Collapsing dynamics of a laser-induced cavitation bubble near the edge of a rigid wall

In the present paper, the collapsing dynamics of a laser-induced cavitation bubble near the edge of a rigid wall is experimentally investigated with a high-speed photography system. For a symmetrical setup, the two primary control parameters of the bubble collapsing behavior include the equivalent maximum bubble radius and the distance between the bubble and the edge of the rigid wall. Based on the bubble interface deformation during the collapsing process, three typical cases are identified for the categorization of the phenomenon with the influences of the parameters revealed. Through a quantitative analysis of the obtained high-speed photos, the motions of the bubble interface in different directions are given together with the calculations of the bubble centroid. The primary findings of the present paper could be summarized in terms of the bubble-edge distance as follows. When the bubble is close to the edge, the movement of the bubble interface near the edge will be restricted with a clear neck formation in the middle part of the bubble. For this case, the edge could delay the bubble collapsing time up to 22% of the Rayleigh collapsing time. When the bubble is of the medium distance to the edge, the differences of the expansion or shrinkage of the bubble interface among different directions will be reduced with an olive-shaped bubble formed during the collapsing process. For this range of parameters, the bubble moves rapidly toward the edge especially during the final collapsing stage. When the bubble is far away from the edge, the bubble will be a nearly spherical one.     

放缩,反演和障碍问题

代替移动平面法和滑动区域法，作者利用放缩和反演变换研究某些半线性椭圆型分分下等方程解的单调性和对称性，这些变换依赖某一参数，在关于数据的单调性的适当假定下，当参数近某一初始值最大值时，解和其变换的差在某一“窄区域”满足一个椭圆型不等式，利用Ｖａｒａｄｈａｎ的极值原理，即得这个差是正的并得到解的单调性。     

Reinforcement Learning-Based Reactive Obstacle Avoidance Method for Redundant Manipulators

Redundant manipulators are widely used in fields such as human-robot collaboration due to their good flexibility. To ensure efficiency and safety, the manipulator is required to avoid obstacles while tracking a desired trajectory in many tasks. Conventional methods for obstacle avoidance of redundant manipulators may encounter joint singularity or exceed joint position limits while tracking the desired trajectory. By integrating deep reinforcement learning into the gradient projection method, a reactive obstacle avoidance method for redundant manipulators is proposed. We establish a general DRL framework for obstacle avoidance, and then a reinforcement learning agent is applied to learn motion in the null space of the redundant manipulator Jacobian matrix. The reward function of reinforcement learning is redesigned to handle multiple constraints automatically. Specifically, the manipulability index is introduced into the reward function, and thus the manipulator can maintain high manipulability to avoid joint singularity while executing tasks. To show the effectiveness of the proposed method, the simulation of 4 degrees of planar manipulator freedom is given. Compared with the gradient projection method, the proposed method outperforms in a success rate of obstacles avoidance, average manipulability, and time efficiency.     

An Improved Hybrid Method for Inverse Obstacle Scattering Problems

An improved hybrid method is introduced in this paper as a numerical method to reconstruct the scatterer by far-field pattern for just one incident direction with unknown physical properties of the scatterer. The improved hybrid method inherits the idea of the hybrid method by Kress and Serranho which is a combination of Newton and decomposition method, and it improves the hybrid method by introducing a general boundary condition. The numerical experiments show the feasibility of this method.     

Wang's Harnack inequalities for space–time white noises driven SPDEs with two reflecting walls and their applications

In this paper, we establish Wang's Harnack inequalities for Gaussian space–time white noises driven the stochastic partial differential equation with double reflecting walls, which is of the infinite dimensional Skorokhod equation. We first establish both the Harnack inequality with power and the log-Harnack inequality for the special case of additive noises by the coupling approach. Then we investigate the log-Harnack inequality for the Markov semigroup associated with the reflected SPDE driven by multiplicative noises using the penalization method and the comparison principle for SPDEs. As their applications, we study the strong Feller property, uniqueness of invariant measures, the entropy-cost inequality, and some other important properties of the transition density.     

Research anouncement uniqueness theorems for inverse obstacle scattering problems in lipschitz domains

For the Neumann and Robin boundary conditiom the uniqueness theorema for inveme obstade scattering pmblema are proved in Lipachitz domains. The role of nonsmoothness of the boundary is analyzed.     

Stability of the determination of the surface impedance of an obstacle from the scattering amplitude

We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof, which is essentially based on an elliptic Carleman inequality. Copyright © 2013 John Wiley & Sons, Ltd.     

Elliptic gradient constraint problem

We study the existence and regularity of gradient constraint problem. It arises in elastoplasticity and finance. First, we consider linear double obstacle problem which comes from viscosity solution to Hamilton–Jacobi equation and find the solution has C^1,α regularity by estimating Campanato-type integral oscillation. Then, by perturbation method and fixed point theorem in C^1,α space, we prove the existence of C^1,α solution.     

Effect of surface modification of montmorillonite on the properties of rigid polyurethane foam composites

<正>This study investigated the influence of various organically modified montmorillonites(organoclays) on the structure and properties of rigid polyurethane foam(RPUF) nanocomposites.The organoclays were modified with cetyltrimethyl ammonium bromide(CTAB),methyl tallow bis(2-hydroxyethyl) quaternary ammonium chloride (MT2ETOH) and tris(hydroxymethyl)aminomethane(THMA) and denoted as CMMT,Cloisite 30B and OMMT, respectively.MT2ETOH and THMA contain hydroxyl groups,while THMA does not have long aliphatic tail in its molecule. X-ray diffraction and transmission electron microscopy show that OMMT and Cloisite 30B can be partially exfoliated in the RPUF nanocomposites because their intercalating agents MT2ETOH and THMA can react with isocyanate.However, CMMT modified with nonreactive CTAB is mainly intercalated in the RPUF matrices.At a relatively low filler content,the RPUF/CMMT composite foam has a higher specific compressive strength(the ratio of compressive strength against the apparent density of the foams),while at relatively high filler contents,RPUF/Cloisite 30B and RPUF/OMMT composites have higher specific compressive strengths,higher modulus and more uniform pore size than the RPUF/CMMT composite.