Performance of explicit and IMEX MRI multirate methods on complex reactive flow problems within modern parallel adaptive structured grid frameworks

Large-scale multiphysics simulations are computationally challenging due to the coupling of multiple processes with widely disparate time scales. The advent of exascale computing systems exacerbates these challenges, since these enable ever increasing size and complexity. Recently, there has been renewed interest in developing multirate methods as a means to handle the large range of time scales, as these methods may afford greater accuracy and efficiency than more traditional approaches of using IMEX and low-order operator splitting schemes. However, there have been few performance studies that compare different classes of multirate integrators on complex application problems. We study the performance of several newly developed multirate infinitesimal (MRI) methods, implemented in the SUNDIALS solver package, on two reacting flow model problems built on structured mesh frameworks. The first model revisits the work of Emmet et al. (2014) on a compressible reacting flow problem with complex chemistry that is implemented using BoxLib but where we now include comparisons between a new explicit MRI scheme with the multirate spectral deferred correction (SDC) methods in the original paper. The second problem uses the same complex chemistry as the first problem, combined with a simplified flow model, but run at a large spatial scale where explicit methods become infeasible due to stability constraints. Two recently developed implicit-explicit MRI multirate methods are tested. These methods rely on advanced features of the AMReX framework on which the model is built, such as multilevel grids and multilevel preconditioners. The results from these two problems show that MRI multirate methods can offer significant performance benefits on complex multiphysics application problems and that these methods may be combined with advanced spatial discretization to compound the advantages of both

A Staggered Scheme for the Compressible Fluctuating Hydrodynamics of Multispecies Fluid Mixtures

We present a numerical formulation for the solution of non-isothermal, compressible, Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are significantly simplified and compact discretization of the diffusive and stochastic momentum fluxes, and an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously in Balakrishnan et al., Phys. Rev. E 89:013017, 2014. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients, and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo (DSMC) method.Comment: 20 pages, 9 figures, 9 pages supplementary materia

Low Mach Number Fluctuating Hydrodynamics of Diffusively Mixing Fluids

We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fast isentropic fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatio-temporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions. We construct several explicit Runge-Kutta temporal integrators that strictly maintain the equation of state constraint. The resulting spatio-temporal discretization is second-order accurate deterministically and maintains fluctuation-dissipation balance in the linearized stochastic equations. We apply our algorithms to model the development of giant concentration fluctuations in the presence of concentration gradients, and investigate the validity of common simplications neglecting the spatial non-homogeneity of density and transport properties. We perform simulations of diffusive mixing of two fluids of different densities in two dimensions and compare the results of low Mach number continuum simulations to hard-disk molecular dynamics simulations. Excellent agreement is observed between the particle and continuum simulations of giant fluctuations during time-dependent diffusive mixing

Surface Coverage Dynamics for Reversible Dissociative Adsorption on Finite Linear Lattices

Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, $N$, and the ratio of the adsorption and desorption rates. Using these results, we show that the system has finite size effects. For comparable $N$'s, the finite size effect is significantly larger when $N$ is even than when $N$ is odd. Moreover, as $N$ increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also investigate the time evolution of the surface coverage and discuss why cluster-expansion-based approximations fail to provide the correct kinetics. Finally, we analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites and show that the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion

The NEI/NCBI dbGAP database: Genotypes and haplotypes that may specifically predispose to risk of neovascular age-related macular degeneration

