让学生看到音乐的数理之美--通过“乐音研究”再谈大学文科物理实验的设计与实施

针对新开设的大学文科物理实验“乐音研究”实验教学实践,着重强调了实验的设计理念、目的和思路。通过“乐音研究”实验,使文科学生区分噪音和乐音差异,了解其作为一种特殊力学振动的时域特征、频域特征,理解乐音“听起来好听”的悦耳和谐原理,并通过展示各个音符间的关系,让学生学会示波器以及LabView 分析界面的使用,通过分析归纳出“十二平均律”,最后利用“三分损益”方法构建管箫,体验音乐中包含物理学和数学在内的科学原理。     

单稳系统的脉冲响应研究

针对单稳系统检测脉冲信号的参数调节方法很难达到理想随机共振效果的难点, 本文提出了脉冲序列整体平移的方法. 该方法不采用系统参数调节, 而是通过偏移量的设置来实现并达到增强单稳随机共振的目的. 为了减小单稳脉冲响应波形的失真, 探讨了该方法减小脉冲响应失真的机理. 在噪声存在的情况下, 揭示了该平移方法调节噪声使噪声产生积极作用从而改善单稳随机共振的机理, 表明所提方法有利于含噪脉冲信号的检测.     

Optically referenced broadband electronic synthesizer with 15 digits of resolution

Fundamental science, as well as all communications and navigation systems, are heavily reliant on the phase, timing, and synchronization provided by low‐noise and agile frequency sources. Although research into varied photonic and electronic schemes have strived to improve upon the spectral purity of microwave and millimeter‐wave signals, the reliance on conventional electronic synthesis for tuning has resulted in limited progress in broadband sources. Using a digital‐photonic synthesizer architecture that derives its time‐base from a high‐stability optical reference cavity, we generate frequency‐agile and wideband microwave signals with exceptional dynamic range and with a fractional frequency instability of 1 × 10⁻¹⁵ at 1 s. The presented architecture demonstrates digitally controlled, user defined and broadband frequency tuning from RF to 100 GHz with orders‐of‐magnitude improvement in noise performance over room‐temperature electronic wide‐bandwidth synthesis schemes.

     

Stochastic averaging of quasi-integrable Hamiltonian systems under combined harmonic and white noise excitations

A stochastic averaging method is proposed to predict approximately the response of quasi-integrable Hamiltonian systems to combined harmonic and white noise excitations. According to the proposed method, an n+α+β-dimensional averaged Fokker-Planck-Kolmogorov (FPK) equation governing the transition probability density of n action variables or independent integrals of motion, α combinations of angle variables and β combinations of angle variables and excitation phase angles can be constructed when the associated Hamiltonian system has α internal resonant relations and the system and harmonic excitations have β external resonant relations. The averaged FPK equation is solved by using the combination of the finite difference method and the successive over relaxation method. Two coupled Duffing-van der Pol oscillators under combined harmonic and white noise excitations is taken as an example to illustrate the application of the proposed procedure and the stochastic jump and its bifurcation as the system parameters change are examined.     

A rod-airfoil experiment as a benchmark for broadband noise modeling

A low Mach number rod-airfoil experiment is shown to be a good benchmark for numerical and theoretical broadband noise modeling. The benchmarking approach is applied to a sound computation from a 2D unsteady-Reynolds-averaged Navier–Stokes (U-RANS) flow field, where 3D effects are partially compensated for by a spanwise statistical model and by a 3D large eddy simulation. The experiment was conducted in the large anechoic wind tunnel of the Ecole Centrale de Lyon. Measurements taken included particle image velocity (PIV) around the airfoil, single hot wire, wall pressure coherence, and far field pressure. These measurements highlight the strong 3D effects responsible for spectral broadening around the rod vortex shedding frequency in the subcritical regime, and the dominance of the noise generated around the airfoil leading edge. The benchmarking approach is illustrated by two examples:

A variational formulation for physical noised image segmentation

Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others,these results show that our proposed model and algorithms are effective.     

Nonlinear PDEs with Modulated Dispersion I: Nonlinear Schrödinger Equations

We start a study of various nonlinear PDEs under the effect of a modulation in time of the dispersive term. In particular in this paper we consider the modulated non-linear Schrödinger equation (NLS) in dimension 1 and 2 and the derivative NLS in dimension 1. We introduce a deterministic notion of “irregularity” for the modulation and obtain local and global results similar to those valid without modulation. In some situations, we show how the irregularity of the modulation improves the well–posedness theory of the equations. We develop two different approaches to the analysis of the effects of the modulation. A first approach is based on novel estimates for the regularizing effect of the modulated dispersion on the non-linear term using the theory of controlled paths. A second approach is an extension of a Strichartz estimated first obtained by Debussche and Tsutsumi in the case of the Brownian modulation for the quintic NLS.