Dynamical systems

Distribution function (physics)

In molecular kinetic theory in physics, a system's distribution function is a function of seven variables, , which gives the number of particles per unit volume in single-particle phase space. It is the number of particles per unit volume having approximately the velocity near the position and time . The usual normalization of the distribution function is where, N is the total number of particles, and n is the number density of particles – the number of particles per unit volume, or the density divided by the mass of individual particles. A distribution function may be specialised with respect to a particular set of dimensions. E.g. take the quantum mechanical six-dimensional phase space, and multiply by the total space volume, to give the momentum distribution, i.e. the number of particles in the momentum phase space having approximately the momentum . Particle distribution functions are often used in plasma physics to describe wave–particle interactions and velocity-space instabilities. Distribution functions are also used in fluid mechanics, statistical mechanics and nuclear physics. The basic distribution function uses the Boltzmann constant and temperature with the number density to modify the normal distribution: Related distribution functions may allow bulk fluid flow, in which case the velocity origin is shifted, so that the exponent's numerator is , where is the bulk velocity of the fluid. Distribution functions may also feature non-isotropic temperatures, in which each term in the exponent is divided by a different temperature. Plasma theories such as magnetohydrodynamics may assume the particles to be in thermodynamic equilibrium. In this case, the distribution function is Maxwellian. This distribution function allows fluid flow and different temperatures in the directions parallel to, and perpendicular to, the local magnetic field. More complex distribution functions may also be used, since plasmas are rarely in thermal equilibrium. The mathematical analogue of a distribution is a measure; the time evolution of a measure on a phase space is the topic of study in dynamical systems. * v * t * e (Wikipedia).

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Probability Distribution Functions and Cumulative Distribution Functions

In this video we discuss the concept of probability distributions. These commonly take one of two forms, either the probability distribution function, f(x), or the cumulative distribution function, F(x). We examine both discrete and continuous versions of both functions and illustrate th

From playlist Probability

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Cumulative Distribution Functions and Probability Density Functions

This statistics video tutorial provides a basic introduction into cumulative distribution functions and probability density functions. The probability density function or pdf is f(x) which describes the shape of the distribution. It can tell you if you have a uniform, exponential, or nor

From playlist Statistics

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Probability Density Function of the Normal Distribution

More resources available at www.misterwootube.com

From playlist Random Variables

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From playlist Mathematics 1B (Algebra)

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From playlist Probability Distributions

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From playlist Probability Theory

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Overview and definition of a uniform probability distribution. Worked examples of how to find probabilities.

From playlist Probability Distributions

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From playlist QUSS GS 260

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From playlist Statistical Physics of Machine Learning 2020

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Top Eigenvalue of a Random Matrix: A tale of tails - Satya Majumdar

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From playlist Top Eigenvalue of a Random Matrix: A tale of tails - Satya Majumdar

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Frank Noé: "Connection between Statistics and Machine Learning"

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From playlist Machine Learning for Physics and the Physics of Learning 2019

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Extremal statistics in 1d Coulomb gas by Anupam Kundu

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From playlist Large deviation theory in statistical physics: Recent advances and future challenges

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From playlist Large deviation theory in statistical physics: Recent advances and future challenges

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From playlist Summer of Math Exposition 2 videos

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From playlist Large deviation theory in statistical physics: Recent advances and future challenges

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From playlist Unit 7 Probability C: Sampling Distributions & Simulation

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Indian Statistical Physics Community Meeting 2018 DATE:16 February 2018 to 18 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community which is attended by scientists, postdoctoral fellows, and graduate s

From playlist Indian Statistical Physics Community Meeting 2018

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A First-Order Dynamical Transition in the displacement distribution by Satya N Majumdar

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From playlist Indian Statistical Physics Community Meeting 2019

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Inverse normal with Z Table

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From playlist Unit 2: Normal Distributions

Related pages

Boltzmann constant | Momentum | Phase space | Number density | Measure (mathematics) | Density | Probability density function | Cumulative distribution function | Normal distribution | Thermodynamic equilibrium | Maxwell–Boltzmann distribution