Photoreactions of aromatic compounds—XXXV: Nucleophilic photosubstitution of methoxy substituted aromatic compounds. Monophotonic ionization of the triplet

Methoxy groups exert an activating and ortho/para directing influence in light induced nucleophilic substitution reactions (cyanation, hydroxylation, etc) of aromatic compounds in aqueous media. The first chemical step in these processes is monophotonic ionization of the aromatic compound in its lowest triplet state, followed by reaction of the radical cation with the nucleophile Quantum yields of photocyanation of 4-fluoro- and 4-chloroanisole indicate that in 99% (mole fraction) water virtually all triplets formed undergo electron ejection.This hypothesis is in agreement with the results of charge density calculations for the radical cations. It is directly supported by the similarity of the product composition of these photochemical substitutions with that of anodic substitutions, where the intermediacy of an aromatic cation is generally accepted. The presence of an oxidizing agent (oxygen, or persulphate) is required only when a hydrogen is replaced. The nucleophilic photosubstitution at electron rich aromatic systems in solvents as water can therefore be classified as an S_r⁺n¹(³Ar^*) process.     

A New Method for the Syntiiesis of 1-Aryl Phthalazines

A simple versatile method for the conversion of 1 -aroyl-2-(substituted benzylidene)-hydrazines to 1-aryl-phthalazines using polyphosphate ester (PPE) is described.     

Optimal control for reinitialization in finite element level set methods

A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first‐order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE‐based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

An Euler system source term that develops prototype Z‐pinch implosions intended for the evaluation of shock‐hydro methods

In this paper, a phenomenological model for a magnetic drive source term for the momentum and total energy equations of the Euler system is described. This body force term is designed to produce a Z‐pinch like implosion that can be used in the development and evaluation of shock‐hydrodynamics algorithms that are intended to be used in Z‐pinch simulations. The model uses a J × B Lorentz force, motivated by a 0‐D analysis of a thin shell (or liner implosion), as a source term in the equations and allows for arbitrary current drives to be simulated. An extension that would include the multi‐physics aspects of a proposed combined radiation hydrodynamics (rad‐hydro) capability is also discussed. The specific class of prototype problems that are developed is intended to illustrate aspects of liner implosions into a near vacuum and with idealized pre‐fill plasma effects. In this work, a high‐resolution flux‐corrected‐transport method implemented on structured overlapping meshes is used to demonstrate the application of such a model to these idealized shock‐hydrodynamic studies. The presented results include an asymptotic solution based on a limiting‐case thin‐shell analytical approximation in both (x, y) and (r, z). Additionally, a set of more realistic implosion problems that include density profiles approximating plasma pre‐fill and a set of perturbed liner geometries that excite a hydro‐magnetic like Rayleigh–Taylor instability in the implosion dynamics are demonstrated. Finally, as a demonstration of including and evaluating multiphysics effects in the Euler system, a simple radiation model is included and self‐convergence results for two types of (r, z) implosions are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Stability of operator splitting methods for systems with indefinite operators: Advection–diffusion–reaction systems

This brief paper presents an A-stability result for operator splitting type time integration methods applied to advection–diffusion–reaction equations with possibly indefinite source terms. These results extend our earlier work on diffusion–reaction systems [D.L. Ropp, J.N. Shadid, Stability of operator splitting methods for systems with indefinite operators: reaction–diffusion systems, J. Comput. Phys. 203 (2) (2005) 449–466]. The A-stability result presents sufficient conditions that control both low and high wave number instabilities. A corollary shows that if L-stable methods are used for the diffusion term the high wave number instability will be controlled more easily. Numerical results are presented that verify second-order convergence for the operator splitting methods and demonstrate control of instabilities on a chemotaxis problem by use of an L-stable diffusion integrator.     

A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier–Stokes equations

In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier–Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of the Navier–Stokes system first presented in [A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the numerical approximation of Navier–Stokes equations, Computational Methods in Applied Mechanical Engineering 188 (2000) 505–526]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code.     

Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods

This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, including both low-Lundquist number (e.g., an MHD Faraday conduction pump and a hydromagnetic Rayleigh–Bernard linear stability calculation) and moderately-high Lundquist number (magnetic island coalescence problem) examples. Initial results that explore the scaling of the solution methods are presented on up to 4096 processors for problems with up to 64M unknowns on a CrayXT3/4. Additionally, a large-scale proof-of-capability calculation for 1 billion unknowns for the MHD Faraday pump problem on 24,000 cores is presented.     

Towards large-scale multi-socket,multicore parallel simulations: Performance of an MPI-only semiconductor device simulator

This preliminary study considers the scaling and performance of a finite element (FE) semiconductor device simulator on a set of multi-socket, multicore architectures with nonuniform memory access (NUMA) compute nodes. These multicore architectures include two linux clusters with multicore processors: a quad-socket, quad-core AMD Opteron platform and a dual-socket, quad-core Intel Xeon Nehalem platform; and a dual-socket, six-core AMD Opteron workstation. These platforms have complex memory hierarchies that include local core-based cache, local socket-based memory, access to memory on the same mainboard from another socket, and then memory across network links to different nodes. The specific semiconductor device simulator used in this study employs a fully-coupled Newton–Krylov solver with domain decomposition and multilevel preconditioners. Scaling results presented include a large-scale problem of 100+ million unknowns on 4096 cores and a comparison with the Cray XT3/4 Red Storm capability platform. Although the MPI-only device simulator employed for this work can take advantage of all the cores of quad-core and six-core CPUs, the efficiency of the linear system solve is decreasing with increased core count and eventually a different programming paradigm will be needed.     

Stabilization and scalable block preconditioning for the Navier–Stokes equations

This study compares several block-oriented preconditioners for the stabilized finite element discretization of the incompressible Navier–Stokes equations. This includes standard additive Schwarz domain decomposition methods, aggressive coarsening multigrid, and three preconditioners based on an approximate block LU factorization, specifically SIMPLEC, LSC, and PCD. Robustness is considered with a particular focus on the impact that different stabilization methods have on preconditioner performance. Additionally, parallel scaling studies are undertaken. The numerical results indicate that aggressive coarsening multigrid, LSC and PCD all have good algorithmic scalability. Coupling this with the fact that block methods can be applied to systems arising from stable mixed discretizations implies that these techniques are a promising direction for developing scalable methods for Navier–Stokes.     

Synthesis and Antiproliferative Activity of Some Newly Synthesized Pyrazolopyridine Derivatives

Russian Journal of General Chemistry - A series of pyrazolopyridine derivatives is synthesized from emyl-4-amino-6-memyl-1-(mphtha[1,2-d]-[1,3]tmazol-2-yl)-1H-pyrazolo[3,4-b]pyridine-5-carboxylate...