Particle size distribution refers to the proportion of particles with specific size ranges in a sample. It’s crucial in understanding material properties and behavior, influencing factors such as flowability, reactivity, and stability. Closely related concepts include measurement techniques, physical properties, mathematical parameters, statistical distributions, and influencing factors. Particle size distribution finds applications in industries like…

The Korteweg de Vries (KdV) equation is a nonlinear partial differential equation that models the propagation of shallow water waves and other soliton-like phenomena. Solitons are stable, localized wave-like entities that interact elastically and maintain their shape and velocity over long distances. The KdV equation describes the evolution of solitons and has been extensively studied…

The Feynman-Kac formula, developed by Richard Feynman and Mark Kac, bridges quantum mechanics and probability theory. It represents the solution to the Schrödinger equation as a path integral over Brownian paths. The formula provides a powerful tool for studying quantum systems with a stochastic component and has applications in nuclear physics, quantum computing, finance, and…

The Kohn-Sham equations are a system of self-consistent equations used to calculate the electron density of a system in density functional theory (DFT). They are derived from the Hohenberg-Kohn theorem, which states that the ground state energy of a system is a unique functional of its electron density. The Kohn-Sham equations can be solved numerically…

The Klein-Gordon equation is a fundamental equation in physics that describes the behavior of scalar fields. Scalar fields are mathematical objects that exist throughout spacetime and can have a variety of properties, such as mass, charge, and spin. The Klein-Gordon equation is a differential equation that describes how scalar fields change over time and space….

The Nernst-Einstein equation, a cornerstone of electrochemistry, relates the diffusion coefficient of an ion to its mobility, charge, electric field, and temperature. Advanced by Walther Nernst and Albert Einstein, it elucidates the relationship between the random motion of ions and the macroscopic movement under an electric field. These principles underpin practical applications such as diffusion,…

The Johnson-Mehl-Avrami equation is a mathematical model that describes the kinetics of phase transformations. It was developed by William Austin Johnson, Robert Francis Mehl, and Melvin Avrami in the early 20th century. The equation is used to predict the rate of transformation from one phase to another, such as the transformation from a solid to…

The Hamilton-Jacobi-Bellman equation with terminal constraint is a partial differential equation that arises in optimal control theory. It provides necessary conditions for the optimal solution to a problem where the objective is to minimize a cost function over time, subject to certain constraints. The equation describes the evolution of the value function, which represents the…

The Hamilton-Jacobi equation, derived by William Rowan Hamilton and Carl Gustav Jacobi, provides a powerful tool in classical mechanics. It allows the formulation of a dynamical system’s equations of motion as a single partial differential equation. This equation offers insights into a system’s energy and momentum conservation, as well as facilitating the determination of particle…

Outline for Peng-Robinson Equation of State Key Concepts: The Peng-Robinson equation of state (PR EOS) is a cubic equation of state used to predict the behavior of non-ideal gases and liquids. It accounts for intermolecular forces and is widely used in chemical engineering and other fields. Variables: Pressure, temperature, volume, molecular weight, and two temperature-dependent…

The Coffin-Manson equation is an empirical relationship that describes the fatigue life of a material under cyclic loading. It states that the fatigue life (N) of a material is inversely proportional to the plastic strain amplitude (εp) raised to the power of b, which is a material constant. This equation is widely used in fatigue…

Billy Meier, a Swiss farmer, claimed extraterrestrial contact with the Pleiadians. His Contact Group (FIGU) published “The Contact Notes” and “And They Come from the Pleiades,” which detailed his experiences. Critics questioned the authenticity of his photographs and alleged sightings, while supporters defended his credibility. Meier’s claims remain a controversial topic in UFO investigations, sparking…