Optimal Transport Control an Application to the Steel Industry

荷兰的塔塔钢铁公司需要钢铁结构的模型来测试其机械性能，一旦他们有了一种看起来很有趣的钢，他们就可以生产它，看看它是否具有理想的性能。这是利用最优输运控制理论来产生拉盖尔图来模拟钢中的晶粒。博士学位的开始将关注使用数值线性代数的技术在MATLAB中实现和加速当前的方法，在那之后我可以进入许多不同的方向。其中之一就是提出新的方法来制作更精确的钢模型，并考虑到钢的任何其他特性。我们目前指定的是颗粒的体积，但我们可能希望指定其他东西，如纵横比。我们还可能希望改变模型输出的颗粒形状，以便更准确地表示颗粒。除此之外，这将取决于塔塔钢铁的需求。

TaTa Steel, a steel company based in the Netherlands need models of the strucutre of steel to test out the mechanical properties, once they have a steel that looks interesting they can produce it and see if it has desirable properties. This is done using the theory of optimal transport control to produce Laguerre diagrams which model the grains in the steel. The start of the PhD will be concerned with implementing and speeding up current methods in MATLAB using techniques from numerical linear algebra, there are a number of different directions in which I could go in after that. One of which, would be coming up with new ways to produce more accurate models of steel and take into account any other properties of the steel. We currently specify the volumes of the grains but we may wish to specify other things such as aspect ratio. We also may wish to alter the shape of the grains outputted by the model to more acurately represent the grains. Beyond this, it would depend on the needs of TaTa steel.