Pulling on grafted flexible polymers can cause twisted bundles.

Bundles of semiflexible polymers can twist at low temperatures to balance energy gain from attraction and energy cost from bending. This raises the question whether twisting can be also observed for bundles of rather flexible grafted polymers stretched out by pulling force. Here, we address this question using Monte Carlo computer simulations of small bundles. Our data show that for weak forces F < Fl, intertwined globular conformations are favored, whereas for strong forces F > Fu, rod-like bundles emerge. In the intermediate force window Fl < F < Fu, bundles with a helical twist can be clearly identified. Applying a field to all monomers yields qualitatively the same effect. This suggests the conclusion that rather flexible polymers under pulling force or field behave effectively like semiflexible polymers without external pull.

Aging following a zero-temperature quench in the d=3 Ising model.

Aging in phase-ordering kinetics of the d=3 Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator C_{ag} is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent λ. Previous work indicated that the lower Fisher-Huse bound of λ≥d/2=1.5 is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for λ we obtain at late times does not disagree with this bound. By conducting systematic fits to the data of C_{ag} using different Ansätze for the leading correction term, we find λ=1.58(14), with most of the error attributed to the systematic uncertainty regarding the Ansätze. This result is in contrast to the recent report that below the roughening transition universality might be violated.

Separation of the Chlorofluorocarbon (CFC) CCl2F2 from N2 in NaY Zeolite, in MIL-127(Fe) and in the two Carbon Nanotubes CNT (9,9) and CNT (11,11).

Four well-suited porous materials for the selective adsorption of the most prominent CFC, which is CCl2F2, from the air are carbon nanotubes CNT (9,9) and CNT (11,11), NaY zeolite, and the Metal Organic Framework MIL-125(Fe). The adsorption has been investigated through molecular simulations. Simulation results and theoretical considerations show that reasons for the extraordinarily high selectivity in all four cases were found to be the differences in the enthalpy of adsorption for the various adsorbed gases rather than steric reasons. The four adsorbate-adsorbent systems have been examined at different temperatures, pressures, and concentration ratios in the mixture. Among them, the carbon nanotube CNT (11,11) exhibited the highest selectivity, reaching up to 104.

Superdiffusion-like behavior in zero-temperature coarsening of the [Formula: see text] Ising model.

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.

Resampling schemes in population annealing: Numerical and theoretical results.

The population annealing algorithm is a population-based equilibrium version of simulated annealing. It can sample thermodynamic systems with rough free-energy landscapes more efficiently than standard Markov chain Monte Carlo alone. A number of parameters can be fine-tuned to improve the performance of the population annealing algorithm. While there is some numerical and theoretical work on most of these parameters, there appears to be a gap in the literature concerning the role of resampling in population annealing which this work attempts to close. The two-dimensional Ising model is used as a benchmarking system for this study. At first various resampling methods are implemented and numerically compared. In a second part the exact solution of the Ising model is utilized to create an artificial population annealing setting with effectively infinite Monte Carlo updates at each temperature. This limit is first performed on finite population sizes and subsequently extended to infinite populations. This allows us to look at resampling isolated from other parameters. Many results are expected to generalize to other systems.

Collapse transition of a Lennard-Jones polymer.

Using the recently introduced parsimonious Metropolis Monte Carlo algorithm, bead-stick polymers both with infinite-range Lennard-Jones interaction and with truncation are simulated. The focus lies on determining the Boyle temperature for long chains with thousands of repeat units and on testing for theoretically predicted logarithmic corrections. Subsequently the behavior at the infinite-chain transition temperature, i.e., the Θ temperature, is studied for chains with up to N=32768 repeat units by investigation of the scaling of the end-to-end distance, the radius of gyration, the specific heat, and their derivatives with N.

Phase-Separation Kinetics in the Two-Dimensional Long-Range Ising Model.

