Related papers: Solving functional flow equations with pseudo-spec…
In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different…
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We derive a linear…
We describe a supersymmetric RG flow between conformal fixed points of a two-dimensional quantum field theory as an analytic domain wall solution of the three-dimensional SO(4) x SO(4) gauged supergravity. Its ultraviolet fixed point is an…
We show that convexity of the effective action follows from its functional flow equation. Our analysis is based on a new, spectral representation. The results are relevant for the study of physical instabilities. We also derive constraints…
In this article, we propose an efficient time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations. The method achieves second-order accuracy in time and spectral accuracy in phase space, both of which…
This paper surveys machine-learning-based super-resolution reconstruction for vortical flows. Super resolution aims to find the high-resolution flow fields from low-resolution data and is generally an approach used in image reconstruction.…
Mixed-dimensional mathematical models for flow in fractured media have been prevalent in the modeling community for almost two decades, utilizing the explicit representation of fractures by lower-dimensional manifolds embedded in the…
We develop a diffuse solid method that is versatile and accurate for modeling wetting and multiphase flows in highly complex geometries. In this scheme, we harness N + 1-component phase field models to investigate interface shapes and flow…
A new framework for two-fluids flow using a Finite Element/Level Set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red…
In fluid flow imaging, intensity gradients are a good measure of spatial variations in scalar properties, which play an important role in controlling transport processes. However, current flow imaging techniques exhibit system-limited…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…
Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this…
We compute three-point functions for the $SL(2,\mathbb R)$-WZNW model. After reviewing the case of the two-point correlator, we compute spectral flow preserving and nonpreserving correlation functions in the space-time picture involving…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in…
Although many deep-learning-based super-resolution approaches have been proposed in recent years, because no ground truth is available in the inference stage, few can quantify the errors and uncertainties of the super-resolved results. For…
We demonstrate an application of the spectral method as a numerical approximation for solving Hyperbolic PDEs. In this method a finite basis is used for approximating the solutions. In particular, we demonstrate a set of such solutions for…
The double distribution function approach is an efficient route towards extension of kinetic solvers to compressible flows. With a number of realizations available, an overview and comparative study in the context of high speed compressible…