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Mangioni SE, dell'Erba MG, Combi B. Structure formation in a conserved mass model of a set of individuals interacting with attractive and repulsive forces. Phys Rev E 2021; 104:014212. [PMID: 34412252 DOI: 10.1103/physreve.104.014212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2019] [Accepted: 06/29/2021] [Indexed: 11/07/2022]
Abstract
We study a set of interacting individuals that conserve their total mass. In order to describe its dynamics we resort to mesoscopic equations of reaction diffusion including currents driven by attractive and repulsive forces. For the mass conservation we consider a linear response parameter that maintains the mass in the vicinity of a optimal value which is determined by the set. We use the reach and intensity of repulsive forces as control parameters. When sweeping a wide range of parameter space we find a great diversity of localized structures, stationary as well as other ones with cyclical and chaotic dynamics. We compare our results with real situations.
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Affiliation(s)
- Sergio E Mangioni
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| | - Matías G dell'Erba
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Argentina
| | - Bruno Combi
- IFIMAR (Universidad Nacional de Mar del Plata and CONICET), Deán Funes 3350, B7602AYL Mar del Plata, Argentina
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2
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Abstract
We study the dynamics of a system of overdamped Brownian particles governed by the generalized stochastic Smoluchowski equation associated with a generalized form of entropy and involving a long-range potential of interaction [P.H. Chavanis, Entropy 17, 3205 (2015)]. We first neglect fluctuations and provide a macroscopic description of the system based on the deterministic mean field Smoluchowski equation. We then take fluctuations into account and provide a mesoscopic description of the system based on the stochastic mean field Smoluchowski equation. We establish the main properties of this equation and derive the Kramers escape rate formula, giving the lifetime of a metastable state, from the theory of instantons. We relate the properties of the generalized stochastic Smoluchowski equation to a principle of maximum dissipation of free energy. We also discuss the connection with the dynamical density functional theory of simple liquids.
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Kharchenko VO, Kharchenko DO, Yanovsky VV. Nano-sized Adsorbate Structure Formation in Anisotropic Multilayer System. NANOSCALE RESEARCH LETTERS 2017; 12:337. [PMID: 28482649 PMCID: PMC5419960 DOI: 10.1186/s11671-017-2096-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2016] [Accepted: 04/20/2017] [Indexed: 05/15/2023]
Abstract
In this article, we study dynamics of adsorbate island formation in a model plasma-condensate system numerically. We derive the generalized reaction-diffusion model for adsorptive multilayer system by taking into account anisotropy in transfer of adatoms between neighbor layers induced by electric field. It will be found that with an increase in the electric field strength, a structural transformation from nano-holes inside adsorbate matrix toward separated nano-sized adsorbate islands on a substrate is realized. Dynamics of adsorbate island sizes and corresponding distributions are analyzed in detail. This study provides an insight into details of self-organization of adatoms into nano-sized adsorbate islands in anisotropic multilayer plasma-condensate systems.
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Affiliation(s)
- Vasyl O. Kharchenko
- Institute of Applied Physics, National Academy of Sciences of Ukraine, 58 Petropavlivska St., Sumy, Ukraine
| | - Dmitrii O. Kharchenko
- Institute of Applied Physics, National Academy of Sciences of Ukraine, 58 Petropavlivska St., Sumy, Ukraine
| | - Vladimir V. Yanovsky
- Institute for Single Crystals, National Academy of Sciences of Ukraine, 60 Nauky Avenue, Kharkiv, Ukraine
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Bozdech S, Krischer K, Crespo-Yapur DA, Savinova E, Bonnefont A. 1/f 2 noise in bistable electrocatalytic reactions on mesoscale electrodes. Faraday Discuss 2016; 193:187-205. [PMID: 27711827 DOI: 10.1039/c6fd00115g] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
The formation of a self-organized spatial domain during current-controlled CO oxidation, a kinetically bistable reaction, is investigated experimentally and by deterministic simulations as a function of the electrode size and of the supporting electrolyte concentration. Decreasing the microelectrode size leads to the suppression of the spatial instability at the electrode and thus stabilizes the S-NDR branch of the reaction. The critical microelectrode size capable of supporting sustained domain formation is shown to be strongly affected by the sulfuric acid concentration, the characteristic time of the positive feedback loop increasing with the sulfate concentration. Furthermore, we demonstrate that for microelectrode diameters close to the instability threshold, small amplitude electrochemical potential fluctuations appear in the system. These potential fluctuations cannot be captured by deterministic mathematical models and are attributed to a strong enhancement of molecular fluctuations or intrinsic noise in the vicinity of the spatial instability. Analysis of the electrochemical noise revealed a 1/f 2 frequency dependence and several common features with neuronal shot noise.
