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Harmonic decomposition of the trace of 1D transfer matrices in layered media

Antonio Joaquin Garcia Suarez

The Transfer Matrix formalism is ubiquitous when it comes to study wave propagation in various stratified media, applications ranging from Seismology to Quantum Mechanics. A relation between variables at two points in two different layers can be establishe ...

2022

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

EPFL2022

A Characterisation Of The Continuum Gaussian Free Field In Arbitrary Dimensions

Juhan Aru

We prove that under certain mild moment and continuity assumptions, the d-dimensional continuum Gaussian free field is the only stochastic process satisfying the usual domain Markov property and a scaling assumption. Our proof is based on a decomposition o ...

ECOLE POLYTECHNIQUE2022

Slice Estimation in Diffusion MRI of Neonatal and Fetal Brains in Image and Spherical Harmonics Domains Using Autoencoders

Meritxell Bach Cuadra, Gabriel Girard, Erick Jorge Canales Rodriguez, Thomas Yu

Diffusion MRI (dMRI) of the developing brain can provide valuable insights into the white matter development. However, slice thickness in fetal dMRI is typically high (i.e., 3-5 mm) to freeze the in-plane motion, which reduces the sensitivity of the dMRI s ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

TCB-spline-based isogeometric analysis method with high-quality parameterizations

Xiaodong Wei

Isogeometric analysis (IGA) was introduced to integrate methods for analysis and computer-aided design (CAD) into a unified process. High-quality parameterization of a physical domain plays a crucial role in IGA. However, obtaining high-quality parameteriz ...

ELSEVIER SCIENCE SA2022

Koopmans Spectral Functionals in Periodic Boundary Conditions

Nicola Marzari, Nicola Colonna, Edward Baxter Linscott, Riccardo De Gennaro

Koopmans spectral functionals aim to describe simultaneously ground-state properties and charged excitations of atoms, molecules, nanostructures, and periodic crystals. This is achieved by augmenting standard density functionals with simple but physically ...

AMER CHEMICAL SOC2022

HP - A code for the calculation of Hubbard parameters using density-functional perturbation theory

Nicola Marzari, Iurii Timrov, Matteo Cococcioni

We introduce HP, an implementation of density-functional perturbation theory, designed to compute Hubbard parameters (on-site U and inter-site V ) in the framework of DFT+U and DFT+U+V. The code does not require the use of computationally expensive superce ...

ELSEVIER2022

Spectral analysis for transmission eigenvalue problems with and without the complementing conditions

Jean Louis-Alexandre Fornerod

The interior transmission eigenvalue problem is a system of partial differential equations equipped with Cauchy data on the boundary: the transmission conditions. This problem appears in the inverse scattering theory for inhomogeneous media when, for some ...

EPFL2022

Two-dimensional Hubbard model at finite temperature: Weak, strong, and long correlation regimes

Riccardo Rossi

We investigate the momentum-resolved spin and charge susceptibilities, as well as the chemical potential and double occupancy in the two-dimensional Hubbard model as functions of doping, temperature, and interaction strength. Through these quantities, we i ...

AMER PHYSICAL SOC2022

Optimal radial basis for density-based atomic representations

Michele Ceriotti, Félix Benedito Clément Musil, Jigyasa Nigam, Sergey Pozdnyakov, Alexander Jan Goscinski

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

2021

Physics-enhanced machine learning with symmetry-adapted and long-range representations

Andrea Grisafi

Theoretical and computational approaches to the study of materials and molecules have, over the last few decades, progressed at an exponential rate. Yet, the possibility of producing numerical predictions that are on par with experimental measurements is t ...

EPFL2021

Impact of quantum-chemical metrics on the machine learning prediction of electron density

Anne-Clémence Corminboeuf, Alberto Fabrizio, Ksenia Briling

Machine learning (ML) algorithms have undergone an explosive development impacting every aspect of computational chemistry. To obtain reliable predictions, one needs to maintain a proper balance between the black-box nature of ML frameworks and the physics ...

AMER INST PHYSICS2021