154 research outputs found
The wave equation as a port-Hamiltonian system and a finite-dimensional approximation
The problem of approximating a distributed parameter system with free boundary conditions is solved for the 2-dimensional wave equation. To this end we first model the wave equation as a distributed-parameter port-Hamiltonian system. Then we employ the idea that it is natural to use different finite elements for the approximation of di?erent geometric variables (forms) describing a distributed-parameter system, to spatially discretize the system and we show that we obtain a ?nite-dimensional port-Hamiltonian system, which also preserves the conservation laws
Interconnection structures in physical systems: a mathematical formulation
The power-conserving structure of a physical system is known as interconnection structure. This paper presents a mathematical formulation of the interconnection structure in Hilbert spaces. Some properties of interconnection structures are pointed out and their three natural representations are treated. The developed theory is illustrated on two examples: electrical circuit and one-dimensional transmission lin
Harmonic oscillators in the Nos\'e - Hoover thermostat
We study the dynamics of an ensemble of non-interacting harmonic oscillators
in a nonlinear dissipative environment described by the Nos\'e - Hoover model.
Using numerical simulation we find the histogram for total energy, which agrees
with the analysis of the Nos\'e - Hoover equations effected with the method of
averaging. The histogram does not correspond to Gibbs' canonical distribution.
We have found oscillations at frequency proportional to ,
the dissipative parameter of thermostat and the characteristic
mass of particle, about the stationary state corresponding to equilibrium. The
oscillations could have an important bearing upon the analysis of simulating
molecular dynamics in the Nos\'e - Hoover thermostat.Comment: 7 pages, 4 figure
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