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Because surface-grafted polyelectrolyte brushes (PEBs) are responsive to external stimuli, such as electric fields and ionic strength, PEBs are attractive for applications ranging from drug delivery to separations technologies. Essential to PEB utilization is understanding how critical parameters like grafting density (σ) impact PEB structure and the dynamics of the PEB and counterions. To study the effect of σ on PEB and counterion structure and dynamics, we fine-tune a coarse-grained model that retains the chemical specificity of a strong polyelectrolyte, poly[(2-(methacryloyloxy)ethyl) trimethylammonium chloride] (PMETAC), using the MARTINI forcefield. Using “salt-free” conditions where the counterion concentration balances the charge on the brush, we build coarse-grained (CG) molecular dynamics simulations for MARTINI PMETAC brushes (N=150 monomers; MW = 31.2 kg/mol) at experimentally relevant values of σ = 0.05, 0.10, 0.20, and 0.40 chains/nm2. Using 5 µs simulations, we investigate the effects of grafting density on PEB structure, ion dissociation dynamics, polymer mobility, and counterion diffusivity. Results show that competition between electrostatic interactions, steric hindrance, and polymer mobility controls counterion diffusivity. The interplay of these factors leads to diffusivity that depends non-monotonically on σ, with counterion diffusivity peaking at an intermediate σ = 0.10 chains/nm2. 

Abstract Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our Universe. 

Abstract We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods.