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In this paper, the general and supplementary conditions are used to determine the inverse heat conduction in the parabolic equation. The measured conditions ensure that the inverse problem has a unique solution, but the solution is not stable, so the problem is ill-posed. Using the boundary element method to discretize the original problem, it is used to solve the problem. On this basis, the direct method, the least square method and the regular method are tried. Finally, the minimal energy method is used to solve the system. Numerical experiments are carried out and the results are discussed.

A fluorescent sulfur and oxygen co-doped graphitic carbon nitride quantum dots (S,O-CNQDs) were prepared from ethylenediaminetetraacetic acid disodium salt dihydrate and thiourea as the carbon and sulfur sources. The morphology and surface functional groups of S,O-CNQDs were characterized by X-ray diffraction, transmission electron microscopy, X-ray photoelectron spectroscopy and Fourier transform infrared spectroscopy. The fluorescence of S,O-CNQDs could be quenched efficiently by Cu2+ under the optimum conditions. The S,O-CNQDs could function as an excellent fluorescent probe for Cu2+ detection with a wide linear range of 0.50–15 μM and a low detection limit of 0.58 nM. In addition, this fluorescent probe was employed for monitoring Cu2+ in samples of tap water, lake water, human serum and urine with good recoveries from 99.0% to 110.0%. Moreover, the S,O-CNQDs with high cell penetration and low cytotoxicity were utilized for Cu2+ detection in living cells. Owing to the excellent properties of S,O-CNQDs, the as-prepared S,O-CNQDs can be a potential candidate for biological applications.

This study aims at developing a green sustainable bio-inspired composite film by combining the flexible chitin/silk fibroin matrix (CT/SF) and the rigid cellulose nanocrystals (CNC) with the multi-layer chiral nematic structure. The effects of CNC concentration on the chemical bonding, optical- and micro-morphology, thermal stability and mechanical properies of chitin/silk fibroin/cellulose nanocrystal (CT/SF/CNC) were comprehensively investigated. The results indicate that a critical concentration for CNC at 2 wt% can display the obvious iridescent color domains of biocomposite films with potential optical functional property. There is a color shift from blue to yellow-red corresponding to the higher concentrations at 3.5 and 5.0 wt%, respectively. The concentration of CNC also affects the transition of conformation of SF from the random to the β-turn as well as the bonding ability between SF and CT. The CT/SF/CNC-3.5 wt% with the excellent optical and mechanical properties as well as the improved thermal stability breaks the conventional conflict between increased strength and compromised ductility. Its tensile strength and elongation at break effectively elevate by 282% and 42%, respectively.

Impedance characteristics and frequency dispersion of typical lossy patterned resistive films are extensively investigated. And on this basis we put forward an improved Circuit-Pattern Direct Extraction Method (CPDEM) for patterned lossy resistive film based broadband absorber design. The pattern parameters are directly extracted from the numerically calculated circuit model and further optimized to meet the design requirements. Herein, two broadband designs are demonstrated, whose relative bandwidth is 127% with the thickness of 0.086 λL at lowest operating frequency of the absorption band and 178% with the thickness of 0.102 λL. Our numerical calculation and full-wave electromagnetic simulation are in good agreement with the experimental results, which proves that this design method is feasible and accurate. This CPDEM design method might also give the guideline for the resistive film absorber design.

A polarization-insensitive tunable frequency selective surface absorber for oblique incidence broadband applications is presented. The design method of combining anisotropy pattern and adjustable impedance is put forward. The influence of the parasitic or additional parameters of the PIN diode on the performance of the FSS absorber is analyzed by circuit model. An improved anisotropy capacitive absorbing circuit is designed and then realized by FSS patterns. Variable resistance PIN devices are loaded in FSS elements, and the impedance of FSS absorber structure is dynamically turned by changing the bias voltage of PIN devices. Far-field simulation results show that the absorber achieves prominent omnidirectional radar cross section (RCS) reduction in the absorbing band by overlaying it to metallic plate. Simulation and measurement results all illustrate that the reflectivity envelope covers a broadband of 1.6–5.1 GHz below -10 dB for both TE and TM polarizations at incident angle from 30° to 50°.

A flexible design of a wideband double-layer microwave absorber is proposed. In order to break through the limitation of single-layer absorbers at finite resonant frequencies, a special double-layered structure is adopted. The middle layer functional frequency selective surface is the core of the double-layer absorber. It exhibits two functions, which are resonant or lossy in a low frequency and strong reflective in a high frequency. As a result, the coupling between the two layers is weak, and this feature leads to the absorber having two different absorption bands which are provided by two single-layer absorbers (named as functional layers (FLs)), respectively. It means that an engineer could target the design for a particular band according to requirements without degrading the performance on the other band. For the flexible design, two FLs, a dual-band absorption precursor and a continuous absorption modified absorber are proposed successively. During the whole design process, all structures are fabricated and measured. The measurement result shows that the reflection of the modified absorber below −10 dB covers a bandwidth of 2.98–16.62 GHz in normal incidence. The good agreement between simulation and measurement validates the proposed absorber.