Field Theory Simulations Research Articles

Polymer field-theory simulations on graphics processing units

We report the first CUDA™ graphics-processing-unit (GPU) implementation of the polymer field-theoretic simulation framework for determining fully fluctuating expectation values of equilibrium properties for periodic and select aperiodic polymer systems. Our implementation is suitable both for self-consistent field theory (mean-field) solutions of the field equations, and for fully fluctuating simulations using the complex Langevin approach. Running on NVIDIA® Tesla T20 series GPUs, we find double-precision speedups of up to 30× compared to single-core serial calculations on a recent reference CPU, while single-precision calculations proceed up to 60× faster than those on the single CPU core. Due to intensive communications overhead, an MPI implementation running on 64 CPU cores remains two times slower than a single GPU.

Lattice Boltzmann method for multiscale self-consistent field theory simulations of block copolymers

A new Lattice Boltzmann (LB) approach is introduced to solve for the block copolymer propagator in polymer field theory. This method bridges two desired properties from different numerical techniques, namely: (i) it is robust and stable as the pseudo-spectral method and (ii) it is flexible and allows for grid refinement and arbitrary boundary conditions. While the LB method is not as accurate as the pseudo-spectral method, full self-consistent field theoretic simulations of block copolymers on graphoepitaxial templates yield essentially indistinguishable results from pseudo-spectral calculations. Furthermore, we were able to achieve speedups of ~100× compared to single CPU core implementations by utilizing graphics processing units. We expect this method to be very useful in multi-scale studies where small length scale details have to be resolved, such as in strongly segregating block copolymer blends or nanoparticle-polymer interfaces.

Inverse Design of Topographical Templates for Directed Self-Assembly of Block Copolymers.

A computational inverse design algorithm is presented that predicts the necessary topographical template to direct the self-assembly of a diblock copolymer thin film into a desired complex morphology. This topographical template is determined from the spatial configuration of a template that results in an energy minimum for the system. Degenerate solutions are accounted for by performing multiple simulations with random starting configurations of the topographical template and making a statistically weighted template that is tested using self-consistent field theory simulations. The final template is, thus, the inverse design solution of the desired block copolymer morphology. The results also yield nonintuitive post-configuration design principles.

Reliability analysis of beams on random elastic foundations

The classical problem of a beam on an elastic foundation has long been of practical interest to geotechnical engineers, because it provides a framework for computing deflections not only of foundations, but also of vertically oriented laterally loaded piles. The supporting soil can be modelled as an elastic medium, which can be calibrated to represent the stiffness of the soils adjacent to the beam (or pile). The objective of this paper is to study the influence of spatially random soil stiffness on deformations of transversely loaded homogeneous piles and beams, using a combination of finite-element analysis, random field theory and Monte Carlo simulations. Following code validation against alternative solutions, the method investigates how the statistically defined soil stiffness (mean, standard deviation and spatial correlation length) influences the mean and standard deviation of pile or beam deflection. The goal of such an approach is to estimate the probability of deflections exceeding some design threshold.

Self-assembly of graft copolymers in backbone-selective solvents: a route toward stable hierarchical vesicles

We employ self-consistent field theory and dissipative particle dynamics simulation to investigate self-assembly of graft copolymers in a backbone-selective solvent. It is found that the graft copolymers are capable of forming hierarchical vesicles such as multilamellar vesicles and large-compound vesicles in dilute solution. The self-consistent field calculations demonstrate that the formed hierarchical vesicles are thermodynamically stable, due to the nature of the graft copolymers. In addition, the dissipative particle dynamics simulations reveal that the pathway of the spontaneous vesicle formation in an initially homogeneous dilute solution is hierarchical. Unilamellar vesicles are first formed along the “standard” pathway, then gradually coalesced to compound or multilamellar sub-vesicles, and finally organized into large-compound or multilamellar vesicles. The results demonstrate the possibility of using two-component copolymers to generate stable aggregates with complex structures, and suggest a versatile and promising route to obtain the advanced nanostructured materials.