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Affiliation(s)
- S Bozdech
- Institut de Chimie et Procédés pour l'Energie, l'Environnement et la Santé, UMR 7515 of CNRS-Université de Strasbourg-ECPM, 25 rue Becquerel, 67087 Strasbourg, France
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Ooshida T, Goto S, Matsumoto T, Otsuki M. Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids. Phys Rev E 2016; 94:022125. [PMID: 27627264 DOI: 10.1103/physreve.94.022125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2016] [Indexed: 06/06/2023]
Abstract
As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, a displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the analytical calculation is to relate the displacement correlation tensor, which is a kind of four-point space-time correlation, to the Lagrangian two-time correlation of the deformation gradient tensor. Tensorial treatment of the statistical quantities, including the displacement correlation itself, allows capturing the vortical structure of the cooperative motion. The calculated displacement correlation also implies a negative long-time tail in the velocity autocorrelation, which is a manifestation of the cage effect. Both the longitudinal and transverse components of the displacement correlation are found to be expressible in terms of a similarity variable, suggesting that the cages are nested to form a self-similar structure in the space-time.
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Affiliation(s)
- Takeshi Ooshida
- Department of Mechanical and Aerospace Engineering, Tottori University, Tottori 680-8552, Japan
| | - Susumu Goto
- Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Takeshi Matsumoto
- Division of Physics and Astronomy, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Michio Otsuki
- Department of Materials Science, Shimane University, Matsue 690-8504, Japan
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7
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Mesoscale model for heterogeneous catalysis based on the principle of compromise in competition. Chem Eng Sci 2016. [DOI: 10.1016/j.ces.2016.03.019] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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8
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Reigada R, Mikhailov AS. Equilibrium microphase separation in the two-leaflet model of lipid membranes. Phys Rev E 2016; 93:010401. [PMID: 26871009 DOI: 10.1103/physreve.93.010401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2015] [Indexed: 06/05/2023]
Abstract
Because of the coupling between local lipid composition and the thickness of the membrane, microphase separation in two-component lipid membranes can take place; such effects may underlie the formation of equilibrium nanoscale rafts. Using a kinetic description, this phenomenon is analytically and numerically investigated. The phase diagram is constructed through the stability analysis for linearized kinetic equations, and conditions for microphase separation are discussed. Simulations of the full kinetic model reveal the development of equilibrium membrane nanostructures with various morphologies from the initial uniform state.
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Affiliation(s)
- Ramon Reigada
- Departament de Química Física i Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, Avinguda Diagonal 647, 08028 Barcelona, Spain
| | - Alexander S Mikhailov
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
- Department of Mathematics and Life Sciences, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8530, Japan
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Wettmann L, Bonny M, Kruse K. Effects of molecular noise on bistable protein distributions in rod-shaped bacteria. Interface Focus 2014; 4:20140039. [PMID: 25485085 DOI: 10.1098/rsfs.2014.0039] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The distributions of many proteins in rod-shaped bacteria are far from homogeneous. Often they accumulate at the cell poles or in the cell centre. At the same time, the copy number of proteins in a single cell is relatively small making the patterns noisy. To explore limits to protein patterns due to molecular noise, we studied a generic mechanism for spontaneous polar protein assemblies in rod-shaped bacteria, which are based on cooperative binding of proteins to the cytoplasmic membrane. For mono-polar assemblies, we find that the switching time between the two poles increases exponentially with the cell length and with the protein number. This feature could be beneficial to organelle maintenance in ageing bacteria.
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Affiliation(s)
- L Wettmann
- Theoretische Physik , Universität des Saarlandes , Postfach 151150, 66041 Saarbrücken , Germany
| | - M Bonny
- Theoretische Physik , Universität des Saarlandes , Postfach 151150, 66041 Saarbrücken , Germany
| | - K Kruse
- Theoretische Physik , Universität des Saarlandes , Postfach 151150, 66041 Saarbrücken , Germany
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Pazzona FG, Demontis P, Suffritti GB. Thermodynamics of the one-dimensional parallel Kawasaki model: exact solution and mean-field approximations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022118. [PMID: 25215700 DOI: 10.1103/physreve.90.022118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2014] [Indexed: 06/03/2023]
Abstract
The adsorption isotherm for the recently proposed parallel Kawasaki (PK) lattice-gas model [Phys. Rev. E 88, 062144 (2013)] is calculated exactly in one dimension. To do so, a third-order difference equation for the grand-canonical partition function is derived and solved analytically. In the present version of the PK model, the attraction and repulsion effects between two neighboring particles and between a particle and a neighboring empty site are ruled, respectively, by the dimensionless parameters ϕ and θ. We discuss the inflections induced in the isotherms by situations of high repulsion, the role played by finite lattice sizes in the emergence of substeps, and the adequacy of the two most widely used mean-field approximations in lattice gases, namely, the Bragg-Williams and the Bethe-Peierls approximations.
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Affiliation(s)
- Federico G Pazzona
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, 07100 Sassari, Italy
| | - Pierfranco Demontis
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, 07100 Sassari, Italy
| | - Giuseppe B Suffritti
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, 07100 Sassari, Italy
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Pazzona FG, Demontis P, Suffritti GB. Conciliating synchronicity with spatial discretization, exclusion, interactions, and detailed balance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062114. [PMID: 24483393 DOI: 10.1103/physreve.88.062114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2013] [Indexed: 06/03/2023]
Abstract
The construction of a discrete stochastic system of interacting particles that evolves through a fully synchronous evolution rule while satisfying detailed balance is a highly demanding task. As a consequence, the presence of nontrivial interaction fields can make synchronicity and thermodynamic equilibrium look as two conflicting counterparts. We show that, with the proper prescriptions, the process of migration of particles in a lattice of mutually exclusive nodes can be simulated with a fully synchronous algorithm, which we call parallel Kawasaki dynamics (PKD), that incorporates site exclusion, local interactions, and detailed balance without the need of system partitioning schemes. We show that the underlying pseudo-Hamiltonian (which is derived from the PKD dynamics instead of being assumed a priori as usual in a sequential Monte Carlo scheme) is temperature dependent and causes the resulting equilibrium properties to differ substantially from the conventional hopping model when the system is near critical conditions.
