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Rohrbach PB, Kobayashi H, Scheichl R, Wilding NB, Jack RL. Multilevel simulation of hard-sphere mixtures. J Chem Phys 2022; 157:124109. [DOI: 10.1063/5.0102875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a mixture of size-asymmetric hard spheres, in the grand canonical ensemble. A three-level version of the method is compared with a previously-studied two-level version. The extra level interpolates between the full mixture and a coarse-grained description where only the large particles are present -- this is achieved by restricting the small particles to regions close to the large ones. The three-level method improves the performance of the estimator, at fixed computational cost. We analyse the asymptotic variance of the estimator, and discuss the mechanisms for the improved performance.
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Affiliation(s)
- Paul B Rohrbach
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge Department of Applied Mathematics and Theoretical Physics, United Kingdom
| | | | | | - Nigel B. Wilding
- School of Physics, University of Bristol School of Physics, United Kingdom
| | - Robert L. Jack
- DAMTP, University of Cambridge Department of Applied Mathematics and Theoretical Physics, United Kingdom
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Yadav M, Singh Y. Coarse-grained Hamiltonian and effective one component theory of colloidal suspensions. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.120233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/31/2022]
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Kobayashi H, Rohrbach PB, Scheichl R, Wilding NB, Jack RL. Critical point for demixing of binary hard spheres. Phys Rev E 2021; 104:044603. [PMID: 34781560 DOI: 10.1103/physreve.104.044603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2021] [Accepted: 09/22/2021] [Indexed: 11/07/2022]
Abstract
We use a two-level simulation method to analyze the critical point associated with demixing of binary hard-sphere mixtures. The method exploits an accurate coarse-grained model with two- and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble and matching to the universal form for the 3D Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions and the geometry of the underlying hard-sphere packings.
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Affiliation(s)
- Hideki Kobayashi
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Paul B Rohrbach
- DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Robert Scheichl
- Institute for Applied Mathematics, Heidelberg University, INF 205, 69120 Heidelberg, Germany.,Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom
| | - Nigel B Wilding
- H. H. Wills Physics Laboratory, University of Bristol, Royal Fort, Bristol BS8 1TL, United Kingdom
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.,DAMTP, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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Campos-Villalobos G, Boattini E, Filion L, Dijkstra M. Machine learning many-body potentials for colloidal systems. J Chem Phys 2021; 155:174902. [PMID: 34742191 DOI: 10.1063/5.0063377] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Simulations of colloidal suspensions consisting of mesoscopic particles and smaller species such as ions or depletants are computationally challenging as different length and time scales are involved. Here, we introduce a machine learning (ML) approach in which the degrees of freedom of the microscopic species are integrated out and the mesoscopic particles interact with effective many-body potentials, which we fit as a function of all colloid coordinates with a set of symmetry functions. We apply this approach to a colloid-polymer mixture. Remarkably, the ML potentials can be assumed to be effectively state-independent and can be used in direct-coexistence simulations. We show that our ML method reduces the computational cost by several orders of magnitude compared to a numerical evaluation and accurately describes the phase behavior and structure, even for state points where the effective potential is largely determined by many-body contributions.
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Affiliation(s)
- Gerardo Campos-Villalobos
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Emanuele Boattini
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Laura Filion
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
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Wang J, Charron N, Husic B, Olsson S, Noé F, Clementi C. Multi-body effects in a coarse-grained protein force field. J Chem Phys 2021; 154:164113. [PMID: 33940848 DOI: 10.1063/5.0041022] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
The use of coarse-grained (CG) models is a popular approach to study complex biomolecular systems. By reducing the number of degrees of freedom, a CG model can explore long time- and length-scales inaccessible to computational models at higher resolution. If a CG model is designed by formally integrating out some of the system's degrees of freedom, one expects multi-body interactions to emerge in the effective CG model's energy function. In practice, it has been shown that the inclusion of multi-body terms indeed improves the accuracy of a CG model. However, no general approach has been proposed to systematically construct a CG effective energy that includes arbitrary orders of multi-body terms. In this work, we propose a neural network based approach to address this point and construct a CG model as a multi-body expansion. By applying this approach to a small protein, we evaluate the relative importance of the different multi-body terms in the definition of an accurate model. We observe a slow convergence in the multi-body expansion, where up to five-body interactions are needed to reproduce the free energy of an atomistic model.
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Affiliation(s)
- Jiang Wang
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Nicholas Charron
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Brooke Husic
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Simon Olsson
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Cecilia Clementi
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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Turci F, Wilding NB. Phase Separation and Multibody Effects in Three-Dimensional Active Brownian Particles. PHYSICAL REVIEW LETTERS 2021; 126:038002. [PMID: 33543975 DOI: 10.1103/physrevlett.126.038002] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 12/14/2020] [Indexed: 06/12/2023]
Abstract
Simulation studies of the phase diagram of repulsive active Brownian particles in three dimensions reveal that the region of motility-induced phase separation between a high and low density phase is enclosed by a region of gas-crystal phase separation. Near-critical loci and structural crossovers can additionally be identified in analogy with simple fluids. Motivated by the striking similarity to the behavior of equilibrium fluids with short-ranged pairwise attractions, we show that a direct mapping to pair potentials in the dilute limit implies interactions that are insufficiently attractive to engender phase separation. Instead, this is driven by the emergence of multibody effects associated with particle caging that occurs at sufficiently high number density. We quantify these effects via information-theoretical measures of n-body effective interactions extracted from the configurational structure.
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Affiliation(s)
- Francesco Turci
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - Nigel B Wilding
- H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
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Yadav M, Singh Y. The solvent mediated interaction potential between solute particles: theory and applications. SOFT MATTER 2020; 16:9780-9788. [PMID: 33001128 DOI: 10.1039/d0sm01168a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In this paper we develop a theory to calculate the solvent mediated interaction potential between solute particles dispersed in a solvent. The potential is a functional of the instantaneous distribution of solute particles and is expressed in terms of the solute-solvent direct pair correlation function and the density-density correlation function of the bulk solvent. The dependence of the direct pair correlation function on multi-point correlations of the solute distribution is simplified with a mean field approximation. A self consistent approach is developed to calculate the effective potential between solute particles, the solute-solvent and the solute-solute correlation functions. The significance of the solvent fluctuations on the range of the effective potential is elucidated. The theory is applied to calculate equilibrium properties of the Asakura-Oosawa (AO) model for several values of solute and solvent densities and for several values of the particles size ratio. The results give a quantitative description of many-body effect on the effective potential and on the pair correlation functions.
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Affiliation(s)
- Mamta Yadav
- Department of Physics, Banaras Hindu University, Varanasi-221005, India.
| | - Yashwant Singh
- Department of Physics, Banaras Hindu University, Varanasi-221005, India.
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