A note on the fluctuation–dissipation relation for the generalized Langevin equation with hydrodynamic backflow

Tóthová, Jana; Lisý, V.

doi:10.1016/j.physleta.2016.05.053

Cited by 20 publications

(7 citation statements)

References 32 publications

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“…(1) becomes the standard memoryless LE with the white noise force and the purely viscous Stokes friction force (t). To our opinion, the most simple method of solving the GLE equations, which goes back to the old work by Vladimirsky [42,43], is as follows [44][45][46][47][48]. If we are interested in finding the mean square displacement (MSD) of the particle,…”

Section: Harmonically Bounded Particle Described By the Fractional Lamentioning

confidence: 99%

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NMR signals within the generalized Langevin model for fractional Brownian motion

Lisý

Tóthová

2018

Physica A: Statistical Mechanics and its Applications

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The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the longtime limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S(t) for an ensemble of spinbearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S(t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

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Section: Harmonically Bounded Particle Described By the Fractional Lamentioning

confidence: 99%

“…must hold. For more details see the above cited articles [42][43][44][45][46][47][48]. The new equation,…”

Section: Harmonically Bounded Particle Described By the Fractional La...mentioning

confidence: 99%

NMR signals within the generalized Langevin model for fractional Brownian motion

Lisý

Tóthová

2018

Physica A: Statistical Mechanics and its Applications

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“…(1) becomes the standard memoryless LE with the white noise force and a purely viscous Stokes friction force −γυ (t). To our opinion, the simplest method of solving linear GLE equations, which goes back to the old work [14], is as follows [15][16][17][18][19]. If we are interested in finding the MSD of the particle,…”

Section: Harmonically Bounded Particle Described By the Fractional Lementioning

confidence: 99%

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

Lisý

Tóthová

2018

EPJ Web Conf.

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Abstract. Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.

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“…In 2017, Liemert et al (2017) studied a generalized Langevin equation for a free particle in the presence of a truncated power-law and Mittag-Leffler memory kernel. In 2016, the solution of the generalized Langevin equation (GLE) with the Boussinesq-Basset force was obtained in Tóthová and Lisý (2016). Ulam-Hyers stability of nonlinear fractional Langevin equations by using the boundedness, monotonicity and nonnegative properties of classical and generalized Mittag-Leffler functions was investigated by Wang and Li (2015) in 2015.…”

Section: Introductionmentioning

confidence: 99%

Existence Results for a New Class of Nonlinear Langevin Equations of Fractional Orders

Khalili

Yadollahzadeh

2019

Iran J Sci Technol Trans Sci

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A note on the fluctuation–dissipation relation for the generalized Langevin equation with hydrodynamic backflow

Cited by 20 publications

References 32 publications

NMR signals within the generalized Langevin model for fractional Brownian motion

NMR signals within the generalized Langevin model for fractional Brownian motion

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

Existence Results for a New Class of Nonlinear Langevin Equations of Fractional Orders

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