1
|
Liu J, Sun K, Wang H. Anomalous diffusion in external-force-affected deterministic systems. Phys Rev E 2024; 110:014204. [PMID: 39160918 DOI: 10.1103/physreve.110.014204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2024] [Accepted: 06/20/2024] [Indexed: 08/21/2024]
Abstract
This study investigates the impact of external forces on the movement of particles, specifically focusing on a type of box piecewise linear map that generates normal diffusion akin to Brownian motion. Through numerical methods, the research delves into the effects of two distinct external forces: linear forces linked to the particle's current position and periodic sinusoidal forces related to time. The results uncover anomalous dynamical behavior characterized by nonlinear growth in the ensemble-averaged mean-squared displacement (EAMSD), aging, and ergodicity breaking. Notably, the diffusion pattern of particles under linear external forces resembles an Ehrenfest double urn model, with its asymptotic EAMSD coinciding with the Langevin equation under linear potential. Meanwhile, particle movement influenced by periodic sinusoidal forces corresponds to an inhomogeneous Markov chain, with its external force amplitude and diffusion coefficient function exhibiting a "multipeak" fractal structure. The study also provides insights into the formation of this structure through the turnstiles dynamics.
Collapse
|
2
|
Kazakevičius R, Kononovicius A. Anomalous diffusion and long-range memory in the scaled voter model. Phys Rev E 2023; 107:024106. [PMID: 36932606 DOI: 10.1103/physreve.107.024106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 01/10/2023] [Indexed: 06/18/2023]
Abstract
We analyze the scaled voter model, which is a generalization of the noisy voter model with time-dependent herding behavior. We consider the case when the intensity of herding behavior grows as a power-law function of time. In this case, the scaled voter model reduces to the usual noisy voter model, but it is driven by the scaled Brownian motion. We derive analytical expressions for the time evolution of the first and second moments of the scaled voter model. In addition, we have derived an analytical approximation of the first passage time distribution. By numerical simulation, we confirm our analytical results as well as showing that the model exhibits long-range memory indicators despite being a Markov model. The proposed model has steady-state distribution consistent with the bounded fractional Brownian motion, thus we expect it to be a good substitute model for the bounded fractional Brownian motion.
Collapse
Affiliation(s)
- Rytis Kazakevičius
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257 Vilnius, Lithuania
| | - Aleksejus Kononovicius
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257 Vilnius, Lithuania
| |
Collapse
|
3
|
Zhang N, Liao Z, Yang Y, Huang Y, Zhang X, Ye J, Xiao M. Preparation and intrinsic kinetics study of the scale-up production of hydroxypropyl agar by heterogeneous hydroxypropylation reaction. Int J Biol Macromol 2022; 200:218-225. [PMID: 34995660 DOI: 10.1016/j.ijbiomac.2021.12.115] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Revised: 11/28/2021] [Accepted: 12/18/2021] [Indexed: 12/20/2022]
Abstract
Hydroxypropylation is effective in modifying the structure and properties of agar. So far, the industrial scale-up production of hydroxypropylated agar has not been evaluated. Therefore, the large-scale production of the hydroxypropylation of agar using a heterogeneous reaction system was evaluated in the present this study. The structures and properties of the hydroxypropyl agar (HPA) product were measured and the intrinsic kinetics of the heterogeneous reaction were determined and analyzed. The results showed that the large-scale HPA had good thermal stability, and lower viscosity, gelling temperature and melting temperature compared with those of agar. The SEM indicated that the improvement of solubility of HPA was not only due to the hydrophilic effect of hydroxypropyl group, but also due to the formation of cluster structure and grid structure. The characteristic of heterogeneous hydroxypropylation reaction were determined by preliminary kinetic experiments, which demonstrated that the reaction order of propylene oxide was 2, while that for agar was approximately 0. The reaction activation energy of heterogeneous hydroxypropylation reaction was calculated to be 83.50 kJ/mol using the Arrhenius formula. Taken together, the results would provide guidances for the industrialization of hydroxypropyl agar.
Collapse
Affiliation(s)
- Na Zhang
- College of Chemical Engineering, Huaqiao University, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China; Xiamen Engineering and Technological Research Center for Comprehensive Utilization of Marine Biological Resources, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China.
| | - Zhensheng Liao
- College of Chemical Engineering, Huaqiao University, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China
| | - Yucheng Yang
- College of Chemical Engineering, Huaqiao University, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China; Xiamen Engineering and Technological Research Center for Comprehensive Utilization of Marine Biological Resources, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China.
| | - Yayan Huang
- College of Chemical Engineering, Huaqiao University, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China; Xiamen Engineering and Technological Research Center for Comprehensive Utilization of Marine Biological Resources, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China.
| | - Xueqin Zhang
- College of Chemical Engineering, Huaqiao University, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China; Xiamen Engineering and Technological Research Center for Comprehensive Utilization of Marine Biological Resources, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China.
