that it is one of the most vulnerable masonry construction typologies, there are few experimental campaigns giv ...

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...

Glacial moulins (cylindrical meltwater drainage shafts) provide valuable insights into glacier dynamics, but are inaccessible and hazardous environments for humans to study. Exploring them using passive sensor probes has revealed their complex geometry, wh ...

Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Localization errors of the stochastic heat equation

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Hitting with Probability One for Stochastic Heat Equations with Additive Noise

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

An interior penalty coupling strategy for isogeometric non-conformal Kirchhoff-Love shell patches

Geometric Learning: Leveraging differential geometry for learning and control

The Advection Boundary Law in presence of mean-flow and spinning modes

Spectral Estimators for High-Dimensional Matrix Inference

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

Frustrated magnets in the limit of infinite dimensions: Dynamics and disorder-free glass transition

Verification of the Fourier-enhanced 3D finite element Poisson solver of the gyrokinetic full-f code PICLS

Stable cones in the thin one-phase problem

Anomalous and Chern topological waves in hyperbolic networks

Radiative transfer in luminescent solar concentrators

First-principle based predictions of the effects of negative triangularity on DTT scenarios

Exploiting the Signal-Leak Bias in Diffusion Models

Experimental Investigation on Size-Effect of Rubble Stone Masonry Walls Under In-Plane Horizontal Loading: Overview and Preliminary Results

Stability of the Faber-Krahn inequality for the short-time Fourier transform

Into the ice: Exploration and data capturing in glacial moulins by a tethered robot

Residual-based attention in physics-informed neural networks