Fermi-Bose Correspondence and Bose-Einstein Condensation in The Two-Dimensional Ideal Gas

The ideal uniform two-dimensional (2D) Fermi and Bose gases are considered both in the thermodynamic limit and the finite case. We derive May's Theorem, viz. the correspondence between the internal energies of the Fermi and Bose gases in the thermodynamic limit. This results in both gases having the same heat capacity. However, as we shall show, the thermodynamic limit is never truly reached in two dimensions and so it is essential to consider finite-size effects. We show in an elementary manner that for the finite 2D Bose gas, a pseudo-Bose-Einstein condensate forms at low temperatures, incompatible with May's Theorem. The two gases now have different heat capacities, dependent on the system size and tending to the same expression in the thermodynamic limit.Comment: 18 pages, 3 figures in EPS format, to be published in Journal of Low Temperature Physic

Canonical decompositions of 3-manifolds

We describe a new approach to the canonical decompositions of 3-manifolds along tori and annuli due to Jaco-Shalen and Johannson (with ideas from Waldhausen) - the so-called JSJ-decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus-torus theorems, and the theory of Seifert fibrations does not need to be developed in advance.Comment: 20 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper3.abs.htm

Splittings of groups and intersection numbers

We prove algebraic analogues of the facts that a curve on a surface with self-intersection number zero is homotopic to a cover of a simple curve, and that two simple curves on a surface with intersection number zero can be isotoped to be disjoint.Comment: 40 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper6.abs.htm

Tracking Control Design for Quadrotor Unmanned Aerial Vehicle

The model of a quadrotor unmanned aerial vehicle (UAV) is nonlinear and dynamically unstable. A flight controller design is proposed on the basis of Lyapunov stability theory which guarantees that all the states remain and reach on the sliding surfaces. The control strategy uses sliding mode with a backstepping control to perform the position and attitude tracking control. This proposed controller is simple and effectively enhance the performance of quadrotor UAV. In order to demonstrate the robustness of the proposed control method, White Gaussian Noise and aerodynamic moment disturbances are taken into account. The performance of the nonlinear control method is evaluated by comparing the performance with developed linear quadratic regulator and existing backstepping control technique and proportional-integral-derivative from the literature. The comparative performance results demonstrate the superiority and effectiveness of the proposed control strategy for the quadrotor UAV

MPPT Schemes for PV System Under Normal and Partial Shading Condition: a Review

The photovoltaic system is one of the renewable energy device, which directly converts solar radiation into electricity. The I-V characteristics of PV system are nonlinear in nature and under variable Irradiance and temperature, PV system has a single operating point where the power output is maximum, known as Maximum Power Point (MPP) and the point varies on changes in atmospheric conditions and electrical load. Maximum Power Point Tracker (MPPT) is used to track MPP of solar PV system for maximum efficiency operation. The various MPPT techniques together with implementation are reported in literature. In order to choose the best technique based upon the requirements, comprehensive and comparative study should be available. The aim of this paper is to present a comprehensive review of various MPPT techniques for uniform insolation and partial shading conditions. Furthermore, the comparison of practically accepted and widely used techniques has been made based on features, such as control strategy, type of circuitry, number of control variables and cost. This review work provides a quick analysis and design help for PV systems. Article History: Received March 14, 2016; Received in revised form June 26th 2016; Accepted July 1st 2016; Available online How to Cite This Article: Sameeullah, M. and Swarup, A. (2016). MPPT Schemes for PV System under Normal and Partial Shading Condition: A Review. Int. Journal of Renewable Energy Development, 5(2), 79-94. http://dx.doi.org/10.14710/ijred.5.2.79-9