Two timescales asymptotes of the weakly compressible Stokes system

We establish a two timescale asymptotics of the weakly compressible Stokes system which has dissipation of order $\epsilon >0$. For any $L^2$ initial data, over time scale of order 1, the solutions of the weakly compressible Stokes system converge strongly to those of the acoustic system as $\epsilon \to 0$. Over time scale of order $1/\epsilon$, the limit system is the incompressible Stokes system with the initial data projected on the incompressible mode. For the periodic domain, the convergence is weak due to the fast oscillation generated by acoustic waves. For the Navier-slip boundary condition with the reciprocal of slip length being square of the Knudsen number, the acoustic waves are damped by the viscous boundary layer, and consequently the strong convergence is justified.     

Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

Pattern transition and regulation in a subthalamopallidal network under electromagnetic effect

Although the significant roles of magnetic induction and electromagnetic radiation in the neural system have been widely studied, their influence on Parkinson's disease (PD) has yet to be well explored. By virtue of the magnetic flux variable, this paper studies the transition of firing patterns induced by magnetic induction and the regulation effect of external magnetic radiation on the firing activities of the subthalamopallidal network in basal ganglia. We find: (i) The network reproduces five typical waveforms corresponding to the severity of symptoms: weak cluster, episodic, continuous cluster, episodic, and continuous wave. (ii) Magnetic induction is a double-edged sword for the treatment of PD. Although the increase of magnetic coefficient may lead the physiological firing activity to transfer to pathological firing activity, it also can regulate the pathological intensity firing activity with excessive β-band power transferring to the physiological firing pattern with weak β-band power. (iii) External magnetic radiation could inhibit continuous tremulous firing and β-band power of subthalamic nucleus (STN), which means the severity of symptoms weakened. Especially, the bi-parameter plane of the regulation region shows that a short pulse period of magnetic radiation and a medium level of pulse percentage can well regulate pathological oscillation. This work helps to understand the firing activity of the subthalamopallidal network under electromagnetic effect. It may also provide insights into the mechanisms behind the electromagnetic therapy of PD-related firing activity.     

兴城地区岩石光谱特征与物性参数、金属元素间响应关系研究

岩石物性参数、元素含量和光谱特征三者之间的相互关系并非独立存在, 研究三者之间的相互关系，对于探索通过遥感信息进行岩石矿物成分、物性参数的定量反演方法奠定基础。采集了兴城地区590块岩样本，分析其物性参数（密度、介电常数、电阻率、磁化率）、金属成分含量（Fe, Ti, V, Mn, Zr, Co, Zn, Nb, Bi, Pb）以及岩石光谱之间的关系。将各物化参数与原始光谱、光谱吸收深度、光谱小波包分解后的高低频做相关性分析，找出各物化参数影响光谱吸收和反射的特征波段，探究关系密切的参数。该研究为岩石岩性分类、某种金属元素和物理特性的反演以及用某种参数来预测关系密切的参数奠定了基础，取得如下结论：（1）获得了火成岩中Fe，Ti，Mn，V，Zn，Bi和Pb等元素的特征谱带，其中Fe元素含量更高，与光谱的相关性更显著。在0.4和0.54 μm波段附近存在Fe的特征反射波段，1.0~1.5 μm波段范围内存在Fe元素的特征吸收波段；在0.4~0.55和0.6~0.65 μm波段范围内，Ti元素与光谱的相关性更显著，在2.28 μm波段附近存在Ti的特征吸收波段；在0.41 μm波段附近存在Mn的特征反射波段；火成岩、沉积岩V元素与光谱相关性差异性较大，在0.76，0.81，0.89，0.95 μm波段附近可能存在火成岩的特征吸收波段和沉积岩的特征反射波段；沉积岩的Zn元素含量与光谱的相关性比火成岩要显著，在0.41，1.36，1.59 μm波段附近可能存在火成岩Zn的特征反射波段，在2.34 μm波段附近可能存在沉积岩Zn的特征波段；2.14 μm波段附近，Bi元素对沉积岩光谱的吸收有一定的作用；Pb的特征谱带可能存在于0.45，0.54，2.29 μm附近；（2）在岩石各物理特性和光谱的关系研究中，在0.57~0.85 μm波段范围内，密度对光谱有很好的吸收反射特征，在0.53 μm波段附近，磁化率使光谱有较强的反射，在1.08 μm波段附近，磁化率使光谱产生较强的吸收；电阻率和光谱的相关关系与密度和光谱的相关关系极为相似；（3）在岩石各物性参数间的关系中发现，密度和电阻率呈显著正相关的关系；（4）在岩石各物性参数与金属元素的关系中研究发现，密度与各金属元素相关性较弱；磁化率与Fe和Ti元素呈显著的正相关关系；电阻率与各金属元素间的相关关系较弱；介电常数与各金属元素含量呈正相关关系，其中与V，Zn，Bi元素的相关关系最显著；（5）在金属元素间，Fe与Ti有较显著的正相关关系，Ti与Fe，V元素间有较强的正相关关系，Zn和Pb存在较强的正相关。     

