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## 1. chinaXiv:202002.00066 [pdf]

Subjects: Mathematics >> Modeling and Simulation

 基于经典动力学模型和模型参数自动优化算法, 本文分析了全国当前累计确诊感染病例数大于100（截止到2020年2月16日）的24个省市自治区, 以及湖北省除神农架以外的16个地市从2020年1月20日至2月16日的累计确诊病例数, 并对相应省市地区疫情可能的结束时间和总感染人数的进行了长期预测. 我们的研究表明, 在目前严防严控措施下, 全国大部分省市的疫情将于2月底前基本结束, 而湖北省内疫情也有望于3月中旬结束, 但是武汉市的疫情可能要持续到4月初. 通过对比公开数据与预测值, 我们建议加强对黑龙江、河北、江西、安徽、贵州和四川六省, 以及湖北省内武汉、荆州、鄂州、随州、天门和恩施六个地市的的监控, 以防疫情死灰复燃. 此外, 分析结果提示, 在疫情发展前期, 天津、河北、重庆、四川、海南和广西等省, 以及湖北省下辖多个地市可能存在着聚集性感染, 这有待于疫后进一步的流行病学调查确认.

## 2. chinaXiv:201910.00071 [pdf]

Subjects: Mathematics >> Modeling and Simulation

 Radiation symmetry evaluation is critical to the laser driven Inertial Confinement Fusion (ICF), which is usually done by solving a view-factor equation model. The model is nonlinear, and the number of equations can be very large when the size of discrete mesh element is very small to achieve a prescribed accuracy, which may lead to an intensive equation solving process. In this paper, an efficient radiation symmetry analysis approach based on sparse representation is presented, in which, 1) the Spherical harmonics, annular Zernike polynomials and Legendre-Fourier polynomials are employed to sparsely represent the radiation flux on the capsule and cylindrical cavity, and the nonlinear energy equilibrium equations are transformed into the equations with sparse coefficients, which means there are many redundant equations, 2) only a few equations are selected to recover such sparse coefficients with Latin hypercube sampling, 3) a Conjugate Gradient Subspace Thresholding Pursuit (CGSTP) algorithm is then given to rapidly obtain such sparse coefficients equation with as few iterations as possible. Finally, the proposed method is validated with two experiment targets for Shenguang II and Shenguang III laser facility in China. The results show that only one tenth of computation time is required to solve one tenth of equations to achieve the radiation flux with comparable accuracy. Further more, the solution is much more efficient as the size of discrete mesh element decreases, in which, only 1.2% computation time is required to obtain the accurate result.