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Affiliation(s)
- Federico G Pazzona
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, via Vienna 2, I-07100 Sassari, Italy
| | - Pierfranco Demontis
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, via Vienna 2, I-07100 Sassari, Italy
| | - Giuseppe B Suffritti
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari, via Vienna 2, I-07100 Sassari, Italy
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12
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Pazzona FG, Demontis P, Suffritti GB. Synchronous equilibrium model for the diffusion of mutually exclusive particles in a heterogeneous lattice of adsorption sites. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:063306. [PMID: 23848805 DOI: 10.1103/physreve.87.063306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2013] [Indexed: 06/02/2023]
Abstract
Through straight synchronization and proper manipulation of a sequential Monte Carlo glass-forming rule introduced by Fröbose and Jäckle [J. Stat. Phys. 42, 551 (1986)], we constructed a synchronous, non-glass-forming rule for diffusion of mutually exclusive particles in a lattice of adsorption sites. The rule satisfies detailed balance in the presence of both homogeneous and heterogeneous adsorption energies. Our model differs from the usual lattice-gas cellular automata diffusion rules in that the mutual exclusion holds on the lattice sites rather than on the channels which connect neighboring sites, and from the mass-conserving cellular automata rules in the use of a no-partitioning scheme. The first aim of this work is to show that, although some prescriptions in the synchronous rule are introduced just to allow that both detailed balance and mutual exclusion can coexist with synchronicity, the diffusion process produced by the rule is not anomalous so that the rule can be regarded as a diffusion model. We then compare the diffusion isotherms of several test systems with the ones obtained by means of sequential Monte Carlo simulations of Arrhenius jumps of particles on a lattice. Finally, we apply the rule to the case of a (100) fcc model surface and estimate the amount of time correlation in the migration process, and show that the synchronous rule produces higher correlations and slightly lower diffusivity than the sequential Monte Carlo counterpart.
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Affiliation(s)
- Federico G Pazzona
- Dipartimento di Chimica e Farmacia, Università degli Studi di Sassari and Consorzio Interuniversitario Nazionale per la Scienza e Tecnologia dei Materiali (INSTM), Unità di Ricerca di Sassari, via Vienna, 2, I-07100 Sassari, Italy.
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13
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Kharchenko VO, Kharchenko DO. Nanosize pattern formation in overdamped stochastic reaction-diffusion systems with interacting adsorbate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041143. [PMID: 23214565 DOI: 10.1103/physreve.86.041143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2012] [Revised: 09/17/2012] [Indexed: 05/28/2023]
Abstract
We study overdamped stochastic model describing adsorption or desorption processes with nonequilibrium chemical reactions on the surface. It is shown that internal noise satisfying the fluctuation-dissipation relation at small intensities governs transitions between ordered thermodynamical dense and diluted phases. These phase transitions are characterized by an increase of fluctuations of the coverage filed and correlation radius of spatial modulation. At large noise intensity a transition towards disordered phase with chaotic spatial configuration is realized. We have shown that organized stationary patterns are of nanometer range. We define that both period of stationary structures and corresponding correlation radius depend on the noise intensity.
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Affiliation(s)
- Vasyl O Kharchenko
- Institute of Applied Physics, National Academy of Sciences of Ukraine, 58 Petropavlivska St., 40000 Sumy, Ukraine.
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14
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Rao T, Zhang Z, Hou ZH, Xin HW. Coarse-grained Simulations of Chemical Oscillation in Lattice Brusselator System. CHINESE J CHEM PHYS 2011. [DOI: 10.1088/1674-0068/24/04/425-433] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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15
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Mangioni SE, Deza RR. Nonequilibrium pattern formation by subdominant attractive forces: a simple model and a stabilization strategy by means of noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:042101. [PMID: 21230330 DOI: 10.1103/physreve.82.042101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2010] [Indexed: 05/30/2023]
Abstract
We introduce a simple model describing a mechanism for transient pattern formation driven by subdominant attractive forces. The patterns can be stabilized if they are confined by means of a particular multiplicative noise into the region where such mechanism is active. The scope of the results appears to transcend the original application context.