Toeplitz quantization on Fock space

For Toeplitz operators $T_f^{(t)}$ acting on the weighted Fock space $H_t^2$, we consider the semi-commutator $T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}$, where $t>0$ is a certain weight parameter that may be interpreted as Planck's constant ? in Rieffel's deformation quantization. In particular, we are interested in the semi-classical limit

($?$)$\underset{t\to 0}{\lim }?{6T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}6}_t.$

It is well-known that ${6T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}6}_t$ tends to 0 under certain smoothness assumptions imposed on f and g. This result was recently extended to $f,g\in \mathrm{BUC}({\mathbb{C}}^n)$ by Bauer and Coburn. We now further generalize (?) to (not necessarily bounded) uniformly continuous functions and symbols in the algebra $\mathrm{VMO}\cap L^{\infty }$ of bounded functions having vanishing mean oscillation on ${\mathbb{C}}^n$. Our approach is based on the algebraic identity $T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}=?{(H_{\overline{f}}^{(t)})}^{?}{H}_g^{(t)}$, where $H_g^{(t)}$ denotes the Hankel operator corresponding to the symbol g, and norm estimates in terms of the (weighted) heat transform. As a consequence, only f (or likewise only g) has to be contained in one of the above classes for (?) to vanish. For g we only have to impose ${\lim \sup }_{t\to 0}{6H_g^{(t)}6}_t<\infty$, e.g. $g\in L^{\infty }({\mathbb{C}}^n)$. We prove that the set of all symbols $f\in L^{\infty }({\mathbb{C}}^n)$ with the property that ${\lim }_{t\to 0}?{6T_f^{(t)}{T}_g^{(t)}?T_{fg}^{(t)}6}_t={\lim }_{t\to 0}?{6T_g^{(t)}{T}_f^{(t)}?T_{gf}^{(t)}6}_t=0$ for all $g\in L^{\infty }({\mathbb{C}}^n)$ coincides with $\mathrm{VMO}\cap L^{\infty }$. Additionally, we show that $\underset{t\to 0}{\lim }?{6T_f^{(t)}6}_t={6f6}_{\infty }$ holds for all $f\in L^{\infty }({\mathbb{C}}^n)$. Finally, we present new examples, including bounded smooth functions, where (?) does not vanish.     

秋千参数自激振动的数学模型与数值模拟

将秋千视为变长度单摆,基于归一化高斯函数构造了摆球相对摆杆的速度表达式.在此基础上建立了秋千的非线性动力学微分方程,并据此数学模型对秋千运动进行了数值模拟,得到了秋千的运动规律和功能转化的机制.     

HgCdTe薄膜的输运特性及其应力调控

窄禁带直接带隙半导体材料碲镉汞(Hg1–xCdxTe)是一种在红外探测与自旋轨道耦合效应基础研究方面都具有重要应用意义的材料.本文对单晶生长的体材料Hg0.851Cd0.149Te进行阳极氧化以形成表面反型层,将样品粘贴在压电陶瓷上减薄后进行磁输运测试,在压电陶瓷未加电压时观察到了明显的SdH振荡效应.对填充因子与磁场倒数进行线性拟合,获得样品反型层二维电子气的载流子浓度为ns=1.25×10^16m^-2.在不同磁场下,利用压电陶瓷对样品进行应力调控,观测到具有不同特征的现象,分析应是样品中存在二维电子气与体材料两个导电通道.零磁场下体材料主导的电阻的变化应来源于应力导致的带隙的改变;而高场下产生类振荡现象的原因应为应力导致的二维电子气能级的分裂.     

由多平衡态快子系统所诱发的簇发振荡及机理

通过引入子电路模块, 并选取适当的参数及非线性电阻特性, 建立了多时间尺度下具有多平衡态的四维广义哈特利(Hartley) 电路模型. 基于快子系统的多平衡态及其稳定性, 给出了参数空间的分岔集, 得到了不同区域中的动力学特性及其相应的分岔模式和临界条件. 针对两种典型具有不同分岔特征的情形, 分别给出了多平衡态参与下的两种不同的周期簇发振荡行为, 结合快子系统的分岔分析, 揭示了沉寂态和激发态之间相互转化的产生机制, 指出多平衡态不仅会导致多种沉寂态和激发态同时参与同一周期簇发振荡, 也会导致簇发振荡模式的多样性.     

Oscillation and breakup of a bubble under forced vibration

Coupled shape oscillations and translational motion of an incompressible gas bubble in a vibrating liquid container is studied numerically. The bubble oscillation characteristics are mapped based on the bubble Bond number (Bo) and the ratio of the vibration amplitude of the container to the bubble diameter (A/D). At small Bo and A/D, the bubble oscillation is found to be linear with small amplitudes, and at large Bo and A/D, it is nonlinear and chaotic. This chaotic bubble oscillation is similar to those observed in two coupled nonlinear systems, here being the gas inside the bubble and its surrounding liquid. Further increases in the forcing, results in the bubble breakup due to large liquid inertia.