Critical time scales for advection–diffusion–reaction processes

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and coworkers in 2010–2011 to give a finite measure of the time required for the transient solution of a reaction–diffusion equation to approach the steady–state solution (Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb in 1991 (IMA J Appl Math. 47, 193 (1991)). Although McNabb’s initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one–dimensional linear advection–diffusion–reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform–to-uniform transitions; these results provide a practical interpretation for MAT, by directly linking the stochastic microscopic processes to a meaningful macroscopic timescale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using the MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

Analysis of modes in a freestanding microsquare resonator by 3-D finite-difference time-domain

Modes in a microsquare resonator slab with strong vertical waveguide consisting of air/semiconductor/air are analyzed by three-dimensional (3-D) finite-difference time-domain simulation, and compared with that of two-dimensional (2-D) simulation under effective index approximation. Mode frequencies and field distributions inside the resonator obtained by the 3-D simulation are in good agreement with those of the 2-D approximation. However, field distributions at the boundary of the resonator obtained by 3-D simulation are different from that of the 2-D simulation, especially the vertical field distribution near the boundary is great different from that of the slab waveguide, which is used in the effective index approximation. Furthermore the quality factors obtained by 3-D simulation are much larger. than that by 2-D simulation for the square resonator slab with the strong vertical waveguide.

Finite-difference time-domain analysis of deformed square cavity filters with a traveling-wave-like filtering response by mode coupling

An add-drop filter based on a perfect square resonator can realize a maximum of only 25% power dropping because the confined modes are standing-wave modes. By means of mode coupling between two modes with inverse symmetry properties, a traveling-wave-like filtering response is obtained in a two-dimensional single square cavity filter with cut or circular corners by finite-difference time-domain simulation. The optimized deformation parameters for an add-drop filter can be accurately predicted as the overlapping point of the two coupling modes in an isolated deformed square cavity. More than 80% power dropping can be obtained in a deformed square cavity filter with a side length of 3.01 mu m. The free spectral region is decided by the mode spacing between modes, with the sum of the mode indices differing by 1. (c) 2007 Optical Society of America.

Investigation of mode characteristics for a square cavity with a pedestal by a three-dimensional finite-difference time-domain technique

Mode characteristics of a strongly confined square cavity suspended in air via a pedestal on the substrate are investigated by a three-dimensional finite-difference time-domain technique. The mode wavelengths and mode quality factors (Q factors) are calculated as the functions of the size of the pedestal and the slope angle 0 of the sidewalls of the square slab, respectively For the square slab with side length of 2 mu m, thickness of 0.2 mu m, and refractive index of 3.4, on a square pedestal with refractive index of 3.17, the Q factor of the whispering-gallery (WG)-like mode transverse-electric TE(3.5)o first increases with the side length b of the square pedestal and then quickly decreases as b > 0.4 mu m, but the Q factor of the WG-like mode TE(4.6)o drops down quickly as b > 0.2 mu m, owing to their different symmetries. The results indicate that the pedestal can also result in mode selection in the WG-like modes. In addition, the numerical results show that the Q factors decrease 50% as the slope angle of the sidewalls varies from 90 degrees to 80 degrees. The mode characteristics of WG-like modes in the square cavity with a rectangular pedestal are also discussed. The results show that the nonsquare pedestal largely degrades the WG-like modes. (c) 2006 Optical Society of America

Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique

The mode characteristics of a three-dimensional (3D) microdisk with a vertical refractive index distribution of n(2)/3.4/n(2) are investigated by the S-matrix method and 3D finite-difference time-domain (FDTD) technique. For the microdisk with a thickness of 0.2 mu m. and a radius of 1 mu m, the mode wavelengths and quality factors for the HE7,1 mode obtained by 3D FDTD simulation and the S-matrix method are in good agreement as n(2) increases from 1.0 to 2.6. But the Q factor obtained by the 3D FDTD rapidly decreases from 1.12 X 10(4) to 379 as n2 increases from 2.65 to 2.8 owing to the vertical radiation losses, which cannot be predicted by the proposed S-matrix method. The comparisons also show that quality factors obtained from the analytical solution of two-dimensional microdisks under the effective index approximation are five to seven times smaller than those of the 3D FDTD as n(2) = 1 and R = 1 mu m. (c) 2006 Optical Society of America.

Mode-coupling analysis of three-dimensional microdisk resonators by the finite-difference time-domain technique

Quality factor enhancement due to mode coupling is observed in a three-dimensional microdisk resonator. The microdisk, which is vertically sandwiched between air and a substrate, with a radius of 1 mu m, a thickness of 0.2 mu m, and a refractive index of 3.4, is considered in a finite-difference time-domain (FDTD) numerical simulation. The mode quality factor of the fundamental mode HE71 decreases with an increase of the refractive index of the substrate, n(sub), from 2.0 to 3.17. However, the mode quality factor of the first-order mode HE72 reaches a peak value at n(sub) = 2.7 because of the mode coupling between the fundamental and the first-order modes. The variation of mode field distributions due to the mode coupling is also observed. This mechanism may be used to realize high-quality-factor modes in microdisks with high-refractive-index substrates. (c) 2006 Optical Society of America.

Coupled 3-D finite difference time domain and finite volume methods for solving microwave heating in porous media

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of temperature and moisture fields as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

Finite-Element Time-Step Coupled Generator, Load, AVR and Brushless Exciter Modelling

This paper presented results from a details and comprehensive simulation using finite element method of the practical operation of an electrical machine. The results it displayed have been used in practice to design more efficient equipment.

Finite difference time domain modeling of phase grating diffusion

In this paper, a method for modeling diffusion caused by non-smooth boundary surfaces in simulations of room acoustics using finite difference time domain (FDTD) technique is investigated. The proposed approach adopts the well-known theory of phase grating diffusers to efficiently model sound scattering from rough surfaces. The variation of diffuser well-depths is attained by nesting allpass filters within the reflection filters from which the digital impedance filters used in the boundary implementation are obtained. The presented technique is appropriate for modeling diffusion at high frequencies caused by small surface roughness and generally diffusers that have narrow wells and infinitely thin separators. The diffusion coefficient was measured with numerical experiments for a range of fractional Brownian diffusers.