Related papers: The gradient flow formulation of the electroweak H…

Quantum algorithms have been identified as a potential means to accelerate computational fluid dynamics (CFD) simulations, with the lattice Boltzmann method (LBM) being a promising candidate for realizing quantum speedups. Here, we extend…

We present a second-order strictly length-preserving and unconditionally energy-stable rotational discrete gradient (Rdg) scheme for the numerical approximation of the Oseen-Frank gradient flows with anisotropic elastic energy functional.…

We compute the hadronic running of the electromagnetic and weak couplings in lattice QCD with $N_{\mathrm{f}}=2+1$ flavors of $\mathcal{O}(a)$ improved Wilson fermions. Using two different discretizations of the vector current, we compute…

Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…

Comprehension of metabolic pathways is considerably enhanced by metabolic flux analysis (MFA-ILE) in isotope labeling experiments. The balance equations are given by hundreds of algebraic (stationary MFA) or ordinary differential equations…

Hamiltonian learning is crucial to the certification of quantum devices and quantum simulators. In this paper, we propose a hybrid quantum-classical Hamiltonian learning algorithm to find the coefficients of the Pauli operator components of…

We calculate the gravitational form factors (GFFs) and pressure, shear and energy distributions for a quark state dressed with a gluon at one loop in QCD. We use the light-front Hamiltonian approach. In the light-front gauge, we use a…

We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…

Many observables of interest in lattice QCD are extracted from correlation functions involving the vector current. If Wilson fermions are used, it is therefore of practical importance that, besides the action, the current be O($a$) improved…

We report on the determination of the gradient flow scales in $N_f=2+1$ QCD using highly improved staggered quark (HISQ) ensembles generated by the HotQCD Collaboration for bare gauge couplings ranging from $\beta = 6.423$ to $8.400$. Using…

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.

Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that…

Lattice scales defined using gradient flow are typically very precise, while also easy to calculate. However, different definitions of flows and operators can differ significantly, suggesting possible systematical effects. Using a subset of…

We employ a new strategy for a non perturbative determination of the renormalized energy momentum tensor. The strategy is based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow.…

Our ability to resolve new physics effects is, largely, limited by the precision with which we calculate. The calculation of observables in the Standard (or a new physics) Model requires knowledge of associated hadronic contributions. The…

We calculate the PCAC mass for $(2+1)$ flavor full QCD with Wilson-type quarks. We adopt the Small Flow-time eXpansion (SFtX) method based on the gradient flow which provides us a general way to compute correctly renormalized observables…

The lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon are calculated on the lattice. The calculation is done with Wilson fermions and for three values of the hopping parameter $\kappa$, so that…

We present the complete one-loop matching of the baryon- and lepton-number-conserving low-energy effective field theory (LEFT) to the QCD gradient flow. Using Euclidean conventions and the background-field formulation of the gradient flow,…

Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…

We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of the Hele-Shaw…