A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$ -Superlinear Convergence for Stochastic Games on Domains

In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the \(H^2\)-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.

     

Development of health monitoring method for pecan nut trees using side video data and computer vision

Optical Review - Increasing efficiency and productivity in the field of agriculture is important to provide sufficient food to the world’s increasing population. It is important to monitor...     

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N₂ atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Graphical Abstract

     

Gibbsian dynamics and ergodicity of magnetohydrodynamics and related systems forced by random noise

The magnetohydrodynamics system consists of the Navier-Stokes equations from fluid mechanics, coupled with the Maxwell’s equations from electromagnetism through multiples of non-linear terms involving derivatives. Following the approach of [1 Weinan, E., Mattingly, J. C., Sinai, Y. (2001). Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. Commun. Math. Phys. 224:83–106. DOI:10.1007/s002201224083.[Crossref], [Web of Science ®] , [Google Scholar]], we prove the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes. Its proof requires taking advantage of the structure of the non-linear terms carefully and is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as the magneto-micropolar fluid system from the theory of microfluids.     

污泥基吸附剂对亚甲基蓝和环丙沙星的吸附性能研究

亚甲基蓝和环丙沙星是水体中2种污染物, 对生态环境有潜在危害. 本文以市政剩余活性污泥为原料, 氯化锌为活化剂热解制备污泥基吸附剂, 研究盐酸酸洗浓度、氯化锌浓度、热解温度、热解时间等对污泥基吸附剂吸附水中亚甲基蓝和环丙沙星性能的影响. 结果表明 (1)污泥基吸附剂对亚甲基蓝的吸附性能随盐酸酸洗浓度的增大而增加, 对环丙沙星的吸附性能则随盐酸酸洗浓度的增大呈先降后增趋势, 两者均在1.500mol·L-1盐酸浓度下取得最优值. (2)污泥基吸附剂对亚甲基蓝和环丙沙星的吸附性能随氯化锌浓度和热解温度的增加呈先升后降趋势, 在氯化锌浓度为4.0mol·L-1、热解温度为500℃时有最优值; 随着热解时间的延长, 污泥基吸附剂对亚甲基蓝和环丙沙星的吸附性能分别在500℃热解70min和80min时有最优值. (3)污泥基吸附剂的最佳制备条件为 氯化锌4.0mol·L-1活化2h、500℃热解70min和80min、1.500mol·L-1盐酸酸洗; 以此制得的污泥基吸附剂对亚甲基蓝和环丙沙星的去除率分别为97.7%和96.4%, 平衡吸附量分别为97.9mg·g-1和3.9mg·g-1, 且污泥基吸附剂对亚甲基蓝和环丙沙星的吸附过程均符合准二级动力学方程.     

Photoinduced dynamics of a cyanine dye: parallel pathways of non-radiative deactivation involving multiple excited-state twisted transients

Cyanine dyes are broadly used for fluorescence imaging and other photonic applications. 3,3′-Diethylthiacyanine (THIA) is a cyanine dye composed of two identical aromatic heterocyclic moieties linked with a single methine, –CH. The torsional degrees of freedom around the methine bonds provide routes for non-radiative decay, responsible for the inherently low fluorescence quantum yields. Using transient absorption spectroscopy, we determined that upon photoexcitation, the excited state relaxes along two parallel pathways producing three excited-state transients that undergo internal conversion to the ground state. The media viscosity impedes the molecular modes of ring rotation and preferentially affects one of the pathways of non-radiative decay, exerting a dominant effect on the emission properties of THIA. Concurrently, the polarity affects the energy of the transients involved in the decay pathways and further modulates the kinetics of non-radiative deactivation.     

Direct Introduction of a Dimesitylboryl Group Using Base‐Mediated Substitution of Aryl Halides with Silyldimesitylborane

The first dimesitylboryl substitution of aryl halides with a silylborane bearing a dimesitylboryl group in the presence of alkali‐metal alkoxides is described. The reactions of aryl bromides or iodides with Ph₂MeSi?BMes₂ and Na(OtBu) afforded the desired aryl dimesitylboranes in good to high yields and with high borylation/silylation ratios. Selective reaction of the sterically less‐hindered C?Br bond of dibromoarenes provided monoborylated products. This reaction was used to rapidly construct a D‐π‐A aryl dimesityl borane with a non‐symmetrical biphenyl spacer.     

NMR‐based analysis of the chemical composition of Japanese persimmon aqueous extracts

Japanese persimmon (Diospyros kaki L.) is recognized as an outstanding source of biologically active compounds relating to many health benefits. In the present study, NMR spectroscopy provided a comprehensive metabolic overview of Japanese persimmon juice. Detailed signal assignments of Japanese persimmon juice were carried out using various 2D NMR techniques incorporated with broadband water suppression enhanced through T₁ effects (BB‐WET) or WET sequences, and 26 components, including minor components, were identified. In addition, most components were quantitatively evaluated by the integration of signals using conventional ¹H NMR and BB‐WET NMR. This is the first detailed analysis combined with quantitative characterization of chemical components using NMR for Japanese persimmon. Copyright © 2015 John Wiley & Sons, Ltd.     

Chemical equilibrium controlled synthesis of polyoxymethylene dimethyl ethers over sulfated titania

The chemical equilibrium and reaction kinetic behavior in the synthesis of polyoxymethylene dimethyl ethers(DMMn) were investigated over sulfated titania in order to reveal the decisive factor controlling the reaction. The results showed that the molar ratio of adjacent DMMn products in equilibrium solution had the same value, which depended absolutely on the reaction temperature. Meanwhile, the reactions had the same DMMn products distributions under varied reaction conditions. The equilibrium constants of the related step-wise reactions for DMMn formation were equal, which were calculated based on the bulk compositions of the reaction solution. And thus, the selectivity to DMMn was mainly controlled by the chemical equilibrium, i.e., thermodynamic control. In brief, the present results provide some guidance for future synthesis of DMMn.