基于神经网络改进WENO-Z重构方法

本文通过使用深度神经网络对WENO-Z格式的非线性权重进行改进,提出了一种新的WENO-Z-NN格式．新格式首先用神经网络去随机扰动有限体积系数集,然后用代表偏微分方程解的波形生成的数据,采用L2正则化来学习扰动的最优函数,最后引入测试函数并结合最小总变差和最小总偏差作为评估依据进行后处理,从而得到新的权重．一维波动方程和一维Euler方程的数值结果表明,无论是在粗网格还是在细网格,本文所提出的WENO-Z-NN格式的激波捕捉能力明显优于传统的WENO-Z和WENO-JS-NN格式．     

Determination of molecular weights and Mark–Houwink constants for soluble electronically conducting polymers

Intrinsic viscosities and gel permeation chromatography data were used to evaluate the Mark–Houwink constants of the soluble electronically conducting polymer, poly(3-hexylthiophene) (P3HT):K and a are 2.28 × 10^-3 cm³/g and 0.96, respectively, in tetrahydrofuran (THF) at 25°C. Mark–Houwink constants were used to calibrate gel permeation chromatography (GPC) columns for P3HT. Number-average molecular weights of P3HT determined with modified calibration curves agreed well with those determined by an absolute method, embulliometry. Molecular weights estimated using unmodified polystyrene calibration procedures were significantly larger than true values.     

加权半线性椭圆系统稳定正解的Liouville定理

研究加权半线性椭圆系统■其中,p>1,w(x)、w₁(x)和w₂(x)是非负连续函数.对于w₁≠w₂和w₁≡w₂,指数p属于次临界、临界和超临界的部分区间时,证明了椭圆系统不存在稳定正解.     

物理信息神经网络的一种自适应配置点算法

物理信息神经网络(PINN)能够将方程模型融入到损失最小化训练中, 能同时学习输入数据分布和物理规律, 大多数PINN是通过均匀采样配置点来覆盖整个求解区域, 且各个配置点间都同等发挥作用, 其配置点策略简便易行, 但也使得PINN增加了部分不必要的配置点, 且对部分复杂规律的学习能力不足. 文章提出一种配置点自适应设置策略, 以提高PINN学习能力和学习效率. 首先通过损失函数残差及梯度联合分布确定配置点选择概率, 同时在迭代一定次数后进行重采样, 避免过早陷入局部最优, 这样可以使一部分配置点分布在损失较高或变化较明显处, 从而改善配置点的分布情况, 达到以较少的配置点也能准确反映方程模型的效果, 提升学习效率; 其次引入配置点的变权重设定, 使每个配置点对方程残差的影响有所侧重, 在网络迭代训练中自动提高损失值较高部分配置点的权重, 从而使PINN更专注于损失较大的部分, 即复杂规律的学习. 最后通过Burgers方程、Schrodinger方程、Helmholtz方程和Navier-Stokes方程4种典型算例与传统PINN及其各种改进方法进行比较实验. 数值结果表明, 该算法可以在较少的配置点数量和迭代次数设定下, 有效提升求解精度和计算效率.

     

IR laser ablation of doped poly(methyl methacrylate)

We investigate the TEA CO₂ laser ablation of films of poly(methyl methacrylate), PMMA, with average M_W 2.5, 120 and 996 kDa doped with photosensitive compounds iodo-naphthalene (NapI) and iodo-phenanthrene (PhenI) by examining the induced morphological and physicochemical modifications. The films casted on CaF₂ substrates were irradiated with a pulsed CO₂ laser (10P(20) line at 10.59 μm) in resonance with vibrational modes of PMMA and of the dopants at fluences up to 6 J/cm². Laser induced fluorescence probing of photoproducts in a pump and probe configuration is carried out at 266 nm. Formation of naphthalene (NapH) and phenanthrene (PhenH) is observed in NapI and PhenI doped PMMA, respectively, with relatively higher yields in high M_W polymer, in similarity with results obtained previously upon irradiation in the UV at 248 nm. Above threshold, formation of photoproducts is nearly complete after 200 ms. As established via optical microscopy, bubbles are formed in the irradiated areas with sizes that depend on polymer M_W and filaments are observed to be ejected out of the irradiated volume in the samples made with high M_W polymer. The implications of these results for the mechanisms of polymer IR laser ablation are discussed and compared with UV range studies.