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  2. Automatic calculation of particle interaction or decay

    en.wikipedia.org/wiki/Automatic_calculation_of...

    The Automatic Calculation project is to create the tools to make those steps as automatic (or programmed) as possible: I Feynman rules, coupling and mass generation LanHEP is an example of Feynman rules generation. Some model needs an additional step to compute, based on some parameters, the mass and coupling of new predicted particles.

  3. Smoothed-particle hydrodynamics - Wikipedia

    en.wikipedia.org/wiki/Smoothed-particle...

    where denotes the surface normal direction of the solid structure, and the imaginary particle density is calculated through the equation of state. Accordingly, the interaction forces f a F : p {\displaystyle \mathbf {f} _{a}^{F:p}} and f a F : v {\displaystyle \mathbf {f} _{a}^{F:v}} acting on a solid particle a {\displaystyle a} are given by

  4. Euler's three-body problem - Wikipedia

    en.wikipedia.org/wiki/Euler's_three-body_problem

    The problem of two fixed centers conserves energy; in other words, the total energy is a constant of motion.The potential energy is given by =where represents the particle's position, and and are the distances between the particle and the centers of force; and are constants that measure the strength of the first and second forces, respectively.

  5. Brownian motion - Wikipedia

    en.wikipedia.org/wiki/Brownian_motion

    2-dimensional random walk of a silver adatom on an Ag(111) surface [1] Simulation of the Brownian motion of a large particle, analogous to a dust particle, that collides with a large set of smaller particles, analogous to molecules of a gas, which move with different velocities in different random directions.

  6. Verlet integration - Wikipedia

    en.wikipedia.org/wiki/Verlet_integration

    Verlet integration (French pronunciation:) is a numerical method used to integrate Newton's equations of motion. [1] It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics.

  7. Tautochrone curve - Wikipedia

    en.wikipedia.org/wiki/Tautochrone_curve

    This is called Abel's integral equation and allows us to compute the total time required for a particle to fall along a given curve (for which / would be easy to calculate). But Abel's mechanical problem requires the converse – given T ( y 0 ) {\displaystyle T(y_{0})\,} , we wish to find f ( y ) = d ℓ / d y {\displaystyle f(y)={d\ell }/{dy ...

  8. Langevin equation - Wikipedia

    en.wikipedia.org/wiki/Langevin_equation

    The equation for Brownian motion above is a special case. An essential step in the derivation is the division of the degrees of freedom into the categories slow and fast . For example, local thermodynamic equilibrium in a liquid is reached within a few collision times, but it takes much longer for densities of conserved quantities like mass and ...

  9. List of equations in fluid mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in_fluid...

    Defining equation (physical chemistry) List of electromagnetism equations; List of equations in classical mechanics; List of equations in gravitation; List of equations in nuclear and particle physics; List of equations in quantum mechanics; List of photonics equations; List of relativistic equations; Table of thermodynamic equations

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