1
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Yuan J, Curk T. Collapse and expansion kinetics of a single polyelectrolyte chain with hydrodynamic interactions. J Chem Phys 2024; 160:161103. [PMID: 38656439 DOI: 10.1063/5.0201740] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 03/29/2024] [Indexed: 04/26/2024] Open
Abstract
We investigate the collapse and expansion dynamics of a linear polyelectrolyte (PE) with hydrodynamic interactions. Using dissipative particle dynamics with a bead-spring PE model, long-range electrostatics, and explicit ions, we examine how the timescales of collapse tcol and expansion texp depend on the chain length N and obtain scaling relationships tcol ∼ Nα and texp ∼ Nβ. For neutral polymers, we derive values of α = 0.94 ± 0.01 and β = 1.97 ± 0.10. Interestingly, the introduction of electrostatic interaction markedly shifts α to α ≈ 1.4 ± 0.1 for salt concentrations within c = 10-4 to 10-2 M. A reduction in the ion-to-monomer size ratio noticeably reduces α. On the other hand, the expansion scaling remains approximately constant, β ≈ 2, regardless of the salt concentration or ion size considered. We find β > α for all conditions considered, implying that expansion is always slower than collapse in the limit of long polymers. This asymmetry is explained by distinct kinetic pathways of collapse and expansion processes.
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Affiliation(s)
- Jiaxing Yuan
- Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
| | - Tine Curk
- Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
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2
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Jain N, Thakur S. Structure and dynamics of chemically active ring polymers: swelling to collapse. SOFT MATTER 2023; 19:7358-7369. [PMID: 37740385 DOI: 10.1039/d3sm00839h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/24/2023]
Abstract
The ring structures are common in many synthetic or natural systems and experience both local and long-range forces by chemical sensing. This work is an effort to investigate the structural and dynamical properties of a chemically active ring in an explicit solvent bath utilizing hybrid molecular dynamics (MD) and multiparticle collision dynamics (MPCD) simulation techniques. We show that by tuning the chemical properties of the ring, it can be converted from a chemo-attractant to a chemo-repellent, thereby changing the steady state to be either collapsed or swelled as compared to its passive limit. We quantify these observations by comparing the scaling laws, local structures and the dynamics of active and passive rings. Furthermore, we show the impact of varying numbers of active sites by calculating the contact probability of the collapse state that highlights diverse structures. We also analyze the dynamics of the ring by finding the relaxation time and the mean square displacement of the centre of mass. A faster relaxation with enhanced diffusion is observed for the active rings.
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Affiliation(s)
- Namita Jain
- Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, India.
| | - Snigdha Thakur
- Department of Physics, Indian Institute of Science Education and Research Bhopal, Bhopal 462066, India.
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3
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Gessert D, Christiansen H, Janke W. Superdiffusion-like behavior in zero-temperature coarsening of the [Formula: see text] Ising model. Sci Rep 2023; 13:13270. [PMID: 37582791 PMCID: PMC10427613 DOI: 10.1038/s41598-023-39328-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2023] [Accepted: 07/24/2023] [Indexed: 08/17/2023] Open
Abstract
One key aspect of coarsening following a quench below the critical temperature is domain growth. For the non-conserved Ising model a power-law growth of domains of like spins with exponent [Formula: see text] is predicted. Including recent work, it was not possible to clearly observe this growth law in the special case of a zero-temperature quench in the three-dimensional model. Instead a slower growth with [Formula: see text] was reported. We attempt to clarify this discrepancy by running large-scale Monte Carlo simulations on simple-cubic lattices with linear lattice sizes up to [Formula: see text] employing an efficient GPU implementation. Indeed, at late times we measure domain sizes compatible with the expected growth law-but surprisingly, at still later times domains even grow superdiffusively, i.e., with [Formula: see text]. We argue that this new problem is possibly caused by sponge-like structures emerging at early times.
