The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Aleksandra Delić - One of the best experts on this subject based on the ideXlab platform.
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Finite Difference Approximation of Fractional Wave Equation with Concentrated Capacity
Computational methods in applied mathematics, 2016Co-Authors: Aleksandra Delić, Boško S. JovanovićAbstract:AbstractWe consider the time fractional wave equation with coefficient which contains the Dirac Delta Distribution. The existence of generalized solutions of this initial-boundary value problem is proved. An implicit finite difference scheme approximating the problem is developed and its stability is proved. Estimates for the rate of convergence in special discrete energetic Sobolev norms are obtained. A numerical example confirms the theoretical results.
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Convergence of a finite difference method for the time‐fractional diffusion equation with concentrated capacity
Pamm, 2013Co-Authors: Aleksandra DelićAbstract:We investigate the convergence of difference scheme for the time-fractional differential equation with fractional derivative of an order with the coefficient at the time derivative containing Dirac Delta Distribution. Convergence order of is proved. A numerical example demonstrates the theoretical results. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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NAA - A Finite Difference Approach for the Time-Fractional Diffusion Equation with Concentrated Capacity
Lecture Notes in Computer Science, 2012Co-Authors: Aleksandra DelićAbstract:In this paper we consider finite-difference scheme for the time-fractional diffusion equation with Caputo fractional derivative of order αi¾?∈i¾?0,1 with the coefficient at the time derivative containing Dirac Delta Distribution.
Cesare Corrado - One of the best experts on this subject based on the ideXlab platform.
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On the Stability of the Immersed finite element Method with High Order structural Elements
Computers & Structures, 2012Co-Authors: Cesare CorradoAbstract:The Immersed Finite Element Method (IFEM) is a mathematical formulation for fluid-structure interaction problem like the Immersed Boundary method; in IFEM the immersed structure has the same space dimension of the fluid domain. We present a stability of IFEM for a scheme where the Dirac Delta Distribution is treated variationally, as in \cite{IBBoffiGastaldiHeltai}; moreover the finite element space related to the structure displacement consists of piecewise continuous Lagrangian elements, at least quadratic. The analysis is performed on two different time-stepping scheme. We demonstrate also that when the structure density is smaller than the fluid one, the stability is assured only if the time step size is bounded from below.
Manfred Fähnle - One of the best experts on this subject based on the ideXlab platform.
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Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing
Journal of Theoretical and Applied Physics, 2016Co-Authors: Christian Illg, Michael Haag, Nicolas Teeny, Jens Wirth, Manfred FähnleAbstract:Scatterings of electrons at quasiparticles or photons are very important for many topics in solid-state physics, e.g., spintronics, magnonics or photonics, and therefore a correct numerical treatment of these scatterings is very important. For a quantum-mechanical description of these scatterings, Fermi’s golden rule is used to calculate the transition rate from an initial state to a final state in a first-order time-dependent perturbation theory. One can calculate the total transition rate from all initial states to all final states with Boltzmann rate equations involving Brillouin zone integrations. The numerical treatment of these integrations on a finite grid is often done via a replacement of the Dirac Delta Distribution by a Gaussian. The Dirac Delta Distribution appears in Fermi’s golden rule where it describes the energy conservation among the interacting particles. Since the Dirac Delta Distribution is a not a function it is not clear from a mathematical point of view that this procedure is justified. We show with physical and mathematical arguments that this numerical procedure is in general correct, and we comment on critical points.
