In this paper,nonconforming mixed finite element method is proposed to simulate the wave propagation in *** error estimate of the semi-discrete scheme is given by convergence order O(h 2),which is less than 40 percent...
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In this paper,nonconforming mixed finite element method is proposed to simulate the wave propagation in *** error estimate of the semi-discrete scheme is given by convergence order O(h 2),which is less than 40 percent of the computational costs comparing with the same effect by using Nédélec-Raviart element.A Crank-Nicolson full discrete scheme is also presented with O(τ2+h 2)by traditional discrete formula without using penalty *** examples of 2D TE,TM cases and a famous re-focusing phenomena are shown to verify our theories.
The inherently low electrical conductivity of TiO2-based electrodes as well as the high electrical resistance between an electrode and a current collector represents a major obstacle to their use as an anode for lithi...
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The inherently low electrical conductivity of TiO2-based electrodes as well as the high electrical resistance between an electrode and a current collector represents a major obstacle to their use as an anode for lithium ion batteries. In this study, we report on high-density TiO2 nanotubes (NTs) branched onto a carbon nanofiber (CNF) “tree” that provide a low resistance current path between the current collector and the TiO2 NTs. Compared to a TiO2 NT array grown directly on the current collector, the branched TiO2 NTs tree, coupled with the CNF electrode, exhibited ∼10 times higher areal energy density and excellent rate capability (discharge capacity of ∼150 mA·h·g−1 at a current density of 1,000 mA·g−1). Based on the detailed experimental results and associated theoretical analysis, we demonstrate that the introduction of CNFs with direct electric contact with the current collector enables a significant increase in areal capacity (mA·h·cm−2) as well as excellent rate capability.
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