This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: There is an elegant mathematical equation behind many different natural phenomena. From the fractal pattern of a romanesco cauliflower sitting on a grocery store shelf to the flow of rivers, they all have underlying mathematical properties.
The way heat propagates from one object to another also has a strikingly complex mathematical basis. Simulating how heat propagates through rods when multiple rods are heated simultaneously is a major feat—as the temperatures of the rods influence one another. However, a research team at Tohoku University and Islamic Azad University found a method to rapidly simulate this situation.
The paper is published in the journal Linear Algebra and its Applications. Professor Amir Sadeghi (Islamic Azad University) and Professor Shinya Miyajima (Tohoku University) achieved this by starting with a matrix. A matrix is an array of real numbers arranged in rows and columns.
The complementary error function takes real numbers as inputs and has values between 0 and 2. By computing the value of the complementary error function, it can be simulated on a computer how heat propagates through a heated rod. The complementary error matrix function is a matrix-valued extension of the complementary error function.
"A matrix is a way of organizing numbers, so we can better understand how certain systems work," explains Miyajima. "The hard part is figuring out how to arrange the numbers." To achieve this simulation, the input matrix must satisfy a certain assumption. However, it is not always valid, and even when it is satisfied, the simulation may not be successful.
Furthermore, a method for computing the value of the matrix complementary error function had not previously been reported in the literature. The team had a lot of work to do to figure out how to properly build their matrix to ensure the simulation was accurate. "This is a complex error function that would require an enormous amount of computational time to evaluate normally," explains Sadeghi.
Extract — continue reading at the source.