Using Monte Carlo computer simulations, we investigate the kinetics of phase separation in the two-dimensional conserved Ising model with power-law decaying long-range interactions, the prototypical model for many long-range interacting systems. A long-standing analytical prediction for the characteristic length is shown to be applicable. In the simulation, we relied on our novel algorithm which provides a massive speedup for long-range interacting systems.

Activity mediated globule to coil transition of a flexible polymer in a poor solvent.

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.

Exceptionally high selectivity in the separation of light hydrocarbons by adsorption on MIL-127(Fe) and on a (9,9) carbon nanotube.

Porous solids with channel sizes that are not much above the size of small hydrocarbons can yield extremely large adsorption selectivity. Our Grand Canonical Monte-Carlo simulations indicate exceptionally high selectivity for the separation of methane, ethane and propane from natural gas. At 250 K the C3H8/CH4 separation on MIL-127 at low pressure has a selectivity of more than 1000 and the C3H8/CH4 separation on CNT (9,9) is even above 2000. This is due to the strong molecule lattice interaction in narrow channels which leads to large enthalpies of adsorption. The Arrhenius law for the Henry coefficients is analysed in order to show that the effect is due to this enthalpy rather than to steric reasons.

Effects of alignment activity on the collapse kinetics of a flexible polymer.

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.

Adsorption and the Chemical Reaction N2O4 ↔ 2NO2 in the Presence of N2 in a Gas Phase Connected with a Carbon Nanotube.

The paper shows, by molecular simulations, that a CNT (9,9) carbon nanotube allows very efficient separation of nitrogen oxides (NO x ) from N2, that has in good approximation properties of the complete air mixture. Gibbs ensemble Monte Carlo simulations are used to describe the adsorption. The permanent chemical reaction between N2O4 and NO2, which occurs simultaneously to adsorption, is treated by the reactive Monte Carlo simulation. A very high selectivity has been found. For a low pressure and at T = 298 K, an adsorption/reaction selectivity between NO x and N2 can reach values up to 3 × 103.

Understanding population annealing Monte Carlo simulations.

Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and it proves to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest caliber. Here we study population annealing using as the main example the two-dimensional Ising model, which allows for particularly clean comparisons due to the available exact results and the wealth of published simulational studies employing other approaches. We analyze in depth the accuracy and precision of the method, highlighting its relation to older techniques such as simulated annealing and thermodynamic integration. We introduce intrinsic approaches for the analysis of statistical and systematic errors and provide a detailed picture of the dependence of such errors on the simulation parameters. The results are benchmarked against canonical and parallel tempering simulations.

Zero-temperature coarsening in the two-dimensional long-range Ising model.

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.

Nonflat histogram techniques for spin glasses.

We study the bimodal Edwards-Anderson spin glass comparing established methods, namely the multicanonical method, the 1/k ensemble, and parallel tempering, to an approach where the ensemble is modified by simulating power-law-shaped histograms in energy instead of flat histograms as in the standard multicanonical case. We show that by this modification a significant speed-up in terms of mean round-trip times can be achieved for all lattice sizes taken into consideration.

Aging in the Long-Range Ising Model.

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.

Combined Adsorption and Reaction in the Ternary Mixture N2, N2O4, NO2 on MIL-127 Examined by Computer Simulations.

A high selectivity of NO x over N2 (simulating air) is found in silico when studying the adsorption of the ternary mixture N2O4/NO2/N2 on the metal-organic framework MIL-127(Fe) by molecular simulations under consideration of the recombination reaction N2O4 ↔ 2NO2. The number of N atoms in nitrogen oxides NO x and that in N2 is used to define a selectivity of the combined adsorption and chemical recombination that can reach values of about 1000.

Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse.

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.

Accelerating Molecular Dynamics Simulations with Population Annealing.

Population annealing is a powerful tool for large-scale Monte Carlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors, and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.

Phase ordering kinetics of the long-range Ising model.

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.

Acceptance rate is a thermodynamic function in local Monte Carlo algorithms.

We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the three- and four-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.