Self-assembly in a mixed polymer brush with inhomogeneous grafting density composition

While theoretical and numerical studies have shown the possibility of obtaining long-range ordering from the self-assembly of A–B binary mixed brushes similar to diblock copolymer thin films, such ordered patterns are not currently obtainable experimentally. In addition, most experimental observations of mixed brushes show relatively short range order with many defective structures. One explanation for poor microdomain ordering in experimental mixed brushes is a strong correlation between the spatial distribution of the grafting points and the self-assembly. To investigate this relationship in detail, we use self-consistent field theory (SCFT) simulations to study the phase-separated morphologies of melt mixed brushes with spatially varying grafting density compositions. Variations in the grafting density composition are implemented by modulating the grafting chain end distribution function to locally control the ratio of A and B chains attached to the surface, while maintaining uniform total grafting density. Three different types of grafting density composition variations are investigated: a linear ramping of the grafting density composition, deterministic sinusoidal variations, and random fluctuations with various correlation lengths and strengths. The resulting patterns in the micro-phase separated brush are seen to depend sensitively on both the wavelengths and amplitudes of the imposed grafting density fluctuations.

Complexation between weakly basic dendrimers and linear polyelectrolytes: effects of grafts, chain stiffness, and pOH

We develop and implement a new hybrid methodology combining self-consistent field theory (SCFT) and Monte Carlo simulations to study the complexation between negatively charged semiflexible linear polyelectrolyte (LPE) molecules and a positively charged dendrimer containing grafts of neutral polymers. We examine the influence of LPE stiffness, length of the dendrimer grafts, and solution pOH upon the characteristics of the resulting complexes. Our results indicate that increasing LPE stiffness reduces the dendrimer–LPE binding affinity and results in an overall higher net charge carried within the dendrimer molecule. When we varied the size of the grafts, the dendrimer–LPE binding strength was seen to decrease with increasing grafting chain length for the flexible LPE chains. In contrast, for stiff LPE chains, the binding strength was not seen to vary significantly with the grafting lengths. Overall, longer grafting lengths were seen to reduce the fraction of exposed LPE molecules, suggesting that grafted dendrimers may better shield nucleic acid material from serum nucleases. Lastly, we found that increasing the solution pOH was seen to enhance both the binding between the dendrimer and LPE molecules and the total positive charge carried by the complex.

Accurate calibration of the velocity-dependent one-scale model for domain walls

We study the asymptotic scaling properties of standard domain wall networks in several cosmological epochs. We carry out the largest field theory simulations achieved to date, with simulation boxes of size 20483, and confirm that a scale-invariant evolution of the network is indeed the attractor solution. The simulations are also used to obtain an accurate calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values cw=0.34±0.16 and kw=0.98±0.07, which are of higher precision than (but in agreement with) earlier estimates.

Simulations of long term methane hydrate dissociation by pressure reduction using an extended RetrasoCodeBright simulator

Methane hydrates in sediments are generally not in thermodynamic equilibrium. This implies that there may be several competing hydrate phase transitions in naturally existing hydrate reservoirs. In addition to dissociation due to instability imposed by changes in temperature and/or pressure which can bring hydrate outside stability also gradients in chemical potential caused by concentration gradients may lead to dissociation or formation of hydrate. Mineral surfaces bring additional thermodynamic phases of impact for hydrate phase transitions. The limited numbers of reservoir simulators which have incorporated hydrate are normally simplified by considering only pressure and temperature as criteria for hydrate stability region. In cases where kinetic description is used it is normally based on oversimplified models, typically models derived from experiments in pressure, temperature volume controlled laboratory cells. In the case of hydrate production through pressure reduction heat transport might dominate the kinetics and simplified heat transport kinetic models are frequently in use for this purpose. In lack of reliable data from full scale hydrate production the reservoir simulators are the only tools which can be used to evaluate efficiency of different production scenarios. Several research groups have been recently working on this subject. The approaches for inclusion of hydrates as a phase, and corresponding production simulation results from different simulators vary. In this work we have applied a fundamentally different approach, in which we have reworked a reactive transport reservoir simulator, namely RetrasoCodeBright into a hydrate simulator. This has been accomplished by adding hydrates as pseudo-mineral components. This opens up for non equilibrium thermodynamic description since kinetic models for different competing hydrate phase transitions can be included through their respective kinetic models. The main theoretical tool for generating these kinetic models has been phase field theory simulations, with thermodynamic properties derived from molecular modeling. The detailed results from these types of simulations provide information on the relative impact of mass transport, heat transport and thermodynamics of the phase transition, which enable qualified simplifications for implementation into RetrasoCodeBright. Details of the simulator, and numerical algorithms, are discussed in detail and some relevant examples are shown. In particular we applied the reservoir simulator to data from Mount Elbert methane hydrate deposits from North Slope, Alaska. Pressure reduction is used as gas production method.

