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Luo X, Bao JD, Fan WY. Multiple diffusive behaviors of the random walk in inhomogeneous environments. Phys Rev E 2024; 109:014130. [PMID: 38366502 DOI: 10.1103/physreve.109.014130] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2023] [Accepted: 12/20/2023] [Indexed: 02/18/2024]
Abstract
Anomalous diffusive behaviors are observed in highly inhomogeneous but relatively stable environments such as intracellular media and are increasingly attracting attention. In this paper we develop a coupled continuous-time random walk model in which the waiting time is power-law coupled with the local environmental diffusion coefficient. We provide two forms of the waiting time density, namely, a heavy-tailed density and an exponential density. For different waiting time densities, anomalous diffusions with the diffusion exponent between 0 and 2 and Brownian yet non-Gaussian diffusion can be realized within the present model. The diffusive behaviors are analyzed and discussed by deriving the mean-squared displacement and probability density function. In addition we derive the effective jump length density corresponding to the decoupled form to help distinguish the diffusion types. Our model unifies two kinds of anomalous diffusive behavior with different characteristics in the same inhomogeneous environment into a theoretical framework. The model interprets the random motion of particles in a complex inhomogeneous environment and reproduces the experimental results of different biological and physical systems.
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Affiliation(s)
- Xiao Luo
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Wen-Yue Fan
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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2
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Chen Y, Wang X, Ge M. Lévy-walk-like Langevin dynamics with random parameters. CHAOS (WOODBURY, N.Y.) 2024; 34:013109. [PMID: 38198676 DOI: 10.1063/5.0174613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 12/05/2023] [Indexed: 01/12/2024]
Abstract
Anomalous diffusion phenomena have been widely found in systems within an inhomogeneous complex environment. For Lévy walk in an inhomogeneous complex environment, we characterize the particle's trajectory through an underdamped Langevin system coupled with a subordinator. The influence of the inhomogeneous environment on the particle's motion is parameterized by the random system parameters, relaxation timescale τ, and velocity diffusivity σ. We find that the two random parameters make different effects on the original superdiffusion behavior of the Lévy walk. The random σ contributes to a trivial result after an ensemble average, which is independent of the specific distribution of σ. By contrast, we find that a specific distribution of τ, a modified Lévy distribution with a finite mean, slows down the decaying rate of the velocity correlation function with respect to the lag time. However, the random τ does not promote the diffusion behavior in a direct way, but plays a competition role to the superdiffusion of the original Lévy walk. In addition, the effect of the random τ is also related to the specific subordinator in the coupled Langevin model, which corresponds to the distribution of the flight time of the Lévy walk. The random system parameters are capable of leading to novel dynamics, which needs detailed analyses, rather than an intuitive judgment, especially in complex systems.
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Affiliation(s)
- Yao Chen
- College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China
| | - Xudong Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
| | - Mengyan Ge
- College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China
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3
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Davis S, Avaria G, Bora B, Jain J, Moreno J, Pavez C, Soto L. Kappa distribution from particle correlations in nonequilibrium, steady-state plasmas. Phys Rev E 2023; 108:065207. [PMID: 38243483 DOI: 10.1103/physreve.108.065207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 11/12/2023] [Indexed: 01/21/2024]
Abstract
Kappa-distributed velocities in plasmas are common in a wide variety of settings, from low-density to high-density plasmas. To date, they have been found mainly in space plasmas, but are recently being considered also in the modeling of laboratory plasmas. Despite being routinely employed, the origin of the kappa distribution remains, to this day, unclear. For instance, deviations from the Maxwell-Boltzmann distribution are sometimes regarded as a signature of the nonadditivity of the thermodynamic entropy, although there are alternative frameworks such as superstatistics where such an assumption is not needed. In this work we recover the kappa distribution for particle velocities from the formalism of nonequilibrium steady-states, assuming only a single requirement on the dependence between the kinetic energy of a test particle and that of its immediate environment. Our results go beyond the standard derivation based on superstatistics, as we do not require any assumption about the existence of temperature or its statistical distribution, instead obtaining them from the requirement on kinetic energies. All of this suggests that this family of distributions may be more common than usually assumed, widening its domain of application in particular to the description of plasmas from fusion experiments. Furthermore, we show that a description of kappa-distributed plasma is simpler in terms of features of the superstatistical inverse temperature distribution rather than the traditional parameters κ and the thermal velocity v_{th}.