| | - Jing Ye
- College of Chemical Engineering, Huaqiao University, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China; Xiamen Engineering and Technological Research Center for Comprehensive Utilization of Marine Biological Resources, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China.
| | - Meitian Xiao
- College of Chemical Engineering, Huaqiao University, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China; Xiamen Engineering and Technological Research Center for Comprehensive Utilization of Marine Biological Resources, Jimei Road, Jimei District, Xiamen 361021, Fujian, PR China.
| |
Collapse
|
4
|
Wang W, Cherstvy AG, Kantz H, Metzler R, Sokolov IM. Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes. Phys Rev E 2021; 104:024105. [PMID: 34525678 DOI: 10.1103/physreve.104.024105] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2021] [Accepted: 07/14/2021] [Indexed: 12/12/2022]
Abstract
How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x)=D_{0}|x|^{γ} and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity-breaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB∼(1/r)-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.
Collapse
Affiliation(s)
- Wei Wang
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany.,Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Holger Kantz
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.,IRIS Adlershof, Zum Großen Windkanal 6, 12489 Berlin, Germany
| |
Collapse
|
5
|
Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems. ENTROPY 2021; 23:e23091125. [PMID: 34573750 PMCID: PMC8470578 DOI: 10.3390/e23091125] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/04/2021] [Revised: 08/25/2021] [Accepted: 08/25/2021] [Indexed: 11/17/2022]
Abstract
In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models-reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.
Collapse
|
6
|
Kazakevičius R, Kononovicius A. Anomalous diffusion in nonlinear transformations of the noisy voter model. Phys Rev E 2021; 103:032154. [PMID: 33862826 DOI: 10.1103/physreve.103.032154] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 03/04/2021] [Indexed: 11/07/2022]
Abstract
Voter models are well known in the interdisciplinary community, yet they have not been studied from the perspective of anomalous diffusion. In this paper, we show that the original voter model exhibits a ballistic regime. Nonlinear transformations of the observation variable and time scale allow us to observe other regimes of anomalous diffusion as well as normal diffusion. We show that numerical simulation results coincide with derived analytical approximations describing the temporal evolution of the raw moments.
Collapse
Affiliation(s)
- Rytis Kazakevičius
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257 Vilnius, Lithuania
| | - Aleksejus Kononovicius
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257 Vilnius, Lithuania
| |
Collapse
|
7
|
Dos Santos MAF, Dornelas V, Colombo EH, Anteneodo C. Critical patch size reduction by heterogeneous diffusion. Phys Rev E 2020; 102:042139. [PMID: 33212705 DOI: 10.1103/physreve.102.042139] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Accepted: 10/13/2020] [Indexed: 06/11/2023]
Abstract
Population survival depends on a large set of factors and on how they are distributed in space. Due to landscape heterogeneity, species can occupy particular regions that provide the ideal scenario for development, working as a refuge from harmful environmental conditions. Survival occurs if population growth overcomes the losses caused by adventurous individuals that cross the patch edge. In this work, we consider a single species dynamics in a patch with a space-dependent diffusion coefficient. We show analytically, within the Stratonovich framework, that heterogeneous diffusion reduces the minimal patch size for population survival when contrasted with the homogeneous case with the same average diffusivity. Furthermore, this result is robust regardless of the particular choice of the diffusion coefficient profile. We also discuss how this picture changes beyond the Stratonovich framework. Particularly, the Itô case, which is nonanticipative, can promote the opposite effect, while Hänggi-Klimontovich interpretation reinforces the reduction effect.
Collapse
Affiliation(s)
- M A F Dos Santos
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900, Rio de Janeiro, RJ, Brazil
| | - V Dornelas
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900, Rio de Janeiro, RJ, Brazil
- ICTP-SAIFR & IFT-UNESP, Rua Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP, Brazil
| | - E H Colombo
- Department of Ecology & Evolutionary Biology, Princeton University, Princeton, New Jersey 08544, USA
- Department of Ecology, Evolution, and Natural Resources, Rutgers University, New Brunswick, New Jersey 08901, USA
| | - C Anteneodo
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente 225, 22451-900, Rio de Janeiro, RJ, Brazil
- Institute of Science and Technology for Complex Systems (INCT-SC), Rio de Janeiro, Brazil
| |
Collapse
|
8
|
Safdari H, Cherstvy AG, Chechkin AV, Bodrova A, Metzler R. Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation. Phys Rev E 2017; 95:012120. [PMID: 28208482 DOI: 10.1103/physreve.95.012120] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Indexed: 06/06/2023]
Abstract
We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.
Collapse
Affiliation(s)
- Hadiseh Safdari
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Department of Physics, Shahid Beheshti University, 19839 Tehran, Iran
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Aleksei V Chechkin
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine
- Department of Physics & Astronomy, University of Padova, "Galileo Galilei" - DFA, 35131 Padova, Italy
| | - Anna Bodrova
- Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany
- Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| |
Collapse
|