相关论文: Refining and classifying finite-time Lyapunov expo…
Anomalous diffusion is a common phenomenon observed in underground solute transport, soil water infiltration and sediment movement, etc. Time and space fractional derivative advection-dispersion equation (FADE) has been widely employed as…
We develop a coarse-graining procedure for two-dimensional models of fluctuating loops by mapping them to interface models. The result is an effective field theory for the scaling limit of loop models, which is found to be a Liouville…
Choose a random degree d poly f with coefficients in a finite field F. We estimate the ultimate period of f under compositional iteration. We also determine the joint distribution of the small cycle lengths in the graph with edges (x,f(x)),…
Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional field space. To this end, the underlying exact flow equation of the…
The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial…
A weighted residual collocation methodology for simulating two-dimensional shear-driven and natural convection flows has been presented. Using a dyadic mesh refinement, the methodology generates a basis and a multiresolution scheme to…
Orbital-free density functional theory (OF-DFT) for real-space systems has historically depended on Lagrange optimization techniques, primarily due to the inability of previously proposed electron density approaches to ensure the…
Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located…
We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
Many important physical problems, such as fluid structure interaction or conjugate heat transfer, require numerical methods that compute boundary derivatives or fluxes to high accuracy. This paper proposes a novel alternative to calculating…
A novel random field model or the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities in terms of stochastic Fourier-type integrals has recently been introduced and analyzed by the authors.…
Fluid-solid interaction (FSI) problems are fundamental in many scientific and engineering applications, yet effectively capturing the highly nonlinear two-way interactions remains a significant challenge. Most existing deep learning methods…
A finite element method for solving nonlinear differential equations on a grid, with potential applicability to computational fluid dynamics (CFD), is developed and tested. The current method facilitates the computation of solutions of a…
The fluid flow around a bluff body is complex and time dependent, which also contains a wide range of time and length scales. The first few eigenmodes of the proper orthogonal decomposition (POD) of such a flow provide significant insight…
We consider a vector-Laplace problem posed on a 2D surface embedded in a 3D domain, which results from the modeling of surface fluids based on exterior Cartesian differential operators. The main topic of this paper is the development and…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
In this paper, we present the numerical solution of two-phase flow problems of engineering significance with a space-time finite element method that allows for local temporal refinement. Our basis is the method presented in [3], which…
The models that are based of fractional derivatives should be highlighted among promising new models to describe turbulent fluid flows. In the present work, a steady-state flow in a duct is considered under the condition that the turbulent…
This work presents an arbitrary Lagrangian Eulerian (ALE) method for the compressible two-phase flow ejecta transporting model with the HLLC-2D Riemann solver. We focus on researching the precise equation to describe the interactions…