Random Skew Plane Partitions and the Pearcey Process

We study random skew 3D partitions weighted by q ^vol and, specifically, the q → 1 asymptotics of local correlations near various points of the limit shape. We obtain sine-kernel asymptotics for correlations in the bulk of the disordered region, Airy kernel asymptotics near a general point of the frozen boundary, and a Pearcey kernel asymptotics near a cusp of the frozen boundary.     

Universality for the Pearcey process

Consider non-intersecting Brownian motions on the line leaving from the origin and forced to two arbitrary points. Letting the number of Brownian particles tend to infinity, and upon rescaling, there is a point of bifurcation, where the support of the density of particles goes from one interval to two intervals. In this paper, we show that at that very point of bifurcation a cusp appears, near which the Brownian paths fluctuate like the Pearcey process. This is a universality result within this class of problems. Tracy and Widom obtained such a result in the symmetric case, when the two target points are symmetric with regard to the origin. This asymmetry enabled us to improve considerably a result concerning the non-linear partial differential equations governing the transition probabilities for the Pearcey process, obtained by Adler and van Moerbeke.     

Riemann–Hilbert approach to multi-time processes: The Airy and the Pearcey cases

We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels à la Its–Izergin–Korepin–Slavnov (IIKS) and hence related to suitable Riemann–Hilbert problems, thus extending the known results for the single-time case. We focus on the Airy and Pearcey processes. As an example of applications we re-deduce a third order PDE, found by Adler and van Moerbeke, for the two-time Airy process.     

Propagation of a Pearcey beam in uniaxial crystals

An analytical propagation expression of a Pearcey beam in uniaxial crystals orthogonal to the optical axis is derived.The propagations of the Pearcey beam in the tourmaline and the quartz are investigated. The phase distribution and the angular momentum of the Pearcey beam in the tourmaline are also performed. The result shows that the positions of the auto-focusing and the inversion simply relate to the extraordinary refractive index of the crystals. In other words, we can choose the suitable crystals to adjust the positions of auto-focusing and inversion of the Pearcey beam to meet the actual needs.     

A Rotationally Symmetric Multifocal Pearcey Beam with a Polygonal Profile

The polygonal multifocal propagation properties and particle trapping experiments of a new kind of power-exponential-phase vortex chirped circular Pearcey Gaussian beam are investigated. Theoretical and experimental results show that it is possible to adjust the position and transverse spatial distribution of the beam in focal plane, as well as to make the transverse intensity distribution emerge an arbitrary polygonal profile by changing the distribution factor and vortex topological charge. Stable trapping of multiple particles is achieved in the experiment with transverse intensity fields in the polygon plane with different topological charges.     

Pearcey光束簇的实验产生和光学结构研究

基于微分几何理论和衍射光学理论, 给出了决定Pearcey光束光学结构的因素. 通过数值模拟和实验, 理论构造并实际产生了一簇光学拓扑结构不同的Pearcey光束. 随后, 它们的基本光学性质被研究. 研究结果表明, Pearcey光束的结构灵活可控, 因而有望在科学实验中发挥新的作用.     

Generation and control of dynamically tunable circular Pearcey beams with annular spiral-zone phase

Light-field shaping technology plays an important role in optics and nanophotonics. For instance, the spatially structured light field, which exhibits characteristic features in complex phases, light intensity, and polarization, is crucial to understanding new physical phenomena and exploring practical applications. Herein, we propose and demonstrate a new class of tunable circular Pearcey beams(TCPBs) by imposing the annular spiral-zone phase(ASZP). Through experiments, we used a spatial light modulator to generate TCPBs based on their spiral phase distribution, and numerically analyzed the generation and control of the beams with unusual autofocusing and self-rotating dynamics. ASZP is a general term for complex phases composed of the spiral phase,equiphase, and radial phase. TCPB typically exhibits dynamical properties, including abrupt autofocusing, automatic generation of optical bottles, and self-rotation of the beam pattern, during propagation. Besides, the number of generated optical bottles can be modulated by the superposition mode of ASZP and the number of subphases. We found that an inappropriate superposition mode leads to distortion, and we analyzed the underlying mechanism. Potential applications of TCPBs in optical manipulation are also discussed, presenting an exemplary role desired for light-field manipulation.     

Dynamic Optical Vortex Trajectory Guided by the Symmetric Pearcey Gaussian Vortex Beam in the Uniformly Moving Parabolic Potential

This paper analytically and numerically proposes the propagation dynamics of the symmetric Pearcey Gaussian vortex beam (SPGVB) in the uniformly moving parabolic potential. The optical vortex located in the initial plane produces a vortex channel in the presence of the uniformly moving parabolic potential, called the vortex trajectory. The vortex trajectory can be manipulated dynamically by configuring different combinations of the parameters, and the optical intensity and the focal position can also be affected. Moreover, the spatial dynamic vortex trajectory is derived analytically, and the 2D on-axis and off-axis vortex scenarios are also presented. Our work expands the methods of the vortex trajectory manipulation and may broaden more practical potential applications in the particle manipulation.     

