Modification of Spatial Coherence by Means of Low-Order Zernike-Mode Adaptive Optics

Spatial coherence of the field modified by low-order adaptive optics is analyzed to establish a theoretical basis for the recent idea of using adaptive optics as a spatial coherence modifier. In this context low-order adaptive optics has the ability to correct some of the low-order aberrations specified by Zernike polynomials. The initial field to be modified is assumed to be a spatially partially coherent one resulting from phase disturbance. It is demonstrated, as in the previous study, that low-order adaptive optics serves to enhance the spatial coherence of the resultant field and that the effect of the enhancement becomes stronger as the spatial coherence of the initially partially coherent field increases. Potential applications of low-order adaptive optics as a spatial coherence modifier are briefly discussed.     

Note on the surface wave due to the prescribed elevation

In the present paper, a study of the deep-sea water wave caused by an oscillatory wind stress due to the atmospheric depression, resulting in spiral cyclonic wind pressure on the surface of the sea is made. It has been observed that the motion of the water wave in the case of wind stress exhibits a greater elevation on the sea surface asg the acceleration due to gravity decreases and maintains the oscillatory nature with the increase of time. For the case of spiral cyclonic motion for which the sea surface experiences the elliptical pressure on the surface, the motion diminishes asg diminishes and oscillates with the variation of time. The motion also diminishes asymptotically as the radius vector of the elliptical pressure approaches unity.     

Temperature dependent small-angle neutron scattering of CTABr—magnetic fluid emulsion

Small-angle neutron scattering studies have been carried out to check the structural integrity of citryltrimethylammonium bromide (CTABr) micelles in a magnetic fluid for different magnetic fluid concentrations at two different temperatures 303 and 333 K. It is found that the CTABr micelles grow with increasing magnetic fluid concentration and there is a decrease in the micellar size with increase in temperature.     

Fast and precise algorithm based on maximum radial symmetry for single molecule localization

We present an algorithm to estimate the location of single fluorescent molecule with both high speed and high precision. This algorithm is based on finding the subpixel position with maximum radial symmetry in a pixelated single molecule fluorescence image. Compared with conventional algorithms, this algorithm does not rely on point-spread-function or noise model. Through numerical simulation and experimental analysis, we found that this algorithm exhibits localization precision very close to the maximum likelihood estimator (MLE), while executes ～1000 times faster than the MLE and ～6 times faster than the fluoroBancroft algorithm.     

非偏振贝塞尔高斯光束的球散射

无衍射光束球散射性质的研究目前一般采用贝塞尔光束,但是贝塞尔光束在物理上是不可实现的。贝塞尔高斯光束作为近似无衍射光束,是亥姆霍兹方程在傍轴条件下的解,并且可以用激光振荡器直接产生,但其光束宽是有限的。应用傅里叶变换,平面波谱展开和球面矢量波函数展开法,推导了非偏振贝塞尔高斯光束的球散射远场的无量纲散射函数。通过数值模拟,对非偏振的贝塞尔高斯光束与贝塞尔光束,高斯光束的球散射远场进行了比较,比较发现:当球散射体偏离光轴时,非偏振贝塞尔高斯光束跟贝塞尔光束散射远场的差异主要是散射强度的差异,但是散射极点所在的方向基本保持不变;贝塞尔高斯光束和贝塞尔光束的散射在光束圆锥角方向上比较显著,但高斯光束的前向散射比较显著。     

Interaction of two parallel plane jets of different velocities

The interaction of two parallel plane jets of different velocities is studied by flow visualization and PIV measurement to examine the influence of velocity ratio on the development ofjets in the initial region. It is found that the parallel plane jets develop toward the high velocity side and the jet width is reduced with a decrease in the jet velocity ratio. Corresponding to the variation of mean velocity field to the velocity ratio, the magnitudes of turbulence intensities, Reynolds stress and static pressure are weakened in the merging region of the jets and their peak locations of the properties are shifted to the high velocity side. These results indicate that the interaction of two parallel jets is weakened with a decrease in the velocity ratio of the jets.     

Derivation of the Keldysh Path Integral from the Master Equation of a Harmonic Oscillator in a Thermal Bath Via Supercoherent States

We consider a harmonic oscillator coupled to a Markovian environment, i.e. a thermal reservoir. We derive the Keldysh path integral and the corresponding lesser, greater, time-ordered, antitime-ordered, retarded, advanced, and Keldysh Green’s functions for this system. In order to give a conceptually clear derivation, we use the superoperator formalism and also define supercoherent states. The supercoherent states and the creation and annihilation superoperators provide a natural way to rewrite the master equation into a path integral.     

Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

We prove tail triviality of determinantal point processes \( \mu \) on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for \(\hbox {Sine}_2 , \hbox {Airy}_2 , \hbox {Bessel}_2 \), and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.     

Statistical Analysis of the First Passage Path Ensemble of Jump Processes

The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas.