langevin equation वाक्य
उदाहरण वाक्य
मोबाइल
- It is based on the Generalized Langevin Equation ( GLE ).
- On small timescales, inertial effects are prevalent in the Langevin equation.
- In physics, however, stochastic integrals occur as the solutions of Langevin equations.
- However, the Langevin equation is more general.
- On long timescales, the mathematical Brownian motion is well described by a Langevin equation.
- In those cases, the Langevin equation, which looks at particle acceleration, must be used.
- The equipartition theorem can be used to derive the Brownian motion of a particle from the Langevin equation.
- The " Langevin equation " describes advection, diffusion, and other phenomena in an explicitly stochastic way.
- In 1991, he derived, with Bedeaux, the Langevin equation for a Brownian particle using only causality and time reversal invariance.
- In the white noise setting described so far, the quantum Langevin equation for an arbitrary system operator a takes a simpler form:
- In this scenario the equation of motion for an arbitrary system operator Y is called the " quantum Langevin equation " and may be written as:
- This differential equation is interpreted as defining the system operator a as the quantum ItM integral of the right hand side, and is equivalent to the Langevin equation ( ).
- Another prototypical feature of the Langevin equation is the occurrence of the damping coefficient \ lambda in the correlation function of the random force, a fact also known as Einstein relation.
- There is, however, an analogue of the formula that is both fully quantum and relativistic, called the " Abraham Lorentz Dirac Langevin equation " see Johnson and Hu.
- Using the Langevin equation to model Brownian motion, the path integral formation can be used to determine an effective action and pre-exponential model to see the effect of dissipation on tunnelling.
- One of the simplest forms of the Langevin equation is when its " noise term " is Gaussian; in this case, the Langevin equation is exactly equivalent to the convection diffusion equation.
- One of the simplest forms of the Langevin equation is when its " noise term " is Gaussian; in this case, the Langevin equation is exactly equivalent to the convection diffusion equation.
- This differential equation is interpreted as defining the system operator a as the quantum Stratonovich integral of the right hand side, and is in the same form as the Langevin equation ( ).
- The self-diffusion mechanism itself was not directly investigated, although it had been indirectly investigated by behavior of impurity diffusion in a pure material as shown in the Einstein s Brown theory and the Langevin equation.
- The time evolution of the position of the Brownian particle itself is best described using Langevin equation, an equation which involves a random force field representing the effect of the thermal fluctuations of the solvent on the particle.
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