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

For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…

Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of…

We present the results of a detailed set of one-zone models that account for the coupling between pulsation and convection following the original prescriptions of Stellingwerf (1986). Motivated by the arbitrary nature of the input…

We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an…

In general terms, intermittency is the property for which time evolving systems alternate among two or more different regimes. Predicting the instance when the regime switch will occur is extremely challenging, often practically impossible.…

The Lorenz equations [1] are a severe Galerkin-truncation of the Oberbeck-Boussinesq (OB) equations describing Rayleigh-B\'enard convection (RBC). Here we examine the mathematical connections between the chaotic lobe-switching behavior of a…

We present a model of groundwater dynamics under stationary flow and governed by Darcy's Law of water motion through porous media, we apply it to study a 2D aquifer with water table of constant slope comprised of an homogeneous and…

We investigate stationary states, including their existence and stability, in a class of nonlocal aggregation-diffusion equations with linear diffusion and symmetric nonlocal interactions. For the scalar case, we extend previous results by…

In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…

Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…

Many dynamical systems are difficult or impossible to model using high fidelity physics based models. Consequently, researchers are relying more on data driven models to make predictions and forecasts. Based on limited training data,…

We consider a stochastic version of the point vortex system, in which the fluid velocity advects single vortices intermittently for small random times. Such system converges to the deterministic point vortex dynamics as the rate at which…

This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…

We investigate a lattice of coupled logistic maps where, in addition to the usual diffusive coupling, an advection term parameterized by an asymmetry in the coupling is introduced. The advection term induces periodic behavior on a…

The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly…

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one.…

Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…

We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…

Treating diffusion and advection/reaction separately is an effective strategy for solving semilinear advection-diffusion-reaction equations. However, such an approach is prone to suffer from order reduction, especially in the presence of…

This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…