Langevin original approach and Ornstein–Uhlenbeck-type processes

Contreras-Vergara, O.; Lucero-Azuara, N.; Sánchez-Salas, N.; Jiménez–Aquino, J. I.

doi:10.1016/j.physa.2021.126349

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…This stochastic differential equation rules a process well known as Ornstein-Uhlenbeck and it becomes stationary in long time limit, t → ∞, for which κ(t) → κ =const. This stochastic differential equation can be transformed into a macroscopic one following Langevin's strategy as reported in [36]. From Eq.…”

Section: Stochastic Heat Enginementioning

confidence: 99%

“…Once this is done, the efficiency at maximum power characterized by finite-time cycles can be obtained using the low-dissipation approach. This work is organized as follows: Section II obtains the macroscopic equation (ensemble property) for the overdamped harmonic oscillator associated with the mean value x 2 (t) , using the original method proposed by Langevin in 1908 [34][35][36]. Then, by means of the state-like equation, the equilibrium thermodynamic properties for the Carnot-, Stirling-, and Ericsson-like cycles are calculated.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Carnot, Stirling, Ericsson stochastic heat engines: Efficiency at maximum power

O.¹,

Sánchez-Salas²,

Valencia-Ortega³

et al. 2022

Preprint

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This work obtains the efficiency at maximum power for a stochastic heat engine performing Carnot-like, Stirling-like and Ericsson-like cycles. For the mesoscopic engine a Brownian particle trapped by an optical tweezers is considered. The dynamics of this stochastic engine is described as an overdamped Langevin equation with a harmonic potential, whereas is in contact with two thermal baths at different temperatures, namely, hot (T h ) and cold (T c ). The harmonic oscillator Langevin equation is transformed into a macroscopic equation associated with the mean value x 2 (t) using the original Langevin approach. At equilibrium stationary state this quantity satisfies a state-like equation from which the thermodynamic properties are calculated. To obtained the efficiency at maximum power it is considered the finite-time cycle processes under the framework of low dissipation approach.

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Section: Stochastic Heat Enginementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Carnot, Stirling, Ericsson stochastic heat engines: Efficiency at maximum power

O.¹,

Sánchez-Salas²,

Valencia-Ortega³

et al. 2022

Preprint

View full text Add to dashboard Cite

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An overdamped Langevin approach to parallel diffusion and energy dissipation in the presence of low-frequency circularly polarized electromagnetic waves

Nariyuki

2023

AIP Advances

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Brownian motion of charged particles in the presence of low-frequency, circularly polarized electromagnetic waves is discussed. By using the wave rest frame, the Langevin system including low-frequency waves can be treated as a periodic system with a constant external force. In an overdamped limit, parallel diffusion is formulated by the Brownian motion whose diffusion coefficient includes wave amplitude. The nonequilibrium work by low-frequency waves satisfies a nonequilibrium relation corresponding to the fluctuation–dissipation relation with the effective temperature defined by wave amplitude.

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The permeability effect on the diffusion and correlation process of fluid flow in porous media

Hana

Hader

Tanasehte

et al. 2023

Int. J. Mod. Phys. B

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This study numerically examines the fluid flow in porous media used in desalination. This topic is of significant current interest in the fields of science, engineering and technology, particularly in the process of water filtration. Moreover, in this work, we are attracted to correlation and diffusion process of the porous medium below the effect of permeability, dynamic pressure and friction coefficient. These parameters characterized the fluid flow in porous medium. To study numerically this phenomenon, many models have been proposed. However, we developed our investigation by using the Langevin dynamics model. Furthermore, this dynamic framework is based on Newton’s second law and Darcy’s law. Hence, we modeled the medium as a set of random diameters pores, which are dispersed randomly. The obtained results indicate that the average velocity time evolution presents an exponential profile with two different states: the first is transient and the second is permanent. The two regimes are separated by a cross-over time. Furthermore, time evolution exhibits an increasing profile versus the permeability, then it presents a decreasing profile versus the friction coefficient. Likewise, the diffusion process and correlation are tested for different parameters, especially the permeability and the dynamic pressure. We remark that the effective diffusion coefficient decreases exponentially with permeability and increases linearly with dynamic pressure. Hence, the fluid flow correlation in porous media presents a Gaussian function profile, with standard deviation function which increases exponentially with permeability.

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Langevin original approach and Ornstein–Uhlenbeck-type processes

Cited by 3 publications

References 29 publications

Carnot, Stirling, Ericsson stochastic heat engines: Efficiency at maximum power

Carnot, Stirling, Ericsson stochastic heat engines: Efficiency at maximum power

An overdamped Langevin approach to parallel diffusion and energy dissipation in the presence of low-frequency circularly polarized electromagnetic waves

The permeability effect on the diffusion and correlation process of fluid flow in porous media

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