SUPG-YZβ formulation for solving convection-dominated steady linear reaction-convection-diffusion equations

In this computational study, stabilized finite element solutions of convection-dominated steady linear reaction-convection-diffusion equations are examined. Although the standard Galerkin finite element method (GFEM) is one of the most robust, efficient, and reliable methods for many engineering simulations, it suffers from instability issues in solving convection-dominated problems. To this end, this work deals with a stabilized version of the standard GFEM, called the streamline-upwind/Petrov-Galerkin (SUPG) formulation, to overcome the instability issues in solving such problems. The stabilized formulation is further supplemented with YZβ shock-capturing to provide additional stability around sharp gradients. A comprehensive set of test computations is provided to compare the results obtained by using the GFEM, SUPG, and SUPG-YZβ formulations. It is observed that the GFEM solutions involve spurious oscillations for smaller values of the diffusion parameter, as expected. These oscillations are significantly eliminated when the SUPG formulation is employed. It is also seen that the SUPG-YZβ formulation provides better solution profiles near steep gradients, in general.

Moving Mountains: Reshaping the Activity Volcano of Electrocatalysis with Fluxional Subnano Clusters

The activity volcano derived from Sabatier analysis provides intuitive guide for catalyst design, but it also imposes fundamental limitations on the maximal activity and the pool of high-performance elements. Here we show that the activity volcano for oxygen reduction reaction (ORR) can be shifted and reshaped in the subnano regime. The fluxional behavior of subnano clusters, in both isolated and graphite-supported forms, not only breaks the linear scaling relationships but also causes an overall strengthening in adsorbate binding. The metals with optimal adsorbate binding in the bulk form (Pt/Pd) thus suffer over-binding issues, while the metals that under-bind in the bulk form (Ag/Au) gain optimal reaction energetics. In addition, the potential-dependence of isomer energies differ, causing non-linear reaction free energy-potential relations and enabling population-tuning of specific isomers, thereby surpassing the apex of the activity volcano. The shift of the volcano that puts under-binding elements closer to the top is likely general in fluxional cluster catalysis, and can be used for cluster catalyst design.

PSVII-27 Genetic analysis of disease resilience of nursery-to-finish pigs under a natural disease challenge model using reaction norms

Disease resilience is the ability of an animal to maintain performance across environments with different disease challenge loads (CL) and can be quantified using random regression reaction norm models that describe phenotype as a function of CL. Objectives of this study were to: 1) develop measures of CL using growth rate and clinical disease phenotypes under a natural disease challenge; 2) evaluate genetic variation in disease resilience. Data used were late nursery and finisher growth rates and clinical disease phenotypes, including medical treatment and mortality rates, and subjective health scores, collected on 50 batches of 60/75 crossbred (LRxY) barrows under a polymicrobial natural disease challenge. All pigs were genotyped using a 650K SNP panel. Different CL were derived from estimates of contemporary group effects and used as environmental covariates in reaction norm analyses of average daily gain (ADG) and treatment rate (TRT). The CL were compared based on model loglikelihoods and estimates of genetic variance, using both linear and cubic spline reaction norm models. Linear reaction norm models fitted the data significantly better than the standard genetic model and the cubic spline models fitted the data significantly better than the linear reaction norm model for most traits. CL based on early finisher ADG provided the best fit for nursery ADG, while CL based on clinical disease phenotypes was best for finisher ADG and TRT. With increasing CL, estimates of heritability for ADG initially decreased and then increased, while estimates of heritability for TRT generally increased with CL. Genetic correlations were low between ADG or TRT at high versus low CL but high for close CLs. Results can be used to select more resilient pigs across different CL levels, or high-performance animals at a given CL level, or a combination of these. Funded by Genome Canada, Genome Alberta, USDA-NIFA, and PigGenCanada.

EDP-convergence for a linear reaction-diffusion system with fast reversible reaction

We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system as a gradient flow of the free energy in the space of probability measures equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh-type functions for the reaction part. The fast-reaction limit is done on the level of the gradient structure by proving EDP-convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow-manifold. Moreover, the limit gradient system can be equivalently described by a coarse-grained gradient system, which induces a diffusion equation with a mixed diffusion constant for the coarse-grained slow variable.

State-constrained controllability of linear reaction-diffusion systems

We study the controllability of a coupled system of linear parabolic equations, with nonnegativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with an “approximate” nonnegativity constraint, and a another stronger one, with “exact” nonnegativity constraint, when all the diffusion coefficients are equal. The proofs are based on a “staircase” method. Finally, we show that state-constrained controllability admits a positive minimal time, even with weaker unilateral constraint on the state.