Existence of frequency modes coupling seismic waves and vibrating tall buildings

We prove in this paper an existence result for frequency modes coupling seismic waves and vibrating tall buildings. The derivation from physical principles of a set of equations modeling this phenomenon was done in previous studies. In this model all vibrations are assumed to be anti-plane and time harmonic so the two dimensional Helmholtz equation can be used. A coupling frequency mode is obtained once we can determine a wavenumber such that the solution of the corresponding Helmholtz equation in the lower half plane with relevant Neumann and Dirichlet conditions at the interface satisfies a specific integral equation at the base of an idealized tall building. Although numerical simulations suggest that such wavenumbers should exist, as far as we know, to date, there is no theoretical proof of their existence. This is what this present study offers to provide.     

Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations

The numerical simulation of electric circuits including multirate signals can be done by a model based on partial differential algebraic equations. In the case of frequency modulated signals, a local frequency function appears as a degree of freedom in the model. Thus the determination of a solution with a minimum amount of variation is feasible, which allows for resolving on relatively coarse grids. We prove the existence and uniqueness of the optimal solutions in the case of initial-boundary value problems as well as biperiodic boundary value problems. The minimisation problems are also investigated and interpreted in the context of optimal control. Furthermore, we construct a method of characteristics for the computation of optimal solutions in biperiodic problems. Numerical simulations of test examples are presented.     

Modeling and simulations of interface properties with first‐principles electronic structure computations

We report extensive first‐principles electronic structure modeling and calculations for the SiC–SiO₂ interface, a solid–solid interface formed during oxidation of silicon carbide (SiC). The interface modeling provides atomic‐scale understanding about the nature of the interface defects as well as passivation effects due to the modification of the interface bonding. In particular, simulation results show that incorporation of hydrogen and fluorine decreases the defect density, thus enhancing the performance of SiC‐based electronic devices. Copyright © 2013 John Wiley & Sons, Ltd.     

基于跳频通信的移动机械遥控系统

为解决在同一个工作区域多个无线通信网络容易彼此干扰无法协同工作的问题,以移动机械工程车辆为控制对象,设计JRCJ500无线遥控系统,由用户手持终端接收用户操作指令,现场控制器驱动远程设备动作,实现对车辆的远程操作控制与状态信息反馈;采用STM32L低功耗处理器设计无线通信模块,选择公用通信频段,基于跳频扩频通信技术,约定无线通信数据格式与跳频频点,通过简单高效的跳频图案生成算法,在每一帧数据中添加同步字头,实现了无线通信网络的快速同步组网,保证了通信的稳定性,实现了在限定工作区域多台无线通信设备同时工作的应用需求。由于采用模块化设计,系统具有良好的通用性和可移植性,能够在多种复杂恶劣工作场合实现远程控制功能。     

Q波段回旋行波管新型盒型输出窗的设计

利用等效电路理论,初步设计了窗片厚度为1.32mm的回旋行波管盒型输出窗,再加入感性膜片,更改窗片形状,最终设计出了能承受25kW平均功率、相对带宽达到14%、窗片厚度达到1.7mm的Q波段新型宽频带回旋行波管盒型输出窗;采用高频软件HFSS与有限元分析软件ANSYS协同仿真的新方法对回旋行波管盒型窗进行热特性研究表明,盒型窗理论上功率容量达到62kW平均功率,说明输出窗窗片承受25kW平均功率的可行性,窗片中心与边缘的温差为66℃,没有达到陶瓷窗片的临界温差158℃,验证了新型盒型窗设计的合理性。     

部分相干平顶光束在非Kolmogorov湍流中的湍流距离

给出了部分相干平顶光束通过非Kolmogorov湍流传输的湍流距离解析表达式,并研究了非Kolmogorov湍流的湍流广义指数、内尺度、外尺度和光束参数对部分相干平顶光束湍流距离的影响。研究表明:湍流距离随相干参数、束腰、外尺度(当湍流广义指数的取值为3.6~4.0时)的增大而减小;随光束阶数、内尺度的增大而增大;随湍流广义指数先减小后增大,且在湍流广义指数取3.11时存在极小值,即光束扩展的极大值。同时利用湍流广义指数及光束参数,具体比较了湍流距离与瑞利区间的大小,并指出光束参数及湍流广义指数决定了湍流是否在瑞利区间内就能对光束扩展构成明显的影响。     

绝缘微堆质子直线加速器关键技术研究进展

基于绝缘微堆技术的直线加速器由于其能够实现较高的粒子加速梯度,尤其在质子加速及肿瘤治疗领域的优势得到高度关注。目前该种加速器处于研发阶段,有一系列技术和工程问题有待解决。介绍了课题组在过去的两年里围绕建立一台1 MeV质子注入器原型样机在固态脉冲功率系统、绝缘微堆及质子束源等方面取得的研究进展。实现了耐压梯度接近20 MV/m的环形绝缘微堆样品,样品内径30 mm,外径50mm,厚度15mm,基本达到设计要求;固态脉冲功率系统实现了光导开关多路稳定工作模式,开关直流偏置耐压达到20kV,采用激光二极管触发同步系统在15路同步时实现了低于1ns的抖动,输出300kV的电压脉冲,输出电压脉冲宽度10ns;进行了低能质子加速束流动力学的初步分析和模拟工作,模拟结果表明采用微堆结构可以实现质子束的有效加速和传输。     

Cohen–Macaulayness and Limit Behavior of Depth for Powers of Cover Ideals

Let 𝕂 be a field, and let R = 𝕂[x ₁,…, x _n ] be the polynomial ring over 𝕂 in n indeterminates x ₁,…, x _n . Let G be a graph with vertex-set {x ₁,…, x _n }, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J ^(k) and J ^[k], respectively. In this paper, we give necessary and sufficient conditions for R/J ^k , R/J ^(k), and R/J ^[k] to be Cohen–Macaulay. We also study the limit behavior of the depths of these rings.     

Robust investment–reinsurance optimization with multiscale stochastic volatility

This paper investigates the investment and reinsurance problem in the presence of stochastic volatility for an ambiguity-averse insurer (AAI) with a general concave utility function. The AAI concerns about model uncertainty and seeks for an optimal robust decision. We consider a Brownian motion with drift for the surplus of the AAI who invests in a risky asset following a multiscale stochastic volatility (SV) model. We formulate the robust optimal investment and reinsurance problem for a general class of utility functions under a general SV model. Applying perturbation techniques to the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation associated with our problem, we derive an investment–reinsurance strategy that well approximates the optimal strategy of the robust optimization problem under a multiscale SV model. We also provide a practical strategy that requires no tracking of volatility factors. Numerical study is conducted to demonstrate the practical use of theoretical results and to draw economic interpretations from the robust decision rules.     

Derivatives of molecular surface area and volume: simple and exact analytical formulas

The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy-to-use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear-scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header-only template library.