Shock-layer bounds for a singularly perturbed equation

The size of the shock-layer governed by a conservation law is studied. The conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum-principle arguments. The bounding functions demonstrate that the size of the shock-layer is proportional to the parameter multiplying the diffusion term

Interface conditions for domain decomposition with radical grid refinement

Interface conditions for coupling the domains in a physically motivated domain decomposition method are discussed. The domain decomposition is based on an asymptotic-induced method for the numerical solution of hyperbolic conservation laws with small viscosity. The method consists of multiple stages. The first stage is to obtain a first approximation using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problem via a domain decomposition. The method is derived and justified via singular perturbation techniques

An iterative method for systems of nonlinear hyperbolic equations

An iterative algorithm for the efficient solution of systems of nonlinear hyperbolic equations is presented. Parallelism is evident at several levels. In the formation of the iteration, the equations are decoupled, thereby providing large grain parallelism. Parallelism may also be exploited within the solves for each equation. Convergence of the interation is established via a bounding function argument. Experimental results in two-dimensions are presented

Asymptotic-induced numerical methods for conservation laws

Asymptotic-induced methods are presented for the numerical solution of hyperbolic conservation laws with or without viscosity. The methods consist of multiple stages. The first stage is to obtain a first approximation by using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problems identified by using techniques derived via asymptotics. Finally, a residual correction increases the accuracy of the scheme. The method is derived and justified with singular perturbation techniques

Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups

An asymptotic induced numerical method for the convection-diffusion-reaction equation

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method

Optimal control of thermally coupled Navier Stokes equations

The optimal boundary temperature control of the stationary thermally coupled incompressible Navier-Stokes equation is considered. Well-posedness and existence of the optimal control and a necessary optimality condition are obtained. Optimization algorithms based on the augmented Lagrangian method with second order update are discussed. A test example motivated by control of transport process in the high pressure vapor transport (HVPT) reactor is presented to demonstrate the applicability of our theoretical results and proposed algorithm

The control of purity and stoichiometry of compound semiconductors by high vapor pressure transport

In this report we summarize the results of a three year research program on high pressure vapor transport (HPVT) of compound semiconductors. Most of our work focused onto pnictides, in particular ZnGeP2, as a model system. Access to single crystals of well controlled composition of this material is desired for advancing the understanding and control of its point defect chemistry in the contest of remote, real-time sensing of trace impurities, e.g., greenhouse gases, in the atmosphere by ZnGeP2 optical parametric oscillators (OPO's)

Deciphering the past to inform the future: preparing for the next (“really big”) extreme event

Climate change will bring more extremes in temperature and precipitation that will impact productivity and ecosystem resilience throughout agroecosystems worldwide. Historical events can be used to identify drivers that impact future events. A catastrophic drought in the US in the 1930s resulted in an abrupt boundary between areas severely impacted by the Dust Bowl and areas that were less severely affected. Historical primary production data confirmed the location of this boundary at the border between two states (Nebraska and Iowa). Local drivers of weather and soils explained production responses across the boundary before and after the drought (1926–1948). During the drought, however, features at the landscape scale (soil properties and wind velocities) and regional scale (the Missouri River, its floodplain, and the nearby Loess Hills) explained most of the observed variance in primary production. The impact of future extreme events may be affected by land surface properties that either accentuate or ameliorate the effects of these events. Consideration of large-scale geomorphic processes may be necessary to interpret and manage for catastrophic events

Cold stress induces differential gene expression of retained homeologs in Camelina sativa cv Suneson

Camelina sativa (L.) Crantz, a member of the Brassicaceae, has potential as a biofuel feedstock which is attributable to the production of fatty acids in its seeds, its fast growth cycle, and low input requirements. While a genome assembly is available for camelina, it was generated from short sequence reads and is thus highly fragmented in nature. Using long read sequences, we generated a chromosome-scale, highly contiguous genome assembly (644,491,969 bp) for the spring biotype cultivar ‘Suneson’ with an N50 contig length of 12,031,512 bp and a scaffold N50 length of 32,184,682 bp. Annotation of protein-coding genes revealed 91,877 genes that encode 133,355 gene models. We identified a total of 4,467 genes that were significantly up-regulated under cold stress which were enriched in gene ontology terms associated with “response to cold” and “response to abiotic stress”. Coexpression analyses revealed multiple coexpression modules that were enriched in genes differentially expressed following cold stress that had putative functions involved in stress adaptation, specifically within the plastid. With access to a highly contiguous genome assembly, comparative analyses with Arabidopsis thaliana revealed 23,625 A. thaliana genes syntenic with 45,453 Suneson genes. Of these, 24,960 Suneson genes were syntenic to 8,320 A. thaliana genes reflecting a 3 camelina homeolog to 1 Arabidopsis gene relationship and retention of all three homeologs. Some of the retained triplicated homeologs showed conserved gene expression patterns under control and cold-stressed conditions whereas other triplicated homeologs displayed diverged expression patterns revealing sub- and neo-functionalization of the homeologs at the transcription level. Access to the chromosome-scale assembly of Suneson will enable both basic and applied research efforts in the improvement of camelina as a sustainable biofuel feedstock