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Affiliation(s)
- Sergio Davis
- Research Center in the intersection of Plasma Physics, Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, piso 7, 8370136, Santiago, Chile
| | - Gonzalo Avaria
- Departamento de Física, Universidad Técnica Federico Santa María, Av. Vicuña Mackenna 3939, 8940000, Santiago, Chile
| | - Biswajit Bora
- Research Center in the intersection of Plasma Physics, Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, piso 7, 8370136, Santiago, Chile
| | - Jalaj Jain
- Research Center in the intersection of Plasma Physics, Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
| | - José Moreno
- Research Center in the intersection of Plasma Physics, Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, piso 7, 8370136, Santiago, Chile
| | - Cristian Pavez
- Research Center in the intersection of Plasma Physics, Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, piso 7, 8370136, Santiago, Chile
| | - Leopoldo Soto
- Research Center in the intersection of Plasma Physics, Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
- Departamento de Física, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, piso 7, 8370136, Santiago, Chile
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4
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Waigh TA, Korabel N. Heterogeneous anomalous transport in cellular and molecular biology. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:126601. [PMID: 37863075 DOI: 10.1088/1361-6633/ad058f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 10/20/2023] [Indexed: 10/22/2023]
Abstract
It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.
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Affiliation(s)
- Thomas Andrew Waigh
- Biological Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - Nickolay Korabel
- Department of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom
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5
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Liang Y, Wang W, Metzler R. Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift. Phys Rev E 2023; 108:024143. [PMID: 37723819 DOI: 10.1103/physreve.108.024143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 08/11/2023] [Indexed: 09/20/2023]
Abstract
The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the trapping phase) in a disordered medium is considered in the presence of an external drift. In particular, we consider trapping events whose times follow a scale-free distribution with diverging mean trapping time. We construct this process in terms of fractional Brownian motion with constant forcing in which the trapping effect is introduced by the subordination technique, connecting "operational time" with observable "real time." We derive the statistical properties of this process such as non-Gaussianity and nonergodicity, for both ensemble and single-trajectory (time) averages. We demonstrate nice agreement with extensive simulations for the probability density function, skewness, kurtosis, as well as ensemble and time-averaged mean-squared displacements. We place a specific emphasis on the comparisons between the cases with and without drift.
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Affiliation(s)
- Yingjie Liang
- College of Mechanics and Materials, Hohai University, 211100 Nanjing, China
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
| | - Wei Wang
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
- Asia Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea
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6
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Itto Y. Conditional Entropic Approach to Nonequilibrium Complex Systems with Weak Fluctuation Correlation. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25040556. [PMID: 37190346 PMCID: PMC10137531 DOI: 10.3390/e25040556] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Revised: 03/21/2023] [Accepted: 03/21/2023] [Indexed: 05/17/2023]
Abstract
A conditional entropic approach is discussed for nonequilibrium complex systems with a weak correlation between spatiotemporally fluctuating quantities on a large time scale. The weak correlation is found to constitute the fluctuation distribution that maximizes the entropy associated with the conditional fluctuations. The approach is illustrated in diffusion phenomenon of proteins inside bacteria. A further possible illustration is also presented for membraneless organelles in embryos and beads in cell extracts, which share common natures of fluctuations in their diffusion.
