Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals

In this paper,a high-accuracy numerical scheme is developed for long-time dynamic simulations of 2D and 3D wave propagation phenomena.In the derivation of the present approach,the second order time derivative of the physical quantity in the wave equation is treated as a substitution variable.Based on the temporal discretization with the Krylov deferred correction(KDC)technique,the original wave problem is then converted into the modified Helmholtz equation.The transformed boundary value problem(BVP)in space is efficiently simulated by using the meshless generalized finite difference method(GFDM)with Taylor series after truncating the second and fourth order approximations.The developed scheme is finally verified by four numerical experiments including cases with complicated domains or the temporally piecewise defined source function.Numerical results match with the analytical solutions and results by the COMSOL software,which demonstrates that the developed KDC-GFDM can allow large time-step sizes for wave propagation problems in longtime intervals.

Consideration of transmembrane water exchange in pharmacokinetic model significantly improves the accuracy of DCE-MRI in estimating cellular density:A pilot study in glioblastoma multiforme

Transmembrane water exchange(TWE)including transcytolemmal water exchange and transvascular water exchange is involved in many in vivo measurements and makes different contributions to the measuring results.In this study,we focus on the potential influence of TWE on the cell density parameter,intracellular water mole fraction pi,derived by dynamic contrast enhanced-magnetic resonance imaging(DCE-MRI)which has been reported as a technique to characterize perfusion and vascularization of tissues,but its accuracy in measuring cell density(or interstitial space)has been questioned.Sixteen patients with glioblastoma multiforme(GBM)were enrolled since GBM shows strong intratumor heterogeneity in both cell density and TWE.All the subjects were collected with DCE-MRI and apparent diffusion coefficient(ADC)map.The latter was considered as a valid surrogate of cell density.Extended Tofts(eTofts)model considering TWE as infinitely large variables and shutter-speed model(SSM)considering TWE as finite ones were used to fit DCE-MRI data.Monte Carlo(MC)and finite difference(FD)methods were used to simulate the influence of TWE on DCE-MRI-derived pi and ADC,respectively.The eTofts model shows a significant overestimation of pi in comparison with SSM in GBM(P<0.001),which is in accordance with MC simulations,and this overestimation shows dependence on the intra-to-extracellular water exchange rate constant(kio).Significant negative correlations between ADC and SSM-derived pi were found in both voxel-wise analyses(t-test P<0.001,average r=-0.74)and inter-subject comparisons(r=-0.63,P=0.009).But no consistent voxel-wise correlations(P>0.05)and a weaker inter-subject negative correlation(r=-0.56,P=0.02)were found between ADC and eTofts-derived pi.Further experimental and FD results revealed that kio made a limited contribution to ADC values in the physiological kio range in GBM,supporting ADC as a valid biomarker of cell density.These results suggest that the DCE-MRI pharmacokinetic shutter-speed model could significantly improve its accuracy in cell density estimation because of the considering transmembrane water exchange.

A compact frequency selective stop-band splitter by using Fabry Perot nanocavity in a T-shaped waveguide

By utilizing a Fabry–Perot （FP） nanocavity adjacent to T-shaped gap waveguide ports, spectrally selective filtering is realized. When the wavelength of incident light corresponds to the resonance wavelength of the FP nanocavity, the surface plasmons are captured inside the nanocavity, and light is highly reflected from this port. The resonance wavelength is determined by using Fabry–Perot resonance condition for the nanocavity. For any desired filtering frequency the dimension of the nanocavity can be tailored. The numerical results are based on the two-dimensional finite difference time domain simulation under a perfectly matched layer absorbing boundary condition. The analytical and simulation results indicate that the proposed structure can be utilized for filtering and splitting applications.

Recent status and advanced progress of tip effect induced by micro-nanostructure

The unique structural features represented by micro-nanoneedle tip structure reflect wonderful physical and chemical properties.The tip effect includes the concentration of energy such as electrons,photons and magnetism in the tip region,which has promising applications in the fields of energy conversion,water capture,environmental restoration and so on.In this review,a comprehensive and systematic summary of the latest advances in the application of the tip effect in different fields is provided.Utilizing advanced Finite Difference Time Domain simulation,we further propose our understanding of the fundamental mechanism of the tip effect induced by micro-nanostructure.However,we need to forge the present study to further reveal the essential law of the tip effect from the perspective of theoretical calculations.This review would provide a solid foundation for further development and application of the tip effect.