arXiv subjects

Glenn H. Fredrickson

Publications and source records attributed to Glenn H. Fredrickson.

At least 19 recordsLinked to original sources

arXiv2026

Exact kinetic propagators for coherent state complex Langevin simulations

We introduce and benchmark an improved algorithm for complex Langevin simulations of bosonic coherent state path integrals. Our approach utilizes a Strang splitting of the imaginary-time propagator rather than the conventional linear-order Taylor expansion, allowing us to construct an action that incorporates higher-order terms at negligible computational cost. The resulting algorithm enjoys guaranteed linear stability independent of the imaginary-time discretization, enabling more resource-efficient simulations. We demonstrate this improved performance for single-species bosons and for two-component bosons with Rashba spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2025

Fast phase prediction of charged polymer blends by white-box machine learning surrogates

Compatibilized polymer blends are a complex, yet versatile and widespread category of material. When the components of a binary blend are immiscible, they are typically driven towards a macrophase-separated state, but with the introduction of electrostatic interactions, they can be either homogenized or shifted to microphase separation. However, both experimental and simulation approaches face significant challenges in efficiently exploring the vast design space of charge-compatibilized polymer blends, encompassing chemical interactions, architectural properties, and composition. In this work, we introduce a white-box machine learning approach integrated with polymer field theory to predict the phase behavior of these systems, which is significantly more accurate than conventional black-box machine learning approaches. The random phase approximation (RPA) calculation is used as a testbed to determine polymer phases. Instead of directly predicting the polymer phase output of RPA calculations from a large input space by a machine learning model, we build a parallel partial Gaussian process model to predict the most computationally intensive component of the RPA calculation that only involves polymer architecture parameters as inputs. This approach substantially reduces the computational cost of the RPA calculation across a vast input space with nearly 100% accuracy for out-of-sample prediction, enabling rapid screening of polymer blend charge-compatibilization designs. More broadly, the white-box machine learning strategy offers a promising approach for dramatic acceleration of polymer field-theoretic methods for mapping out polymer phase behavior.

cond-mat.soft↗

arXiv2025

A projected complex Langevin sampling method for bosons in the canonical and microcanonical ensembles

We introduce a projected complex Langevin (CL) numerical sampling method -- a fictitious Langevin dynamics scheme that uses numerical projection to sample a constrained stationary distribution with highly oscillatory character. Despite the complex-valued degrees of freedom and associated sign-problem, the projected CL method succeeds as a natural extension of real-valued projected Langevin processes. In the new proposed method, complex-valued Lagrange multipliers are determined to enforce constraints to machine precision at each iteration. To illustrate the efficacy of this approach, we adapt the projected CL method to sample coherent state quantum field theories describing interacting Bose gases, which are realized in modern cold-atom experiments. We apply projected CL to two scenarios with holomorphic constraints, the canonical and microcanonical ensembles, and show that projected CL reproduces the correct thermodynamic observables. We further observe improved numerical stability and accuracy at larger timesteps when compared to the previous state-of-the-art method for performing constrained CL sampling.

cond-mat.quant-gas↗

arXiv2024

Finite temperature stability of quantized vortex structures in rotating Bose-Einstein condensates via complex Langevin simulation

The thermodynamic stability of quantized vortex patterns in rotating Bose-Einstein condensates is assessed at finite temperature using complex Langevin sampling. We construct a temperature-rotation frequency phase diagram and find that that vortices are stabilized at lower rotation speeds by the addition of quantum and thermal fluctuations. The coherent states field theoretic representation of the imaginary time path integral enables efficient simulation of large systems at finite temperature, and the complex Langevin simulation scheme bypasses the sign problems that arise from the complex-valued coherent states fields as well as the gauge potential describing solid body rotation. Field operators allow us to generate high-resolution images of particle and momentum density of the cloud. Quantized vortices appear as dark spots on density images, and vector plots of cloud momentum detail circulation around each vortex.

cond-mat.quant-gas↗

arXiv2024

Emergence of Disordered Hyperuniformity in Melts of Linear Diblock Copolymers

Disordered hyperuniform (DHU) systems are recently discovered exotic states of matter, where (normalized) large-scale density fluctuations are completely suppressed as in crystals, even though the systems are isotropic and lack conventional long-range order. Despite recent success, realizing such systems using bottom-up approaches remains challenging. Here, we study the large-scale behavior of neat melts of linear diblock copolymers using large-cell self-consistent field theory (SCFT) simulations. We initialize SCFT simulations using point patterns that correspond to the local energy minimum of the so-called Quantizer energy, a geometric functional related to the free energy of copolymeric self-assemblies. Upon relaxation via the SCFT simulations, we obtain a new class of metastable disordered micelle mesophases that are hyperuniform. Moreover, we find that DHU micelle mesophases possess very similar free energies to the thermodynamically stable body-centered cubic sphere mesophases and are also much more favorable energetically than previously obtained liquid-like packings. Our findings shed light on the design of novel disordered hyperuniform materials using bottom-up approaches, and suggest new possibilities for technological applications, e.g., novel non-iridescent structural colors.