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Affiliation(s)
- Yuichi Itto
- Science Division, Center for General Education, Aichi Institute of Technology, Toyota 470-0392, Aichi, Japan
- Institut für Computerphysik, Universität Stuttgart, 70569 Stuttgart, Germany
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7
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Bogachev M, Sinitca A, Grigarevichius K, Pyko N, Lyanova A, Tsygankova M, Davletshin E, Petrov K, Ageeva T, Pyko S, Kaplun D, Kayumov A, Mukhamedshina Y. Video-based marker-free tracking and multi-scale analysis of mouse locomotor activity and behavioral aspects in an open field arena: A perspective approach to the quantification of complex gait disturbances associated with Alzheimer's disease. Front Neuroinform 2023; 17:1101112. [PMID: 36817970 PMCID: PMC9932053 DOI: 10.3389/fninf.2023.1101112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Accepted: 01/12/2023] [Indexed: 02/05/2023] Open
Abstract
Introduction Complex gait disturbances represent one of the prominent manifestations of various neurophysiological conditions, including widespread neurodegenerative disorders such as Alzheimer's and Parkinson's diseases. Therefore, instrumental measurement techniques and automatic computerized analysis appears essential for the differential diagnostics, as well as for the assessment of treatment effectiveness from experimental animal models to clinical settings. Methods Here we present a marker-free instrumental approach to the analysis of gait disturbances in animal models. Our approach is based on the analysis of video recordings obtained with a camera placed underneath an open field arena with transparent floor using the DeeperCut algorithm capable of online tracking of individual animal body parts, such as the snout, the paws and the tail. The extracted trajectories of animal body parts are next analyzed using an original computerized methodology that relies upon a generalized scalable model based on fractional Brownian motion with parameters identified by detrended partial cross-correlation analysis. Results We have shown that in a mouse model representative movement patterns are characterized by two asymptotic regimes characterized by integrated 1/f noise at small scales and nearly random displacements at large scales separated by a single crossover. More detailed analysis of gait disturbances revealed that the detrended cross-correlations between the movements of the snout, paws and tail relative to the animal body midpoint exhibit statistically significant discrepancies in the Alzheimer's disease mouse model compared to the control group at scales around the location of the crossover. Discussion We expect that the proposed approach, due to its universality, robustness and clear physical interpretation, is a promising direction for the design of applied analysis tools for the diagnostics of various gait disturbances and behavioral aspects in animal models. We further believe that the suggested mathematical models could be relevant as a complementary tool in clinical diagnostics of various neurophysiological conditions associated with movement disorders.
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Affiliation(s)
- Mikhail Bogachev
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
- Institute for Fundamental Medicine and Biology, Kazan Federal University, Kazan, Russia
| | - Aleksandr Sinitca
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
| | - Konstantin Grigarevichius
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
| | - Nikita Pyko
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
| | - Asya Lyanova
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
| | - Margarita Tsygankova
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
| | - Eldar Davletshin
- Institute for Fundamental Medicine and Biology, Kazan Federal University, Kazan, Russia
| | - Konstantin Petrov
- FRC Kazan Scientific Center of RAS, Arbuzov Institute of Organic and Physical Chemistry, Kazan, Russia
| | - Tatyana Ageeva
- Institute for Fundamental Medicine and Biology, Kazan Federal University, Kazan, Russia
| | - Svetlana Pyko
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
| | - Dmitrii Kaplun
- Centre for Digital Telecommunication Technologies, St. Petersburg Electrotechnical University “LETI”, St. Petersburg, Russia
| | - Airat Kayumov
- Institute for Fundamental Medicine and Biology, Kazan Federal University, Kazan, Russia
| | - Yana Mukhamedshina
- Institute for Fundamental Medicine and Biology, Kazan Federal University, Kazan, Russia
- Department of Histology, Cytology and Embryology, Kazan State Medical University, Kazan, Russia
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8
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Dos Santos MAF, Nobre FD, Curado EMF. Entropic form emergent from superstatistics. Phys Rev E 2023; 107:014132. [PMID: 36797946 DOI: 10.1103/physreve.107.014132] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 12/23/2022] [Indexed: 06/18/2023]
Abstract
The Beck-Cohen superstatistics became an important theory in the scenario of complex systems because it generates distributions representing regions of a nonequilibrium system, characterized by different temperatures T≡β^{-1}, leading to a probability distribution f(β). In superstatistics, some classes have been most frequently considered for f(β), like χ^{2}, χ^{2} inverse, and log-normal ones. Herein we investigate the superstatistics resulting from a χ_{η}^{2} distribution through a modification of the usual χ^{2} by introducing a real index η (0<η≤1). In this way, one covers two common and relevant distributions as particular cases, proportional to the q-exponential (e_{q}^{-βx}=[1-(1-q)βx]^{1/1-q}) and the stretched exponential (e^{-(βx)^{η}}). Furthermore, an associated generalized entropic form is found. Since these two particular-case distributions have been frequently found in the literature, we expect that the present results should be applicable to a wide range of classes of complex systems.
