子集模拟中马尔可夫链蒙特卡洛抽样算法比较

文章着重研究子集模拟中马尔可夫链蒙特卡洛(MCMC)抽样算法的抽样效率与计算精度。首先，阐述可靠度子集模拟的基本原理与中间状态样本生成的各种MCMC抽样算法，在稳态马尔可夫链构造基础上提出延迟拒绝MMH(Modified Metropolis Hasting)算法，通过在MMH算法上增加备选样本的延迟拒绝步提高MMH算法的抽样效率；阐述基于随机游走与基于扩散方程MCMC方法中建议分布的差异，进一步对备选样本接受率为1的preconditioned Crank-Nicolson(pCN)算法和条件抽样(Conditional sampling, CS)算法开展研究，证明两种算法的等价性；推导有效样本量的计算方法，提出采用有效样本量与总样本量的比值定义MCMC方法的抽样效率。通过复杂目标分布的样本生成研究不同MCMC抽样算法建议分布及其参数对备选样本接受率与抽样效率的影响，最后通过计算实例研究子集模拟过程采用不同MCMC抽样算法得到失效概率的相对误差及其变异性，揭示不同MCMC抽样算法对失效概率计算精度的影响。研究表明：不同MCMC抽样算法生成备选样本的接受率及其自相关性受建议分布及其参数影响较大，对于复杂的目标分布，pCN算法和CS算法的抽样效率较高，延迟拒绝MMH算法次之；采用CS算法和延迟拒绝MMH算法进行子集模拟得到的失效概率精度较高且变异性较低；增加子集模拟中间状态样本量可以提高失效概率计算精度并降低其变异性。     

Co?N graphene encapsulated cobalt catalyst for H2O2 decomposition under acidic conditions

Hydrogen peroxide (H₂O₂) has been listed as one of the 100 most important chemicals in the world. However, huge amount of residual H₂O₂ is hard to timely decomposed into O₂ and H₂O under acidic condition, easily resulting in explosion hazard. Here, we reported a core–shell structure catalyst, that is graphene with Co N structure encapsulated Co nanoparticles. Co N graphene shell serves as the active site for the H₂O₂ decomposition, and Co core further enhance this decomposition. Benefiting from it, the H₂O₂ decomposition were close to 100% after 6 cycles without pH adjustment, which increased 6 orders of magnitude compared with no catalyst. At the same time, the O₂ generation reached 99.67% in 2 h with little metal leaching, and ·OH has been greatly inhibited to only 0.08%. This work can cleanly remove H₂O₂ with little deep oxidation and protect the process of H₂O₂ utilization to achieve a safer world.     

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Stabilization for Schrödinger Equation with Internal Damping and Boundary Disturbance

In this paper, the stabilization for Schrödinger equation subject to internal damping and boundary disturbance at the control end is investigated. Due to its immeasurability, the nonlinear observer system is designed to obtain the state information, and the existence of weak solution and its convergence for the nonlinear observer system are proved. The feedback control is realized by the backstepping transformation. In addition, the adaptive disturbance rejection control is applied to estimate the disturbance. According to the observer and disturbance estimation, the feedback control is finally designed to stabilize the system asymptotically.

     

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Effects of structural parameters on water film properties of transpiring wall reactor

Corrosion and salt deposition problems severely restrict the industrialization of supercritical water oxidation. Transpiring wall reactor can effectively weaken these two problems by a protective water film. In this work, methanol was selected as organic matter, and the influences of vital structural parameters on water film properties and organic matter removal were studied via numerical simulation. The results indicate that higher than 99% of methanol conversion could be obtained and hardly affected by transpiration water layer, transpiring wall porosity and inner diameter. Increasing layer and porosity reduced reactor center temperature, but inner diameter's influence was lower relatively. Water film temperature reduced but coverage rate raised as layer, porosity, and inner diameter increased. Notably, the whole reactor was in supercritical state and coverage rate was only approximately 85% in the case of one layer. Increasing reactor length affected slightly the volume of the upper supercritical zone but enlarged the subcritical zone.     

Ensemble relation network with multi-level measure

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