Electrically charged curvaton

We consider the possibility that the primordial curvature perturbation was generated through the curvaton mechanism from a scalar field with an electric charge, or precisely the Standard Model U(1) weak hypercharge. This links the dynamics of the very early universe concretely to the Standard Model of particle physics, and because the coupling strength is known, it reduces the number of free parameters in the curvaton model. The gauge coupling also introduces several new physical effects.Charge fluctuations are generated during inflation, but they are screened by electron-positron pairs therefore do not violate observational constraints. After inflation, the curvaton interacts with thermal radiation which destroys the curvaton condensate and prevents the generation of curvature perturbations, unless the inflaton dynamics satisfy strong constraints. The curvaton also experiences a period of parametric resonance with the U(1) gauge field. Using the standard perturbative approach, we find that the model can generate the observed density perturbation for Hubble rate H*≳108GeV and curvaton mass m≳10−2H*, but with a level of non-Gaussianity (fNL≳130) that violates observational constraints. However, previous studies have shown that the parametric resonance changes the predicted perturbations significantly, and therefore fully non-linear numerical field theory simulations are required.

Morphological control of grafted polymer films via attraction to small nanoparticle inclusions

Control of the morphologies of polymer films and layers by addition of nanosize particles is a novel technique for design of nanomaterials and is also at the core of some important biological processes. In order to facilitate the analysis of experimental data and enable predictive engineering of such systems, solid theoretical understanding is necessary. We study theoretically and computationally the behavior of plane-grafted polymer layers (brushes) in athermal solvent, decorated with small nanoparticle inclusions, using mean field theory and coarse-grained simulations. We show that the morphology of such layers is very sensitive to the interaction between the polymers and the nanoparticles and to the nanoparticle density. In particular, the mean field model shows that for a certain range of parameters, the nanoparticles induce a sharp transition in the layer height, accompanied by a sharp increase in the number of adsorbed nanoparticles. At other parameter values, the layer height depends smoothly on the nanoparticle concentration. Predictions of the theoretical model are verified by Langevin dynamics simulations. The results of the paper are in qualitative agreement with experiments on in vitro models of biological transport and suggest strategies for morphological control of nanocomposite materials.

Self-Assembly of a Mixture System Containing Polypeptide Graft and Block Copolymers: Experimental Studies and Self-Consistent Field Theory Simulations

Self-assembly behavior of mixture systems containing poly(γ-benzyl-L-glutamate)-poly(ethylene glycol) graft (PBLG-g-PEG) and block (PBLG-b-PEG) copolymers in aqueous solution was investigated by both experiments and computer simulations. Pure graft copolymers self-assembled into vesicles, and pure block copolymers aggregated into spherical micelles or vesicles, while, for the mixture systems, hybrid cylindrical micelles were observed. In addition to the experimental observations, self-consistent field theory (SCFT) simulations were performed on the self-assembly behavior of graft/block copolymer mixtures. Simulation results reproduced the morphological transitions observed in the experiments. Moreover, from the SCFT simulations, the chain distributions of copolymers in the aggregates were obtained. For the hybrid cylindrical micelles, block copolymers were found to mainly locate at the ends of aggregates, which prevents the fusion of cylinders to vesicles. By combining experimental findings with simulation results, the mechanism regarding the morphological transition of the aggregates formed by graft/block copolymer mixtures is proposed.

Symmetric partitioned Runge–Kutta methods for differential equations on Lie groups

In this paper, we develop a higher order symmetric partitioned Runge–Kutta method for a coupled system of differential equations on Lie groups. We start with a discussion on partitioned Runge–Kutta methods on Lie groups of arbitrary order. As symmetry is not met for higher orders, we generalize the method to a symmetric partitioned Runge–Kutta (SPRK) scheme. Furthermore, we derive a set of coefficients for convergence order 4. The SPRK integration method can be used, for example, in simulations of quantum field theories. Finally, we compare the new SPRK scheme numerically with the Störmer–Verlet scheme, one of the state-of-the-art schemes used in this subject.

Interorbital correlation effects on heavy-electron systems

We study an extended periodic Anderson model, which includes correlations between conduction and $f$ electrons, by employing dynamical mean field theory and continuous-time quantum Monte Carlo simulations. It is clarified how the antiferromagnetic phase, which is stabilized in the ordinary periodic Anderson model, changes into a charge ordered (CO) phase in the strong $c$-$f$ interaction region. A systematic analysis of the effects due to the hybridization and the $c$-$f$ interaction evidences the existence of a critical end point for the CO transition; the quantum phase transition between the CO phase and the paramagnetic phase is of first (second) order in the weak (moderate) hybridization region. We also address the effects of the Hubbard-type correlations among conduction electrons on the phase diagram.