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Affiliation(s)
- Maike A F Dos Santos
- Department of Physics, PUC-Rio, Rua Marquês de São Vicente, 225, 22451-900, Rio de Janeiro, Brazil
- Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
| | - Fernando D Nobre
- Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
- National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
| | - Evaldo M F Curado
- Centro Brasileiro de Pesquisas Físicas Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
- National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ Brazil
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9
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Costa MO, Silva R, Anselmo DHAL. Superstatistical and DNA sequence coding of the human genome. Phys Rev E 2022; 106:064407. [PMID: 36671113 DOI: 10.1103/physreve.106.064407] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 11/16/2022] [Indexed: 12/14/2022]
Abstract
In this work, by considering superstatistics we investigate the short-range correlations (SRCs) and the fluctuations in the distribution of lengths of strings of nucleotides. To this end, a stochastic model provides the distributions of the size of the exons based on the q-Gamma and inverse q-Gamma distributions. Specifically, we define a time series for exon sizes to investigate the SRC and the fluctuations through the superstatistics distributions. To test the model's viability, we use the Project Ensembl database of genes to extract the time evolution of exon sizes, calculated in terms of the number of base pairs (bp) in these biological databases. Our findings show that, depending on the chromosome, both distributions are suitable for describing the length distribution of human DNA for lengths greater than 10 bp. In addition, we used Bayesian statistics to perform a selection model approach, which revealed weak evidence for the inverse q-Gamma distribution for a considerable number of chromosomes.
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Affiliation(s)
- M O Costa
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal - RN, 59072-970, Brasil
| | - R Silva
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal - RN, 59072-970, Brasil and Programa de Pós-Graduação em Física, Universidade do Estado do Rio Grande do Norte, Mossoró - Rio Grande do Norte, 59610-210, Brasil
| | - D H A L Anselmo
- Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal - RN, 59072-970, Brasil and Programa de Pós-Graduação em Física, Universidade do Estado do Rio Grande do Norte, Mossoró - Rio Grande do Norte, 59610-210, Brasil
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10
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Runfola C, Vitali S, Pagnini G. The Fokker-Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm. ROYAL SOCIETY OPEN SCIENCE 2022; 9:221141. [PMID: 36340511 PMCID: PMC9627453 DOI: 10.1098/rsos.221141] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/21/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live Escherichia coli cells, we obtain the probability density function of molecules' displacement and we derive the corresponding Fokker-Planck equation. Molecules' distribution emerges to be related to the Krätzel function and its Fokker-Planck equation to be a fractional diffusion equation in the Erdélyi-Kober sense. The irreducibility of the derived Fokker-Planck equation to those of other literature models is also discussed.
