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Gershenzon I, Lacroix-A-Chez-Toine B, Raz O, Subag E, Zeitouni O. On-Site Potential Creates Complexity in Systems with Disordered Coupling. PHYSICAL REVIEW LETTERS 2023; 130:237103. [PMID: 37354403 DOI: 10.1103/physrevlett.130.237103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Accepted: 04/04/2023] [Indexed: 06/26/2023]
Abstract
We calculate the average number of critical points N[over ¯] of the energy landscape of a many-body system with disordered two-body interactions and a weak on-site potential. We find that introducing a weak nonlinear on-site potential dramatically increases N[over ¯] to exponential in system size and give a complete picture of the organization of critical points. Our results extend solvable spin-glass models to physically more realistic models and are of relevance to glassy systems, nonlinear oscillator networks, and many-body interacting systems.
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Affiliation(s)
- I Gershenzon
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - B Lacroix-A-Chez-Toine
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
- Department of Mathematics, Kings College London, London WC2R 2LS, United Kingdom
| | - O Raz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - E Subag
- Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - O Zeitouni
- Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
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Chen G, Qu CK, Gong P. Anomalous diffusion dynamics of learning in deep neural networks. Neural Netw 2022; 149:18-28. [DOI: 10.1016/j.neunet.2022.01.019] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Revised: 12/17/2021] [Accepted: 01/26/2022] [Indexed: 11/17/2022]
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Nguyen D, Tao L, Li Y. Integration of Machine Learning and Coarse-Grained Molecular Simulations for Polymer Materials: Physical Understandings and Molecular Design. Front Chem 2022; 9:820417. [PMID: 35141207 PMCID: PMC8819075 DOI: 10.3389/fchem.2021.820417] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2021] [Accepted: 12/31/2021] [Indexed: 12/21/2022] Open
Abstract
In recent years, the synthesis of monomer sequence-defined polymers has expanded into broad-spectrum applications in biomedical, chemical, and materials science fields. Pursuing the characterization and inverse design of these polymer systems requires our fundamental understanding not only at the individual monomer level, but also considering the chain scales, such as polymer configuration, self-assembly, and phase separation. However, our accessibility to this field is still rudimentary due to the limitations of traditional design approaches, the complexity of chemical space along with the burdened cost and time issues that prevent us from unveiling the underlying monomer sequence-structure-property relationships. Fortunately, thanks to the recent advancements in molecular dynamics simulations and machine learning (ML) algorithms, the bottlenecks in the tasks of establishing the structure-function correlation of the polymer chains can be overcome. In this review, we will discuss the applications of the integration between ML techniques and coarse-grained molecular dynamics (CGMD) simulations to solve the current issues in polymer science at the chain level. In particular, we focus on the case studies in three important topics—polymeric configuration characterization, feed-forward property prediction, and inverse design—in which CGMD simulations are leveraged to generate training datasets to develop ML-based surrogate models for specific polymer systems and designs. By doing so, this computational hybridization allows us to well establish the monomer sequence-functional behavior relationship of the polymers as well as guide us toward the best polymer chain candidates for the inverse design in undiscovered chemical space with reasonable computational cost and time. Even though there are still limitations and challenges ahead in this field, we finally conclude that this CGMD/ML integration is very promising, not only in the attempt of bridging the monomeric and macroscopic characterizations of polymer materials, but also enabling further tailored designs for sequence-specific polymers with superior properties in many practical applications.
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Affiliation(s)
- Danh Nguyen
- Department of Mechanical Engineering, University of Connecticut, Mansfield, CT, United States
| | - Lei Tao
- Department of Mechanical Engineering, University of Connecticut, Mansfield, CT, United States
| | - Ying Li
- Department of Mechanical Engineering, University of Connecticut, Mansfield, CT, United States
- Polymer Program, Institute of Materials Science, University of Connecticut, Mansfield, CT, United States
- *Correspondence: Ying Li,
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Szulc A, Gat O, Regev I. Forced deterministic dynamics on a random energy landscape: Implications for the physics of amorphous solids. Phys Rev E 2020; 101:052616. [PMID: 32575307 DOI: 10.1103/physreve.101.052616] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Accepted: 04/21/2020] [Indexed: 06/11/2023]
Abstract
The dynamics of supercooled liquids and plastically deformed amorphous solids is known to be dominated by the structure of their rough energy landscapes. Recent experiments and simulations on amorphous solids subjected to oscillatory shear at athermal conditions have shown that for small strain amplitudes these systems reach limit cycles of different periodicities after a transient. However, for larger strain amplitudes the transients become longer and for strain amplitudes exceeding a critical value the system reaches a diffusive steady state. This behavior cannot be explained using the current mean-field models of amorphous plasticity. Here we show that this phenomenology can be described and explained using a simple model of forced dynamics on a multidimensional random energy landscape. In this model, the existence of limit cycles can be ascribed to confinement of the dynamics to a small part of the energy landscape which leads to self-intersection of state-space trajectories and the transition to the diffusive regime for larger forcing amplitudes occurs when the forcing overcomes this confinement.
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Affiliation(s)
- Asaf Szulc
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Omri Gat
- Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Ido Regev
- The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84990, Israel
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