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Nizama M, Cáceres MO. Intermittent Kac's flights and the generalized telegrapher's equation. Phys Rev E 2024; 109:024116. [PMID: 38491600 DOI: 10.1103/physreve.109.024116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 01/23/2024] [Indexed: 03/18/2024]
Abstract
A generalized one-dimensional telegrapher equation associated with an intermittent change of sign in the velocity of a Kac's flight has been proposed. To solve this random differential equation, we used the enlarged master equation approach to obtain the exact differential equation for the evolution of a normalized positive distribution. This distribution is associated with a generalized finite-velocity diffusionlike process. We studied the robustness of the ballistic regime, the cutoff of its domain, and the time-dependent Gaussian convergence. The second moment for the evolution of the profile has been studied as a function of non-Poisson statistics (possibly intermittent) for the time intervals Δ_{ij} in the Kac's flight. Numerical results for the evolution of sharp and wide initial profiles have also been presented. In addition, for comparison with a non-Gaussian process at all times, we have revisited the non-Markov Poisson's flight with exponential pulses. A theory for generalized random flights with intermittent stochastic velocity and in the presence of a force is also presented, and the stationary distribution for two classes of potential has been obtained.
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Affiliation(s)
- Marco Nizama
- Departamento de Fisica, Facultad de Ingenieria and CONICET, Universidad Nacional del Comahue, CP 8300, Neuquen, Argentina
| | - Manuel O Cáceres
- Comision Nacional de Energia Atomica, Centro Atomico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina
- CONICET, Centro Atomico Bariloche, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina
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Influence of the catalyst layer thickness on the determination of the OER activity of Fe3O4@CoFe2O4 Core-Shell Nanoparticles. Electrochim Acta 2023. [DOI: 10.1016/j.electacta.2023.141981] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
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Cáceres MO, Nizama M. Stochastic telegrapher's approach for solving the random Boltzmann-Lorentz gas. Phys Rev E 2022; 105:044131. [PMID: 35590552 DOI: 10.1103/physreve.105.044131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 03/31/2022] [Indexed: 06/15/2023]
Abstract
The 1D random Boltzmann-Lorentz equation has been connected with a set of stochastic hyperbolic equations. Therefore, the study of the Boltzmann-Lorentz gas with disordered scattering centers has been transformed into the analysis of a set of stochastic telegrapher's equations. For global binary disorder (Markovian and non-Markovian) exact analytical results for the second moment, the velocity autocorrelation function, and the self-diffusion coefficient are presented. We have demonstrated that time-fluctuations in the lost of energy in the telegrapher's equation, can delay the entrance to the diffusive regime, this issue has been characterized by a timescale t_{c} which is a function of disorder parameters. Indeed, producing a longer ballistic dynamics in the transport process. In addition, fluctuations of the space probability distribution have been studied, showing that the mean value of a stochastic telegrapher's Fourier mode is a good statistical object to characterize the solution of the random Boltzmann-Lorentz gas. In a different context, the stochastic telegrapher's equation has also been related to the run-and-tumble model in Biophysics. Then a discussion devoted to the potential applications when swimmers' speed and tumbling rate have time fluctuations has been pointed out.
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Affiliation(s)
- Manuel O Cáceres
- Comision Nacional de Energia Atomica, Centro Atomico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina
- CONICET, Centro Atomico Bariloche, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina
| | - Marco Nizama
- Departamento de Fisica, Facultad de Ingenieria and CONICET, Universidad Nacional del Comahue, CP 8300, Neuquen, Argentina
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Angelani L, Garra R. Run-and-tumble motion in one dimension with space-dependent speed. Phys Rev E 2019; 100:052147. [PMID: 31869950 DOI: 10.1103/physreve.100.052147] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2019] [Indexed: 11/07/2022]
Abstract
We consider a particle performing run-and-tumble dynamics with space-dependent speed. The model has biological relevance as it describes motile bacteria or cells in heterogeneous environments. We give exact expression for the probability density function in the case of free motion in unbounded space. We then analyze the case of a particle moving in a confined interval in the presence of partially absorbing boundaries, reporting the probability density in the Laplace (time) domain and the mean time to absorption. We also discuss the relaxation to the steady state in the case of confinement with reflecting boundaries and drift effects due to direction-dependent tumbling rates, modeling taxis phenomena of cells. The case of diffusive particles with spatially variable diffusivity is obtained as a limiting case.
