Related papers: Hamiltonian Lorenz-like models
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
For the discrete model suggested by Lorenz in 1996 a one-dimensional long wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low order truncation weak external…
The modal analysis is revisited through the symplectic formalism, what leads to two intertwined eigenproblems. Studying the properties of the solutions, we prove that they form a canonical basis. The method is general and works even if the…
We construct different equivalent non-equilibrium statistical ensembles in a simple yet instructive $N$-degrees of freedom model of atmospheric turbulence, introduced by Lorenz in 1996. The vector field can be decomposed into an…
Liquid-liquid phase transitions have been found experimentally or by computer simulations in many compounds such as water, hydrogen, sulfur, phosphorus, carbon, silica, and silicon. Limited valence model implemented via event-driven…
The current study formulates a convective model of the Lorenz type near the temperature of maximum density. The existence of this temperature actualizes water dynamics in temperate lakes. There is a conceptual interest what this feature…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
A simplified model of natural convection, similar to the Lorenz (1963) system, is compared to computational fluid dynamics simulations in order to test data assimilation methods and better understand the dynamics of convection. The…
We discuss Hamiltonian model of oscillator lattice with local coupling. Model describes spatial modes of nonlinear Schr\"{o}dinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of Topaj - Pikovsky…
Slow flows of an ideal compressible fluid (gas) in the gravity field in the presence of two isentropic layers are considered, with a small difference of specific entropy between them. Assuming irrotational flows in each layer [that is ${\bf…
The recently proposed low degree-of-freedom model of Moffat and Kimura [1,2] for describing the approach to finite-time singularity of the incompressible Euler fluid equations is investigated. The model assumes an initial finite-energy…
Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…
Fluid reductions of the Vlasov-Amp{\`e}re equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all…
The problem of energy conservation in the lattice Boltzmann method is solved. A novel model with energy conservation is derived from Boltzmann's kinetic theory. It is demonstrated that the full thermo-hydrodynamics pertinent to the…
In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…
We study the geometric particle-in-cell methods for an electrostatic hybrid plasma model. In this model, ions are described by the fully kinetic equations, electron density is determined by the Boltzmann relation, and space-charge effects…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
Dynamics of complex systems is studied by first considering a chaotic time series generated by Lorenz equations and adding noise to it. The trend (smooth behavior) is separated from fluctuations at different scales using wavelet analysis…
We consider on a symplectic manifold M with Poisson bracket {,} an Hamiltonian H with complete flow and a family Phi=(Phi_1,...,Phi_d) of observables satisfying the condition {{Phi_j,H},H}=0 for each j. Under these assumptions, we prove a…
Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model…