A port-Hamiltonian approach to modeling and interconnections of canal systems

We show how the port-Hamiltonian formulation of distributed parameter systems, which incorporates energy flow through the boundary of the spatial domain of the system, can be used to model networks of canals and study interconnections of such systems. We first formulate fluid flow with 1-d spatial variable whose dynamics are given by the well-known shallow water equations, with respect to a Stokes-Dirac structure, and then consider a slightly more complicated case where we have a modified (a non-constant) Stokes-Dirac structure. We also explore the existence of Casimir functions for such systems and highlight their implications on control of fluid dynamical systems.

A Finite Dimensional Approximation of the shallow water Equations: The port-Hamiltonian Approach

We look into the problem of approximating a distributed parameter port-Hamiltonian system which is represented by a non-constant Stokes-Dirac structure. We here employ the idea where we use different finite elements for the approximation of geometric variables (forms) describing a infinite-dimensional system, to spatially discretize the system and obtain a finite-dimensional port-Hamiltonian system. In particular we take the example of a special case of the shallow water equations.

On interconnections of infinite-dimensional port-Hamiltonian systems

Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving interconnection of Dirac structures is again a Dirac structure. In this paper we study interconnection properties of mixed finite and infinite dimensional port-Hamiltonian systems and show that this interconnection again defines a port-Hamiltonian system. We also investigate which closed-loop port-Hamiltonian systems can be achieved by power conserving interconnections of finite and infinite dimensional port-Hamiltonian systems. Finally we study these results with particular reference to the transmission line

Abundance analysis of the recurrent nova RS Ophiuchi (2006 outburst)

We present an analysis of elemental abundances of ejecta of the recurrent nova RS Oph using published optical and near-infrared spectra during the 2006 outburst. We use the CLOUDY photoionization code to generate synthetic spectra by varying several parameters, the model generated spectra are then matched with the observed emission line spectra obtained at two epochs. We obtain the best fit model parameters through the $\chi^{2}$ minimization technique. Our model results fit well with observed optical and near-infrared spectra. The best-fit model parameters are compatible with a hot white dwarf source with T$_{BB}$ of 5.5 - 5.8 $\times$ 10$^{5}$ K and roughly constant a luminosity of 6 - 8 $\times$ 10$^{36}$ ergs s$^{-1}$. From the analysis we find the following abundances (by number) of elements with respect to solar: He/H = 1.8 $\pm$ 0.1, N/H = 12.0 $\pm$ 1.0, O/H = 1.0 $\pm$ 0.4, Ne/H = 1.5 $\pm$ 0.1, Si/H = 0.4 $\pm$ 0.1, Fe/H = 3.2 $\pm$ 0.2, Ar/H = 5.1 $\pm$ 0.1, and Al/H = 1.0 $\pm$ 0.1, all other elements were set at the solar abundance. This shows the ejecta are significantly enhanced, relative to solar, in helium, nitrogen, neon, iron and argon. Using the obtained parameter values, we estimate an ejected mass in the range of 3.4 - 4.9 $\times$ 10$^{-6}$ M$_{\odot}$ which is consistent with observational results.Comment: Accepted in New Astronom

Population balances in case of crossing characteristic curves: Application to T-cells immune response

The progression of a cell population where each individual is characterized by the value of an internal variable varying with time (e.g. size, weight, and protein concentration) is typically modeled by a Population Balance Equation, a first order linear hyperbolic partial differential equation. The characteristics described by internal variables usually vary monotonically with the passage of time. A particular difficulty appears when the characteristic curves exhibit different slopes from each other and therefore cross each other at certain times. In particular such crossing phenomenon occurs during T-cells immune response when the concentrations of protein expressions depend upon each other and also when some global protein (e.g. Interleukin signals) is also involved which is shared by all T-cells. At these crossing points, the linear advection equation is not possible by using the classical way of hyperbolic conservation laws. Therefore, a new Transport Method is introduced in this article which allowed us to find the population density function for such processes. The newly developed Transport method (TM) is shown to work in the case of crossing and to provide a smooth solution at the crossing points in contrast to the classical PDF techniques.Comment: 18 pages, 10 figure