The Applied Mathematics Laboratory is a research laboratory within the Mathematics Department of the Courant Institute. It was established to carry out physical experiments, modeling, and associated numerical studies in a variety of problems of interest to Courant faculty, postdocs, and graduate and undergraduate students. Most of the research to date has involved fluid mechanics, and we focus ...

The classical multiwinner rules are designed for particular purposes. For example, variants of kBorda are used to find k best competitors in judging contests while the Chamberlin-Courant rule is used to select a diverse set of k products. These rules represent two extremes of the multiwinner world. At times, however, one might need to find an appropriate trade-off between these two extremes. We...

Accurate prediction of pollution control and environmental protection need a good understanding of pollutant dynamics. Numerical model techniques are important apparatus in this research area. So a 2500 line FORTRAN 95 version code was conducted in which using approximate Riemann solver, couples the shallow water and pollution transport agents in two dimensions by the aid of unstructured meshes...

The "odd transgression" introduced by the authors in an earlier article is applied to construct and study inverse image functor theory of Courant algebroids.

In this paper, a behavioural model of photovoltaic grid connected system is presented and simulated. The photovoltaic generator and a single phase inverter are modelled both by the well known one diode model and a current controlled voltage source respectively. The indirect current control method has been applied to achieve the inverter current control in order to feed a sinusoidal current wave...

In this article algorithms are developed for nonlinear n-term Courant element approximation of functions in Lp (0 < p ≤ ∞) on bounded polygonal domains in R2. Redundant collections of Courant elements, which are generated by multilevel nested triangulations allowing arbitrarily sharp angles, are investigated. Scalable algorithms are derived for nonlinear approximation which both capture the rat...

Nijenhuis tensors N on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form N + N = λI for irreducible Courant algebroids, in particular for the extended tangent bundles T M = TM ⊕ TM . It is proved that compatible Nijenhuis tensors on irreducible Courant algebroids must satisfy quadratic relations N −λN + γI = 0, so that the corre...

We analyse the different situations where a fluctuation theorem can be proved for a single macroscopic current of a system in a nonequilibrium steady state sustaining several transport processes. We express the conditions under which such a fluctuation theorem will hold in terms of the cycles and transport processes of the network. In this case, a given macroscopic current obeys a fluctuation t...