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Affiliation(s)
- C. Runfola
- Department of Physics and Astronomy, University of Bologna, Viale Berti Pichat 6/2, I-40127 Bologna, Italy
- BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain
| | - S. Vitali
- BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain
- Eurecat, Centre Tecnológic de Catalunya, Unit of Digital Health, Data Analytics in Medicine, E-08005 Barcelona, Catalunya, Spain
| | - G. Pagnini
- BCAM – Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain
- Ikerbasque – Basque Foundation for Science, Plaza Euskadi 5, E-48009 Bilbao, Basque Country, Spain
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11
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Balcerek M, Burnecki K, Thapa S, Wyłomańska A, Chechkin A. Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions. CHAOS (WOODBURY, N.Y.) 2022; 32:093114. [PMID: 36182362 DOI: 10.1063/5.0101913] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Accepted: 08/12/2022] [Indexed: 06/16/2023]
Abstract
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The correlation and diffusion properties of this random motion are fully characterized by its index of self-similarity or the Hurst exponent. However, recent single-particle tracking experiments in biological cells revealed highly complicated anomalous diffusion phenomena that cannot be attributed to a class of self-similar random processes. Inspired by these observations, we here study the process that preserves the properties of the fractional Brownian motion at a single trajectory level; however, the Hurst index randomly changes from trajectory to trajectory. We provide a general mathematical framework for analytical, numerical, and statistical analysis of the fractional Brownian motion with the random Hurst exponent. The explicit formulas for probability density function, mean-squared displacement, and autocovariance function of the increments are presented for three generic distributions of the Hurst exponent, namely, two-point, uniform, and beta distributions. The important features of the process studied here are accelerating diffusion and persistence transition, which we demonstrate analytically and numerically.
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Affiliation(s)
- Michał Balcerek
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
| | - Krzysztof Burnecki
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
| | - Samudrajit Thapa
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Agnieszka Wyłomańska
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
| | - Aleksei Chechkin
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
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12
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Szarek D, Maraj-Zygmąt K, Sikora G, Krapf D, Wyłomańska A. Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2021.107401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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13
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Wang W, Metzler R, Cherstvy AG. Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models. Phys Chem Chem Phys 2022; 24:18482-18504. [DOI: 10.1039/d2cp01741e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...
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14
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Schäfer B, Heppell CM, Rhys H, Beck C. Fluctuations of water quality time series in rivers follow superstatistics. iScience 2021; 24:102881. [PMID: 34401665 PMCID: PMC8348929 DOI: 10.1016/j.isci.2021.102881] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 06/02/2021] [Accepted: 07/14/2021] [Indexed: 10/26/2022] Open
Abstract
Superstatistics is a general method from nonequilibrium statistical physics which has been applied to a variety of complex systems, ranging from hydrodynamic turbulence to traffic delays and air pollution dynamics. Here, we investigate water quality time series (such as dissolved oxygen concentrations and electrical conductivity) as measured in rivers and provide evidence that they exhibit superstatistical behavior. Our main example is time series as recorded in the River Chess in South East England. Specifically, we use seasonal detrending and empirical mode decomposition to separate trends from fluctuations for the measured data. With either detrending method, we observe heavy-tailed fluctuation distributions, which are well described by log-normal superstatistics for dissolved oxygen. Contrarily, we find a double peaked non-standard superstatistics for the electrical conductivity data, which we model using two combinedχ 2 -distributions.
