We've been trying to solve the equation without changing the underlying assumption about time.

我们一直以来试图个方程的前提条件是时间不变。

In it was a series of equations describing how complex shapes like these can arise spontaneously from simple initial conditions.

其中有一系列方程，描述了像样的复杂形状如何从简单的初始条件自发产生。

What you want to do for the math underlying this is to basically feed some software, a differential equation and an initial condition and just say, how does this initial condition evolve?

你想要做的就是给一些软件输入一个微分方程和初始条件，然后问，个初始条件会如何演变？

But to know the two things in physics to solve a partial differential equation are the initial conditions and the boundary conditions.

但要知道在物理学中求偏微分方程所需的两个要素是初始条件和边界条件。

Conditions are right for nuclear fusion, slowly turning mass into energy according to the equation E equals mc squared.

条件行核聚变，根据E等于mc平方的方程， 将质量缓慢转化为能量。

The unit length is l. According to the finite difference principle, the finite difference form of Equation (4) is For the boundary conditions of the existing tunnel, it is assumed that both ends of the tunnel are free.

单位长度为 l。根据有限差分原理，方程（4）的有限差分形式为：对于现有隧道的边界条件，假设隧道的两端都是自由的。

The conditions at the solar centre were sufficiently hot and dense to allow nuclear reactions to take place and mass to be destroyed, thus producing the energy that Einstein's equation predicted.

太阳中心的条件足够炽热和密集， 足以引发核反应并摧毁质量，从而产生爱因斯坦方程所预言的能量。

And so I love simplified, give me a simplified model with, you know, a dynamical equation, some initial conditions, I'm very happy.

所以我喜欢简化，给我一个简化的模型，你知道， 一个动力学方程，一些初始条件，我很高兴。

They derived and solved the differential equation of pipeline deformation under high-fill conditions.

他们推导并求了高填充条件下管道变形的微分方程。