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Affiliation(s)
- Sergio E Mangioni
- IFIMAR, UNMdP-CONICET, Deán Funes 3350, B7602AYL Mar del Plata, Argentina
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16
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Guo X, De Decker Y, Evans JW. Metastability in Schloegl's second model for autocatalysis: Lattice-gas realization with particle diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:021121. [PMID: 20866789 DOI: 10.1103/physreve.82.021121] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2009] [Revised: 07/24/2010] [Indexed: 05/29/2023]
Abstract
We analyze metastability associated with a discontinuous nonequilibrium phase transition in a stochastic lattice-gas realization of Schloegl's second model for autocatalysis. This model realization involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires an adjacent diagonal pair of particles. This model, also known as the quadratic contact process, exhibits discontinuous transition between a populated active state and a particle-free vacuum or "poisoned" state, as well as generic two-phase coexistence. The poisoned state exists for all particle annihilation rates p>0 and hop rates h≥0 and is an absorbing state in the sense of Markovian processes. The active or reactive steady state exists only for p below a critical value, p{e}=p{e}(h) , but a metastable extension appears for a range of higher p up to an effective upper spinodal point, p{s+}=p{s+}(h) (i.e., p{s+}>p{e} ). For selected h , we assess the location of p{s+}(h) by characterizing both the poisoning kinetics and the propagation of interfaces separating vacuum and active states as a function of p .
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Affiliation(s)
- Xiaofang Guo
- Department of Physics & Astronomy, Iowa State University, Ames, 50011, USA
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Reversible formation of nanodomains in monolayers of DPPC studied by kinetic modeling. Biophys J 2009; 96:4896-905. [PMID: 19527648 DOI: 10.1016/j.bpj.2009.03.041] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2008] [Revised: 03/15/2009] [Accepted: 03/23/2009] [Indexed: 12/13/2022] Open
Abstract
Dipalmitoylphosphatidylcholine (DPPC) is the most abundant component in pulmonary surfactants and is believed to be responsible for maintaining low surface tension in alveoli during breathing. In this work, a kinetic model is introduced that describes the phase separation in DPPC films that produces the liquid-condensed (LC) and liquid-expanded (LE) fractions, which differ according to the area density of DPPC. The phase separation in an initially homogeneous film has been investigated numerically. Furthermore, explicit simulations of periodic compression-expansion cycles are reported. In this process, a moderate change of the surface area resulted in a dramatic change in the total amount of LC fraction, as well as in the surface morphology. Depending on the extent of the film's compression, the simulated surface morphologies comprised individual nanosized LC domains embedded in the LE fraction, interconnected networks of such domains, or continuous LC films with nanopores. Equilibration of the total area of the LC nanodomains occurred over a few milliseconds, indicating that the rate of the LE-LC phase transformation is sufficient for maintaining low surface tension during breathing, and that nanoscale LC domains are likely to play a major role in this process. Unlike the total content of the LC fraction, which stabilized quickly, the average size of LC nanodomains showed a tendency to increase slowly, at a rate determined by the diffusivity of DPPC. The computed average domain size seems to be compatible with published experiments for DPPC films. The numeric results also elucidate the distinction between thermodynamically determined and kinetically limited structural properties during phase separation in the major structure-forming component of pulmonary surfactants.
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Mikhailov AS, Ertl G. Nonequilibrium microstructures in reactive monolayers as soft matter systems. Chemphyschem 2009; 10:86-100. [PMID: 19040249 DOI: 10.1002/cphc.200800277] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Chemical systems provide classical examples of nonequilibrium pattern formation. Reactions in weak aqueous solutions, such as the extensively investigated Belousov-Zhabotinsky reaction, demonstrate a rich variety of patterns, ranging from travelling fronts to rotating spiral waves and chemical turbulence. Pattern formation in such systems is based on interplay between the reactions and diffusion. Intrinsically, this puts a restriction on the minimum length scale of the developing structures, which cannot be shorter than the diffusion length of the reactants. However, much smaller nonequilibrium structures, with characteristic lengths reaching down to nanoscales, are also possible. They are found in reactive soft matter, where energetic interactions between molecules are present as well. In these systems, chemical reactions and diffusion interfere with phase transitions, yielding active, stationary or dynamic microstructures. Nonequilibrium soft-matter microstructures are of fundamental importance for biological cells and may have interesting engineering applications. In this Minireview, we focus on the microstructures found in reactive soft-matter monolayers at solid surfaces or liquid-air interfaces.
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Affiliation(s)
- Alexander S Mikhailov
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin-Dahlem, Germany.
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Guo X, Liu DJ, Evans JW. Schloegl's second model for autocatalysis with particle diffusion: Lattice-gas realization exhibiting generic two-phase coexistence. J Chem Phys 2009; 130:074106. [PMID: 19239283 DOI: 10.1063/1.3074308] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We analyze a discontinuous nonequilibrium phase transition between an active (or reactive) state and a poisoned (or extinguished) state occurring in a stochastic lattice-gas realization of Schloegl's second model for autocatalysis. This realization, also known as the quadratic contact process, involves spontaneous annihilation, autocatalytic creation, and diffusion of particles on a square lattice, where creation at empty sites requires a suitable nearby pair of particles. The poisoned state exists for all annihilation rates p>0 and is an absorbing particle-free "vacuum" state. The populated active steady state exists only for p below a critical value, p(e). If p(f) denotes the critical value below which a finite population can survive, then we show that p(f)<p(e). This strict inequality contrasts a postulate of Durrett, and is a direct consequence of the occurrence of coexisting stable active and poisoned states for a finite range p(f)<or=p<or=p(e) (which shrinks with increasing diffusivity). This so-called generic two-phase coexistence markedly contrasts behavior in thermodynamic systems. However, one still finds metastability and nucleation phenomena similar to those in discontinuous equilibrium transitions.