The Enskog Process

In this paper we give a new proof of the second order Boltzmann–Gibbs principle introduced in Gonçalves and Jara (Arch Ration Mech Anal 212(2):597–644, 2014). The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions. In addition, we fully derive the convergence of the equilibrium fluctuations towards (1) a trivial process in case of super-diffusive systems, (2) an Ornstein–Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, as defined in Gubinelli and Jara (SPDEs Anal Comput (1):325–350, 2013) and Gubinelli and Perkowski (Arxiv:1508.07764, 2015), in case of weakly asymmetric diffusive systems. Examples and applications are presented for weakly and partial asymmetric exclusion processes, weakly asymmetric speed change exclusion processes and hamiltonian systems with exponential interactions.     

The Asymmetric Avalanche Process

An asymmetric stochastic process describing the avalanche dynamics on a ring is proposed. A general kinetic equation which incorporates the exclusion and avalanche processes is considered. The Bethe ansatz method is used to calculate the generating function for the total distance covered by all particles. It gives the average velocity of particles which exhibits a phase transition from an intermittent to continuous flow. We calculated also higher cumulants and the large deviation function for the particle flow. The latter has the universal form obtained earlier for the asymmetric exclusion process and conjectured to be common for all models of the Kardar–Parisi–Zhang universality class.     

组合发电仪的制作

仪器应用生活中常见的材料,仅仅围绕物理学科知识,通过巧妙设计,组装出一系列发电机。旨在让学生明白各种发电机的工作原理,以及能量之间是如何相互转化的,培养学生节约能源,保护环境利用清洁能源的意识。此外本仪器制作简单,便于学生亲手制作,锻炼动手能力的同时,又可提高学习兴趣。     

高功率垂直腔面发射激光器的湿法腐蚀工艺

为提高高功率垂直腔面发射激光器(VCSEL)光电性能,对氧化限制型高功率VCSEL湿法腐蚀工艺进行了实验研究。实验中采用H₃PO₄系溶液替代以往制备此类器件常用的H₂SO₄系溶液作为高功率VCSEL外延片的腐蚀液,利用扫描电镜(SEM)研究了腐蚀后外延片氧化窗口的腐蚀形貌变化与腐蚀液浓度的关系,消除了以往采用H₂SO₄系溶液腐蚀时,高功率VCSEL氧化层侧壁出现的"燕尾"结构;通过改变湿法腐蚀工艺的外部温度条件和腐蚀液的浓度配比,实验研究了高功率VCSEL湿法腐蚀速率规律,最后得出了制备高功率VCSEL时湿法腐蚀工艺的最佳外部温度条件与腐蚀液的最佳浓度配比。     

Linux的进程地址空间研究

本文研究了Linux进程的虚拟地址空间管理，包括页表结构、内存分配策略、线性地址区间结构，线性地址到物理地址的映射等。     

磁感应发电仪的制作

实验教具利用变化的磁场可以产生感应电流之一原理制成。设计巧妙,现象奇特,紧紧围绕物理学科知识,取材于生活,制作简单,便于学生亲手完成,可以让学生锻炼动手能力的同时,理解感应电流是如何产生的,进而改变实验条件,激发学生思考,加深对知识的理解。     

The Two-Nucleon Stripping Process with Skyrme Type Potential

Theory of two-nucleon stripping reactions is reconsidered. The nucleon-nucleon interactions are taken as Skyrme type potentials. Differential cross-sections for two-nucleon stripping reactions are calculated using DWBA approximation with different Skyrme type potentials of different parameters. The angular distributions for different two-nucleon stripping reactions (t, p) with incident triton on the different targets of ³¹P, ⁴⁰Ca, ⁹⁶Zr, ¹¹⁸Sn and ²⁰⁶Pb are calculated giving good agreement with the experimental data. Better values are extracted for the spectroscopic factors.     

The Initial Process of Superfluorescence in Microscopic Description

The initiation of superfluorescence is studied by a method starting from the N-atom master equation in the high-excitation limit. By numerical calculation cooperation numbers and the temporal growth of the radiation pattern are determined for atomic numbers between 24 and 48. For randomly distributed atoms there is a particle density of maximum cooperation.     

The Largest Fragment of a Homogeneous Fragmentation Process

We show that in homogeneous fragmentation processes the largest fragment at time t has size

$$\begin{aligned} e^{-t \Phi '(\overline{p})}t^{-\frac{3}{2} (\log \Phi )'(\overline{p})+o(1)}, \end{aligned}$$

where \(\Phi \) is the Lévy exponent of the fragmentation process, and \(\overline{p}\) is the unique solution of the equation \((\log \Phi )'(\bar{p})=\frac{1}{1+\bar{p}}\). We argue that this result is in line with predictions arising from the classification of homogeneous fragmentation processes as logarithmically correlated random fields.

     

The Entropy of a Binary Hidden Markov Process

The entropy of a binary symmetric Hidden Markov Process is calculated as an expansion in the noise parameter ε. We map the problem onto a one-dimensional Ising model in a large field of random signs and calculate the expansion coefficients up to second order in ε. Using a conjecture we extend the calculation to 11th order and discuss the convergence of the resulting series