相关论文: On the Lorenz '96 Model and Some Generalizations

We have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions…

Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…

Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many cases, random ordinary differential equations (RODEs) are…

Isaac Newton formulated the central difference algorithm (Eur. Phys. J. Plus (2020) 135:267) when he derived his second law. The algorithm is under various names ("Verlet, leap-frog,...") the most used algorithm in simulations of complex…

Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…

We introduce a low-order dynamical system to describe thermal convection in an annular domain. The model derives systematically from a Fourier-Laurent truncation of the governing Navier-Stokes Boussinesq equations and accounts for spatial…

We present a systematic approach to deriving normal forms and related amplitude equations for flows and discrete dynamics on the center manifold of a dynamical system at local bifurcations and unfoldings of these. We derive a general,…

In this work, we consider a system of differential equations modeling the dynamics of some populations of preys and predators, moving in space according to rapidly oscillating time-dependent transport terms, and interacting with each other…

We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial…

Constraints in power consumption and computational power limit the skill of operational numerical weather prediction by classical computing methods. Quantum computing could potentially address both of these challenges. Herein, we present…

The group focused on a model problem of idealised moist air convection in a single column of atmosphere. Height, temperature and moisture variables were chosen to simplify the mathematical representation (along the lines of the Boussinesq…

We consider cross-diffusion systems describing evolution of two species $u$ and $v$ moving according to Darcy's law with the pressure law $p(s) = \frac{1}{\alpha-1} s^{\alpha-1}$ where $s=u+v$. One of the most challenging questions in the…

A novel view for the emergence of chaos in Lorenz-like systems is presented. For such purpose, the Lorenz problem is reformulated in a classical mechanical form and it turns out to be equivalent to the problem of a damped and forced one…

We present an analysis of existence, uniqueness, and smoothness of the solution to a class of fractional ordinary differential equations posed on the whole real line that models a steady state behavior of a certain anomalous diffusion,…

A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic…

Motivated by challenges in Earth mantle convection, we present a massively parallel implementation of an Eulerian-Lagrangian method for the advection-diffusion equation in the advection-dominated regime. The advection term is treated by a…

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…

We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant…

This work studies two-dimensional fixed-flux Rayleigh-B\'enard convection with periodic boundary conditions in both horizontal and vertical directions and analyzes its dynamics using numerical continuation, secondary instability analysis…

With the accumulation of meteorological big data, data-driven models for short-term precipitation forecasting have shown increasing promise. We focus on Koopman operator analysis, which is a data-driven scheme to discover governing laws in…