Deforming SW curve

A system of Bethe-Ansatz type equations, which specify a unique array of Young tableau responsible for the leading contribution to the Nekrasov partition function in the $\epsilon_2\rightarrow 0$ limit is derived. It is shown that the prepotential with generic $\epsilon_1$ is directly related to the (rescaled by $\epsilon_1$) number of total boxes of these Young tableau. Moreover, all the expectation values of the chiral fields \langle \tr \phi^J \rangle are simple symmetric functions of their column lengths. An entire function whose zeros are determined by the column lengths is introduced. It is shown that this function satisfies a functional equation, closely resembling Baxter's equation in 2d integrable models. This functional relation directly leads to a nice generalization of the equation defining Seiberg-Witten curve.Comment: 14 page

Exotic prepotentials from D(-1)D7 dynamics

We compute the partition functions of D(-1)D7 systems describing the multi-instanton dynamics of SO(N) gauge theories in eight dimensions. This is the simplest instance of the so called exotic instantons. In analogy with the Seiberg-Witten theory in four space-time dimensions, the prepotential and correlators in the chiral ring are derived via localization formulas and found to satisfy relations of the Matone type. Exotic prepotentials of SO(N) gauge theories with N=2 supersymmetries in four-dimensions are also discussed.Comment: 19 page

Electromagnetic wave propagation in spatially homogeneous yet smoothly time-varying dielectric media

We explore the propagation and transformation of electromagnetic waves through spatially homogeneous yet smoothly time-dependent media within the framework of classical electrodynamics. By modelling the smooth transition, occurring during a finite period {\tau}, as a phenomenologically realistic and sigmoidal change of the dielectric permittivity, an analytically exact solution to Maxwell's equations is derived for the electric displacement in terms of hypergeometric functions. Using this solution, we show the possibility of amplification and attenuation of waves and associate this with the decrease and increase of the time-dependent permittivity. We demonstrate, moreover, that such an energy exchange between waves and non-stationary media leads to the transformation (or conversion) of frequencies. Our results may pave the way towards controllable light-matter interaction in time-varying structures.Comment: 5 figure

Eco-labelling and product development: potentials and experiences

In this contribution, we concentrate on voluntary eco-labels, i.e., labels applied for reasons other than prescription by public regulation. Typical examples are the European eco-label, the Nordic White Swan or the German Blue Angel. Section 2, The concept of eco-labelling, gives an overview of the history and ‘landscape’ of eco-labels. It provides information on countries using such a scheme, presents an important categorisation elaborated in this context, explains objectives and mechanisms and hints at the distinction between direct and indirect effects. Section 3,Eco-labelling and product development, refers to the potential and some experiences within business, i.e., on a micro-economic level. The following Section 4 Assessing the impacts presents an empirical view on the state, successes and failures of eco-labelling; primarily based on a meso- and macro-economic view. The final Section 5, Conclusions, deduces the consequences and challenges, both for business and policy, for strengthening eco-labelling

System Level Analysis of a Water PCM HX Integrated into Orion's Thermal Control System

In a cyclical heat load environment such as low Lunar orbit, a spacecraft's radiators are not sized to reject the full heat load requirement. Traditionally, a supplemental heat rejection device (SHReD) such as an evaporator or sublimator is used to act as a "topper" to meet the additional heat rejection demands. Utilizing a Phase Change Material (PCM) heat exchanger (HX) as a SHReD provides an attractive alternative to evaporators and sublimators as PCM HXs do not use a consumable, thereby leading to reduced launch mass and volume requirements. In continued pursuit of water PCM HX development an Orion system level analysis was performed using Thermal Desktop for a water PCM HX integrated into Orion's thermal control system in a 100km Lunar orbit. The study verified of the thermal model by using a wax PCM and analyzed 1) placing the PCM on the Internal Thermal Control System (ITCS) versus the External Thermal Control System (ETCS) 2) use of 30/70 PGW verses 50/50 PGW and 3) increasing the radiator area in order to reduce PCM freeze times. The analysis showed that for the assumed operating and boundary conditions utilizing a water PCM HX on Orion is not a viable option for any case. Additionally, it was found that the radiator area would have to be increased by at least 40% in order to support a viable water-based PCM HX