Mathematical structures in the network representation of energy-conserving physical systems

It is shown that network modelling of energy-conserving physical systems naturally leads to the consideration of (nonlinear) implicit generalized Hamiltonian systems. Behavioral systems theory may be invoked to formulate and analyze the system-theoretic properties of these systems.

Port-Hamiltonian systems on graphs

In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac structure relating the flow and effort variables associated to the edges, internal vertices, as well as boundary vertices of the graph, and to formulate energy-storing or energy-dissipating relations between the flow and effort variables of the edges and internal vertices. This allows for state variables associated to the edges, and formalizes the interconnection of networks. Examples from different origins such as consensus algorithms are shown to share the same structure. It is shown how the identified Hamiltonian structure offers systematic tools for the analysis of the resulting dynamics.Comment: 45 pages, 2 figure

Robust Aeroelastic Control of Very Flexible Wings using Intrinsic Models

This paper explores the robust control of large exible wings when their dynamics are written in terms of intrinsic variables, that is, velocities and stress resultants. Assuming 2-D strip theory for the aerodynamics, the resulting nonlinear aeroelastic equations of motion are written in modal coordinates. It is seen that a system which experiences large displacements can nonetheless be accurately described by a system with only weak nonlinear couplings in this description of the wing dynamics. As result, a linear robust controller acting on a control surface is able to effectively provide gust load alleviation and flutter suppression even when the wing structure undergoes large deformations. This is numerically demonstrated on various representative test cases. © 2013 by Yinan Wang, Andrew Wynn and Rafael Palacios

Quantum transport and momentum conserving dephasing

We study numerically the influence of momentum-conserving dephasing on the transport in a disordered chain of scatterers. Loss of phase memory is caused by coupling the transport channels to dephasing reservoirs. In contrast to previously used models, the dephasing reservoirs are linked to the transport channels between the scatterers, and momentum conserving dephasing can be investigated. Our setup provides a model for nanosystems exhibiting conductance quantization at higher temperatures in spite of the presence of phononic interaction. We are able to confirm numerically some theoretical predictions.Comment: 7 pages, 4 figure

Hamiltonian formulation of distributed-parameter systems with boundary energy Kow

Abstract A Hamiltonian formulation of classes of distributed-parameter systems is presented, which incorporates the energy flow through the boundary of the spatial domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. The system is Hamiltonian with respect to an infinite-dimensional Dirac structure associated with the exterior derivative and based on Stokes' theorem. The theory is applied to the telegraph equations for an ideal transmission line, Maxwell's equations on a bounded domain with non-zero Poynting vector at its boundary, and a vibrating string with traction forces at its ends. Furthermore the framework is extended to cover Euler's equations for an ideal fluid on a domain with permeable boundary. Finally, some properties of the Stokes-Dirac structure are investigated, including the analysis of conservation laws