We study the thermodynamics of the heavy quarkonium and string breaking in the anisotropic media by gravity/gauge duality. The degree of anisotropy is characterized by the dynamical exponent v, with v = 1 representing the isotropic case. The free energy of the heavy quarkonium, which is obtained through the Wilson loop, is investigated in an anisotropic background. It is found that the free energy is suppressed by the dynamical exponent v. The results also show that the anisotropy induced by anisotropic pressure significantly influences the free energy of the Coulombic part, in contrast to the effect of anisotropy induced by the magnetic field. Additionally, we find that when v increases, both the absolute value of the imaginary potential and the thermal width increase. Finally, the string breaking is investigated in the confinement phase which corresponds to the zero temperature. It is found that the heavy meson is easier to decay in the presence of anisotropy compared to the isotropic case for the decay mode Q Q -> Qq & thorn; Q q. .

We study Jeans instability with generalized Maxwellian distribution. The results reveal two significant features of the modified Jeans instability. First, the Jeans wavelength of the system covers the original lambda J {\lambda }_{J} when k = 1 k=1 . Second, as k k approaches 0, the modified Jeans wavelength approaches infinity. This means that the system is always gravitationally stable. Furthermore, we examine the implications of the modified Maxwellian distribution on the Friedmann equation. Our analysis suggests that the effective gravitational constant should incorporate the contribution of temperature T T in order to describe the system dynamics.

The partition function of three-dimensional gravity in the quantum regime is dual to the Ising model when the central charge c = 1/2. Mathematically, we show that the three-dimensional gravity can be described by Schramm–Loewner evolution (SLE) with certain κ. In fact, SLE depends on the parameter κ, which controls the diffusion of the Brownian motion. Each value of c < 1 corresponds to two values of κ, which may hint that the three-dimensional gravity has two different phases at certain central charge c. Moreover, phase transition is also discussed in AdS and Ising model.

The partition functions of Jackiw–Teitelboim (JT) gravity corresponds to random matrix integral. And we can define three different versions of bosonic JT gravity which are dual to matrix integrals of GUE, GOE, and GSE, respectively. In fact, the largest eigenvalue λ_max of the Gaussian unitary random matrix GUE is described by the Tracy–Widom distribution. Then we show that there is a third-order order phase transition in the JT gravity as λ_max crosses its mean value from left weakly coupled tail to right strongly coupled tail.

The evolution of Cos−Gaussian beams in periodic potential optical lattices is theoretically and numerically investigated. By theoretical analysis, a breathing soliton solution of the Gross–Pitaevskii equation with periodic potential is obtained, and the period of the breathing soliton is solved. In addition, the evolution of Cos−Gaussian beams in periodic potential optical lattices is numerically simulated. It is found that breathing solitons generate by appropriately choosing initial medium and beam parameters. Firstly, the effects of the initial parameters of Cos−Gaussian beams (initial phase and width) on its initial waveform and the propagation characteristics of breathing soliton are discussed in detail. Then, the influence of the initial parameters (modulation intensity and modulation frequency) of a photonic lattice on the propagation characteristics of breathing solitons is investigated. Finally, the effects of modulation intensity and modulation frequency on the width and period of the breathing soliton are analyzed. The results show that the number of breathing solitons is manipulated by controlling the initial parameters of Cos−Gaussian beams. The period and width of a breathing soliton are controlled by manipulating the initial parameters of a periodic photonic lattice. The results provide some theoretical basis for the generation and manipulation of breathing solitons.

Abstract We numerically investigate and statistically analyze the impact of medium parameters (modulation depth P, modulation factor ω, and gain/loss strength W 0) and beam parameters (truncation coefficient a and distribution factor χ 0) on the propagation characteristics of a cosh-Airy beam in the Gaussian parity-time (PT)-symmetric potential. It is demonstrated that the main lobe of a cosh-Airy beam is captured as a soliton, which varies periodically during propagation. The residual beam self-accelerates along a parabolic trajectory due to the self-healing property. With increment in P, the period of a trapped soliton decreases almost monotonically, while the peak power of a trapped soliton increases monotonically. With the increase in ω or decrease in the absolute value of W 0, the period and peak power of a trapped soliton decrease rapidly and then almost remain unchanged. Moreover, it is indicated that the period of a trapped soliton remains basically unchanged no matter a and χ 0 increase or decrease. The peak power of a trapped soliton increases with increment of a, but the peak power of a trapped soliton stays relatively constant irrespective of variation in χ 0.

由于光的衍射极限限制,人们无法观察精细的细胞结构和获得纳米级的蛋白质以及生物分子信息.本研究采用极大似然算法来实现单分子定位.首先,对荧光分子图像进行解卷积和二值化处理降噪;其次,对荧光显微成像过程建立极大似然模型;最后,用优化工具箱函数进行求解.模拟结果表明:相邻20 nm的2条分子带可以分辨;将此算法应用于实际生物样品的超分辨成像时,原本不能区别的2条微丝可以进行区分,且分辨能力得到了提高;极大似然法可以很好地完成分子定位,进而实现超分辨图像的重构.

在超分辨荧光显微成像技术中,单分子定位显微方法是被广泛应用的技术之一.根据荧光显微成像原理构造多测量矢量压缩感知模型(Multiple Measurement Vector-Compressed Sensing,MMV-CS),并采用多重稀疏贝叶斯学习算法进行求解,来实现超分辨荧光图像重建.分析了有效像元大小、荧光分子生成的光子数和背景信号泊松化噪声对重建结果的影响,以及在图像进行分块处理时算法运行时间的分析.模拟和实验计算分析表明,当点扩展函数的标准差在160 nm时,有效像元大小在120、160、200 nm能取得较好的重构效果,而在60 nm时效果较差.探测器收集的光子数越多,重构效果越好,随着背景信号光子数增加时,离得越近的样品结构越不能分辨.在同样的分块处理情况下,MMV-CS比同伦算法(L1-Homotopy,L1-H)和凸优化算法(CVX)分别快一个数量级和三个数量级,因此,在研究三维超分辨荧光显微成像时,MMV-CS算法在运行时间上具有更大的优势.

In order to achieve fast three-dimensional localization of high-density fluorescent molecular images, a three-dimensional compressed sensing model was established and studied using the CVX method, the Orthogonal Matching Pursuit(OMP) algorithm and a homotopy algorithm. The models' measurement matrix was then designed. Firstly, the system's theory and design were both developed using the three-dimensional point-spread function imaging theory of fluorescence microscopy. Then, the process of fluorescence microscopic imaging was simulated, through which the images generated in the established compressed sensing model were analyzed using the CVX method, OMP algorithm and homotopy algorithm. The recall rate, localization accuracy and reconstruction time were compared. Finally, the simulated biological samples and the collected cells in the laboratory were analyzed using the homotopy algorithm, and thus three-dimensional super-resolution imaging was achieved. It can be seen from the comparative results that the homotopy algorithm is two orders of magnitude faster than the CVX method when the reconstruction density and localization accuracy have little deviation. The localization accuracy of the homotopy algorithm is twice higher than that of the OMP algorithm. The homotopy algorithm is meaningful for 3D super-resolution fluorescence microscopy imaging, which can save computing time and achieve real-time imaging.