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Affiliation(s)
- Xiaofang Guo
- Ames Laboratory, USDOE, Iowa State University, Ames, Iowa 50011, USA
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Ma J, Hou ZH, Xin HW. Coherent Resonance for Rate Oscillations During CO Oxidation on Pt(110) Surfaces: Interplay Between Internal and External Noise. CHINESE J CHEM PHYS 2008. [DOI: 10.1088/1674-0068/21/04/339-345] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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21
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Chapter 9 Non-linear Dynamics in Catalytic Reactions. ACTA ACUST UNITED AC 2008. [DOI: 10.1016/s1573-4331(08)00009-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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Juan M, Hou Z, Xin H. Theoretical Study on the Effects of Internal Noise for Rate Oscillations during CO Oxidation on Platinum(110) Surfaces. J Phys Chem A 2007; 111:11500-5. [DOI: 10.1021/jp073890e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Ma Juan
- Department of Chemical Physics, Hefei National Lab of Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Zhonghuai Hou
- Department of Chemical Physics, Hefei National Lab of Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Houwen Xin
- Department of Chemical Physics, Hefei National Lab of Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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Chatterjee A, Vlachos DG. Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes. J Chem Phys 2007; 127:034705. [PMID: 17655453 DOI: 10.1063/1.2748755] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Abstract
While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.
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Affiliation(s)
- Abhijit Chatterjee
- Center for Catalytic Science and Technology (CCST) and Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716, USA
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Pineda M, Schimansky-Geier L, Imbihl R. Fluctuation-induced phase transition in a spatially extended model for catalytic CO oxidation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061107. [PMID: 17677220 DOI: 10.1103/physreve.75.061107] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2006] [Revised: 03/25/2007] [Indexed: 05/16/2023]
Abstract
A reaction-diffusion master equation has been introduced in order to model the bistable CO oxidation on single crystal metal surfaces at high pressure where the diffusion length becomes small and local fluctuations are important. Analytical solutions can be found in a reduced one-component nonlinear master equation after applying the Weiss mean-field approximation together with the adiabatic elimination of oxygen. It is shown that the Weiss mean-field approximation predicts a symmetry-breaking bifurcation associated with a phase transition. The corresponding stationary solutions of the nonlinear master equation are supported by Gillespie-type Monte Carlo simulations.
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Affiliation(s)
- M Pineda
- Institut für Physikalische Chemie und Elektrochemie, Leibniz Universität Hannover, Callinstrasse 3-3a, D-30167 Hannover, Germany
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25
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Meacci G, Kruse K. Min-oscillations in Escherichia coli induced by interactions of membrane-bound proteins. Phys Biol 2007; 2:89-97. [PMID: 16204861 DOI: 10.1088/1478-3975/2/2/002] [Citation(s) in RCA: 48] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
During division it is of primary importance for a cell to correctly determine the site of cleavage. The bacterium Escherichia coli divides in the center, producing two daughter cells of equal size. Selection of the center as the correct division site is in part achieved by the Min-proteins. They oscillate between the two cell poles and thereby prevent division at these locations. Here, a phenomenological description of these oscillations is presented, where lateral interactions between proteins on the cell membrane play a key role. Solutions to the dynamic equations are compared to experimental findings. In particular, the temporal period of the oscillations is measured as a function of the cell length and found to be compatible with the theoretical prediction.
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Affiliation(s)
- Giovanni Meacci
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzerstr. 38, 01187 Dresden, Germany
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26
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Horntrop DJ. Spectral method study of domain coarsening. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:046703. [PMID: 17501012 DOI: 10.1103/physreve.75.046703] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2006] [Revised: 01/15/2007] [Indexed: 05/15/2023]
Abstract
The self-organization of particles in a two phase system in the coexistence region through a diffusive mechanism is known as Ostwald ripening. The late stage of Ostwald ripening is studied here through the use of a mesoscopic model in conjunction with a special configuration that allows for the direct measurement of system characteristics such as domain size. The mesoscopic model is a stochastic partial integrodifferential equation and is studied through the use of recently developed and benchmarked spectral schemes. The size of the growing region is not observed to increase as a power law in this model during the late stages of self-organization in contrast to the power law growth observed in simulations of the earlier stages of self-organization. The results included here also demonstrate the effect of adjusting the interparticle interaction on the morphological evolution of the system.
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Affiliation(s)
- David J Horntrop
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
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27
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Abstract
In the bacterium Escherichia coli, the Min-proteins show pronounced pole-to-pole oscillations. They are functional for suppressing cell division at the cell ends, leaving the center as the only possible site for division. Analyzing different models of Min-protein dynamics in a bacterial geometry, we find waves on the cytoplasmic membrane. Interestingly, the surface wave solutions of different models belong to different symmetry classes. We suggest that experiments on Min-protein surface waves in vitro are helpful in distinguishing between different classes of models of Min-protein dynamics.
