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García-Valladares G, Plata CA, Prados A. Buckling in a rotationally invariant spin-elastic model. Phys Rev E 2023; 107:014120. [PMID: 36797953 DOI: 10.1103/physreve.107.014120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
Scanning tunneling microscopy experiments have revealed a spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between elastic and internal, electronic, degrees of freedom have been proposed to understand this phenomenon. Nevertheless, these models are not fully consistent with the classical theory of elasticity, since they do not preserve rotational invariance. Herein, we develop and analyze an alternative classical spin-elastic model that preserves rotational invariance while giving a qualitative account of the rippled-to-buckled transition. By integrating over the internal degrees of freedom, an effective free energy for the elastic modes is derived, which only depends on the curvature. Minimization of this free energy gives rise to the emergence of different mechanical phases, whose thermodynamic stability is thoroughly analyzed, both analytically and numerically. All phases are characterized by a spatially homogeneous curvature, which plays the role of the order parameter for the rippled-to-buckled transition, in both the one- and two-dimensional cases. In the latter, our focus is put on the honeycomb lattice, which is representative of actual graphene.
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Affiliation(s)
| | - Carlos A Plata
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
| | - Antonio Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, Spain
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2
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Moslonka C, Sekimoto K. Martingale-induced local invariance in progressive quenching. Phys Rev E 2022; 105:044146. [PMID: 35590610 DOI: 10.1103/physreve.105.044146] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 02/24/2022] [Indexed: 06/15/2023]
Abstract
Progressive quenching (PQ) is a stochastic process during which one fixes, one after another, the degrees of freedom of a globally coupled Ising spin system while letting it thermalize through a heat bath. It has previously been shown that during PQ, the mean equilibrium spin value follows a martingale process and this process can characterize the memory of the system. In the present study, we find that the aforementioned martingale implies a local invariance of the path weight for the total quenched magnetization, the Markovian process whose increment is the spin that is fixed last. Consequently, PQ lets the probability distribution for the total quenched magnetization evolve while keeping the Boltzmann-like factor, or a canonical structure, under constraint, which consists of a path-independent potential and a path-counting entropy. Moreover, when the PQ starts from full equilibrium, the probability distribution at each stage of PQ is found to be the limit distribution of what we call recycled quenching, the process in which a randomly chosen quenched spin is unquenched after a single step of PQ. The local invariance is directly derived from the martingale property, and not from other known theorems on martingale processes.
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Affiliation(s)
- Charles Moslonka
- Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, Université PSL 10 rue Vauquelin, 75005 Paris, France
| | - Ken Sekimoto
- Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, Université PSL 10 rue Vauquelin, 75005 Paris, France
- Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université de Paris, 10 Rue Alice Domon et Léonie Duquet, 75013 Paris, France
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Thibado PM, Kumar P, Singh S, Ruiz-Garcia M, Lasanta A, Bonilla LL. Fluctuation-induced current from freestanding graphene. Phys Rev E 2020; 102:042101. [PMID: 33212603 DOI: 10.1103/physreve.102.042101] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2020] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
At room temperature, micron-sized sheets of freestanding graphene are in constant motion, even in the presence of an applied bias voltage. We quantify the out-of-plane movement by collecting the displacement current using a nearby small-area metal electrode and present an Ito-Langevin model for the motion coupled to a circuit containing diodes. Numerical simulations show that the system reaches thermal equilibrium and the average rates of heat and work provided by stochastic thermodynamics tend quickly to zero. However, there is power dissipated by the load resistor, and its time average is exactly equal to the power supplied by the thermal bath. The exact power formula is similar to Nyquist's noise power formula, except that the rate of change of diode resistance significantly boosts the output power, and the movement of the graphene shifts the power spectrum to lower frequencies. We have calculated the equilibrium average of the power by asymptotic and numerical methods. Excellent agreement is found between experiment and theory.
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Affiliation(s)
- P M Thibado
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - P Kumar
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Surendra Singh
- Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - M Ruiz-Garcia
- Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - A Lasanta
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Departamento de Álgebra, Facultad de Educación, Economía y Tecnología de Ceuta, Universidad de Granada, E-51001 Ceuta, Spain
| | - L L Bonilla
- G. Millán Institute for Fluid Dynamics, Nanoscience and Industrial Mathematics and Department of Mathematics, Universidad Carlos III de Madrid, 28911 Leganés, Spain
- Courant Institute for Mathematical Sciences, New York University, New York, New York 10012, USA
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Ruiz-Garcia M, Bonilla LL, Prados A. Bifurcation analysis and phase diagram of a spin-string model with buckled states. Phys Rev E 2018; 96:062147. [PMID: 29347384 DOI: 10.1103/physreve.96.062147] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2017] [Indexed: 11/07/2022]
Abstract
We analyze a one-dimensional spin-string model, in which string oscillators are linearly coupled to their two nearest neighbors and to Ising spins representing internal degrees of freedom. String-spin coupling induces a long-range ferromagnetic interaction among spins that competes with a spin-spin antiferromagnetic coupling. As a consequence, the complex phase diagram of the system exhibits different flat rippled and buckled states, with first or second order transition lines between states. This complexity translates to the two-dimensional version of the model, whose numerical solution has been recently used to explain qualitatively the rippled to buckled transition observed in scanning tunneling microscopy experiments with suspended graphene sheets. Here we describe in detail the phase diagram of the simpler one-dimensional model and phase stability using bifurcation theory. This gives additional insight into the physical mechanisms underlying the different phases and the behavior observed in experiments.
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Affiliation(s)
- M Ruiz-Garcia
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain.,Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - L L Bonilla
- Gregorio Millán Institute for Fluid Dynamics, Nanoscience, and Industrial Mathematics, and Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
| | - A Prados
- Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080, Sevilla, Spain
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Caruel M, Truskinovsky L. Statistical mechanics of the Huxley-Simmons model. Phys Rev E 2016; 93:062407. [PMID: 27415298 DOI: 10.1103/physreve.93.062407] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2015] [Indexed: 06/06/2023]
Abstract
The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.
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Affiliation(s)
- M Caruel
- MSME, CNRS-UMR 8208, 61 Avenue du Général de Gaulle, 94010 Créteil, France
| | - L Truskinovsky
- LMS, CNRS-UMR 7649, Ecole Polytechnique, 91128 Palaiseau Cedex, France
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Prados A, Carpio A, Bonilla LL. Spin-oscillator model for the unzipping of biomolecules by mechanical force. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021919. [PMID: 23005797 DOI: 10.1103/physreve.86.021919] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2012] [Revised: 07/08/2012] [Indexed: 06/01/2023]
Abstract
A spin-oscillator system models unzipping of biomolecules (such as DNA, RNA, or proteins) subject to an external force. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value F(c) of an applied external force F, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates, whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to F-F(c) as in an Arrhenius law.
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Affiliation(s)
- A Prados
- Física Teórica, Universidad de Sevilla Apartado de Correos 1065, E-41080 Sevilla, Spain
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