We prove global existence backwards from the scattering data posed at infinity for Maxwell Klein Gordon equations in Lorenz gauge satisfying weak null condition. The asymptotics of solutions to were shown be wave like and homogeneous towards timelike arXiv:1803.11086 expressed terms radiation fields, thus our will given form fields backward problem. give a refinement results arXiv:1803.11086, t...

We consider the Nambu and Hamiltonian representations of RayleighBénard convection with a nonlinear thermal heating effect proportional to the Eckert number (Ec). The model we use is an extension of the classical Lorenz63 model with 4 kinematic and 6 thermal degrees of freedom. The conservative parts of the dynamical equations which include all nonlinearities satisfy Liouville’s theorem and per...

Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent. In this paper, we investigate the capability of the test to cope with moderate amounts of noisy data. Comparisons are made between an improved version of our...

Reconstruction of processes and fields from noisy data is to solve a set of linear algebraic equations. Three factors affect the accuracy of reconstruction: (a) a large condition number of the coefficient matrix, (b) high noiseto-signal ratio in the source term, and (c) no a priori knowledge of noise statistics. To improve reconstruction accuracy, the set of linear algebraic equations is transf...

Arbitrary truncations in the Galerkin method commonly used to derive low-order models (LOMs) may violate fundamental conservation properties of the original equations, causing unphysical behaviors in LOMs such as unbounded solutions. To avoid these, energy-conserving LOMs are developed in the form of coupled Volterra gyrostats, based on analogies between fluid dynamics and rigid body mechanics....

An attractor is a transitive set of a flow to which all positive orbit close to it converges. An attractor is singular-hyperbolic if it has singularities (all hyperbolic) and is partially hyperbolic with volume expanding central direction [16]. The geometric Lorenz attractor [6] is an example of a singular-hyperbolic attractor with topological dimension ≥ 2. We shall prove that all singular-hyp...

Both ecological systems and convective fluid systems are examples of open systems which operate far-from-equilibrium. This article demonstrates that there is a correspondence between a resource-consumer chemostat ecosystem and the Rayleigh-Bénard (RB) convective fluid system. The Lorenz dynamics of the RB system can be translated into an ecosystem dynamics. Not only is there a correspondence be...

Enforcing sparse structure within learning has led to significant advances in the field of data-driven discovery dynamical systems. However, such methods require access not only timeseries state system, but also time derivative. In many applications, data are available form time-averages as moments and autocorrelation functions. We propose a methodology discover vector fields defining (possibly...

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes closure parameterizations. These models are suitable for situations where the mechanistic description dynamics some variables is unknown, but reasonably accurate observational data can be obtained evolution state system. In this work, we propose machine account missing physics ...