Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).
-This paper presents a novel reaction-diffusion (RD) method for implicit active contours, which is completely free of the costly re-initialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in a RD-LSE equation, to which a piecewise constant solution can be derived.In order to have a stable numerical solution of the RD based LSE, we propose a two-step splitting method (TSSM) to iteratively solve the RD-LSE equation: first iterating the LSE equation, and then solving the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly re-initialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and PDE-based level set method. The RD-LSE method shows very good performance on boundary anti-leakage, and it can be readily extended to high dimensional level set method.The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.
We consider the problem of reconstructing the shape of multi-scale sound-soft large rough surfaces from phases measurements of the scattered field generated by tapered waves with multiple frequencies impinging on a rough surface. To overcome both the ill-posedness and nonlinearity of this problem for a single frequency, the Landweber regularization method based on the adjoint of the nonlinear objective functional is used. When the multi-frequency data is available, an approximation method is introduced to estimate the large-scale structure of the rough surface using the data measurements at the lowest frequency. The obtained estimate serves as an initial guess for a recursive linearization algorithm in frequency, which is used to capture the small scale structure of the rough surface. Numerical experiments are presented to illustrate the effectiveness of the method.
Graphene nanosheets possess a promising potential as electrodes in Li-ion batteries (LIBs); consequently, the development of low-cost and high-productivity synthetic approaches is crucial. Herein, porous graphene-like nanosheets (PGSs) have been synthesized from expandable graphite (EG) by initially intercalating phosphoric acid, and then performing annealing to enlarge the interlayer distance of EG, thus facilitating the successive intercalation of zinc chloride. Subsequently, the following pyrolysis of zinc chloride in the EG interlayer promoted the formation of the porous PGS structure; meanwhile, the gas produced during the formation of the porous structure could exfoliate the EG to graphene-like nanosheets. The synthetic PGS material used as LIB anode exhibited superior Li + storage performance, showing a remarkable discharge capacity of 830.4 mAh·g −1 at 100 mA·g −1 , excellent rate capacity of 211.6 mAh·g −1 at 20,000 mA·g −1 , and excellent cycle performance (near 100% capacity retention after 10,000 cycles). The excellent rate performance is attributed to the Li + ion rapid transport in porous structures and the high electrical conductivity of graphene-like nanosheets. It is expected that PGS may be widely used as anode material for high-rate LIBs via this facile and low-cost route by employing EG as the raw material.
BackgroundThe pollination drop (PD) is a characteristic feature of many wind-pollinated gymnosperms. Although accumulating evidence shows that the PD plays a critical role in the pollination process, the mechanism of PD withdrawal is still unclear. Here, we carefully observed the PD withdrawal process and investigated the underlying mechanism of PD withdrawal, which will aid the understanding of wind-pollination efficiency in gymnosperms.ResultsIn Ginkgo biloba, PDs were secreted on the micropyle during the pollination period and persisted for about 240 h when not pollinated under laboratory conditions. The withdrawal of an isolated PD required only 1 h for evaporation, much less than a PD on the living ovule, which required 100 h. When pollinated with viable pollen, PDs withdrew rapidly within 4 h. In contrast, nonviable pollen and acetone-treated pollen did not cause PD withdrawal. Although 100% relative humidity significantly inhibited PD withdrawal, pollinated PDs still could withdraw completely within 48 h. Pollen grains of Cycas revoluta, which are similar to those of G. biloba, could induce PD withdrawal more rapidly than those of two distantly related gymnosperms (Pinus thunbergii and Abies firma) or two angiosperms (Paeonia suffruticosa and Orychophragmus violaceus). Furthermore, pollen of G. biloba and C. revoluta submerged immediately when encountering the PD, then sank to the bottom and entered the micropyle. The saccate pollen of P. thunbergii and A. firma submerged into the PD, but remained floating at the top and finally accumulated on the micropyle after PD withdrawal. In contrast, pollen of the angiosperms P. suffruticosa, Salix babylonica, and O. violaceus did not submerge, instead remaining clustered at the edge without entering the PD.ConclusionsWe conclude that PD withdrawal is primarily determined by the dynamic balance between evaporation and ovule secretion, of which pollen is a critical stimulator. When conspecific pollen grains were submerged in the PD, ovule secretion was subsequently terminated and active absorption occurred. These processes cooperated to influence PD withdrawal. In addition, pollen grain behavior within PDs varied dramatically among taxa, and PDs played a role in distinguishing and transporting pollen in G. biloba.
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