Aggregation of theta-polymers in spherical confinement

Zierenberg, Johannes; Mueller, Marco; Schierz, Philipp; Marenz, Martin; Janke, Wolfhard

doi:10.1063/1.4893307

Cited by 26 publications

(49 citation statements)

References 42 publications

(37 reference statements)

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“…We assumed that the solution of polymers is sufficiently dilute so that the interchain interactions and the overlapping between different polymers can be neglected and it is sufficient to consider the behaviour of a single polymer chain. Besides, as it was confirmed by multicanonical simulations recently [60], polymers in a dilute solution confined in a spherical cavity can be considered isolated for all temperatures larger than the aggregation temperature, which is a function of the density. As it is known [15,16,61,62], the behaviour of long flexible polymers is determinated by entropy and characterized by detail independence, universality and scaling.…”

Section: The Thermodynamic Description and The Modelmentioning

confidence: 79%

Linear and ring polymers in confined geometries

Usatenko

Kuterba

Chamati

et al. 2017

Eur. Phys. J. Spec. Top.

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Abstract. A short overview of the theoretical and experimental works on the polymer-colloid mixtures is given. The behaviour of a dilute solution of linear and ring polymers in confined geometries like slit of two parallel walls or in the solution of mesoscopic colloidal particles of big size with different adsorbing or repelling properties in respect to polymers is discussed. Besides, we consider the massive field theory approach in fixed space dimensions d = 3 for the investigation of the interaction between long flexible polymers and mesoscopic colloidal particles of big size and for the calculation of the correspondent depletion interaction potentials and the depletion forces between confining walls. The presented results indicate the interesting and nontrivial behavior of linear and ring polymers in confined geometries and give possibility better to understand the complexity of physical effects arising from confinement and chain topology which plays a significant role in the shaping of individual chromosomes and in the process of their segregation, especially in the case of elongated bacterial cells. The possibility of using linear and ring polymers for production of new types of nano-and micro-electromechanical devices is analyzed.

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Section: The Thermodynamic Description and The Modelmentioning

confidence: 79%

Linear and ring polymers in confined geometries

Usatenko

Kuterba

Chamati

et al. 2017

Eur. Phys. J. Spec. Top.

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“…Polymers are extended objects which bring an additional conformational entropy if isolated in the high-temperature phase [59]. Lowering the temperature results in the formation of a macroscopic aggregate surrounded by a gas of isolated chains [45,60,61], for an illustration see Fig. 1 (right).…”

Section: Droplet Formation In a Solution Of Flexible Polymersmentioning

confidence: 99%

From particle condensation to polymer aggregation

Janke¹,

Zierenberg

2018

J. Phys.: Conf. Ser.

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We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the results in perspective, we compare with in part rigorous theoretical scaling laws for canonical condensation in a supersaturated gas at fixed temperature, and derive corresponding scaling predictions for an undercooled gas at fixed density. The latter allows one to efficiently employ parallel multicanonical simulations and to reach previously not accessible scaling regimes. While the asymptotic scaling can not be observed for the comparably small polymer system sizes, they demonstrate an intermediate scaling regime also observable for particle condensation. Altogether, our extensive results from computer simulations provide clear evidence for the close analogy between particle condensation and polymer aggregation in dilute systems.

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“…Note that while in many scalar implementations of multicanonical simulations no thermalization steps are used between iterations, for the large number of parallel walkers employed here and the resulting small number of updates per iteration and walker we find the equilibration steps to be crucial for achieving a stable parallel procedure. Recent applications of the parallel multicanonical method (on CPU clusters) include studies of the Blume-Capel spin model in 2D [28] and 3D [20], lattice and off-lattice particle condensation [29][30][31][32], continuum formulations of the aggregation process of flexible [32,33] as well as semiflexible [34] polymers, the binding transition of grafted flexible polymers [35], the phase diagram of semiflexible polymers [36], and the interplay of semiflexibility with the adsorption propensity of polymers [37]. In all these different cases, the method proved to be very robust and reliable to use routinely in day-by-day practical work.…”

Section: Parallel Multicanonical Samplingmentioning

confidence: 99%

Massively parallel multicanonical simulations

Gross¹,

Zierenberg²,

Weigel

et al. 2018

Computer Physics Communications

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Generalized-ensemble Monte Carlo simulations such as the multicanonical method and similar techniques are among the most efficient approaches for simulations of systems undergoing discontinuous phase transitions or with rugged freeenergy landscapes. As Markov chain methods, they are inherently serial computationally. It was demonstrated recently, however, that a combination of independent simulations that communicate weight updates at variable intervals allows for the efficient utilization of parallel computational resources for multicanonical simulations. Implementing this approach for the many-thread architecture provided by current generations of graphics processing units (GPUs), we show how it can be efficiently employed with of the order of 10 4 parallel walkers and beyond, thus constituting a versatile tool for Monte Carlo simulations in the era of massively parallel computing. We provide the fully documented source code for the approach applied to the paradigmatic example of the two-dimensional Ising model as starting point and reference for practitioners in the field. Solution method: The code uses a parallel variant of the multicanonical method employing many parallel walkers that accumulate a common histogram. The resulting histogram is used to determine the weight function for the next iteration. Once the iteration has converged, simulations visit all possible energies with the same probability. Restrictions: The system size and size of the population of replicas are limited depending on the memory of the GPU device used. Code repository at https://github.com/CQT-Leipzig/ cudamuca. Running time: Depends on system size (approx. 40 s for L=32 on a Tesla K20m)

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Aggregation of theta-polymers in spherical confinement

Cited by 26 publications

References 42 publications

Linear and ring polymers in confined geometries

Linear and ring polymers in confined geometries

From particle condensation to polymer aggregation

Massively parallel multicanonical simulations

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