石英晶体板非线性高频振动的拓展伽辽金法分析

针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。     

A Direct NMR Method To Measure Self-Diffusion Coefficients in Liquids by Monitoring Diffusing Molecules through One-Dimensional Imaging

Diffusion processes can be followed directly by recording one-dimensional images of a selected slice at variable intervals after selective inversion of the magnetization. The resulting diffusion coefficients of H₂O and DMSO are consistent with earlier studies at different temperatures, obtained by monitoring the attenuation of NMR signals as a function of the gradient amplitude in gradient echo sequences.     

Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

Facile Synthesis of Manganese Tellurite Nanoparticles for Magnetic Resonance Imaging-Guided Photothermal Therapy

In this study, manganese tellurite (MnTeO₃) nanoparticles are developed as theranostic agents for magnetic resonance imaging (MRI)-guided photothermal therapy of tumor. MnTeO₃ nanoparticles are synthesized via a simple one-step method. The as-synthesized MnTeO₃ nanoparticles with uniform size show good biocompatibility. In particular, MnTeO₃ nanoparticles exhibit a high photothermal conversion efficiency (η = 26.3%), which is higher than that of gold nanorods. Moreover, MnTeO₃ nanoparticles also have high MRI performance. The longitudinal relaxivity (r₁) value of MnTeO₃ nanoparticles is determined to be 8.08 ± 0.2 mm ⁻¹ s⁻¹, which is higher than that of clinically approved T₁-contrast agents Gd-DTPA (4.49 ± 0.1 mm ⁻¹ s⁻¹). The subsequent MnTeO₃ nanoparticles-mediated photothermal therapy displays a highly efficient ablation of tumor cells both in vitro and in vivo with negligible toxicity. It is demonstrated that MnTeO₃ nanoparticles can serve as promising theranostic agents with great potentials for MRI-guided photothermal therapy.     

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

3.0T MRI检查结合X线钼靶诊断乳腺恶性肿瘤的研究

本研究探讨3.0T磁共振成像(MRI)结合X线钼靶诊断乳腺恶性肿瘤的价值。采用回顾性研究方法,选取乳腺肿块患者110例162个病灶,给予3.0T MRI及X线钼靶检查。经病理确诊为恶性病变101个;恶性病灶形态不规则、边缘毛刺、时间-信号强度曲线(TIC)类型Ⅲ型和早期增强率≥60%比例明显高于良性病灶(P<0.05),而分叶状比例和表观扩散系数(ADC)值明显低于良性病变(P<0.05);恶性病变X线钼靶表现:形态不规则、钙化、结构不对称和大导管征比例明显高于良性病变(P<0.05);MRI联合X线钼靶诊断乳腺恶性病变的灵敏性、准确性和阴性预测值明显高于MRI诊断(P<0.05)。3.0T MRI检查结合X线钼靶诊断乳腺恶性肿瘤有较好的价值。     

Two-Photon Absorption Enhancement by the Inclusion of a Tropone Ring in Distorted Nanographene Ribbons

A new family of distorted ribbon-shaped nanographenes was designed, synthesized, and their optical and electrochemical properties were evaluated, pointing out an unprecedented correlation between their structural characteristics and the two-photon absorption (TPA) responses and electrochemical band gaps. Three nanographene ribbons have been prepared: a seven-membered-ring-containing nanographene presenting a tropone moiety at the edge, its full-carbon analogue, and a purely hexagonal one. We have found that the TPA cross-sections and the electrochemical band gaps of the seven-membered-ring-containing compounds are higher and lower, respectively, than those of the fully hexagonal polycyclic aromatic hydrocarbon (PAH). Interestingly, the inclusion of additional curvature has a positive effect in terms of non-linear optical properties of those ribbons.