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Affiliation(s)
- Denis Gessert
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
- Centre for Fluid and Complex Systems, Coventry University, Coventry, CV1 5FB UK
| | - Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
- Present Address: NEC Laboratories Europe GmbH, Kurfürsten-Anlage 36, 69115 Heidelberg, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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4
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Paul S, Majumder S, Janke W. Activity mediated globule to coil transition of a flexible polymer in a poor solvent. SOFT MATTER 2022; 18:6392-6403. [PMID: 35979819 DOI: 10.1039/d2sm00354f] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Understanding the role of self-propulsion on the conformational properties of active filamentous objects has relevance in biology. In this work, we consider a flexible bead-spring model for active polymers with both attractive and repulsive interactions among the non-bonded monomers. The activity for each monomer works along its intrinsic direction of self-propulsion which changes diffusively with time. We study its kinetics in the overdamped limit, following quenching from good to poor solvent conditions. We observe that with low activities, though the kinetic pathways remain similar, the scaling exponent for the relaxation time of globule formation becomes smaller than that for the case with no activity. Interestingly, for higher activities when self-propulsion dominates over interaction energy, the polymer conformation becomes extended coil-like. There, in the steady state, the variation of the spatial extension of the polymer, measured via its gyration radius, shows two completely different scaling regimes: the corresponding Flory exponent ν changes from 1/3 to 3/5 similar to a transition of the polymer from a globular state to a self-avoiding walk. This can be explained by an interplay among the three energy scales present in the system, viz., the "ballistic", thermal, and interaction energy.
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Affiliation(s)
- Subhajit Paul
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
- International Center for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore-560089, India
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
- Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida 201313, India
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
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5
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Chauhan K, Singh A. Delayed collapse transitions in a pinned polymer system. Phys Rev E 2022; 105:064505. [PMID: 35854509 DOI: 10.1103/physreve.105.064505] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Accepted: 06/05/2022] [Indexed: 11/07/2022]
Abstract
Employing Langevin dynamics simulations, we investigated the kinetics of the collapse transition for a polymer of length N when a particular monomer at a position 1≤X≤N is pinned. The results are compared with the kinetics of a free polymer. The equilibrium θ-point separating the coil from the globule phase is located by a crossover in 〈R_{g}^{2}〉/N plots of different chain lengths. Our simulation supports a three-stage mechanism for free and pinned polymer collapse: the formation of pearls, the coarsening of pearls, and the formation of a compact globule. Pinning the central monomer has negligible effects on the kinetics as it does not break the symmetry. However, pinning a monomer elsewhere causes the process to be delayed by a constant factor ϕ_{X} depending linearly upon X. The total collapse time scales with N as τ_{c}∼ϕ_{X}N^{1.60±0.03}, which implies τ_{c} is maximum when an end monomer is pinned (X=1 or N), while when pinning the central monomer (X=N/2) it is minimum and identical to that of a free polymer. The average cluster size N_{c}(t) grows in time as t^{z}, where z=1.00±0.04 for a free particle, whereas we identify two time regimes separated by a plateau for pinned polymers. At longer times, z=1.00±0.04, while it deviates in early time regimes significantly, depending on the value of X.
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Affiliation(s)
- Keerti Chauhan
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
| | - Ankit Singh
- Department of Physics, Banaras Hindu University, Varanasi 221005, India
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6
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Paul S, Majumder S, Das SK, Janke W. Effects of alignment activity on the collapse kinetics of a flexible polymer. SOFT MATTER 2022; 18:1978-1990. [PMID: 35023525 DOI: 10.1039/d1sm01055g] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The dynamics of various biological filaments can be understood within the framework of active polymer models. Here we consider a bead-spring model for a flexible polymer chain in which the active interaction among the beads is introduced via an alignment rule adapted from the Vicsek model. Following quenching from the high-temperature coil phase to a low-temperature state point, we study the coarsening kinetics via molecular dynamics (MD) simulations using the Langevin thermostat. For the passive polymer case the low-temperature equilibrium state is a compact globule. The results from our MD simulations reveal that though the globular state is also the typical final state in the active case, the nonequilibrium pathways to arrive at such a state differ from the picture for the passive case due to the alignment interaction among the beads. We notice that deviations from the intermediate "pearl-necklace"-like arrangement, which is observed in the passive case, and the formation of more elongated dumbbell-like structures increase with increasing activity. Furthermore, it appears that while a small active force on the beads certainly makes the coarsening process much faster, there exists a nonmonotonic dependence of the collapse time on the strength of active interaction. We quantify these observations by comparing the scaling laws for the collapse time and growth of pearls with the passive case.
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Affiliation(s)
- Subhajit Paul
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
| | - Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore-560064, India.
