用一种分数阶算法研究非马尔可夫过程中阻尼与涨落的竞争机制

基于分数阶朗之万方程和随机行走理论, 建立了一种用于研究非马尔可夫系统中随机变量随时间演化的数值模拟算法, 称之为分数阶随机行走模拟法. 进一步运用此算法分别数值研究了无阻尼有涨落、 有阻尼无涨落和阻尼与涨落兼备三种情况下, 受欠扩散分数阶朗之万方程约束的随机变量随时间的演化行为. 结果显示阻尼和涨落存在竞争关系: 高斯型涨落的影响会随着时间的增长被"抹平", 从而凸显阻尼使系统趋于平衡的作用; 而长尾型涨落则由于包含"小概率大贡献"事件, 使得长时间演化之后系统变量仍以一定概率出现突然变化. 关键词： 非马尔可夫 欠扩散 阻尼与涨落 分数阶朗之万方程     

基于最小电压法的超声换能器谐振频率自动跟踪*

首先分析了最大电流法跟踪超声换能器谐振频率的原理及应用范围。研究了基于由串联电感和并联电容匹配电路下,不同频率时换能器两端电压电流的变化规律。研究表明在串联电感和并联电容匹配电路下发生谐振时,换能器两端的电压最小而电流并非最大。由此形成了采用最小电压法跟踪谐振频率的自动跟踪策略,并给出了该方法的具体实施步骤。论文研究结果为换能器谐振频率的自动跟踪方法提供了新的选择。     

过模波导器件的迭代设计方法

从模式保留和转换的角度, 过模波导器件可分为模式转换器、模式保留器和模式综合器. 传统方法只解决其中一种器件的设计或者对器件的某个指标进行改进. 本文在深入分析耦合波理论之后, 提出了过模波导器件的迭代设计方法, 从原理上解决了过模波导器件的设计问题. 该方法能够统一设计三类过模波导器件, 通过添加不同的结构控制方法, 可得到转换效率更高、带宽更宽、结构更紧凑、满足不同工程需求的器件, 而且还能有效设计一些新型器件. 给出了两个设计实例: 双频TM₀₁–TE₁₁模式变换器和光壁馈源喇叭. 双频TM₀₁–TE₁₁模式变换器的两个工作频点为8.75 GHz和10.3 GHz, 波导半径为16 mm, 在两个频点转换效率为99%以上. 光壁馈源喇叭实现TE₁₁模式向高斯束的转换. CST仿真结果验证了这两个器件设计的正确性和有效性. 关键词： 耦合波理论 模式转换器 模式过渡器 迭代法     

Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.     

On the Brownian motion in a double-well potential in the overdamped limit

The Brownian motion of a particle in a double-well potential is considered and the position correlation function (excluding inertial effects) for the potential V(x)=ax²/2+bx⁴/4 is evaluated first by averaging the governing Langevin equation over its realizations. The exact solution is then obtained via matrix continued fractions by using a representation, which symmetrizes the recurrence relations for the observables generated by the averaging procedure leading to convergence of these recurrence relations unlike the previous approaches to the problem. A reliable approximate solution based on the exponential separation of the time scales of the fast intrawell and low overbarrier relaxation processes associated with the bistable potential is also given. It is shown that a knowledge of the three characteristic relaxation times (the integral, effective and the longest relaxation times) of the position correlation function allows one to accurately predict the relaxation behavior of the system in the overdamped limit for all time scales of interest.     

800Hz Terfenol-D鱼唇式弯张换能器

本文研制了800Hz Terfenol-D鱼唇式弯张换能器，换能器设计中采用永磁偏磁场和能有效抑制涡流损耗的闭合磁路结构，最高声源级185dB，-3dB带宽180Hz,这种鱼唇工弯张换能器克服了连续直流提供偏磁场时发热强的缺点，并且仅需要普通的功率放大器，更适于长时间连续工作，使这一新型低频大功率水声换能器趋于实用化。     

Connection between the Fokker-Planck-Kolmogorov and nonlinear Langevin equations

We recall the general proof of the statement that the behavior of every holonomic nonrelativistic system can be described in terms of the Langevin equation in Euclidean (imaginary) time such that for certain initial conditions, the different stochastic correlators (after averaging over the stochastic force) coincide with the quantum mechanical correlators. The Fokker-Planck-Kolmogorov (FPK) equation that follows from this Langevin equation is equivalent to the Schrödinger equation in Euclidean time if the Hamiltonian is Hermitian, the dynamics are described by potential forces, the vacuum state is normalizable, and there is an energy gap between the vacuum state and the first excited state. These conditions are necessary for proving the limit and ergodic theorems. For three solvable models with nonlinear Langevin equations, we prove that the corresponding Schrödinger equations satisfy all the above conditions and lead to local linear FPK equations with the derivative order not exceeding two. We also briefly discuss several subtle mathematical questions of stochastic calculus.     

Long-Time Bath Correlations in the Pollak–Grabert–Hänggi Theory

We analyze some cases for which the Pollak–Grabert–Hänggi theory on the activated rate processes for generalized Langevin dynamics exhibits unexplained disagreements with numerical results. First we analyze carefully the PGH theory and we show that a kind of Markovian hypothesis implicitly made in the reasoning is sometimes violated. Then we propose modifications of the original theory in order to take into account the possible effects caused by this violation, and we compare the corrected results with simulations.     

同时发射和接收纵波和横波的压电复合材料换能器

通过控制压电复合材料中压电相的分布形式，本文具有在百度模振动的１－３型压电复合材料和具有扭转模振动的拼接２－２型压电复合材料组合在一起，构成一种混俣模式压电材料，并测试了这种压电材料晶片的性能参数，使用这种晶片作的换能器可以根据使用者的要求，单独产生纵波或横波，也可同时产生这两种波。