Relations between three-point configuration space shear and convergence statistics

With the growing interest in and ability of using weak lensing studies to probe the non-Gaussian properties of the matter density field, there is an increasing need for the study of suitable statistical measures, e.g. shear three-point statistics. In this paper we establish the relations between the three-point configuration space shear and convergence statistics, which are an important missing link between different weak lensing three-point statistics and provide an alternative way of relating observation and theory. The method we use also allows us to derive the relations between other two- and three-point correlation functions. We show the consistency of the relations obtained with already established results and demonstrate how they can be evaluated numerically. As a direct application, we use these relations to formulate the condition for E/B-mode decomposition of lensing three-point statistics, which is the basis for constructing new three-point statistics which allow for exact E/B-mode separation. Our work applies also to other two-dimensional polarization fields such as that of the Cosmic Microwave Background.Comment: 17 pages, 5 figures, submitted to A&

Origin of the anapole condition as revealed by a simple expansion beyond the toroidal multipole

Toroidal multipoles are a topic of increasing interest in the nanophotonics and metamaterials communities. In this paper, we separate out the toroidal multipole components of multipole expansions in polar coordinates (two- and three-dimensional) by expanding the Bessel or spherical Bessel functions. We discuss the formation of the lowest order of magnetic anapoles from the interaction between the magnetic toroidal dipole and the magnetic dipole. Our method also reveals that there are higher order current configurations other than the electric toroidal multipole that have the same radiation characteristics as the pure electric dipole. Furthermore, we find that the anapole condition requires that there is a perfect cancellation of all higher order current configurations

Vehicle currency

While in principle, international payments could be carried out using any currency or set of currencies, in practice, the U.S. dollar is predominant in international trade and financial flows. The dollar acts as a "vehicle currency" in the sense that agents in nondollar economies will generally engage in currency trade indirectly using the U.S. dollar rather than using direct bilateral trade among their own currencies. Indirect trade is desirable when there are transactions costs of exchange.> ; This paper constructs a dynamic general equilibrium model of a vehicle currency. We explore the nature of the efficiency gains arising from a vehicle currency, and show how this depends on the total number of currencies in existence, the size of the vehicle currency economy, and the monetary policy followed by the vehicle currency's government. We find that there can be very large welfare gains to a vehicle currency in a system of many independent currencies. But these gains are asymmetry weighted towards the residents of the vehicle currency country. The survival of a vehicle currency places natural limits on the monetary policy of the vehicle country.International trade ; Dollar, American ; Equilibrium (Economics) - Mathematical models ; Monetary policy

Vehicle Currency

While in principle, international payments could be carried out using any currency or set of currencies, in practice, the US dollar is predominant in international trade and financial flows. The dollar acts as a `vehicle currency' in the sense that agents in non-dollar economies will generally engage in currency trade indirectly using the US dollar rather than using direct bilateral trade among their own currencies. Indirect trade is desirable when there are transactions costs of exchange. This paper constructs a dynamic general equilibrium model of a vehicle currency. We explore the nature of the efficiency gains arising from a vehicle currency, and show how this depends on the total number of currencies in existence, the size of the vehicle currency economy, and the monetary policy followed by the vehicle currency's government. We find that there can be very large welfare gains to a vehicle currency in a system of many independent currencies. But these gains are asymmetrically weighted towards the residents of the vehicle currency country. The survival of a vehicle currency places natural limits on the monetary policy of the vehicle country.Vehicle currency; Transactions cost; Welfare gains