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Frenkel M, Fedorets AA, Shcherbakov DV, Dombrovsky LA, Nosonovsky M, Bormashenko E. Branched droplet clusters and the Kramers theorem. Phys Rev E 2022; 105:055104. [PMID: 35706306 DOI: 10.1103/physreve.105.055104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 04/17/2022] [Indexed: 06/15/2023]
Abstract
Scaling laws inherent for polymer molecules are checked for the linear and branched chains constituting two-dimensional (2D) levitating microdroplet clusters condensed above the locally heated layer of water. We demonstrate that the dimensionless averaged end-to-end distance of the droplet chain r[over ¯] normalized by the averaged distance between centers of the adjacent droplets l[over ¯] scales as r[over ¯]/l[over ¯]∼n^{0.76}, where n is the number of links in the chain, which is close to the power exponent ¾, predicted for 2D polymer chains with excluded volume in the dilution limit. The values of the dimensionless Kuhn length b[over ̃]≅2.12±0.015 and of the averaged absolute value of the bond angle of the droplet chains |θ|[over ¯]=22.0±0.5^{0} are determined. Using these values we demonstrate that the predictions of the Kramers theorem for the gyration radius of branched polymers are valid also for the branched droplets' chains. We discuss physical interactions that explain both the high value of the power exponent and the applicability of the Kramers theorem including the effects of the excluded volume, surrounding droplet monomers, and the prohibition of extreme values of the bond angle.
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Affiliation(s)
- Mark Frenkel
- Department of Chemical Engineering, Engineering Faculty, Ariel University, Ariel 407000
| | - Alexander A Fedorets
- X-BIO Institute, University of Tyumen, 6 Volodarskogo St., Tyumen 625003, Russia
| | - Dmitry V Shcherbakov
- X-BIO Institute, University of Tyumen, 6 Volodarskogo St., Tyumen 625003, Russia
| | - Leonid A Dombrovsky
- Department of Chemical Engineering, Engineering Faculty, Ariel University, Ariel 407000
- X-BIO Institute, University of Tyumen, 6 Volodarskogo St., Tyumen 625003, Russia
- Joint Institute for High Temperatures, 17A Krasnokazarmennaya St., Moscow 111116, Russia
| | - Michael Nosonovsky
- X-BIO Institute, University of Tyumen, 6 Volodarskogo St., Tyumen 625003, Russia
- Mechanical Engineering, University of Wisconsin-Milwaukee, 3200 North Cramer St., Milwaukee, Wisconsin 53211, USA
| | - Edward Bormashenko
- Department of Chemical Engineering, Engineering Faculty, Ariel University, Ariel 407000
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Liang Y, Sandev T, Lenzi EK. Reaction and ultraslow diffusion on comb structures. Phys Rev E 2020; 101:042119. [PMID: 32422761 DOI: 10.1103/physreve.101.042119] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 03/20/2020] [Indexed: 11/07/2022]
Abstract
A two-dimensional (2D) comb model is proposed to characterize reaction-ultraslow diffusion of tracers both in backbones (x direction) and side branches (y direction) of the comblike structure with two memory kernels. The memory kernels include Dirac delta, power-law, and logarithmic and inverse Mittag-Leffler (ML) functions, which can also be considered as the structural functions in the time structural derivative. Based on the comb model, ultraslow diffusion on a fractal comb structure is also investigated by considering spatial fractal geometry of the backbone volume. The mean squared displacement (MSD) and the corresponding concentration of the tracers, i.e., the solution of the comb model, are derived for reactive and conservative tracers. For a fractal structure of backbones, the derived MSDs and corresponding solutions depend on the backbone's fractal dimension. The proposed 2D comb model with different kernel functions is feasible to describe ultraslow diffusion in both the backbone and side branches of the comblike structure.
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Affiliation(s)
- Yingjie Liang
- Key Laboratory of Coastal Disaster and Defence of Ministry of Education, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 211100, China
| | - Trifce Sandev
- Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bulevar Krste Misirkov 2, 1000 Skopje, Macedonia; Institute of Physics & Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany; and Institute of Physics, Faculty of Natural Sciences and Mathematics, Saints Cyril and Methodius University, Arhimedova 3, 1000 Skopje, Macedonia
| | - Ervin Kaminski Lenzi
- Departmento de Fisica, Universidade Estadual de Ponta Grossa, Avenida Carlos Cavalcanti 4748, 84030-900 Ponta Grossa, Paraná, Brazil
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Abstract
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study two generalizations of comb models and present a generic method to obtain their transport properties. The first is a continuous time random walk on a many dimensional m + n comb, where m and n are the dimensions of the backbone and branches, respectively. We observe subdiffusion, ultra-slow diffusion and random localization as a function of n. The second deals with a quantum particle in the 1 + 1 comb. It turns out that the comb geometry leads to a power-law relaxation, described by a wave function in the framework of the Schrödinger equation.