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Affiliation(s)
- L Angelani
- ISC-CNR, Institute for Complex Systems, Piazzale Aldo Moro 2, 00185 Rome, Italy.,Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - R Garra
- Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
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Escaff D, Toral R, Van den Broeck C, Lindenberg K. A continuous-time persistent random walk model for flocking. CHAOS (WOODBURY, N.Y.) 2018; 28:075507. [PMID: 30070507 DOI: 10.1063/1.5027734] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A classical random walker is characterized by a random position and velocity. This sort of random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a walker represents an inanimate particle driven by environmental fluctuations. On the other hand, there are many examples of so-called "persistent random walkers," including self-propelled particles that are able to move with almost constant speed while randomly changing their direction of motion. Examples include living entities (ranging from flagellated unicellular organisms to complex animals such as birds and fish), as well as synthetic materials. Here we discuss such persistent non-interacting random walkers as a model for active particles. We also present a model that includes interactions among particles, leading to a transition to flocking, that is, to a net flux where the majority of the particles move in the same direction. Moreover, the model exhibits secondary transitions that lead to clustering and more complex spatially structured states of flocking. We analyze all these transitions in terms of bifurcations using a number of mean field strategies (all to all interaction and advection-reaction equations for the spatially structured states), and compare these results with direct numerical simulations of ensembles of these interacting active particles.
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Affiliation(s)
- Daniel Escaff
- Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Monseñor Alvaro del Portillo 12455, Las Condes, Santiago, Chile
| | - Raúl Toral
- IFISC (Instituto de Física Interdisciplinar y Sistemas Complejos), Universitat de les Illes Balears-CSIC, Palma de Mallorca 07122, Spain
| | - Christian Van den Broeck
- Hasselt University, B-3500 Hasselt, Belgium and Stellenbosch Institute for Advanced Studies, Matieland 7602, South Africa
| | - Katja Lindenberg
- Department of Chemistry and Biochemistry and BioCircuits Institute, University of California San Diego, La Jolla, California 92093-0340, USA
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Altahhan MR, Aboanber AE, Abou-Gabal HH. Analytical solution of the Telegraph Point Reactor Kinetics model during the cold start-up of a nuclear reactor. ANN NUCL ENERGY 2017. [DOI: 10.1016/j.anucene.2017.06.001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Choi Y, Kim HJ. Nonstationary Markovian replication process causing diverse diffusions. Phys Rev E 2017; 96:042144. [PMID: 29347487 DOI: 10.1103/physreve.96.042144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2017] [Indexed: 06/07/2023]
Abstract
We introduce a single generative mechanism that can be used to describe diverse nonstationary diffusions. A nonstationary Markovian replication process for steps is considered for which we derive analytically the time evolution of the probability distribution of the walker's displacement and the generalized telegrapher equation with time-varying coefficients, and we find that diffusivity can be determined by temporal changes of replication of an immediate step. By controlling the replications, we realize diverse diffusions such as alternating diffusion, superdiffusion, subdiffusion, and marginal diffusion, which originate from oscillating, increasing, decreasing, and slowly increasing or decreasing replications with time, respectively.
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Affiliation(s)
- Yichul Choi
- Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA
| | - Hyun-Joo Kim
- Department of Physics Education, Korea National University of Education, Chungbuk 363-791, Korea
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Heizler SI. Asymptotic Telegrapher’s Equation (P1) Approximation for the Transport Equation. NUCL SCI ENG 2017. [DOI: 10.13182/nse09-77] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Shay I. Heizler
- Bar-Ilan University, Department of Physics, Ramat-Gan, Israel and Nuclear Research Center-Negev, Department of Physics P.O. Box 9001, Beer Sheva 84190, Israel
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Masoliver J. Fractional telegrapher's equation from fractional persistent random walks. Phys Rev E 2016; 93:052107. [PMID: 27300830 DOI: 10.1103/physreve.93.052107] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2016] [Indexed: 06/06/2023]
Abstract
We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specifically, transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses.