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
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7
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Ghosh S, Vemparala S. Kinetics of charged polymer collapse in poor solvents. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:045101. [PMID: 34352747 DOI: 10.1088/1361-648x/ac1aef] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Accepted: 08/05/2021] [Indexed: 06/13/2023]
Abstract
Extensive molecular dynamics simulations, using simple charged polymer models, have been employed to probe the collapse kinetics of a single flexible polyelectrolyte (PE) chain under implicit poor solvent conditions. We investigate the role of the charged nature of PE chain (A), valency of counterions (Z) on the kinetics of such PE collapse. Our study shows that the collapse kinetics of charged polymers are significantly different from those of the neutral polymer and that the finite-size scaling behavior of PE collapse times does not follow the Rouse scaling as observed in the case of neutral polymers. The critical exponent for charged PE chains is found to be less than that of neutral polymers and also exhibits dependence on counterion valency. The coarsening of clusters along the PE chain suggests a multi-stage collapse and exhibits opposite behavior of exponents compared to neutral polymers: faster in the early stages and slower in the later stages of collapse.
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Affiliation(s)
- Susmita Ghosh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Satyavani Vemparala
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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8
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Christiansen H, Majumder S, Janke W. Zero-temperature coarsening in the two-dimensional long-range Ising model. Phys Rev E 2021; 103:052122. [PMID: 34134321 DOI: 10.1103/physreve.103.052122] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 04/20/2021] [Indexed: 11/07/2022]
Abstract
We investigate the nonequilibrium dynamics following a quench to zero temperature of the nonconserved Ising model with power-law decaying long-range interactions ∝1/r^{d+σ} in d=2 spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent α, the persistence exponent θ, and the fractal dimension d_{f}. It is found that the growth exponent α≈3/4 is independent of σ and different from α=1/2, as expected for nearest-neighbor models. In the large σ regime of the tunable interactions only the fractal dimension d_{f} of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponents θ this is a direct consequence of the different growth exponents α as can be understood from the relation d-d_{f}=θ/α; they just differ by the ratio of the growth exponents ≈3/2. This relation has been proposed for annihilation processes and later numerically tested for the d=2 nearest-neighbor Ising model. We confirm this relation for all σ studied, reinforcing its general validity.
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Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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9
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Das SK. A scaling investigation of pattern in the spread of COVID-19: universality in real data and a predictive analytical description. Proc Math Phys Eng Sci 2021; 477:20200689. [PMID: 35153541 PMCID: PMC8317978 DOI: 10.1098/rspa.2020.0689] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 01/05/2021] [Indexed: 12/16/2022] Open
Abstract
We analyse the spread of COVID-19, a disease caused by a novel coronavirus, in various countries by proposing a model that exploits the scaling and other important concepts of statistical physics. Quite expectedly, for each of the considered countries, we observe that the spread at early times occurs exponentially fast. We show how the countries can be classified into groups, like universality classes in the literature of phase transitions, based on the rates of infections during late times. This method brings a new angle to the understanding of disease spread and is useful in obtaining a country-wise comparative picture of the effectiveness of lockdown-like social measures. Strong similarity, during both natural and lockdown periods, emerges in the spreads within countries having varying geographical locations, climatic conditions, population densities and economic parameters. We derive accurate mathematical forms for the corresponding scaling functions and show how the model can be used as a predictive tool, with instruction even for future waves, and, thus, as a guide for optimizing social measures and medical facilities. The model is expected to be of general relevance in the studies of epidemics.
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Affiliation(s)
- Subir K. Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, India
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10
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Wicks TJ, Wattis JAD, Graham RS. Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers. POLYMER CRYSTALLIZATION 2021. [DOI: 10.1002/pcr2.10146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Thomas J. Wicks
- School of Mathematical Sciences University of Nottingham Nottingham UK
| | | | - Richard S. Graham
- School of Mathematical Sciences University of Nottingham Nottingham UK
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11
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Christiansen H, Majumder S, Henkel M, Janke W. Aging in the Long-Range Ising Model. PHYSICAL REVIEW LETTERS 2020; 125:180601. [PMID: 33196262 DOI: 10.1103/physrevlett.125.180601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Revised: 08/01/2020] [Accepted: 09/10/2020] [Indexed: 06/11/2023]
Abstract
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with λ=1.25 in the effectively short-range regime, while for stronger long-range interactions the data are consistent with λ=d/2=1. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as subaging.
