User:Kcobus

$${\partial c_i\over\partial t}+{\partial\over\partial x_j}(u_j,c_i) = D_i{\partial^2 c_i\over\partial x_j\partial x_j}+R_i(c_1,...,c_N,T)+ S_i(x,t)$$

$${i=1,2,...,N}$$

$$\langle u_j ',c'\rangle = -K_{jj}{\partial (c)\over\partial x_j}$$

$${\partial c_i\over\partial t}+\overline{u}_j{\partial(c)\over\partial x_j} = {\partial\over\partial x_j}\bigg(K_{jj}{\partial (c)\over\partial x_j}\bigg)$$

$$ \boldsymbol{\psi}(\mathbf{x},\mathit{t}) = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \mathit{Q}(\mathbf{x},\mathit{t}|\mathbf{x}',\mathit{t}')\boldsymbol{\psi}(\mathbf{x}',\mathit{t}') d\mathbf{x}'$$

$$\langle c(\mathbf{x},\mathit{t}\rangle = \sum_{i=1}^{m}\boldsymbol{\psi}_i(\mathbf{x},\mathit{t}) $$

$$ \langle c(\mathbf{x},\mathit{t}\rangle = = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \mathit{Q}(\mathbf{x},\mathit{t}|\mathbf{x}_0,\mathit{t}_0)\langle c\mathbf{x}_0,\mathit{t}_0)\rangle d\mathbf{x}_0 + \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{t_0}^{t}\mathit{Q}(\mathbf{x},\mathit{t}|\mathbf{x}',\mathit{t}')\mathit{S}(\mathbf{x}',\mathit{t}') d\mathit{t}d\mathbf{x}'$$

$$\langle c(x,y,z)\rangle = \frac{q}{2\pi\sigma_y\sigma_z}exp\bigg[-\bigg(\frac{y^2}{\sigma_y^2}+\frac{z^2}{\sigma_z^2}\bigg)\bigg]$$

Where $$\sigma_y^2=\frac{2K_{yy}x}{\overline{u}} \sigma_z^2=\frac{2K_{zz}x}{\overline{u}}$$

blah blah

Fun