The two links are simplified into Euler-Bernoulli beams and the coupled partial differential equation-ordinary differential equation dynamic model is established via Hamiltonian's principle. Two ...

Bernoulli's equation is a simple but incredibly important equation in physics and engineering that can help us understand a lot about the flow of fluids in the world around us. It essentially ...

Mathematical modelling and real-time microfluidics-based measurements of nuclear shuttling dynamics of the transcription factor EB (TFEB) demonstrate its biphasic nature in response to nutrient ...

Turbulence is a notoriously difficult phenomenon to study. Mathematicians are now starting to untangle it at its smallest ...

But the problem, the researchers find, is “differential subsidence,” where the rates differ on a small scale. If one end of a building sinks a quarter of an inch a year and the other end sinks ...

Congress created the "differential pay statute" in 2009, requiring that the federal government pay reserve members their full salaries when called up in support of a declared national emergency.

Abstract: This paper establishes a connection between non-convex optimization and nonlinear partial differential equations (PDEs). We interpret empirically successful relaxation techniques motivated ...

This book is an introduction to the general theory of second order parabolic differential equations, which model many important, time-dependent physical systems. It studies the existence, uniqueness, ...

The contemporary approach of J Kurzweil and R Henstock to the Perron integral is applied to the theory of ordinary differential equations in this book. It focuses mainly on the problems of continuous ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.