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Why the Place that Jang'S Equation Blow Up is Apparent Horiozn? Let's consider a simple example: Let us assume that the three metric is $$ds^2=g_{rr}d 阅读全文
posted @ 2019-09-18 15:41
yuewen_chen
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This total energy is called the ADM mass of slice $\Sigma_t$ $$ \displaystyle \fbox{$ M_{\rm ADM} = {\dfrac{1}{16\pi}} \lim\limits_{{{S}}_{t}\rightarr 阅读全文
posted @ 2019-09-17 22:01
yuewen_chen
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Spherically Symmetric Case For the spherically symmetric case, $f$ is constant. Thus $$ \begin{equation} D_as^a=\frac{1}{\sqrt{\gamma}}\partial_r (\sq 阅读全文
posted @ 2019-09-17 21:28
yuewen_chen
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body { font-family: "仿宋","FangSong", "宋体", "Segoe UI", Tahoma, Arial; font-size: 20px!important; color:blue; } DIV.post DIV.entry { font-family: "仿宋", 阅读全文
posted @ 2019-09-17 20:00
yuewen_chen
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Finding Black Holes 1 The apparent horizon (i.e., the marginally trapped outer surface) is an invaluable tool for finding black holes in numerical rel 阅读全文
posted @ 2019-09-17 17:06
yuewen_chen
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考虑如下的方程组，测试Levenberger Marquardt 方法： $$ \begin{align } \varphi_{rr}+\frac{2}{r}\varphi_{,r}+\frac{1}{8}(A)^2 \frac{1}{12}\varphi^5 &=f_1\\ A_{,r} \fra 阅读全文
posted @ 2019-09-16 10:30
yuewen_chen
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使用 Levenberg Marquardt 方法测试 $$u_{xx}+u^2= sin(x)+sin(x)^2$$, 初值选取 $u(x)=cos(x)sin(x)$ 参考文献：《非线性方程组数值方法》，袁亚湘； 1. 给出初值 $x_0 \in \mathbb{R}^n; k=1,\eta \ 阅读全文
posted @ 2019-09-15 21:49
yuewen_chen
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When travelers arrive in Kyoto for the first time, they often are confused and disappointed. Expecting a place that exudes timeless elegance and peace 阅读全文
posted @ 2019-07-03 18:31
yuewen_chen
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流形的度量改变意味着什么？ 1.首先来看最简单的例子： $S^2:$ 将球面嵌入到 $\mathbb{R}^3$里面， 半径是 $r$, 我们取标准球面坐标 $(\theta,\phi)$, 球面的度量是 $ds^2=r^2（d\theta^2+sin\theta d\phi^2）$ ,改变度量 ， 阅读全文
posted @ 2018-08-26 18:38
yuewen_chen
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$$\| F\|^2=\int_M (F_A,F_A)$$ $$\boxed{ S = \int\nolimits_{t_1}^{t_2} \left\{ \int\nolimits_{\varSigma_t} N \left(R+K_{ij}K^{ij} K^2\right) \sqrt{\gam 阅读全文
posted @ 2018-08-15 20:42
yuewen_chen
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