Science Daily May 29, 2020
The diffusion equation models random movement and is one of the fundamental equations of physics. The analytic solution of the diffusion equation in finite domains, when time and space is continuous, has been known for a long time. However, the diffusion equation in finite space was not solved until now. Researchers in the UK used Chebyshev polynomials, and the method of images which is used to tackle electrostatic problems to construct the solution to the discrete diffusion equation in higher dimension from the one in lower dimensions. The solution could be used to accurately predict encounter and transmission probability between individuals in a closed environment, without the need for time-consuming computer simulations. Other applications include predicting molecules diffusing inside cells, bacteria roaming in a petri dish, animals foraging within their home ranges, or robots searching in a disaster area…read more. TECHNICAL ARTICLE