Related papers: Renormalizing a Viscous Fluid Model for Large Scal…
We present a novel space-time isogeometric discretization of the acoustic wave equation in second-order formulation that is intrinsically unconditionally stable. The method relies on a variational framework inspired by [Walkington 2014],…
A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations…
We introduce a class of multi-scale systems with discrete time, motivated by the problem of inviscid limit in fluid dynamics in the presence of small-scale noise. These systems are infinite-dimensional and defined on a scale-invariant…
The renormalization group equations for large-scale structure (RG-LSS) describe how the bias and stochastic (noise) parameters -- both of matter and biased tracers such as galaxies -- evolve as a function of the cutoff $\Lambda$ of the…
Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for…
In this first part of two papers, we extend the C-method developed in [40] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact…
We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the…
Low-order virtual element methods (VEM) compute a consistent finite-strain contribution through polynomial projections and rely on stabilization to control the unresolved modes in the projector kernel. In current hyperelastic VEM practice,…
We are concerned with the large time behavior of solutions to the Cauchy problem of the one-dimensional compressible micropolar fluid model without viscosity, where the far-field states of the initial data are prescribed to be different. If…
We develop a non-linear distributional renormalisation algebra for Gaussian Quantum Foam, built from sequences of scaled Gaussians on spacelike hypersurfaces of homotopic, globally hyperbolic spacetimes and their distributional limits. The…
This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…
We derive a new formulation of the $3D$ compressible Euler equations with dynamic entropy exhibiting remarkable null structures and regularity properties. Our results hold for an arbitrary equation of state (which yields the pressure in…
This work is a continuation of the authors' work for the stochastic 2D Euler equation driven by transport type noise. Here we lift the incompressibility constraint. Instead we assume a weighted incompressibility condition. This condition is…
We study the renormalization group flow of the average action of the stochastic Navier--Stokes equation with power-law forcing. Using Galilean invariance we introduce a non-perturbative approximation adapted to the zero frequency sector of…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
We propose an algorithm for simulating stochastic relativistic fluid dynamics based on Metropolis updates. Each step of the algorithm begins with an update based on ideal hydrodynamics. This is followed by proposing random (spatial)…
We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary…
We study the Cauchy problem for the nonlinear wave equations (NLW) with random data and/or stochastic forcing on a two-dimensional compact Riemannian manifold without boundary. (i) We first study the defocusing stochastic damped NLW driven…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Amp\`{e}re (MA) equation, $\det \nabla \psi(x,t) = \mathsf{G}…