周毓麟先生在计算数学领域的成就与贡献——纪念周毓麟院士百年诞辰

本文从计算数学的视角,介绍周毓麟先生在离散泛函分析方法和大型科学计算方法等领域的研究工作.     

A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Design of a Rectangular to Circular Groove Waveguide Transition by Finite Element Method

A rectangular to circular groove waveguide transition is described in millimeter-wave band. The transition maintains a constant cutoff wavelength. Using the Finite Element Method, the size of the variable cross-section throughout the transition are calculated and the transition is designed.     

Assessing the relationship between the inter-rod coupling and the efficiency of piezocomposite high-intensity focused ultrasound transducers

The electroacoustic conversion efficiency of the ultrasonic transducer is a critical performance index for high-power applications. The material properties, volume fraction (VF) and aspect ratio (AR) are typically regarded as the design parameters of the piezocomposite transducer. We hypothesized that the spacing between piezoelectric rods was also a dominant factor. Therefore, the inter-rod coupling effects on the efficiency of 1–3 piezocomposite ultrasonic transducers were investigated in this study. The efficiencies of six flat and three curved 1.0 MHz PZT4 epoxy composite transducers with different geometric parameters were measured. Finite element transient analyses of the inter-rod electrical-mechanical coupling in the composites were carried out to explain the measured results. The experimental results showed that for 0.47 AR, the 79% VF transducers had lower efficiency than the 64% VF and 53% VF transducers. For 0.19 AR, the efficiency of the 59% VF transducer was not greater than the efficiency of the 39% VF transducer. Numerical analyses demonstrated that the positive peak voltage induced by the coupling of the side rods was more than twice the level induced by the coupling of the diagonal rods for any spacing. The diagonal coupling voltage peak did not change for spacings larger than 0.2 mm. Moreover, for spacings of 0.05 and 0.1 mm, the inter-rod coupling caused 24% and 20% waveform shifts of the driving voltage, respectively, while the 0.2 mm spacing coupling caused a 14% reduction in the amplitude of the driving voltage. As a result, the asymmetry of the driving voltage degraded the efficiency of the composite transducers and became more severe when the spacing was decreased. We concluded that the efficiency loss induced by inter-rod coupling as a function of spacing should be considered when designing piezocomposite transducers.     

Fabrication and electrochemistry study of multi-thiol coronary molecule monolayers

Single-component monolayer of novel multi-thiol coronary molecule and two-component mixed monolayer composed of coronary molecule and n-alkanethiol on gold substrates are described. The assembly of monolayers is characterized by ellipsometry, infrared spectroscopy and X-ray photoelectron spectroscope. The electrochemical properties of the single- and two-component monolayers are evaluated by cyclic voltammetry and electrochemical impedance spectroscopy experiments. Coronary molecule with multi-thiol groups has the ability to form stable monolayer via the interaction of mercapto groups and Au surface. Electrochemical impedance measurements indicate that 89.9% of the gold surface is blocked by the coronary molecule, which is attributed to the special spatial structure of the coronary molecule. The uncovered site on gold surface in coronary molecule monolayer could be occupied by the second suitable molecule. The mixed monolayer prepared by stepwise assembly of coronary molecule and n-alkanethiol has complete compact packing and few defects.     

Unconditionally Stable Complex Envelope Wave Equation PML Algorithm for Band Limited FDTD Simulations

Unconditionally stable complex envelope (CE) perfectly matched layer (PML) absorbing boundary conditions (ABCs) are presented for truncating the scalar wave-equation finite difference time domain (WE-FDTD) grids. The formulations are based on incorporating the alternating direction implicit (ADI) scheme into the CE FDTD implementations of the scalar wave-equation derived in the PML region at the domain boundaries. Numerical example carried out in two dimensional domain shows that the proposed formulations are more accurate than the classical ADI scalar wave equation PML formulations when it is used for modelling band limited electromagnetic applications.