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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time asymptotics of soliton equations via the nonlinear steepest descent method
非线性 最速下降法 孤立子方程 长时间渐近性
2023/11/13
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Finite-Time Splash for the free boundary incompressible Navier–Stokes equations (I)
自由边界 不可压缩 Navier-Stokes方程 有限时间飞溅
2023/5/18
In this talk, we consider the incompressible Navier-Stokes equations with free boundary, which has a finite-time splash singularity for a large class of specially prepared initial data. The approach i...
【北京大学物理化学讲座】The route going from transition path time distributions and protein folding times, to quantum mechanics, tunneling times and nonadiabatic transition times（图）
route going transition path time distributions quantum mechanics
2023/6/19
【北京大学物理化学讲座】The route going from transition path time distributions and protein folding times, to quantum mechanics, tunneling times and nonadiabatic transition times
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time behavior of Alfven waves in a flowing plasma
阿尔文波 流动 等离子体 长期行为
2023/4/28
In this talk, we consider the long-time behavior of the linearized MHD equations around a steady flowing plasma. We confirm the following physical phenomenon: there will be a generation of a magnetic ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long time behavior of the Sine-Gordon equation
正弦 戈登方程 长时间行为 黎曼-希尔伯特问题
2023/4/26
We use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted So...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Space-time finite and boundary element methods for the wave equation
波动方程 时空有限元 边界元方法
2023/4/21
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Improved error estimates of the splitting methods for the long-time dynamics for the weakly nonlinear Schrodinger equations
弱非线性薛定谔方程 长时间动力学 分裂方法 误差估计
2023/4/21
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonrelativistic limit of the Klein-Gordon equations: convergence rates and long time approximations
克莱因-戈登方程 非相对论极限 收敛率 长时间近似
2023/4/18
We study the nonrelativistic limit of the cubic Klein-Gordon equations. We show the cubic Klein-Gordon equation converges to the cubic Schr\"odinger equation with a convergence rate of order $\epsilon...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Finite-time singularity formations for the Landau-Lifshitz-Gilbert equation in dimension two
Landau–Lifshitz–Gilbert 二维 有限时间 奇点形成
2023/4/19
Landau-Lifshitz-Gilbert equation (LLG) describes magnetization of ferromagnets. In this paper, we consider the singularity formation of LLG from R^2 to S^2. For any prescribed N distinct points q^{j} ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Energy stability of exponential time differencing schemes for the nonlocal Cahn-Hilliard equation
非局部 Cahn-Hilliard方程 指数时间 差分方案 能量稳定性
2023/4/24
In this talk, we consider a class of exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard equation. We first use the Fourier collocation method to discretize the space do...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Estimating Time-Varying Networks for High-Dimensional Time Series
高维 时间序列 时变网络
2023/4/25
We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Policy Choice in Time Series by Empirical Welfare Maximization
经验福利 最大化 时间序列 政策选择
2023/4/25
This paper develops a novel method for policy choice in a dynamic setting where the available data is a multivariate time series. Building on the statistical treatment choice framework, we propose Tim...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Real-time tool path planning using deep learning for subtractive manufacturing
深度学习 减材制造 实时刀具 路径规划
2023/4/25
Tool path planning is a crucial factor of computer-aided design and manufacturing (CAD/CAM). To generate suitable tool paths, the previous methods often transform the problem into local or global opti...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Calculation of high-order harmonic generation of atoms and molecules by combining time series prediction and neural networks
时间序列预测 神经网络计算 原子分子 高阶谐波生成
2023/5/9
High-order harmonic generation (HHG) from the interaction of ultra-intense laser pulses with atoms is an important tabletop short-wave coherent light source. Accurate quantum simulations of it present...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Variable selection for generalized linear models with interval-censored failure time data
区间删失 失效时间数据 广义线性模型 变量选择
2023/5/9
Variable selection is often needed in many fields and has been discussed by many authors in various situations.