Cosmic string evolution with a conserved charge

Cosmic strings with degrees of freedom beyond the standard Abrikosov-Nielsen-Olesen or Nambu-Goto strings are ubiquitous in field theory as well as in models with extra dimensions, such as string theoretic brane inflation scenarios. Here we carry out an analytic study of a simplified version of one such cosmic string model. Specifically, we extend the velocity-dependent one-scale (VOS) string evolution model to the case where there is a conserved microscopic charge on the string worldsheet. We find that whether the standard scale-invariant evolution of the network is preserved or destroyed due to the presence of the charge will crucially depend on the amount of damping and energy losses experienced by the network. This suggests, among other things, that results derived in Minkowski space (field theory) simulations may not extend to the case of an expanding universe.

Validation of a hybrid MD-SCF coarse-grained model for DPPC in non-lamellar phases

In the framework of a recently developed scheme for a hybrid particle-field simulation technique where self-consistent field theory and molecular dynamics simulation method are combined, specific coarse-grained models for aqueous solutions of phospholipids have been validated. In particular, the transferability of the model in the correct reproduction of non-lamellar phases has been validated against reference particle–particle simulations. By varying the water content, the proposed model is able to correctly describe the different morphologies that are experimentally observed such as micelles and reverse micelles. The lower computational costs of the hybrid techniques allow us to perform simulations of large-scale systems that are needed to investigate the applications of self-assembled structures of lipids in nanotechnologies.

Theoretical Studies of Methane Hydrate Dissociation in Porous Media Using RetrasoCodeBright Simulator

Methane hydrates in reservoir are generally not in chemical equilibrium, there may be several competing hydrate phase transitions like for instance hydrate dissociation due to pressure or temperature changes, hydrate reformation, hydrate dissociation due to contact with under saturated fluids and mineral surfaces. The limited numbers of reservoir simulators, which have incorporated hydrate, are normally simplified by considering only pressure and temperature as criteria for hydrate stability region. If kinetic description is used it is very oversimplified and usually extracted from models derived from experiments in pressure, temperature volume controlled laboratory cells. Reservoir scale simulation of hydrate dynamics are important investigations, which enable engineers to predict the production potential of a methane hydrate reservoir and propose efficient production scenarios. Several research groups have been recently working on this subject but there seems to be significant differences in their approaches and results. In this work a reactive transport reservoir simulator, namely Retraso CodeBright (RCB), has been modified to account for hydrate kinetic phase transitions in the reservoir. For this purpose, hydrate has been added as a pseudo-mineral component and advanced kinetic models of hydrate phase transitions have been developed. The main tools for generating these models have been phase field theory simulations, with thermodynamic properties derived from molecular modelling. The detailed results from these types of simulations provides information on the relative impact of mass transport, heat transport and thermodynamics of the phase transition which enable qualified simplifications for implementation into RCB. The primary step was to study dissociation of methane hydrate under depressurization condition with a certain kinetic rate on a model inspired based on real methane reservoir. Messoyakha methane hydrate reservoir from East Siberia was chosen for constructing model for this theoretical study. Details of the simulator, and numerical algorithms, are discussed in detail and some relevant examples are shown.

Quantum Simulation of Quantum Field Theories in Trapped Ions

We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.

Exploring Lateral Microphase Separation in Mixed Polymer Brushes by Experiment and Self-Consistent Field Theory Simulations

Similar to block copolymers, mixed polymer brushes are physically constrained and, upon annealing, microphase separate into nanodomains with morphologies largely dependent on the volume fractions of the polymers. A combination of experimental analysis of polystyrene (PS)/poly(methyl methacrylate) (PMMA) brushes and self-consistent field theory (SCFT) simulations is employed to determine the phases of annealed binary brushes. By annealing the brushes under conditions that maximize lateral versus vertical separation, a rich array of phases are observed with general agreement to predictions by SCFT simulations. The incorporation of random perturbations to the grafting density in SCFT simulations accounts for disorder in the arrangement of the polymer domains for the PS/PMMA brushes. Additionally, autocorrelation of the polymer domains yields an experimental domain spacing that is nearly 2 times greater than SCFT predictions, which is hypothesized to result from polydispersity in the PS/PMMA brushes. These fi...