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Affiliation(s)
- Jaume Masoliver
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal, 647, E-08028 Barcelona, Spain
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Sim A, Liepe J, Stumpf MPH. Goldstein-Kac telegraph processes with random speeds: Path probabilities, likelihoods, and reported Lévy flights. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042115. [PMID: 25974447 DOI: 10.1103/physreve.91.042115] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2014] [Indexed: 06/04/2023]
Abstract
The Goldstein-Kac telegraph process describes the one-dimensional motion of particles with constant speed undergoing random changes in direction. Despite its resemblance to numerous real-world phenomena, the singular nature of the resultant spatial distribution of each particle precludes the possibility of any a posteriori empirical validation of this random-walk model from data. Here we show that by simply allowing for random speeds, the ballistic terms are regularized and that the diffusion component can be well-approximated via the unscented transform. The result is a computationally efficient yet robust evaluation of the full particle path probabilities and, hence, the parameter likelihoods of this generalized telegraph process. We demonstrate how a population diffusing under such a model can lead to non-Gaussian asymptotic spatial distributions, thereby mimicking the behavior of an ensemble of Lévy walkers.
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Affiliation(s)
- Aaron Sim
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, SW7 2AZ, United Kingdom
| | - Juliane Liepe
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, SW7 2AZ, United Kingdom
| | - Michael P H Stumpf
- Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, SW7 2AZ, United Kingdom
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Sevilla FJ, Gómez Nava LA. Theory of diffusion of active particles that move at constant speed in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022130. [PMID: 25215711 DOI: 10.1103/physreve.90.022130] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2014] [Indexed: 06/03/2023]
Abstract
Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.
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Affiliation(s)
- Francisco J Sevilla
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México Distrito Federal, Mexico
| | - Luis A Gómez Nava
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México Distrito Federal, Mexico and Posgrado en Ciencias Físicas, Universidad Nacional Autónoma de México, Circuito de Posgrados, Ciudad Universitaria, Coyoacán, 04510 México Distrito Federal, Mexico
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Wissner-Gross AD, Freer CE. Relativistic statistical arbitrage. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056104. [PMID: 21230542 DOI: 10.1103/physreve.82.056104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2010] [Revised: 10/10/2010] [Indexed: 05/30/2023]
Abstract
Recent advances in high-frequency financial trading have made light propagation delays between geographically separated exchanges relevant. Here we show that there exist optimal locations from which to coordinate the statistical arbitrage of pairs of spacelike separated securities, and calculate a representative map of such locations on Earth. Furthermore, trading local securities along chains of such intermediate locations results in a novel econophysical effect, in which the relativistic propagation of tradable information is effectively slowed or stopped by arbitrage.
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Affiliation(s)
- A D Wissner-Gross
- The MIT Media Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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Sadjadi Z, Miri M. Persistent random walk on a one-dimensional lattice with random asymmetric transmittances. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:061114. [PMID: 19256809 DOI: 10.1103/physreve.78.061114] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2008] [Indexed: 05/27/2023]
Abstract
We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t;{'} not equalt) for photons moving to the right (left) direction. Transmittances at different sites are assumed independent, distributed according to a given probability density F(t,t;{'}) . We use the effective medium approximation and identify two classes of F(t,t;{'}) which lead to the normal diffusion of photons. Monte Carlo simulations confirm our predictions. We mention that the metamaterial introduced by Fedetov [Nano Lett. 7, 1996 (2007)] can be used to realize a lattice of random asymmetric transmittances.
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Affiliation(s)
- Zeinab Sadjadi
- Institute for Advanced Studies in Basic Sciences (IASBS), P. O. Box 45195-1159, Zanjan 45195, Iran
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Miri M, Sadjadi Z, Fouladvand ME. Persistent random walk on a site-disordered one-dimensional lattice: photon subdiffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:031115. [PMID: 16605508 DOI: 10.1103/physreve.73.031115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2005] [Indexed: 05/08/2023]
Abstract
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density f(t). Depending on the behavior of f(t) near t=0, diffusive and subdiffusive transports are predicted by the disorder expansion of the mean square-displacement and the effective medium approximation. Monte Carlo simulations confirm the anomalous diffusion of photons. To observe photon subdiffusion experimentally, we suggest a dielectric film stack for realization of a distribution f(t).
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Affiliation(s)
- MirFaez Miri
- Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159, Iran.
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Shvartsburg AB. Single-cycle waveforms and non-periodic waves in dispersive media (exactly solvable models). ACTA ACUST UNITED AC 1998. [DOI: 10.3367/ufnr.0168.199801e.0085] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2022]
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