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28
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Pineda M, Imbihl R, Schimansky-Geier L, Zülicke C. Theoretical analysis of internal fluctuations and bistability in CO oxidation on nanoscale surfaces. J Chem Phys 2006; 124:044701. [PMID: 16460194 DOI: 10.1063/1.2140709] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The bistable CO oxidation on a nanoscale surface is characterized by a limited number of reacting molecules on the catalytic area. Internal fluctuations due to finite-size effects are studied by the master equation with a Langmuir-Hinshelwood mechanism for CO oxidation. Analytical solutions can be found in a reduced one-component model after the adiabatic elimination of one variable which in our case is the oxygen coverage. It is shown that near the critical point, with decreasing surface area, one cannot distinguish between two macroscopically stable stationary states. This is a consequence of the large fluctuations in the coverage which occur on a fast time scale. Under these conditions, the transition times between the macroscopic states also are no longer separated from the short-time scale of the coverage fluctuations as is the case for large surface areas and far away from the critical point. The corresponding stationary solutions of the probability distribution and the mean first passage times calculated in the reduced model are supported by numerics of the full two-component model.
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Affiliation(s)
- M Pineda
- Institut für Physikalische Chemie und Elektrochemie, Universität Hannover, Callinstrasse 3-3a, D-30167 Hannover, Germany.
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29
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Lam R, Vlachos DG, Katsoulakis MA. Homogenization of mesoscopic theories: Effective properties of model membranes. AIChE J 2006. [DOI: 10.1002/aic.690480517] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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30
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Snyder MA, Vlachos DG. Molecular sieve valves driven by adsorbate-adsorbate interactions: hysteresis in permeation of microporous membranes. J Chem Phys 2005; 122:204706. [PMID: 15945763 DOI: 10.1063/1.1902949] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A recently derived mesoscopic framework describing activated micropore diffusion is employed to explore system criticality in microporous membranes under nonequilibrium conditions. Rapid exploration of parameter space, possible with this continuum framework, elucidates a novel temperature-induced ignition and extinction of the molecular flux under a macroscopic gradient in pressure (chemical potential). Deviation from equilibrium like phase behavior (i.e., shifting and narrowing of phase envelopes and double hysteresis) derives from asymmetry of the coupled boundaries of the nonequilibrium membrane. We confirm this new phase behavior, akin to "opening" and "closing" of a molecular valve, via gradient kinetic Monte Carlo simulations of thin one-dimensional and three-dimensional systems. The heat of adsorption, strength of adsorbate-adsorbate intermolecular forces, and chemical potential gradient are all shown to control 'valve' actuation, suggesting potential implications in chemical sensing and novel diffusion control.
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Affiliation(s)
- M A Snyder
- Department of Chemical Engineering, Center for Catalytic Science and Technology, University of Delaware, Newark, Delaware 19716-3110, USA
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31
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Hou Z, Rao T, Xin H. Effects of internal noise for rate oscillations during CO oxidation on platinum surfaces. J Chem Phys 2005; 122:134708. [PMID: 15847490 DOI: 10.1063/1.1874933] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have studied the influence of internal noise on the reaction rate oscillation during carbon-monoxide oxidation on single crystal platinum surfaces using chemical Langevin equations. Considering that the surface is divided into small well-mixed cells, we have focused on the dynamic behavior inside a single cell. Internal noise can induce rate oscillations and the performance of the stochastic rate oscillations shows double maxima with the variation of the internal noise intensity, demonstrating the occurrence of internal noise coherent biresonance. The relationship between such a phenomenon with the deterministic bifurcation features of the system is also discussed.
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Affiliation(s)
- Zhonghuai Hou
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.
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32
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Snyder M, Chatterjee A, Vlachos D. Net-event kinetic Monte Carlo for overcoming stiffness in spatially homogeneous and distributed systems. Comput Chem Eng 2005. [DOI: 10.1016/j.compchemeng.2004.09.016] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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33
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34
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De Decker Y, Mikhailov AS. Promoter-Induced Nonlinear Pattern Formation in Surface Chemical Reactions. J Phys Chem B 2004. [DOI: 10.1021/jp0485587] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yannick De Decker
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, C.P. 231. B-1050 Brussels, Belgium, and Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
| | - Alexander S. Mikhailov
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, C.P. 231. B-1050 Brussels, Belgium, and Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
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35
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Popescu MN, Dietrich S. Model for spreading of liquid monolayers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061602. [PMID: 15244580 DOI: 10.1103/physreve.69.061602] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2003] [Indexed: 05/24/2023]
Abstract
Manipulating fluids at the nanoscale within networks of channels or chemical lanes is a crucial challenge in developing small scale devices to be used in microreactors or chemical sensors. In this context, ultrathin (i.e., monolayer) films, experimentally observed in spreading of nanodroplets or upon extraction from reservoirs in capillary rise geometries, represent an extreme limit which is of physical and technological relevance since the dynamics is governed solely by capillary forces. In this work we use kinetic Monte Carlo (KMC) simulations to analyze in detail a simple, but realistic model proposed by Phys. Rev. Lett. 76, 86 (1996)]] for the two-dimensional spreading on homogeneous substrates of a fluid monolayer which is extracted from a reservoir. Our simulations confirm the previously predicted time dependence of the spreading, X ( t--> infinity ) =A square root of t, with X (t) as the average position of the advancing edge at time t, and they reveal a nontrivial dependence of the prefactor A on the strength U0 of interparticle attraction and on the fluid density C0 at the reservoir as well as an U0 -dependent spatial structure of the density profile of the monolayer. The asymptotic density profile at long time and large spatial scale is carefully analyzed within the continuum limit. We show that including the effect of correlations in an effective manner into the standard mean-field description leads to predictions both for the value of the threshold interaction above which phase segregation occurs and for the density profiles in excellent agreement with KMC simulation results.
