Non-Gaussian Fluctuations Resulting from Power-Law Trapping in a Lipid Bilayer

Akimoto, Takuma; Yamamoto, Eiji; Yasuoka, Kenji; Hirano, Yoshinori; Yasui, Masato

doi:10.1103/physrevlett.107.178103

Cited by 94 publications

(125 citation statements)

References 31 publications

(54 reference statements)

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“…Thus, the RSD,σ EB (t), is not helpful to characterize the ergodicity breaking in this case. Using the relative fluctuation defined by [8,42] instead of the RSD, we can clearly see the ergodicity breaking in the case of …”

Section: Ordinary Renewal Processmentioning

confidence: 97%

Phase Diagram in Stored-Energy-Driven Lévy Flight

Akimoto

Miyaguchi

2014

J Stat Phys

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Phase diagram based on the mean square displacement (MSD) and the distribution of diffusion coefficients of the time-averaged MSD for the stored-energy-driven Lévy flight (SEDLF) is presented. In the SEDLF, a random walker cannot move while storing energy, and it jumps by the stored energy. The SEDLF shows a whole spectrum of anomalous diffusions including subdiffusion and superdiffusion, depending on the coupling parameter between storing time (trapping time) and stored energy. This stochastic process can be investigated analytically with the aid of renewal theory. Here, we consider two different renewal processes, i.e., ordinary renewal process and equilibrium renewal process, when the mean trapping time does not diverge. We analytically show the phase diagram according to the coupling parameter and the power exponent in the trapping-time distribution. In particular, we find that distributional behavior of time-averaged MSD intrinsically appears in superdiffusive as well as normal diffusive regime even when the mean trapping time does not diverge.

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Section: Ordinary Renewal Processmentioning

confidence: 97%

Phase Diagram in Stored-Energy-Driven Lévy Flight

Akimoto

Miyaguchi

2014

J Stat Phys

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“…The RF and RSD behave in a similar way, and it is reported that these quantities can characterize some dynamical properties of the system [15][16][17].…”

Section: Introductionmentioning

confidence: 93%

“…Thus it is important to calculate the statistical quantities such as the average and standard deviation of the TAMSD. The magnitude of the fluctuation of the TAMSD can be quantitatively characterized by the relative fluctuation (RF) [15,16] or the relative standard deviation (RSD) [12,14,17]: R(t; ∆) ≡ |δ 2 (∆; t) − δ 2 (∆; t) | δ 2 (∆; t) ,…”

Section: Introductionmentioning

confidence: 99%

Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity

2015

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The mean-square displacement (MSD) is widely utilized to study the dynamical properties of stochastic processes. The time-averaged MSD (TAMSD) provides some information on the dynamics which cannot be extracted from the ensemble-averaged MSD. In particular, the relative standard deviation (RSD) of the TAMSD can be utilized to study the long time relaxation behavior. In this work, we consider a class of Langevin equations which are multiplicatively coupled to timedependent and fluctuating diffusivities. Various interesting dynamics models such as entangled polymers and supercooled liquids can be interpreted as the Langevin equations with time-dependent and fluctuating diffusivities. We derive a general formula for the RSD of the TAMSD for the Langevin equation with the time-dependent and fluctuating diffusivity. We show that the RSD can be expressed in terms of the correlation function of the diffusivity. The RSD exhibits the crossover at the long time region. The crossover time is related to a weighted average relaxation time for the diffusivity. Thus the crossover time gives some information on the relaxation time of fluctuating diffusivity which cannot be extracted from the ensemble-averaged MSD. We discuss the universality and possible applications of the formula via some simple examples.

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“…A clear non-Markovian effect was also observed in the time correlation function of the random force. Note that the non-Gaussian fluctuation is a general feature in non-equilibrium systems ranging from the cosmoscopic [40,41], mesoscopic [42,43], to microscopic systems [44]. Furthermore, as discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Energy dependence of the nucleus-nucleus potential and the friction parameter in fusion reactions

Wen

Sakata

et al. 2014

Phys. Rev. C

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Applying a macroscopic reduction procedure on the improved quantum molecular dynamics (ImQMD) model, the energy dependences of the nucleus-nucleus potential, the friction parameter, and the random force characterizing a one-dimensional Langevin-type description of the heavy-ion fusion process are investigated. Systematic calculations with the ImQMD model show that the fluctuation-dissipation relation found in the symmetric head-on fusion reactions at energies just above the Coulomb barrier fades out when the incident energy increases. It turns out that this dynamical change with increasing incident energy is caused by a specific behavior of the friction parameter which directly depends on the microscopic dynamical process, i.e., on how the collective energy of the relative motion is transferred into the intrinsic excitation energy. It is shown microscopically that the energy dissipation in the fusion process is governed by two mechanisms: One is caused by the nucleon exchanges between two fusing nuclei, and the other is due to a rearrangement of nucleons in the intrinsic system. The former mechanism monotonically increases the dissipative energy and shows a weak dependence on the incident energy, while the latter depends on both the relative distance between two fusing nuclei and the incident energy. It is shown that the latter mechanism is responsible for the energy dependence of the fusion potential and explains the fading out of the fluctuation-dissipation relation.

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Non-Gaussian Fluctuations Resulting from Power-Law Trapping in a Lipid Bilayer

Cited by 94 publications

References 31 publications

Phase Diagram in Stored-Energy-Driven Lévy Flight

Phase Diagram in Stored-Energy-Driven Lévy Flight

Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity

Energy dependence of the nucleus-nucleus potential and the friction parameter in fusion reactions

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