cond-mat.soft↗

arXiv2023

Emergence of a spin microemulsion in spin-orbit coupled Bose-Einstein condensates

We report the first numerical prediction of a "spin microemulsion" -- a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions -- in two-dimensional systems of spinor Bose-Einstein condensates with isotropic Rashba spin-orbit coupling. Using field-theoretic numerical simulations, we investigated the melting of a low-temperature stripe phase with supersolid character and find that the stripes lose their superfluidity at elevated temperature and undergo a Kosterlitz--Thouless-like transition into a spin microemulsion. Momentum distribution calculations highlight a thermally broadened occupation of the Rashba circle of low-energy states with macroscopic and isotropic occupation around the ring. We provide a finite-temperature phase diagram that positions the emulsion as an intermediate, structured isotropic phase with residual quantum character before transitioning at higher temperature into a structureless normal fluid.

cond-mat.quant-gas↗

arXiv2023

Machine Learning and Polymer Self-Consistent Field Theory in Two Spatial Dimensions

A computational framework that leverages data from self-consistent field theory simulations with deep learning to accelerate the exploration of parameter space for block copolymers is presented. This is a substantial two-dimensional extension of the framework introduced in [1]. Several innovations and improvements are proposed. (1) A Sobolev space-trained, convolutional neural network (CNN) is employed to handle the exponential dimension increase of the discretized, local average monomer density fields and to strongly enforce both spatial translation and rotation invariance of the predicted, field-theoretic intensive Hamiltonian. (2) A generative adversarial network (GAN) is introduced to efficiently and accurately predict saddle point, local average monomer density fields without resorting to gradient descent methods that employ the training set. This GAN approach yields important savings of both memory and computational cost. (3) The proposed machine learning framework is successfully applied to 2D cell size optimization as a clear illustration of its broad potential to accelerate the exploration of parameter space for discovering polymer nanostructures. Extensions to three-dimensional phase discovery appear to be feasible.

cond-mat.mtrl-sci↗

arXiv2023

Thermodynamic engine with a quantum degenerate working fluid

Can quantum mechanical thermodynamic engines outperform their classical counterparts? To address one aspect of this question, we experimentally realize and characterize an isentropic thermodynamic engine that uses a Bose-condensed working fluid. In this engine, an interacting quantum degenerate gas of bosonic lithium is subjected to trap compression and relaxation strokes interleaved with strokes strengthening and weakening interparticle interactions. We observe a significant enhancement in efficiency and power when using a Bose-condensed working fluid, compared to the case of a non-degenerate thermal gas. We demonstrate reversibility, and measure power and efficiency as a function of engine parameters including compression ratio and cycle time. Results agree quantitatively with interacting finite temperature field-theoretic simulations that closely replicate the length and energy scales of the working fluid.

cond-mat.quant-gas↗

arXiv2022

Multiscale modeling of solute diffusion in triblock copolymer membranes

We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model's predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

cond-mat.soft↗

arXiv2020

Shear Induced Demixing in Bidisperse and Polydisperse Polymer Blends: Predictions From a Multi-Fluid Model

In light of recent advancements in the constitutive modelling of bidisperse and polydisperse entangled linear polymers, we present a new multi fluid generalization of the classic two fluid approximation for flows of inhomogeneous polymer blends. As an application of the model, we consider predictions for the linear and nonlinear dynamics of shear induced demixing (SID) instabilities in blends with bidisperse and lognormal molecular weight distributions. We find that even in the absence of any chemical contrast between component chains, an imposed flow can induce a demixing instability provided there is sufficient contrast in the size of the two chains. The lower bound polydispersity for SID coincides with the point where elastic forces (kT per entanglement) scaled by the contrast between chains (e.g. polydispersity index minus one) exceed the entropic forces for mixing (kT per chain). For bi-disperse blends, we show that the non-linear dynamics of SID strongly resemble what has previously been shown for SID in entangled polymer solutions.

cond-mat.soft↗

arXiv2017

Mechanics of an Asymmetric Hard--Soft Lamellar Nanomaterial

Nanolayered lamellae are common structures in nanoscience and nanotechnology, but most are nearly symmetric in layer thickness. Here, we report on the structure and mechanics of highly asymmetric and thermodynamically stable soft--hard lamellar structures self-assembled from optimally designed PS1-(PI-b-PS2)3 miktoarm star block copolymers. The remarkable mechanical properties of these strong and ductile PS (polystyrene)-based nanomaterials can be tuned over a broad range by varying the hard layer thickness while maintaining the soft layer thickness constant at 13 nm. Upon deformation, thin PS lamellae (\textless{}100 nm) exhibited kinks and predamaged/damaged grains, as well as cavitation in the soft layers. In contrast, deformation of thick lamellae (\textgreater{}100 nm) manifests cavitation in both soft and hard nanolayers. In situ tensile-SAXS experiments revealed the evolution of cavities during deformation and confirmed that the damage in such systems reflects both plastic deformation by shear and residual cavities. The aspects of the mechanics should point to universal deformation behavior in broader classes of asymmetric hard--soft lamellar materials, whose properties are just being revealed for versatile applications.