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Physical and mathematical justification of the numerical Brillouin zone integration of the Boltzmann rate equation by Gaussian smearing
arXiv: Other Condensed Matter, 2015Co-Authors: Christian Illg, Michael Haag, Nicolas Teeny, Jens Wirth, Manfred FähnleAbstract:Scatterings of electrons at quasiparticles or photons are very important for many topics in solid state physics, e.g., spintronics, magnonics or photonics, and therefore a correct numerical treatment of these scatterings is very important. For a quantum-mechanical description of these scatterings Fermi's golden rule is used in order to calculate the transition rate from an initial state to a final state in a first-order time-dependent perturbation theory. One can calculate the total transition rate from all initial states to all final states with Boltzmann rate equations involving Brillouin zone integrations. The numerical treatment of these integrations on a finite grid is often done via a replacement of the Dirac Delta Distribution by a Gaussian. The Dirac Delta Distribution appears in Fermi's golden rule where it describes the energy conservation among the interacting particles. Since the Dirac Delta Distribution is a not a function it is not clear from a mathematical point of view that this procedure is justified. We show with physical and mathematical arguments that this numerical procedure is in general correct, and we comment on critical points.
John M Stockie - One of the best experts on this subject based on the ideXlab platform.
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on regularizations of the dirac Delta Distribution
Journal of Computational Physics, 2016Co-Authors: Bamdad Hosseini, Nilima Nigam, John M StockieAbstract:In this article we consider regularizations of the Dirac Delta Distribution with applications to prototypical elliptic and hyperbolic partial differential equations (PDEs). We study the convergence of a sequence of Distributions S H to a singular term S as a parameter H (associated with the support size of S H ) shrinks to zero. We characterize this convergence in both the weak-* topology of Distributions and a weighted Sobolev norm. These notions motivate a framework for constructing regularizations of the Delta Distribution that includes a large class of existing methods in the literature. This framework allows different regularizations to be compared. The convergence of solutions of PDEs with these regularized source terms is then studied in various topologies such as pointwise convergence on a deleted neighborhood and weighted Sobolev norms. We also examine the lack of symmetry in tensor product regularizations and effects of dissipative error in hyperbolic problems.
A. Mansoor - One of the best experts on this subject based on the ideXlab platform.
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Conversion of Ungrounded Systems to High-Resistance Grounding Systems
2006 IEEE Industrial and Commercial Power Systems Technical Conference - Conference Record, 2006Co-Authors: P.e. Sutherland, A. MansoorAbstract:An innovative method is proposed where charging current can be measured and grounding resistors sized without staging a fault. Overvoltages have caused damage to equipment and voltage transformer fuse blowing an ungrounded 4.8 kV Delta Distribution system. Three causes are suspected: single-line-to-ground faults, multiple restrikes and ferroresonance. The first is the most likely. The existence of ferroresonance can be determined by taking recordings of transient waveforms. The solution evaluated here is conversion to a high-resistance grounded system using banks of Distribution transformers with broken-Delta secondaries. Evaluation of system parameters shows that the grounding resistance should be in the range of 0.5 to 1.0 times the per phase capacitive reactance. This method requires that all equipment in the 4.8 kV Distribution systems be rated for full line-to-line voltage. Ground fault current is limited to less than 10 A. Simulation of multiple restrikes shows that overvoltages is limited to 2.5 per unit. Properly sized high-resistance grounding can eliminate ferroresonance
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A new method for testing and calibration of high-resistance grounding systems
CIRED 2005 - 18th International Conference and Exhibition on Electricity Distribution, 2005Co-Authors: Peter Sutherland, A. MansoorAbstract:An innovative method is proposed where charging current can be measured and grounding resistors sized without staging a fault. Overvoltages have caused damage to equipment and voltage transformer fuse blowing an ungrounded 4.8 kV Delta Distribution system. Three causes are suspected: single-line-to-ground faults, multiple restrikes and ferroresonance. The first is the most likely. The existence of ferroresonance can be determined by taking recordings of transient waveforms. The solution evaluated here is conversion to a high-resistance grounded system using banks of Distribution transformers with broken-Delta secondaries. Evaluation of system parameters shows that the grounding resistance should be in the range of 0.5 to 1.0 times the per phase capacitive reactance. This method will require that all equipment in the 4.8 kV Distribution systems be rated for full line-to-line voltage. Ground fault current will be limited to less than 10 A. Simulation of multiple restrikes shows that overvoltages will be limited to 2.5 per unit. Properly sized high-resistance grounding can eliminate ferroresonance.