本文研究了一类分段光滑的植物病虫害模型,通过研究感染个体的数量在单位时间内的变化,以 决定是否采取移除措施。 利用 F ilippov 理论、非光滑 Lyap-unov 函数等方法,根据基本再生数的 取值情况,讨论系统的无病平衡点、 地方病平衡点的全局动力学行为。 最后,采用数值仿真的方 法展示了全局动力学。This paper studies the global dynamics of a class of piecewise smooth plant disease model, by studying the change in the number of infected individuals per unit time, to determine whether removal measures should be taken. Based on the value of the basic reproduction number and combined with Filippov theory, non-smooth Lyapunov function and other methods, discussing the global dynamical behaviors of the disease- free equilibrium and the endemic equilibrium of the system. Finally, using numerical simulation to show global dynamics.
设μρ,D,{ nk}是由以下离散测度的无限卷积定义的Borel概率测度:μρ,D,{ nk}=δρn1D∗δρn2D∗δρn3D∗⋯,其中0ρ1,D⊂ℝ是一有限集,{ nk}k=1∞是一个严格递增的正整数序列,且supk≥1{ nk+1−nk}∞。本文证明了:若Z(δ^D)包含在Lattice集中且对任意的r>1,无理数ρ∈ℚ1/r:={ ρ=u1/r:0u1 是一有理数 },那么μρ,D,{ nk}不是谱测度。Let μρ,D,{ nk}be a Borel probability measure defined by the following infinite convolution of discrete measures: μρ,D,{ nk}=δρn1D∗δρn2D∗δρn3D∗⋯,where 0ρ1, D⊂ℝis a finite set, and{ nk}k=1∞is a strictly increasing sequence of positive integers with supk≥1{ nk+1−nk}∞. In this paper, we will show that if Z(δ^D)is contained in a Lattice set and for any r>1, the irrational number ρ∈ℚ1/r:={ ρ=u1/r:0u1 is rational }, then μρ,D,{ nk}is not a spectral measure.
文章给出了平面区域中Stokes-Darcy耦合问题的具有二阶收敛精度的统一近似格式。在这项工作中,我们修改了Darcy变分格式并增强了其正定性,使我们能够将P2元改进的Mini元应用于整个Stokes-Darcy耦合问题。此外,由于这种二阶格式在耦合界面上有足够的自由度,因此不需要在界面上添加额外的函数来稳定离散问题。最后,通过两个算例验证了理论分析,证明了该格式对于具有不同形状的耦合界面的问题具有良好的稳定性和准确性。In this paper, a unified approximation with second-order convergence accuracy for the Stokes-Darcy coupled problem in the plane domain is presented. In this work, we modify the Darcy problem and enhance its positive definiteness, which allows us to apply the Mini-element improved with P2-element to the entire coupled Stokes-Darcy problem. Moreover, since this second-order format has sufficient degrees of freedom on the coupled interface, we do not need to add additional functions on the interface to stabilize the discrete problem. Finally, the theoretical analysis is verified by two arithmetic examples, which prove that the scheme has good stability and accuracy for problems with different shapes of coupled interfaces.
主动脉夹层(AD)是一种死亡率很高的致命性心血管疾病。目前,计算机断层扫描(CT)成像是诊断和评估主动脉疾病的主要方式,提供血管结构的详细可视化。然而,CT成像在评估主动脉内血流动力学变化方面存在局限性。最近,计算流体动力学(CFD)作为一种先进的无创技术出现,可以实现血管内血流动力学状况的可视化。这项技术为临床医生提供了对主动脉疾病更全面的了解,有助于改进诊断、治疗计划和预后评估。本研究中,先模拟了一例直管的血流,将出口压力与解析解比较,结果吻合良好,验证了数值模拟的准确性。然后,模拟了一例AD的血流,并定量和定性分析收缩期和舒张期AD的压力和壁剪切应力(WSS)。结果表明,AD真腔和假腔的压差可促进主动脉壁内膜破裂,形成夹层,过低的壁面剪切力可增强血流对主动脉壁的撕裂作用,促进夹层的形成,这为今后AD的研究和临床实践提供参考。Aortic dissection (AD) is a fatal cardiovascular disease with a high mortality rate. Currently, computed tomography (CT) imaging is the primary modality for diagnosing and evaluating aortic diseases, providing detailed visualization of vascular structures. However, CT imaging has limitations in assessing the hemodynamic changes within the aorta. Recently, computational fluid dynamics (CFD) has emerged as an advanced noninvasive technique that enables the visualization of hemodynamic conditions within blood vessels. This technology provides clinicians with a more comprehensive understanding of aortic disease, facilitating improved diagnosis, treatment planning, and prognosis assessment. In this study, the blood flow of a straight tube was simulated first, and the outlet pressure was compared with the analytical solution. The results were in well agreement, which verified the accuracy of the numerical simulation. Then, we simulated the blood flow of an AD and analyzed the pressure and wall shear stress (WSS) during systolic and diastolic. The results suggest that the pressure difference between the true and false cavities may trigger intimal rupture and dissection formation, and low WSS may increase aortic wall tearing and promote dissection, which provides valuable insights for future research and clinical practice of AD.
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