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Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Malte Henkel
- Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy, 54506 Vandœuvre-lès-Nancy Cedex, France
- Centro de Física Teórica e Computacional, Universidade de Lisboa, 1749-016 Lisboa, Portugal
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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12
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Schneider J, Meinel MK, Dittmar H, Müller-Plathe F. Different Stages of Polymer-Chain Collapse Following Solvent Quenching–Scaling Relations from Dissipative Particle Dynamics Simulations. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c01315] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jurek Schneider
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Melissa K. Meinel
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Han Dittmar
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
| | - Florian Müller-Plathe
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie and Profile Area Thermofluids and Interfaces, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, D-64287 Darmstadt, Germany
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13
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Gumus B, Herrera-Alonso M, Ramírez-Hernández A. Kinetically-arrested single-polymer nanostructures from amphiphilic mikto-grafted bottlebrushes in solution: a simulation study. SOFT MATTER 2020; 16:4969-4979. [PMID: 32432304 DOI: 10.1039/d0sm00771d] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Solution self-assembly of molecular bottlebrushes offers a rich platform to create complex functional organic nanostructures. Recently, it has become evident that kinetics, not just thermodynamics, plays an important role in defining the self-assembled structures that can be formed. In this work, we present results from extensive molecular dynamics simulations that explore the self-assembly behavior of mikto-grafted bottlebrushes when the solvent quality for one of the side blocks is changed by a rapid quench. We have performed a systematic study of the effect of different structural parameters and the degree of incompatibility between side chains on the final self-assembled nanostructures in the low concentration limit. We found that kinetically-trapped complex nanostructures are prevalent as the number of macromonomers increases. We performed a quantitative analysis of the self-assembled morphologies by computing the radius of gyration tensor and relative shape anisotropy as the different relevant parameters were varied. Our results are summarized in terms of non-equilibrium morphology diagrams.
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Affiliation(s)
- Bahar Gumus
- Department of Biomedical Engineering and Chemical Engineering, The University of Texas San Antonio, TX 78249, USA.
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14
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Liu X, Jiang H, Hou Z. Non-monotonic dependence of polymer chain dynamics on active crowder size. J Chem Phys 2020; 152:204906. [PMID: 32486672 DOI: 10.1063/5.0007570] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Configuration dynamics of flexible polymer chains is of ubiquitous importance in many biological processes. Here, we investigate a polymer chain immersed in a bath of size-changed active particles in two dimensional space using Langevin dynamics simulations. Particular attention is paid to how the radius of gyration Rg of the polymer chain depends on the size σc of active crowders. We find that Rg shows nontrivial non-monotonic dependence on σc: The chain first swells upon increasing σc, reaching a fully expanded state with maximum Rg, and then, Rg decreases until the chain collapses to a compact coil state if the crowder is large enough. Interestingly, the chain may oscillate between a collapse state and a stretched state at moderate crowder size. Analysis shows that it is the competition between two effects of active particles, one stretching the chain from inside due to persistence motion and the other compressing the chain from outside, that leads to the non-monotonic dependence. Besides, the diffusion of the polymer chain also shows nontrivial non-monotonic dependence on σc. Our results demonstrate the important interplay between particle activity and size associated with polymer configurations in active crowding environments.
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Affiliation(s)
- Xinshuang Liu
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Huijun Jiang
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
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15
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Paciolla M, Arismendi-Arrieta DJ, Moreno AJ. Coarsening Kinetics of Complex Macromolecular Architectures in Bad Solvent. Polymers (Basel) 2020; 12:E531. [PMID: 32121665 PMCID: PMC7182883 DOI: 10.3390/polym12030531] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2019] [Revised: 02/04/2020] [Accepted: 02/20/2020] [Indexed: 11/16/2022] Open
Abstract
This study reports a general scenario for the out-of-equilibrium features of collapsing polymeric architectures. We use molecular dynamics simulations to characterize the coarsening kinetics, in bad solvent, for several macromolecular systems with an increasing degree of structural complexity. In particular, we focus on: flexible and semiflexible polymer chains, star polymers with 3 and 12 arms, and microgels with both ordered and disordered networks. Starting from a powerful analogy with critical phenomena, we construct a density field representation that removes fast fluctuations and provides a consistent characterization of the domain growth. Our results indicate that the coarsening kinetics presents a scaling behaviour that is independent of the solvent quality parameter, in analogy to the time-temperature superposition principle. Interestingly, the domain growth in time follows a power-law behaviour that is approximately independent of the architecture for all the flexible systems; while it is steeper for the semiflexible chains. Nevertheless, the fractal nature of the dense regions emerging during the collapse exhibits the same scaling behaviour for all the macromolecules. This suggests that the faster growing length scale in the semiflexible chains originates just from a faster mass diffusion along the chain contour, induced by the local stiffness. The decay of the dynamic correlations displays scaling behavior with the growing length scale of the system, which is a characteristic signature in coarsening phenomena.
