Gregory H. Miller

Experimental Shock Chemistry of Aqueous Amino Acid Solutions and the Cometary Delivery of Prebiotic Compounds

A series of shock experiments were conducted to assess thefeasibility of the delivery of organic compounds to theEarth via cometary impacts. Aqueous solutions containingnear-saturation levels of amino acids (lysine, norvaline,aminobutyric acid, proline, and phenylalanine) were sealedinside stainless steel capsules and shocked by ballisticimpact with a steel projectile plate accelerated along a12-m-long gun barrel to velocities of 0.5–1.9 km sec-1. Pressure-temperature-time histories of the shocked fluidswere calculated using 1D hydrodynamical simulations. Maximum conditions experienced by the solutions lasted0.85–2.7 μs and ranged from 5.1–21 GPa and 412–870 K. Recovered sample capsules were milled open and liquid wasextracted. Samples were analyzed using high performanceliquid chromatography (HPLC) and mass spectrometry (MS). In all experiments, a large fraction of the amino acidssurvived. We observed differences in kinetic behavior andthe degree of survivability among the amino acids. Aminobutyricacid appeared to be the least reactive, and phenylalanine appeared to be the most reactive of the amino acids. The impact process resulted in the formation of peptide bonds; new compounds included amino acid dimers and cyclic diketopiperazines. In our experiments, and in certain naturally occurring impacts, pressure has a greater influencethan temperature in determining reaction pathways. Our resultssupport the hypothesis that significant concentrations of organic material could survive a natural impact process.

Modeling of the pressure wave associated with arc fault

The development of computerized three-dimensional modeling for electrical arc events is presented. Data from a mathematical simulation of the pressure wave associated with arc faults are compared to experimental data obtained in equipment testing. Consequences of electrical arc faults and mitigation strategies are reviewed.

A Particle-in-cell Method with Adaptive Phase-space Remapping for Kinetic Plasmas

We present a new accurate and efficient particle-in-cell (PIC) method for computing the dynamics of one-dimensional kinetic plasmas. The method overcomes the numerical noise inherent in particle-based methods by periodically remapping the distribution function on a hierarchy of locally refined grids in phase space. Remapping on phase-space grids also provides an opportunity to integrate a collisional model and an associated grid-based solver. The positivity of the distribution function is enforced by redistributing excess phase-space density in a local neighborhood. We demonstrate the method on a number of standard plasma physics problems. It is shown that remapping significantly reduces the numerical noise and results in a more consistent second-order method than the standard PIC method. An error analysis is presented which is based on prior results of Cottet and Raviarts work [SIAM J. Numer. Anal., 21 (1984), pp. 52-76].

Toward a Mesoscale Model for the Dynamics of Polymer Solutions

Toward a Mesoscale Model for the Dynamics of Polymer Solutions G. H. Miller1 and D. Trebotich2 ∗ 1Department of Applied Science, University of California, One Shields Avenue, Davis, CA 95616, USA and Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA 2Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, USA

An Adaptive, High-Order Phase-Space Remapping for the Two Dimensional Vlasov--Poisson Equations

The numerical solution of the high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved using a local redistribution technique. While the one dimensional algorithm has been well established [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537], we present the two dimensional algorithm and its parallel implementation in this paper. A performance study of the parallel implementation is included. We discuss the scalability of the algorithm on massively parallel computers.

Short Note: An efficient solver for the equations of resistive MHD with spatially-varying resistivity

We regularize the variable coefficient Helmholtz equations arising from implicit time discretizations for resistive MHD, in a way that leads to a symmetric positive-definite system uniformly in the time step. Standard centered-difference discretizations in space of the resulting PDE leads to a method that is second-order accurate, and that can be used with multigrid iteration to obtain efficient solvers.

A Duhamel approach for the Langevin equations with holonomic constraints

To simulate polymer flows in microscale environments we have developed a numerical method that couples stochastic particle dynamics with an efficient incompressible Navier–Stokes solver. Here, we examine properties of the particle solver alone. We derive a Duhamel-form stochastic particle method for freely jointed polymers and demonstrate that it achieves 2-order weak convergence and 3/2-order strong convergence with holonomic constraints. For time steps approaching the relaxation time, our method displays greatly enhanced stability relative to comparable solvers based on linearised dynamics. Under these same conditions, our method has solution errors that are approximately six orders of magnitude smaller than that for the linearised algorithm.

A Hard Constraint Algorithm to Model Particle Interactions in DNA-Laden Flows

We present a new numerical method for particle interactions in polymer-fluid models of DNA-laden flows. The DNA is represented by a bead-rod polymer model and is fully-coupled to the fluid. The main objective in this work is to properly model polymer-polymer and polymer-surface interactions by enforcing the physical rod-rod and rod-surface non-crossing constraints. Our new method is based on a rigid constraint algorithm whereby rods elastically bounce off one another to prevent crossing, similar to our previous algorithm used to model polymer-surface interactions.

Minimal Rotationally Invariant Bases for Hyperelasticity

Rotationally invariant polynomial bases of the hyperelastic strain energy function are rederived using methods of group theory, invariant theory, and computational algebra. A set of minimal basis functions is given for each of the 11 Laue groups, with a complete set of rewriting syzygies. The ideal generated from this minimal basis agrees with the classic work of Smith and Rivlin [Trans. Amer. Math. Soc., 88 (1958), pp. 175--193]. However, the structure of the invariant algebra described here calls for fewer terms, beginning with the fourth degree in strain, for most groups.

A higher-order accurate fluid-particle algorithm for polymer flows

We present a new algorithm for the simulation of polymer-laden flows in microscale environments. Our algorithm is based on a hybridisation of high-order accurate continuum and particle methods. The continuum algorithm provides the basic framework for high-performance computations to resolve device length and time scales. It is coupled to a new particle method with an optimised treatment of particle interactions such that the time step is on the level of the fluid continuum. We demonstrate our simulation capability on the flow of polymers in a contraction microchannel used for single-molecule detection.