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Papachristou C.J.,Naval Academy of Greece
Advanced Electromagnetics | Year: 2015

Bäcklund transformations (BTs) are a useful tool for integrating nonlinear partial differential equations (PDEs). However, the significance of BTs in linear problems should not be ignored. In fact, an important linear system of PDEs in Physics, namely, the Maxwell equations of electromagnetism, may be viewed as a BT relating the wave equations for the electric and the magnetic field, these equations representing integrability conditions for solution of the Maxwell system. We examine the BT property of this system in detail, both for the vacuum case and for the case of a linear conducting medium. © 2015 by Advanced Electromagnetics. All rights reserved. Source

Papachristou C.J.,Naval Academy of Greece
Electronic Journal of Theoretical Physics | Year: 2012

A 3-dimensional reduction of the self-dual Yang-Mills (SDYM) equation, named SDYM3, is examined from the point of view of its symmetry and integrability characteristics. By using a non-auto-Bäcklund transformation, this equation is connected to its potential form (PSDYM3) and a certain isomorphism between the Lie algebras of symmetries of the two systems is shown to exist. This isomorphism allows us to study the infinite-dimensional Lie algebraic structure of the "potential symmetries" of SDYM3 by examining the symmetry structure of PSDYM3 (which is an easier task). By using techniques described in a recent paper, the recursion operators for both SDYM3 and PSDYM3 are derived. Moreover, a Lax pair and an infinite set of nonlocal conservation laws for SDYM3 are found, reflecting the fact that SDYM3 is a totally integrable system. This system may physically represent gravitational fields or chiral fields. © Electronic Journal of Theoretical Physics. All rights reserved. Source

Pelland S.,CANMET Energy | Galanis G.,National and Kapodistrian University of Athens | Galanis G.,Naval Academy of Greece | Kallos G.,National and Kapodistrian University of Athens
Progress in Photovoltaics: Research and Applications | Year: 2013

Hourly solar and photovoltaic (PV) forecasts for horizons between 0 and 48 h ahead were developed using Environment Canada's Global Environmental Multiscale model. The motivation for this research was to explore PV forecasting in Ontario, Canada, where feed-in tariffs are driving rapid growth in installed PV capacity. The solar and PV forecasts were compared with irradiance data from 10 North-American ground stations and with alternating current power data from three Canadian PV systems. A 1-year period was used to train the forecasts, and the following year was used for testing. Two post-processing methods were applied to the solar forecasts: spatial averaging and bias removal using a Kalman filter. On average, these two methods lead to a 43% reduction in root mean square error (RMSE) over a persistence forecast (skill score = 0.67) and to a 15% reduction in RMSE over the Global Environmental Multiscale forecasts without post-processing (skill score = 0.28). Bias removal was primarily useful when considering a "regional" forecast for the average irradiance of the 10 ground stations because bias was a more significant fraction of RMSE in this case. PV forecast accuracy was influenced mainly by the underlying (horizontal) solar forecast accuracy, with RMSE ranging from 6.4% to 9.2% of rated power for the individual PV systems. About 76% of the PV forecast errors were within ±5% of the rated power for the individual systems, but the largest errors reached up to 44% to 57% of rated power. © Her Majesty the Queen in Right of Canada 2011. Source

Papachristou C.J.,Naval Academy of Greece | Harrison B.K.,Brigham Young University
Journal of Nonlinear Mathematical Physics | Year: 2010

By using the self-dual Yang-Mills (SDYM) equation as an example, we study a method for relating symmetries and recursion operators of two partial differential equations connected to each other by a non-auto-Bäcklund transformation. We prove the Lie-algebra isomorphism between the symmetries of the SDYM equation and those of the potential SDYM (PSDYM) equation, and we describe the construction of the recursion operators for these two systems. Using certain known aspects of the PSDYM symmetry algebra, we draw conclusions regarding the Lie algebraic structure of the "potential symmetries" of the SDYM equation. © 2010 The Author(s). Source

Papachristou C.J.,Naval Academy of Greece | Magoulas A.N.,Naval Academy of Greece
Advanced Electromagnetics | Year: 2015

In the literature of Electromagnetism, the electromotive force of a “circuit” is often defined as work done on a unit charge during a complete tour of the latter around the circuit. We explain why this statement cannot be generally regarded as true, although it is indeed true in certain simple cases. Several examples are used to illustrate these points. © 2015 by Advanced Electromagnetics. All rights reserved. Source

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