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Affiliation(s)
- Mariarita Paciolla
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain;
| | | | - Angel J. Moreno
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain;
- Donostia International Physics Center, Paseo Manuel de Lardizabal 4, 20018 San Sebastián, Spain;
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16
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Liu X, Jiang H, Hou Z. Configuration dynamics of a flexible polymer chain in a bath of chiral active particles. J Chem Phys 2019; 151:174904. [DOI: 10.1063/1.5125607] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xinshuang Liu
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Huijun Jiang
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhonghuai Hou
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales, University of Science and Technology of China, Hefei, Anhui 230026, China
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17
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Majumder S, Hansmann UHE, Janke W. Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse. Macromolecules 2019; 52:5491-5498. [PMID: 31631912 PMCID: PMC6795215 DOI: 10.1021/acs.macromol.9b00562] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Revised: 05/31/2019] [Indexed: 11/30/2022]
Abstract
![]()
The
collapse of the polypeptide backbone is an integral part of
protein folding. Using polyglycine as a probe, we explore the nonequilibrium
pathways of protein collapse in water. We find that the collapse depends
on the competition between hydration effects and intrapeptide interactions.
Once intrapeptide van der Waal interactions dominate, the chain collapses
along a nonequilibrium pathway characterized by formation of pearl-necklace-like
local clusters as intermediates that eventually coagulate into a single
globule. By describing this coarsening through the contact probability
as a function of distance along the chain, we extract a time-dependent
length scale that grows in a linear fashion. The collapse dynamics
is characterized by a dynamical critical exponent z ≈ 0.5 that is much smaller than the values of z = 1–2 reported for nonbiological polymers. This difference
in the exponents is explained by the instantaneous formation of intrachain
hydrogen bonds and local ordering that may be correlated with the
observed fast folding times of proteins.
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Affiliation(s)
- Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Ulrich H E Hansmann
- Department of Chemistry and Biochemistry, University of Oklahoma, Norman, Oklahoma 73019, United States
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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18
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Roy S, Bera A, Majumder S, Das SK. Aging phenomena during phase separation in fluids: decay of autocorrelation for vapor-liquid transitions. SOFT MATTER 2019; 15:4743-4750. [PMID: 31149698 DOI: 10.1039/c9sm00366e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented: one in the neighborhood of the vapor branch of the coexistence curve and the other being close to the critical density. The nonequilibrium morphologies, growth mechanisms and growth laws in the two cases are vastly different. In the low density case growth occurs via diffusive coalescence of droplets in a disconnected morphology. On the other hand, the elongated structure in the higher density case grows via advective transport of particles inside the tube-like liquid domains. The objective in this work has been to identify how the decay of the order-parameter autocorrelation, an important quantity to understand aging dynamics, differs in the two cases. In the case of the disconnected morphology, we observe a very robust power-law decay, as a function of the ratio of the characteristic lengths at the observation time and at the age of the system, whereas the results for the percolating structure appear rather complex. To quantify the decay in the latter case, unlike the standard method followed in a previous study, here we have performed a finite-size scaling analysis. The outcome of this analysis shows the presence of a strong preasymptotic correction, while revealing that in this case also, albeit in the asymptotic limit, the decay follows a power-law. Even though the corresponding exponents in the two cases differ drastically, this study, combined with a few recent ones, suggests that power-law behavior of this correlation function is rather universal in coarsening dynamics.
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Affiliation(s)
- Sutapa Roy
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany.
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19
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Christiansen H, Majumder S, Janke W. Phase ordering kinetics of the long-range Ising model. Phys Rev E 2019; 99:011301. [PMID: 30780293 DOI: 10.1103/physreve.99.011301] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Indexed: 11/07/2022]
Abstract
We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions perform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.
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Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
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20
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Chen A, Zhao N. Comparative study of the crowding-induced collapse effect in hard-sphere, flexible polymer and rod-like polymer systems. Phys Chem Chem Phys 2019; 21:12335-12345. [DOI: 10.1039/c9cp01731c] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A systematic Langevin simulation is performed to study the crowding-induced collapse effect on a probed chain in three typical systems: hard sphere (HS), flexible polymer and rod-like polymer.
