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Johannes A Russer - One of the best experts on this subject based on the ideXlab platform.
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Differential Form representation of stochastic electromagnetic fields
Advances in Radio Science, 2017Co-Authors: Michael Haider, Johannes A RusserAbstract:Abstract. In this work, we revisit the theory of stochastic electromagnetic fields using exterior Differential Forms. We present a short overview as well as a brief introduction to the application of Differential Forms in electromagnetic theory. Within the framework of exterior calculus we derive equations for the second order moments, describing stochastic electromagnetic fields. Since the resulting objects are continuous quantities in space, a discretization scheme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equations as obtained for the case of Formulating the theory using the traditional notation of vector calculus. We conclude with an analytic calculation of the radiated electric field of two Hertzian dipole, excited by uncorrelated random currents.
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Differential Form representation of stochastic electromagnetic fields
Kleinheubacher Tagung 2016 Talk KH2016-B-13 2016-09, 2016Co-Authors: Michael Haider, Johannes A RusserAbstract:In this work, we revisit the theory of stochastic elec tromagnetic fields using exterior Differential Forms. We present a short overview as well as a brief introdu ction to the application of Differential Forms in electromagnetic theory. A Differential Form is in principle a quantity, which can be integrated. For the case of a three-dimensional space, the domains of integration could either be lines (1D), areas (2D) or volumes (3D). The corresponding Differential Forms are then given as one-Forms, two-Forms and three-Forms. We describe electric-, and magnetic fields by Differential one-Forms while electric-, and magnetic displacement fields are given by two-Forms. Since charge density is a q uantity that is given as a density in space, we use pseudo scalars, or Differential three-Forms to des cribe it. A well-known result from the field of mathematics, the lemma of Poincare, can then be used to ensure the existence of a field, just by the presence of some charge density. Probably the most important advantage, which makes exterior calculus superior to vectors, when considering electromagneti c fields, is that the Formalism becomes completely independent of the choice of a specific coordinate system. Within the framework of exterior calculus, we deri ve equations for the second order moments, describing stochastic electromagnetic fields. Also the equations for the double one-Forms, or two-Forms respectively, relating the second order moments are independent fo r the choice of a particular basis. Since the resulting objects are continuous quantities in sp ace, a discretization sc heme based on the Method of Moments (MoM) is introduced for numerical treatment. The MoM is applied in such a way, that the notation of exterior calculus is maintained while we still arrive at the same set of algebraic equat ions in the end, we would have obtained when Formulating the theory using the traditional notation of vector calculus. Fo r properly setting up the Method of Moments, we introduce an inner product for Differential Forms. We show that our inner product is valid by exploring some important properties, like sesquilinearity and positive semi-definiteness. We conclude our work with an analytic calculation of the propagation of correlations of two Hertzian dipoles using the Formalism of exterior calculus. We see that even though we consider uncorrelated sources, the cross-correlati on spectra of the excited elec tric field are non-vanishing.
Stefan Wewers - One of the best experts on this subject based on the ideXlab platform.
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Fiercely ramified cyclic extensions of p -adic fields with imperfect residue field
Manuscripta Mathematica, 2014Co-Authors: Stefan WewersAbstract:We study the ramification of fierce cyclic Galois extensions of a local field K of characteristic zero with a one-dimensional residue field of characteristic p > 0. Using Kato’s theory of the refined Swan conductor, we associate to such an extension a ramification datum, consisting of a sequence of pairs (δi, ωi), where δi is a positive rational number and ωi a Differential Form on the residue field of K. Our main result gives necessary and sufficient conditions on such sequences to occur as a ramification datum of a fierce cyclic extension of K.
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Fiercely ramified cyclic extensions of p-adic fields with imperfect residue field
arXiv: Number Theory, 2011Co-Authors: Stefan WewersAbstract:We study the ramification of fierce cyclic Galois extensions of a local field $K$ of characteristic zero with a one-dimensional residue field of characteristic $p>0$. Using Kato's theory of the refined Swan conductor, we associate to such an extension a ramification datum, consisting of a sequence of pairs $(\delta_i,\omega_i)$, where $\delta_i$ is a positive rational number and $\omega_i$ a Differential Form on the residue field of $K$. Our main result gives necessary and sufficient conditions on such sequences to occur as a ramification datum of a fierce cyclic extension of $K$.
Loïc Bourdin - One of the best experts on this subject based on the ideXlab platform.
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Nonshifted calculus of variations on time scales with ∇-differentiable σ
Journal of Mathematical Analysis and Applications, 2014Co-Authors: Loïc BourdinAbstract:In calculus of variations on general time scales, an Euler-Lagrange equation of integral Form is usually derived in order to characterize the critical points of nonshifted Lagrangian functionals, see e.g. [R.A.C. Ferreira and co-authors, Optimality conditions for the calculus of variations with higher-order delta derivatives, Appl. Math. Lett., 2011]. In this paper, we prove that the ∇-differentiability of the forward jump operator σ is a sharp assumption on the time scale in order to ∇-differentiate this integral Euler-Lagrange equation. This procedure leads to an Euler-Lagrange equation of Differential Form. Furthermore, from this Differential Form, we prove a Noether-type theorem providing an explicit constant of motion for Euler-Lagrange equations admitting a symmetry.
B T Marinyuk - One of the best experts on this subject based on the ideXlab platform.
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calculation of vacuum evaporative cooling of water taking into account the transfer of heat to the water vapor interface
Chemical and Petroleum Engineering, 2016Co-Authors: B T Marinyuk, N G Shmuilov, A S LeontevAbstract:The existing method of estimating the duration of vacuum-evaporative cooling of fluids based on the heat balance ratio in Differential Form gives an idealized result (an estimation “from the top”). Therefore, the model presented here describes the development of the process and takes into account heat transfer characteristics: the heat transfer coefficient from water and the geometric surface of the vapor–water interface. Methods of intensifying liquid cooling were described.
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Calculation of Vacuum-Evaporative Cooling of Water, Taking Into Account the Transfer of Heat to the Water–Vapor Interface
Chemical and Petroleum Engineering, 2016Co-Authors: B T Marinyuk, N G Shmuilov, A. S. Leont’evAbstract:The existing method of estimating the duration of vacuum-evaporative cooling of fluids based on the heat balance ratio in Differential Form gives an idealized result (an estimation “from the top”). Therefore, the model presented here describes the development of the process and takes into account heat transfer characteristics: the heat transfer coefficient from water and the geometric surface of the vapor–water interface. Methods of intensifying liquid cooling were described.
Chiaki Kojima - One of the best experts on this subject based on the ideXlab platform.
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CDC - Dual Lyapunov stability analysis in behavioral approach
2008 47th IEEE Conference on Decision and Control, 2008Co-Authors: Chiaki KojimaAbstract:This paper considers a Lyapunov stability analysis for continuous-time systems described by high order difference-algebraic equation from the viewpoint of the semidefinite programming (SDP) duality. In the behavioral system theory, a Lyapunov function is described by a quadratic Differential Form (QDF) and equivalently characterized by a two-variable polynomial matrix. We first develop the SDP duality to the non-negativity and positivity of two-variable polynomial matrices. Using the duality, we derive an alternative stability condition in terms of the two-variable polynomial matrix equation and QDFs as a main result.