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Sarracino A, Vulpiani A. On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems. CHAOS (WOODBURY, N.Y.) 2019; 29:083132. [PMID: 31472486 DOI: 10.1063/1.5110262] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Accepted: 08/08/2019] [Indexed: 06/10/2023]
Abstract
We review generalized fluctuation-dissipation relations, which are valid under general conditions even in "nonstandard systems," e.g., out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperturbed dynamics. In these relations, typically, one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.
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Affiliation(s)
- A Sarracino
- Dipartimento di Ingegneria, Università della Campania "L. Vanvitelli," via Roma 29, 81031 Aversa (CE), Italy
| | - A Vulpiani
- Dipartimento di Fisica, Università Sapienza-p.le A. Moro 2, 00185 Roma, Italy
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Abstract
The dynamics of an initial wave packet affected by random noise is considered in the framework of a comb model. The model is relevant to a diffusion problem in neurons where the transport of ions can be accelerated by an external random field due to synapse fluctuations. In the present specific case, it acts as boundary conditions, which lead to a reaction transport equation with multiplicative noise. The temporal behavior of the mean squared displacement is estimated analytically, and it is shown that the spreading of the initial wave packet corresponds to Richardson diffusion.
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Cecconi F, Puglisi A, Sarracino A, Vulpiani A. Anomalous mobility of a driven active particle in a steady laminar flow. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:264002. [PMID: 29762125 DOI: 10.1088/1361-648x/aac4f0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study, via extensive numerical simulations, the force-velocity curve of an active particle advected by a steady laminar flow, in the nonlinear response regime. Our model for an active particle relies on a colored noise term that mimics its persistent motion over a time scale [Formula: see text]. We find that the active particle dynamics shows non-trivial effects, such as negative differential and absolute mobility (NDM and ANM, respectively). We explore the space of the model parameters and compare the observed behaviors with those obtained for a passive particle ([Formula: see text]) advected by the same laminar flow. Our results show that the phenomena of NDM and ANM are quite robust with respect to the details of the considered noise: in particular for finite [Formula: see text] a more complex force-velocity relation can be observed.
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Affiliation(s)
- F Cecconi
- CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy
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Méndez V, Iomin A, Campos D, Horsthemke W. Mesoscopic description of random walks on combs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062112. [PMID: 26764637 DOI: 10.1103/physreve.92.062112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2015] [Indexed: 06/05/2023]
Abstract
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for the effect of the branches by renormalizing the waiting time probability distribution function for the motion along the backbone. We analyze the overall diffusion properties along the backbone and find normal diffusion, anomalous diffusion, and stochastic localization (diffusion failure), respectively, depending on the characteristics of the continuous time random walk along the branches, and compare our analytical results with stochastic simulations.
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Affiliation(s)
- Vicenç Méndez
- Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | | | - Daniel Campos
- Grup de Física Estadística, Departament de Física, Facultat de Ciències, Edifici Cc, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Werner Horsthemke
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275-0314, USA
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Forte G, Cecconi F, Vulpiani A. Transport and fluctuation-dissipation relations in asymptotic and preasymptotic diffusion across channels with variable section. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062110. [PMID: 25615047 DOI: 10.1103/physreve.90.062110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2014] [Indexed: 06/04/2023]
Abstract
We study the asymptotic and preasymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient D(eff) is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one-dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the preasymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes.
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Affiliation(s)
- Giuseppe Forte
- Dipartimento di Fisica Università di Roma "Sapienza," Piazzale Aldo Moro 2, I-00185 Roma, Italy
| | - Fabio Cecconi
- CNR-Istituto dei Sistemi Complessi (ISC), Via dei Taurini 19, I-00185 Roma, Italy
| | - Angelo Vulpiani
- Dipartimento di Fisica Università di Roma "Sapienza," Piazzale Aldo Moro 2, I-00185 Roma, Italy and CNR-Istituto dei Sistemi Complessi (ISC), Piazzale Aldo Moro 2, I-00185 Roma, Italy
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