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Affiliation(s)
- Anpu Chen
- College of Chemistry
- Sichuan University
- Chengdu 610064
- China
| | - Nanrong Zhao
- College of Chemistry
- Sichuan University
- Chengdu 610064
- China
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21
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Moreno AJ, Lo Verso F. Computational investigation of microgels: synthesis and effect of the microstructure on the deswelling behavior. SOFT MATTER 2018; 14:7083-7096. [PMID: 30118116 DOI: 10.1039/c8sm01407h] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We present computer simulations of a realistic model of microgels. Unlike the regular network frameworks usually assumed in the simulation literature, we model and simulate a realistic and efficient synthesis route, mimicking cross-linking of functionalized chains inside a cavity. This model is inspired, e.g., by microfluidic fabrication of microgels from macromolecular precursors and is different from standard polymerization routes. The assembly of the chains is mediated by a low fraction of interchain crosslinks. The microgels are polydisperse in size and shape but globally spherical objects. In order to deeply understand the microgel structure and eventually improve the synthesis protocol we characterize their conformational properties and deswelling kinetics, and compare them with the results found for microgels obtained via underlying regular (diamond-like) structures. For the same molecular weight, monomer concentration and effective degree of cross-linking, the specific microstructure of the microgel has no significant effect on the locus of the volume phase transition (VPT). However, it strongly affects the deswelling kinetics, as revealed by a consistent analysis of the domain growth during the microgel collapse. Though both the disordered and the regular networks exhibit a similar early growth of the domains, an acceleration is observed in the regular network at the late stage of the collapse. Similar trends are found for the dynamic correlations coupled to the domain growth. As a consequence, the fast late processes for the domain growth and the dynamic correlations in the regular network are compensated, and the dynamic correlations follow a power-law dependence on the growing length scale that is independent of the microgel microstructure.
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Affiliation(s)
- Angel J Moreno
- Centro de Física de Materiales (CSIC, UPV/EHU) and Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebastián, Spain.
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22
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Scolari VF, Mercy G, Koszul R, Lesne A, Mozziconacci J. Kinetic Signature of Cooperativity in the Irreversible Collapse of a Polymer. PHYSICAL REVIEW LETTERS 2018; 121:057801. [PMID: 30118310 DOI: 10.1103/physrevlett.121.057801] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Revised: 04/11/2018] [Indexed: 06/08/2023]
Abstract
We investigate the kinetics of a polymer collapse due to the formation of irreversible cross-links between its monomers. Using the contact probability P(s) as a scale-dependent order parameter depending on the chemical distance s, our simulations show the emergence of a cooperative pearling instability. Namely, the polymer undergoes a sharp conformational transition to a set of absorbing states characterized by a length scale ξ corresponding to the mean pearl size. This length and the transition time depend on the polymer equilibrium dynamics and the cross-linking rate. We confirm experimentally this transition using a DNA conformation capture experiment in yeast.
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Affiliation(s)
- Vittore F Scolari
- Spatial Regulation of Genomes, Genomes and Genetics Department, Institut Pasteur, Paris 75015, France
- UMR3525, Centre National de la Recherche Scientifique, Paris 75015, France
| | - Guillaume Mercy
- Spatial Regulation of Genomes, Genomes and Genetics Department, Institut Pasteur, Paris 75015, France
- UMR3525, Centre National de la Recherche Scientifique, Paris 75015, France
| | - Romain Koszul
- Spatial Regulation of Genomes, Genomes and Genetics Department, Institut Pasteur, Paris 75015, France
- UMR3525, Centre National de la Recherche Scientifique, Paris 75015, France
| | - Annick Lesne
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, Paris F-75252, France
- Institut de Génétique Moléculaire de Montpellier, UMR 5535 CNRS, Montpellier, France
- University of Montpellier, Montpellier, France
| | - Julien Mozziconacci
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, Paris F-75252, France
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23
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Wu J, Cheng C, Liu G, Zhang P, Chen T. The folding pathways and thermodynamics of semiflexible polymers. J Chem Phys 2018; 148:184901. [PMID: 29764123 DOI: 10.1063/1.5018114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.
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Affiliation(s)
- Jing Wu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Chenqian Cheng
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Gaoyuan Liu
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Ping Zhang
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
| | - Tao Chen
- Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of the Ministry of Education, College of Chemistry and Materials Science, Northwest University, Xi'an 710127, People's Republic of China
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24
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Paul S, Das SK. Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging. Phys Rev E 2018; 96:012105. [PMID: 29347235 DOI: 10.1103/physreve.96.012105] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2016] [Indexed: 11/07/2022]
Abstract
We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.
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Affiliation(s)
- Subhajit Paul
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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25
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Christiansen H, Majumder S, Janke W. Coarsening and aging of lattice polymers: Influence of bond fluctuations. J Chem Phys 2017; 147:094902. [DOI: 10.1063/1.4991667] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
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