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Boundary Controls and Interconnection for Scalable Hamiltonian Systems Governed by Molecular Dynamics

Gou Nishida, Ryojun Ikeura
This paper derives a unified framework of boundary controls and numerical calculus from a scaling free molecular dynamics, called a renormalized molecular dynamics.
A renormalized molecular dynamics is suitable not only for the fast numerical calculation of microscopic targets like polymers, but also that of macroscopic targets like mechanical systems because of coarse graining.
First, we introduce renormalized Hamiltonian systems.
The problem of developing boundary controls in renormalized Hamiltonian systems is that the boundaries of renormalized Hamiltonian systems are not directly derived from molecular dynamics.
Thus, we derive the continuum representation of renormalized Hamiltonian systems from the inverse limit of coarse graining.
Then, we define a standard boundary control representation of renormalized Hamiltonian systems by using distributed port-Hamiltonian systems.
Finally, we will show some numerical examples.
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