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Affiliation(s)
- M N Popescu
- Max-Planck-Institut für Metallforschung, Heisenbergstrasse 3, D-70569 Stuttgart, Germany.
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36
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De Decker Y, Marbach H, Hinz M, Günther S, Kiskinova M, Mikhailov AS, Imbihl R. Promoter-induced reactive phase separation in surface reactions. PHYSICAL REVIEW LETTERS 2004; 92:198305. [PMID: 15169457 DOI: 10.1103/physrevlett.92.198305] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2003] [Indexed: 05/24/2023]
Abstract
Promoters are adsorbed mobile species which do not directly participate in a catalytic surface reaction, but can influence its rate. Often, they are characterized by strong attractive interactions with one of the reactants. We show that these conditions lead to a Turing instability of the uniform state and to the formation of reaction-induced periodic concentration patterns. Experimentally such patterns are observed in catalytic water formation on a Rh(110) surface in the presence of coadsorbed potassium.
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Affiliation(s)
- Y De Decker
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, C.P. 231. B-1050 Brussels, Belgium
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37
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Reigada R, Mikhailov AS, Sagués F. Nonequilibrium orientational patterns in two-component Langmuir monolayers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:041103. [PMID: 15169004 DOI: 10.1103/physreve.69.041103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2003] [Indexed: 05/24/2023]
Abstract
A model of a phase-separating two-component Langmuir monolayer in the presence of a photoinduced reaction interconverting two components is formulated. An interplay between phase separation, orientational ordering, and reaction is found to lead to a variety of nonequilibrium self-organized patterns, both stationary and traveling. Examples of the patterns, observed in numerical simulations, include flowing droplets, traveling stripes, wave sources, and vortex defects.
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Affiliation(s)
- Ramon Reigada
- Departament de Química-Física, Universitat de Barcelona, Avenida Diagonal 647, 08028 Barcelona, Spain
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38
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Mesoscopic Modeling of Surface Processes. ACTA ACUST UNITED AC 2004. [DOI: 10.1007/978-1-4419-8935-2_12] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/14/2023]
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39
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Matuszak D, Aranovich GL, Donohue MD. Lattice density functional theory of molecular diffusion. J Chem Phys 2004; 121:426-35. [PMID: 15260563 DOI: 10.1063/1.1756131] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A density functional theory of diffusion is developed for lattice fluids with molecular flux as a functional of the density distribution. The formalism coincides exactly with the generalized Ono-Kondo density functional theory when there is no gradient of chemical potential, i.e., at equilibrium. Away from equilibrium, it gives Fick's first law in the absence of a potential energy gradient, and it departs from Fickian behavior consistently with the Maxwell-Stefan formulation. The theory is applied to model a nanopore, predicting nonequilibrium phase transitions and the role of surface diffusion in the transport of capillary condensate.
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Affiliation(s)
- Daniel Matuszak
- Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, Maryland 21218, USA
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40
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Katsoulakis MA, Vlachos DG. Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles. J Chem Phys 2003. [DOI: 10.1063/1.1616513] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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41
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Katsoulakis MA, Majda AJ, Vlachos DG. Coarse-grained stochastic processes for microscopic lattice systems. Proc Natl Acad Sci U S A 2003; 100:782-7. [PMID: 12552105 PMCID: PMC298678 DOI: 10.1073/pnas.242741499] [Citation(s) in RCA: 89] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant length scales. Here a class of coarse-grained stochastic processes and corresponding Monte Carlo simulation methods, describing computationally feasible mesoscopic length scales, are derived directly from microscopic lattice systems. It is demonstrated below that the coarse-grained stochastic models can capture large-scale structures while retaining significant microscopic information. The requirement of detailed balance is used as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or computer time per executive event compared to microscopic Monte Carlo simulations.
