A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

Insights into how mixing layers scatter sound waves could further understanding of acoustic sources in open-jet wind tunnel ...

Abstract: This paper discusses a novel conceptual formulation of the fractional-order Euler-Lagrange equation for the fractional-order variational method, which is based on the fractional-order ...

A recent entry in the visitor’s book of the James Joyce Tower & Museum in Sandycove, Dublin, perplexed the Friends of Joyce’s Tower, the volunteers who run the museum. The entry, reproduced as the ...

Researchers share a model that identifies the optimal location for bowling ball placement. Employing a system of six differential equations derived from Euler's equations for a rotating rigid body, ...

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

ABSTRACT: We examined the fractional second-order singular Lagrangian systems. We wrote the action principal function and equations of motion as fractional total differential equations. Also, we ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

To mathematicians, equations are art. Just as many are moved by a painting or piece of music, to those who appreciate and understand math, expressions of numbers, variables, operations and relations ...