混沌实验数据处理及仿真

大学物理实验中混沌实验大多采用观察现象的方法进行,本实验采用蔡氏电路(Chua s circuit)产生混沌行为.在观察不同初始值条件下出现的倍周期分岔、阵发混沌、奇异吸引子等相图及现象的基础上,通过对采集数据进行处理,对负电阻伏安特性进行分段线性拟合,用功率频谱法、计算机仿真方法(龙格-库塔数值积分法)对混沌现象进行描绘,将实验数据与非线性方程组的数值解相结合,呈现出混沌现象的本质.     

FFT-based algorithms for the string matching with mismatches problem

The string matching with mismatches problem requires finding the Hamming distance between a pattern P of length m and every length m substring of text T with length n. Fischer and Paterson's FFT-based algorithm solves the problem without error in O(σnlogm), where σ is the size of the alphabet Σ [SIAM–AMS Proc. 7 (1973) 113–125]. However, this in the worst case reduces to O(nmlogm). Atallah, Chyzak and Dumas used the idea of randomly mapping the letters of the alphabet to complex roots of unity to estimate the score vector in time O(nlogm) [Algorithmica 29 (2001) 468–486]. We show that the algorithm's score variance can be substantially lowered by using a bijective mapping, and specifically to zero in the case of binary and ternary alphabets. This result is extended via alphabet remappings to deterministically solve the string matching with mismatches problem with a constant factor of 2 improvement over Fischer–Paterson's method.     

Fabrication of material-independent morphology gradients for high-throughput applications

Gradient surfaces allow rapid, high-throughput investigations and systematic studies in many disparate fields, including biology, tribology and adhesion. We describe a novel method for the fabrication of material-independent morphology gradients, involving a two-step process of particle erosion followed by a chemical polishing procedure that preferentially removes features with a small radius of curvature as a function of time. Gradients are fabricated on aluminium surfaces, but they may be readily transferred to other materials via a replication technique, which allows for the production of identical roughness gradient samples with any chosen surface chemistry. The gradients have been characterized by means of scanning electron microscopy and optical profilometry. Standard roughness parameters (Ra, Rq, Rz, Sm and Sk) were calculated from optical profilometry data. The roughness has also been assessed over different wavelength windows by means of a fast Fourier transformation approach.     

Adaptation of a fast Fourier transform-based docking algorithm for protein design

Designing proteins with novel protein/protein binding properties can be achieved by combining the tools that have been developed independently for protein docking and protein design. We describe here the sequence-independent generation of protein dimer orientations by protein docking for use as scaffolds in protein sequence design algorithms. To dock monomers into sequence-independent dimer conformations, we use a reduced representation in which the side chains are approximated by spheres with atomic radii derived from known C2 symmetry-related homodimers. The interfaces of C2-related homodimers are usually more hydrophobic and protein core-like than the interfaces of heterodimers; we parameterize the radii for docking against this feature to capture and recreate the spatial characteristics of a hydrophobic interface. A fast Fourier transform-based geometric recognition algorithm is used for docking the reduced representation protein models. The resulting docking algorithm successfully predicted the wild-type homodimer orientations in 65 out of 121 dimer test cases. The success rate increases to approximately 70% for the subset of molecules with large surface area burial in the interface relative to their chain length. Forty-five of the predictions exhibited less than 1 A C(alpha) RMSD compared to the native X-ray structures. The reduced protein representation therefore appears to be a reasonable approximation and can be used to position protein backbones in plausible orientations for homodimer design.     

基于傅立叶变换的SVJ模型的欧式期权定价

为了更加精确的计算期权价格,将结合随机波动和跳扩散模型(以下简称SVJ模型)以更好的描述期权标的资产价格过程,然而这样的价格过程无法得到概率密度函数的封闭形式,而只能得到包含特殊函数和无限求和的复杂的表达式.不过它们的特征函数都是封闭且是唯一的,因而可以通过它们的特征函数,并运用两种傅立叶变换的方法来求出期权价格.其中FFT算法计算的结果将与Monte Carlo模拟得出的结果进行比较,然后再将SVJ模型的计算结果和Black-Scholes模型进行比较.     

测量光纤外腔Fabry-Perot干涉仪的白光干涉术

提出了一种基于白光干涉术测量低锐度光纤外腔Fabry Perot干涉仪（EFPI）的方法用宽带光源注入F P腔,在接收端用一高锐度的可调谐光纤F P滤波器对EFPI的反射光谱进行扫描,获得了周期性变化的光谱输出为了测量出EFPI的腔长,对光谱信号进行傅里叶变换,得到光谱的周期,由此求出EFPI的绝对腔长证明了用低锐度EFPI的测量准确度由腔长决定F P腔越长,测量准确度越高在腔长分别是200 μm,400 μm和600 μm时,测量的腔长与实际腔长相同.     

数字图像频域相关分析法及其应用

提出了一种以灰度为载体的数字图像频域相关(DFC)计量的方法,通过傅里叶变换和滤波,直接提取物体位移信息。与传统的激光散斑法比较,无需干涉光源,可用白光照明,因此对实验环境的要求很低;与数字图像相关法比较,计算速度更快,对照明要求更低,不受刚体转动影响。新方法不仅设备简单、容易实现,还具有灵敏度可调,测量过程无需人工干预的良好特征,由于充分利用了计算机数字图像处理的功能,抗干扰性强,是一种适合工业现场测量的有发展前途的位移全场测试新技术。     

一种基于谱线幅值归零的加窗插值FFT谐波检测方法

提出了一种基于谱线幅值归零的加窗插值FFT谐波检测方法用于分析复杂电网信号中的各次谐波.该检测方法将每一次在离散频谱中找到的最大谱线及其左右两侧的数根谱线幅值归零,直到各次谐波分析完毕.通过仿真实验分析了在基波频率稳定时对模拟信号的测量精度,研究了基波频率波动对谐波分析的影响.通过对EAST实验数据的分析,验证了该谐波...     

高温拉曼光谱提高信噪比的途径分析

结合累积时间分辨和空间分辨建成了上海大学高温拉曼谱仪SU-HTRS(T/S).由于高温噪声的不可避免,采用了移动平均方法,傅里叶变换滤波和小波分析的方法对其进行了数据降噪处理.在不同噪声水平上分析了不同处理方式对谱峰中心位置、强度、面积的影响及处理后数据的光滑度的影响.三种方法比较起来,移动平均法快而简单,小波分析的去噪效果最好.     

基于傅里叶变换的高精度条纹细分方法

针对传统傅里叶变换法在提取条纹图相位中存在的能量泄漏问题,提出了条纹图整周期裁剪的方法,可有效抑制能量泄漏对检相精度的影响,提高傅里叶变换法相位计算的精度。在此基础上,提出了一种基于傅里叶变换时移特性的叠栅条纹细分新方法。与传统傅里叶变换法相比,该方法求取相邻两帧条纹图间的相移,只需经过两次傅里叶变换,不需要截取条纹图的基频再逆变换回空域,因此计算量至少减少了一倍,计算速度大大提高。数值计算结果表明,对两束单色平面波形成的条纹,理想条件下细分精度高达10-12量级;对高斯包络调制的条纹,细分精度至少可达10-3量级。