On band gaps in photonic crystal fibers

We consider the Maxwell's system for a periodic array of dielectric `fibers' embedded into a `matrix', with respective electric permittivities $\epsilon_0$ and $\epsilon_1$, which serves as a model for cladding in photonic crystal fibers (PCF). The interest is in describing admissible and forbidden (gap) pairs $(\omega,k)$ of frequencies $\omega$ and propagation constants $k$ along the fibers, for a Bloch wave solution on the cross-section. We show that, for "pre-critical" values of $k(\omega)$ i.e. those just below $\omega (\min\{\epsilon_0,\epsilon_1\}\mu)^{1/2}$ (where $\mu$ is the magnetic permeability assumed constant for simplicity), the coupling specific to the Maxwell's systems leads to a particular partially degenerating PDE system for the axial components of the electromagnetic field. Its asymptotic analysis allows to derive the limit spectral problem where the fields are constrained in one of the phases by Cauchy-Riemann type relations. We prove related spectral convergence. We finally give some examples, in particular of small size "arrow" fibers ($\epsilon_0>\epsilon_1$) where the existence of the gaps near appropriate "micro-resonances" is demonstrated by a further asymptotic analysis.Comment: 36 pages, 1 figur

An Econometric Model of the Soviet Iron and Steel Industry

The purpose of this paper is to cover the development of the iron and steel industry in the USSR for the years 1960-1983 in order to find out whether its pattern is unique or rather common to any developed country. The study of this energy-intensive industry furthermore contributes to the identification of the causes of slower growth in energy consumption

Model of Interindustry Interactions as a System of Simultaneous Equations

This paper considers the techniques used to estimate the parameters of the large-scale model of interindustry interactions. Use of the ordinary least squares technique sometimes leads to overestimation of model validity. These questions are of great importance in forecasting if the set of parameters is obtained by econometric techniques. Three examples illustrate the problem and show that the model should be represented as a system of simultaneous equations and therefore appropriate techniques have to be used for parameter estimation

The Maximum Principle of Pontryagin in the Heat-mass Transfer Problem

A flow of a viscous heat-conducting Newtonian fluid in a long and narrow rectangular basin is studied. The heat-physical characteristics depend substantially on the temperature, which, in turn, is a function of coordinates and time. The problem on a flow optimal control with a quadratic quality functional is considered. The heat flow to a free surface of a fluid is assumed to be a control parameter. By the maximum principle of Pontryagin some conditions of a control optimality are found. The problem considered has arosen from studying one of the glass melting problems

Breaking the Energy Coefficient: Cross-Country Analysis for the Iron and Steel Industry

In this paper one of the most long-standing industries and the impact of its technological changes on energy consumption are considered. Econometric analysis of cross-country and time-series data helps to reveal the impact which is widely discussed in detailed engineering reports

Breaking the Energy Coefficient: Cross-Country Analysis of the Pulp and Paper Industry

Our research concentrates primarily on the empirical analysis of interregional and intertemporal economic structural change, on the sources of and constraints on economic growth, on problems of adaptation to sudden changes, and especially on problems arising from changing patterns of international trade, resource availability, and technology. In this paper one of the long-standing industries and the impact of its technological changes on energy consumption are considered. Econometric analysis of cross-country and time-series data helps to reveal the impact which is widely discussed in detailed engineering reports

Breaking the Energy Coefficient: Cross-Country Analysis for the Chemical Industry

In this paper one of the long-standing industries and the impact of its technological changes on energy consumption are considered. Econometric analysis of cross-country and time-series data helps to reveal the impact which is widely discussed in detailed engineering reports