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Affiliation(s)
- Markos A Katsoulakis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA
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42
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De Decker Y, Baras F, Kruse N, Nicolis G. Modeling the NO+H2 reaction on a Pt field emitter tip: Mean-field analysis and Monte Carlo simulations. J Chem Phys 2002. [DOI: 10.1063/1.1518961] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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43
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Liu DJ, Evans JW. Fluctuations and bistability in a “hybrid” atomistic model for CO oxidation on nanofacets: An effective potential analysis. J Chem Phys 2002. [DOI: 10.1063/1.1507105] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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44
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Sachs C, Hildebrand M, Völkening S, Wintterlin J, Ertl G. Reaction fronts in the oxidation of hydrogen on Pt(111): Scanning tunneling microscopy experiments and reaction–diffusion modeling. J Chem Phys 2002. [DOI: 10.1063/1.1453964] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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45
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Hildebrand M. Self-organized nanostructures in surface chemical reactions: Mechanisms and mesoscopic modeling. CHAOS (WOODBURY, N.Y.) 2002; 12:144-156. [PMID: 12779542 DOI: 10.1063/1.1448807] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Nanoscale patterns can form in reactive adsorbates on catalytic surfaces as a result of attractive lateral interactions. These structures can be described within a mesoscopic theory that is derived by coarse graining the microscopic master equation thus providing a link between microscopic lattice models and reaction-diffusion equations. Such mesoscopic models allow to systematically investigate mechanisms responsible for the formation of nanoscale nonequilibrium patterns in reactive condensed matter. We have found that stationary and traveling nanostructures may result from the interplay of the attractive lateral interactions and nonequilibrium reactions. Besides reviewing these results, a detailed investigation of a single reactive adsorbate in the presence of attractive lateral interactions and global coupling through the gas phase is presented. Finally, it is outlined how a mesoscopic theory should be constructed for a particular scanning tunneling microscopy experiment [the oxidation of hydrogen on a Pt(111) surface] in order to overcome the failure of a corresponding reaction-diffusion model to quantitatively reproduce the experiments. (c) 2002 American Institute of Physics.
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Affiliation(s)
- M. Hildebrand
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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46
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Wintterlin J. Microscopic aspects of pattern formation on surfaces. CHAOS (WOODBURY, N.Y.) 2002; 12:108-117. [PMID: 12779539 DOI: 10.1063/1.1448810] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Recent scanning tunneling microscopy (STM) work gives insight into microscopic processes of surface reactions that play a role for spatio-temporal pattern formation. STM allows to resolve adsorbed particles, follow their surface motion, and monitor reactions with other particles on the atomic scale. The data reveal pronounced deviations from the implicite assumptions of the reaction-diffusion equations traditionally used to model spatio-temporal patterns. In contrast to these descriptions, particles are often not randomly distributed, but cluster in islands because of attractive interactions, and particle hopping can be highly correlated. It is shown that such phenomena can even affect the macroscopic kinetics. The article also discusses a case where the atomic processes inside propagating reaction fronts could be resolved. Here particular strong interaction effects were observed, caused by hydrogen bonds between the reacting species. (c) 2002 American Institute of Physics.
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Affiliation(s)
- Joost Wintterlin
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
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47
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Majda AJ, Khouider B. Stochastic and mesoscopic models for tropical convection. Proc Natl Acad Sci U S A 2002; 99:1123-8. [PMID: 11830655 PMCID: PMC123720 DOI: 10.1073/pnas.032663199] [Citation(s) in RCA: 85] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
A new way to parametrize certain aspects of tropical convection through stochastic and mesoscopic models is developed here. The technical idea is to adapt tools from statistical physics and materials science to model important unresolved features of tropical convection. This new strategy consists of modeling the unresolved effects of convective inhibition in a coarse mesh mesoscopic parametrization through a "heat bath" model involving a stochastic spin flip model with very natural interaction rules for convective inhibition combined with a suitable external potential defined by the coarse mesh values. In turn, the values of the order parameter from this heat bath alter the vertical mass flux in regions of deep convection. Both stochastic and systematic deterministic mesoscopic parametrizations are developed here. The deterministic mesoscopic models derived in this fashion exhibit new phenomena such as multiple radiative equilibria in suitable parameter regimes. The simplest first numerical experiments reported here with the mesoscopic deterministic parametrization qualitatively reproduce several key features of the observational record regarding convectively coupled tropical waves. The systematic stochastic modeling strategy proposed here could also be very useful for capturing other features of tropical convection such as those involving cloud radiation feedbacks.
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Affiliation(s)
- Andrew J Majda
- Courant Institute of Mathematical Sciences and Center for Atmosphere and Ocean Sciences, New York University, New York, NY 10012, USA.
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48
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Lam R, Basak T, Vlachos DG, Katsoulakis MA. Validation of mesoscopic theory and its application to computing concentration dependent diffusivities. J Chem Phys 2001. [DOI: 10.1063/1.1415460] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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49
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Reichert C, Starke J, Eiswirth M. Stochastic model of CO oxidation on platinum surfaces and deterministic limit. J Chem Phys 2001. [DOI: 10.1063/1.1391255] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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50
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Sachs C, Hildebrand M, Volkening S, Wintterlin J, Ertl G. Spatiotemporal self-organization in a surface reaction: from the atomic to the mesoscopic scale. Science 2001; 293:1635-8. [PMID: 11533484 DOI: 10.1126/science.1062883] [Citation(s) in RCA: 157] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Scanning tunneling microscopy data revealed the atomic processes in propagating reaction fronts that occur in the catalytic oxidation of hydrogen on Pt(111). The fronts were also characterized on mesoscopic length scales with respect to their velocity and width. Simulations on the basis of a reaction-diffusion model reproduce the experimental findings qualitatively well. The quantitative comparison reveals the limitations of this traditional approach to modeling spatiotemporal pattern formation in nonlinear dynamics.
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Affiliation(s)
- C Sachs
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany
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