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Affiliation(s)
- Benjamin Schäfer
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
- Faculty of Science and Technology, Norwegian University of Life Sciences, 1432 Ås, Norway
| | - Catherine M. Heppell
- School of Geography, Queen Mary University of London, Mile End Road, London E1 4NS, UK
| | - Hefin Rhys
- Flow Cytometry Science Technology Platform, The Francis Crick Institute, London, UK
| | - Christian Beck
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
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15
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Korabel N, Han D, Taloni A, Pagnini G, Fedotov S, Allan V, Waigh TA. Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast Moving Endosomes. ENTROPY (BASEL, SWITZERLAND) 2021; 23:958. [PMID: 34441098 PMCID: PMC8394768 DOI: 10.3390/e23080958] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/14/2021] [Revised: 07/19/2021] [Accepted: 07/23/2021] [Indexed: 01/14/2023]
Abstract
Trajectories of endosomes inside living eukaryotic cells are highly heterogeneous in space and time and diffuse anomalously due to a combination of viscoelasticity, caging, aggregation and active transport. Some of the trajectories display switching between persistent and anti-persistent motion, while others jiggle around in one position for the whole measurement time. By splitting the ensemble of endosome trajectories into slow moving subdiffusive and fast moving superdiffusive endosomes, we analyzed them separately. The mean squared displacements and velocity auto-correlation functions confirm the effectiveness of the splitting methods. Applying the local analysis, we show that both ensembles are characterized by a spectrum of local anomalous exponents and local generalized diffusion coefficients. Slow and fast endosomes have exponential distributions of local anomalous exponents and power law distributions of generalized diffusion coefficients. This suggests that heterogeneous fractional Brownian motion is an appropriate model for both fast and slow moving endosomes. This article is part of a Special Issue entitled: "Recent Advances In Single-Particle Tracking: Experiment and Analysis" edited by Janusz Szwabiński and Aleksander Weron.
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Affiliation(s)
- Nickolay Korabel
- Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK; (D.H.); (S.F.)
| | - Daniel Han
- Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK; (D.H.); (S.F.)
- School of Biological Sciences, The University of Manchester, Manchester M13 9PT, UK;
- Biological Physics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK
| | - Alessandro Taloni
- CNR—Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Via dei Taurini 19, 00185 Roma, Italy;
| | - Gianni Pagnini
- BCAM—Basque Center for Applied Mathematics, Mazarredo 14, 48009 Bilbao, Spain;
- Ikerbasque—Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
| | - Sergei Fedotov
- Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK; (D.H.); (S.F.)
| | - Viki Allan
- School of Biological Sciences, The University of Manchester, Manchester M13 9PT, UK;
| | - Thomas Andrew Waigh
- Biological Physics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK
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16
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Mitsokapas E, Schäfer B, Harris RJ, Beck C. Statistical characterization of airplane delays. Sci Rep 2021; 11:7855. [PMID: 33846509 PMCID: PMC8041857 DOI: 10.1038/s41598-021-87279-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 03/22/2021] [Indexed: 12/23/2022] Open
Abstract
The aviation industry is of great importance for a globally connected economy. Customer satisfaction with airlines and airport performance is considerably influenced by how much flights are delayed. But how should the delay be quantified with thousands of flights for each airport and airline? Here, we present a statistical analysis of arrival delays at several UK airports between 2018 and 2020. We establish a procedure to compare both mean delay and extreme events among airlines and airports, identifying a power-law decay of large delays. Furthermore, we note drastic changes in plane delay statistics during the COVID-19 pandemic. Finally, we find that delays are described by a superposition of simple distributions, leading to a superstatistics.
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Affiliation(s)
- Evangelos Mitsokapas
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
| | - Benjamin Schäfer
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK.
| | - Rosemary J Harris
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
| | - Christian Beck
- School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, UK
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17
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Fluctuating Diffusivity of RNA-Protein Particles: Analogy with Thermodynamics. ENTROPY 2021; 23:e23030333. [PMID: 33808996 PMCID: PMC8002026 DOI: 10.3390/e23030333] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Revised: 03/05/2021] [Accepted: 03/08/2021] [Indexed: 01/01/2023]
Abstract
A formal analogy of fluctuating diffusivity to thermodynamics is discussed for messenger RNA molecules fluorescently fused to a protein in living cells. Regarding the average value of the fluctuating diffusivity of such RNA-protein particles as the analog of the internal energy, the analogs of the quantity of heat and work are identified. The Clausius-like inequality is shown to hold for the entropy associated with diffusivity fluctuations, which plays a role analogous to the thermodynamic entropy, and the analog of the quantity of heat. The change of the statistical fluctuation distribution is also examined from a geometric perspective. The present discussions may contribute to a deeper understanding of the fluctuating diffusivity in view of the laws of thermodynamics.
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