论文标题
与一类水库接触的一维ASEP的流体动力学
Hydrodynamics for one-dimensional ASEP in contact with a class of reservoirs
论文作者
论文摘要
我们研究了尺寸$ n $的晶格中不对称简单排除过程的流体动力行为。在批量上，排除动力学执行向右通量。在边界上，动力学附加到储层上。我们研究了两种类型的储层：（1）对于某些$θ<0 $和（2）仅在右边界处创建粒子的储层，而仅在右边界上歼灭粒子，这些储层被$ n^θ$削弱。我们证明，颗粒的空间密度在双曲线时间尺度下，随着$ [0,1] $在边界条件下的标量保护定律的熵解决方案演变。边界条件的特征在于$ x = 0 $和$ x = 1 $的边界迹线，该值从$ \ {0,1 \} $中获取值。
We study the hydrodynamic behaviour of the asymmetric simple exclusion process on the lattice of size $n$. In the bulk, the exclusion dynamics performs rightward flux. At the boundaries, the dynamics is attached to reservoirs. We investigate two types of reservoirs: (1) the reservoirs that are weakened by $n^θ$ for some $θ<0$ and (2) the reservoirs that create particles only at the right boundary and annihilate particles only at the left boundary. We prove that the spatial density of particles, under the hyperbolic time scale, evolves with the entropy solution to a scalar conservation law on $[0,1]$ with boundary conditions. The boundary conditions are characterised by the boundary traces at $x=0$ and $x=1$ which take values from $\{0,1\}$.