<p>Abstract</p> <p>Background</p> <p>To examine if the significantly associated SNPs derived from the genome wide allelic association study on the AREDS cohort at the NEI (dbGAP) specifically confer risk for neovascular age-related macular degeneration (AMD). We ascertained 134 unrelated patients with AMD who had one sibling with an AREDS classification 1 or less and was past the age at which the affected sibling was diagnosed (268 subjects). Genotyping was performed by both direct sequencing and Sequenom iPLEX system technology. Single SNP analyses were conducted with McNemar's Test (both 2 × 2 and 3 × 3 tests) and likelihood ratio tests (LRT). Conditional logistic regression was used to determine significant gene-gene interactions. LRT was used to determine the best fit for each genotypic model tested (additive, dominant or recessive).</p> <p>Results</p> <p>Before release of individual data, <it>p</it>-value information was obtained directly from the AREDS dbGAP website. Of the 35 variants with <it>P </it>< 10^-6examined, 23 significantly modified risk of neovascular AMD. Many variants located in tandem on 1q32-q22 including those in <it>CFH</it>, <it>CFHR4</it>, <it>CFHR2</it>, <it>CFHR5</it>, <it>F13B</it>, <it>ASPM </it>and <it>ZBTB </it>were significantly associated with AMD risk. Of these variants, single SNP analysis revealed that <it>CFH </it>rs572515 was the most significantly associated with AMD risk (P < 10^-6). Haplotype analysis supported our findings of single SNP association, demonstrating that the most significant haplotype, GATAGTTCTC, spanning <it>CFH</it>, <it>CFHR4</it>, and <it>CFHR2 </it>was associated with the greatest risk of developing neovascular AMD (<it>P </it>< 10^-6). Other than variants on 1q32-q22, only two SNPs, rs9288410 (<it>MAP2</it>) on 2q34-q35 and rs2014307 (<it>PLEKHA1</it>/<it>HTRA1</it>) on 10q26 were significantly associated with AMD status (<it>P </it>= .03 and <it>P </it>< 10^-6respectively). After controlling for smoking history, gender and age, the most significant gene-gene interaction appears to be between rs10801575 (<it>CFH</it>) and rs2014307 (<it>PLEKHA1</it>/<it>HTRA1</it>) (<it>P </it>< 10^-11). The best genotypic fit for rs10801575 and rs2014307 was an additive model based on LRT. After applying a Bonferonni correction, no other significant interactions were identified between any other SNPs.</p> <p>Conclusion</p> <p>This is the first replication study on the NEI dbGAP SNPs, demonstrating that alleles on 1q, 2q and 10q may predispose an individual to AMD.</p

Identification of Antifungal Compounds Active against Candida albicans Using an Improved High-Throughput Caenorhabditis elegans Assay

Candida albicans, the most common human pathogenic fungus, can establish a persistent lethal infection in the intestine of the microscopic nematode Caenorhabditis elegans. The C. elegans–C. albicans infection model was previously adapted to screen for antifungal compounds. Modifications to this screen have been made to facilitate a high-throughput assay including co-inoculation of nematodes with C. albicans and instrumentation allowing precise dispensing of worms into assay wells, eliminating two labor-intensive steps. This high-throughput method was utilized to screen a library of 3,228 compounds represented by 1,948 bioactive compounds and 1,280 small molecules derived via diversity-oriented synthesis. Nineteen compounds were identified that conferred an increase in C. elegans survival, including most known antifungal compounds within the chemical library. In addition to seven clinically used antifungal compounds, twelve compounds were identified which are not primarily used as antifungal agents, including three immunosuppressive drugs. This assay also allowed the assessment of the relative minimal inhibitory concentration, the effective concentration in vivo, and the toxicity of the compound in a single assay

Phylogenetic ctDNA analysis depicts early-stage lung cancer evolution.

The early detection of relapse following primary surgery for non-small-cell lung cancer and the characterization of emerging subclones, which seed metastatic sites, might offer new therapeutic approaches for limiting tumour recurrence. The ability to track the evolutionary dynamics of early-stage lung cancer non-invasively in circulating tumour DNA (ctDNA) has not yet been demonstrated. Here we use a tumour-specific phylogenetic approach to profile the ctDNA of the first 100 TRACERx (Tracking Non-Small-Cell Lung Cancer Evolution Through Therapy (Rx)) study participants, including one patient who was also recruited to the PEACE (Posthumous Evaluation of Advanced Cancer Environment) post-mortem study. We identify independent predictors of ctDNA release and analyse the tumour-volume detection limit. Through blinded profiling of postoperative plasma, we observe evidence of adjuvant chemotherapy resistance and identify patients who are very likely to experience recurrence of their lung cancer. Finally, we show that phylogenetic ctDNA profiling tracks the subclonal nature of lung cancer relapse and metastasis, providing a new approach for ctDNA-driven therapeutic studies

Fluctuating hydrodynamics of reactive liquid mixtures

Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell–Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier–Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability