Several new energy identities of the two dimenslonal（2D） Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new ...
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Several new energy identities of the two dimenslonal（2D） Maxwell equations in a lossy medium in the case of the perfectly electric conducting boundary conditions are proposed and proved. These identities show a new kind of energy conservation in the Maxwell system and provide a new energy method to analyze the alternating direction im- plicit finite difference time domain method for the 2D Maxwell equations （2D-ADI-FDTD）. It is proved that 2D-ADI-FDTD is approximately energy conserved, unconditionally sta- ble and second order convergent in the discrete L2 and H1 norms, which implies that 2D-ADI-FDTD is super convergent. By this super convergence, it is simply proved that the error of the divergence of the solution of 2D-ADI-FDTD is second order accurate. It is also proved that the difference scheme of 2D-ADI-FDTD with respect to time t is second order convergent in the discrete H1 norm. Experimental results to confirm the theoretical analysis on stability, convergence and energy conservation are presented.
In this paper, we present a weak Galerkin （WG） mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled metho...
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In this paper, we present a weak Galerkin （WG） mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the L^2 for the flux and H1 for the scalar function. Also an optimal order error estimate in L^2 is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.
The dependence of viscosity and entropy on temperature, together with energy dissipation and thermal conductivity, all modify the Poiseuille velocity profile for the normal fluid flow of liquid helium II along a tube....
The dependence of viscosity and entropy on temperature, together with energy dissipation and thermal conductivity, all modify the Poiseuille velocity profile for the normal fluid flow of liquid helium II along a tube. We show that the modifications include a significant temperature gradient in the radial direction, a slightly reduced flow of normal fluid along the tube, and an unexpected diverging radial flow.
Similarity equations relating to steady and unsteady vortices in a stratified atmosphere are shown to possess more general solutions than hitherto reported. Solutions with n cells, where n = 1, 2, 3,..., are possible ...
Similarity equations relating to steady and unsteady vortices in a stratified atmosphere are shown to possess more general solutions than hitherto reported. Solutions with n cells, where n = 1, 2, 3,..., are possible such that the axial and radial velocities tend to zero far from the axis of the vortex. For solutions with a finite number of cells, far from the axis the radial mass flow is directed towards the axis, with the exception of a subclass of solutions relating to one-cell and two-cell vortices associated with the unsteady configuration where the radial velocity is directed outwards.
We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evol...
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We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields coupled to marginally stable, fast fluctuation fields. By exploiting this scale separation, an efficient hybrid fast-eigenvalue/slow-initial-value solution algorithm can be developed in which the amplitude of the fast fluctuations is slaved to the slowly evolving mean fields to ensure marginal stability—and temporal scale separation—is maintained. For 2D systems, the fluctuation eigenfunctions are labeled by their Fourier wave numbers characterizing spatial variability in that extended spatial direction, and the marginal mode(s) must coincide with the fastest-growing mode(s) over all admissible Fourier wave numbers. Here we derive an ordinary differential equation governing the slow evolution of the wave number of the fastest-growing fluctuation mode that simultaneously must be slaved to the mean dynamics to ensure the mode has zero growth rate. We illustrate the procedure in the context of a 2D model partial differential equation that shares certain attributes with the equations governing strongly stratified shear flows and other strongly constrained forms of geophysical turbulence in extreme parameter regimes. The slaved evolution follows one or more marginal stability manifolds, which constitute select state-space structures that are not invariant under the full flow dynamics yet capture quasicoherent structures in physical space in a manner analogous to invariant solutions identified in, e.g., transitionally turbulent shear flows. Accordingly, we propose that marginal stability manifolds are central organizing structures in a dynamical systems description of certain classes of multiscale flows in which scale separation justifies a QL approximation of the dynamics.
A well known numerical technique for calculating the optimal control of distributed parameter systems is the spatial discretisation (SD) procedure. In the paper an improved formulation of the SD scheme is studied in t...
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A well known numerical technique for calculating the optimal control of distributed parameter systems is the spatial discretisation (SD) procedure. In the paper an improved formulation of the SD scheme is studied in the case of the boundary control of the diffusion equation. Significantly more accurate results are obtained with no additional computational complexity.
Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain com...
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In this paper, a new multilayer neural networks training algorithm that minimizes the probability of classification error is proposed. The claim is made that such an algorithm posesses some clear advantages over the s...
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In this paper, a new multilayer neural networks training algorithm that minimizes the probability of classification error is proposed. The claim is made that such an algorithm posesses some clear advantages over the standard backpropagation (BP) algorithm. The convergence analysis of the proposed procedure is performed and convergence of the sequence of criterion realizations with probability one is proven. An experimental comparison with the BP algorithm on three artificial pattern recognition problems is also given.
We investigate the dynamics of two interacting electrons confined in a quantum dot molecule under the influence of cosine squared electric fields. The conditions for two-electron localization in the same quantum dot a...
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We investigate the dynamics of two interacting electrons confined in a quantum dot molecule under the influence of cosine squared electric fields. The conditions for two-electron localization in the same quantum dot are analytically derived within the frame of the Floquet formalism. The analytical results are compared to numerical results obtained from the solution of the time-dependent Schtdinger equation.
This paper describes improvements that have been made to a method of inversion of the HF radar Doppler spectrum to provide a measurement of the ocean wave directional spectrum. The ability to make such measurements ov...
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This paper describes improvements that have been made to a method of inversion of the HF radar Doppler spectrum to provide a measurement of the ocean wave directional spectrum. The ability to make such measurements over the whole HF band using the same inversion method is demonstrated. Measurements obtained in storm conditions, in fetch-limited conditions and in mixed swell, wind-sea conditions are presented. The accuracy of these measurements is discussed.
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