cond-mat.soft↗

arXiv2016

A finite element approach to self-consistent field theory calculations of multiblock polymers

Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.

cond-mat.soft↗

arXiv2013

Dynamics of Polymers: a Mean-Field Theory

We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field $ρ$ and a conjugate MSR response field $ϕ$, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method (SCMF).

cond-mat.soft↗

arXiv2013

Coherent States Formulation of Polymer Field Theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field (AF) framework, the CS formulation does not contain an embedded non-linear, non-local functional of the auxiliary fields, and the action of the field theory has a fully explicit, finite-order and semi-local polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.

cond-mat.soft↗

arXiv2012

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 30x compared to single-core serial calculations on a recent reference CPU, while single-precision calculations proceed up to 60x 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.

physics.comp-ph↗

arXiv2010

Phase Separation in Symmetric Mixtures of Oppositely Charged Rodlike Polyelectrolytes

Phase separation in salt-free symmetric mixtures of oppositely charged rodlike polyelectrolytes is studied using quasi-analytical calculations. Stability analyses for the isotropic-isotropic and the isotropic-nematic phase transitions in the mixtures are carried out and demonstrate that electrostatic interactions favor nematic ordering. Coexistence curves for the symmetric mixtures are also constructed and are used to examine the effects of linear charge density and electrostatic interaction strength on rodlike polyelectrolyte complexation. It is found that the counterions are uni- formly distributed in the coexisting phases for low electrostatic interaction strengths dictated by the linear charge density of the polyelectrolytes and Bjerrum's length. However, the counterions also partition along with the rodlike polyelectrolytes with an increase in the electrostatic interaction strength. It is shown that the number density of the counterions is higher in the concentrated (or "coacervate") phase than in the dilute (or supernatant) phase. In contrast to such rodlike mixtures, flexible polyelectrolyte mixtures can undergo only isotropic-isotropic phase separation. A comparison of the coexistence curves for weakly-charged rodlike mixtures with those of analogous flexible polyelectrolyte mixtures reveals that the electrostatic driving force for the isotropic-isotropic phase separation is stronger in the flexible mixtures.

cond-mat.soft↗

arXiv2009

Thermoreversible Associating Polymer Networks: I. Interplay of Thermodynamics, Chemical Kinetics, and Polymer Physics

Hybrid molecular dynamics/Monte Carlo simulations used to study melts of unentangled, thermoreversibly associating supramolecular polymers. In this first of a series of papers, we describe and validate a model that is effective in separating the effects of thermodynamics and chemical kinetics on the dynamics and mechanics of these systems, and is extensible to arbitrarily nonequilibrium situations and nonlinear mechanical properties. We examine the model's quiescent (and heterogeneous) dynamics, nonequilibrium chemical dynamics, and mechanical properties. Many of our results may be understood in terms of the crossover from diffusion-limited to kinetically-limited sticky bond recombination, which both influences and is influenced by polymer physics, i. e. the connectivity of the parent chains.

cond-mat.soft↗

arXiv2009

Theory of polyzwitterion conformations

Conformational characteristics of polyzwitterionic molecules in aqueous solutions are investigated using the variational method. Analytical relations are derived for the radius of gyration of a single polyzwitterionic chain as a function of the chain length, electrostatic interaction strength, added salt concentration, dipole moment and degree of ionization of the zwitterionic monomers. In the absence of the small ions (counterions and coions) near the polyzwitterionic chain, attractive dipole-dipole interactions are shown to induce a collapse of the polyzwitterionic chain. However, in the presence of the small ions, the radius of gyration is shown to be an interplay of the screening of the electrostatic interactions and the counterion adsorption on the zwitterionic sites. In addition to the well-known Debye-Huckel screening of the charge-charge interactions, screening of the charge-dipole and dipole-dipole interactions are found to play important roles in determining the size of the chain. Functional forms for the screened charge-dipole and dipole-dipole interaction potentials are presented. Furthermore, counterion adsorption on the zwitterionic monomers is predicted to be asymmetric depending on the nature of the added salt and the zwitterionic groups. Qualitative remarks regarding the solubility of these molecules in aqueous solutions along with the classical "anti-polyelectrolyte" effect (increase in the solubility in water with the addition of salt) are presented.

cond-mat.stat-mech↗