Blog
The quantum spin Brauer category
We introduce a diagrammatic braided monoidal category, the quantum spin Brauer category, together with a full functor to the category of finite-dimensional, type $1$ modules for $U_q(\mathfrak{so}(N))$ or $U_q(\mathfrak{o}(N))$. This functor becomes essentially surjective after passing to the idempotent completion. The quantum...
An efficient method for magnetic field extrapolation based on a family of analytical three-dimensional magnetohydrostatic equilibria
With current observational methods it is not possible to directly measure the magnetic field in the solar corona with sufficient accuracy. Therefore, coronal magnetic field models have to rely on extrapolation methods using photospheric magnetograms as boundary conditions. In recent years, due...
Fluctuated lattice-driven charge density wave far above the condensation temperature in kagome superconductor KV3Sb5
The kagome material AV$_3$Sb$_5$ exhibits multiple exotic orders, including an unconventional charge density wave (CDW). Elucidating the underlying mechanism behind the CDW transition is crucial for unraveling the complex interactions among these phases. However, the driving force of the CDW remains a...
Ultra-high dose rate 6 MeV electron irradiation generates stable [1-$^{13}$C]alanine radicals suitable for medical imaging with dissolution Dynamic Nuclear Polarisation
Dissolution Dynamic Nuclear Polarisation (dDNP) is an experimental technique that increases the sensitivity of magnetic resonance experiments by more than a factor of $10^5$, permitting isotopically-labelled molecules to be transiently visible in MRI scans with their biochemical fates spatially resolvable over time...
Finite-strain constitutive model for shape memory alloys formulated in the logarithmic strain space
This work presents a finite-strain version of an established three-dimensional constitutive model for polycrystalline shape memory alloys (SMA) that is able to account for the large deformations and rotations that SMA components may undergo. The model is constructed by applying the logarithmic...
Density of states and non-smooth Lyapunov exponent in the localized phase
Localization of wave functions in the disordered models can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is a smooth function of eigenenergy in...
Bridging Econometrics and AI: VaR Estimation via Reinforcement Learning and GARCH Models
In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to adapt to the complexity of the...
Existence and uniqueness of Leray-Hopf weak solution for the inhomogeneous 2D Navier–Stokes equations without vacuum
We prove the existence and uniqueness of weak solutions of the inhomogeneous incompressible Navier–Stokes equations without vacuum using the relative energy method. We present a novel and direct proof of the existence of weak solutions based on approximation with more regular solutions....
$H^1$ local exact controllability of some one-dimensional bilinear Schr{ö}dinger equations
The local exact controllability of the one-dimensional bilinear Schr{\”o}dinger equation with Dirichlet boundary conditions has been extensively studied in subspaces of H 3 since the seminal work of K. Beauchard. Our first objective is to revisit this result and establish the controllability...
Hitting and Covering Affine Families of Convex Polyhedra, with Applications to Robust Optimization
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new variants of these...