Experimental Effervescence and Freezing Point Depression Measurements of Nitrogen in Liquid Methane-Ethane Mixtures

NASA is designing an unmanned submarine to explore the depths of the hydrocarbon-rich seas on Saturn's moon Titan. Data from Cassini indicates that the Titan north polar environment sustains stable seas of variable concentrations of ethane, methane, and nitrogen, with a surface temperature near 93 K. The submarine must operate autonomously, study atmosphere/sea exchange, interact with the seabed, hover at the surface or any depth within the sea, and be capable of tolerating variable hydrocarbon compositions. Currently, the main thermal design concern is the effect of effervescence on submarine operation, which affects the ballast system, science instruments, and propellers. Twelve effervescence measurements on various liquid methane-ethane compositions with dissolved gaseous nitrogen are thus presented from 1.5 bar to 4.5 bar at temperatures from 92 K to 96 K to simulate the conditions of the seas. After conducting effervescence measurements, two freezing point depression measurements were conducted. The freezing liquid line was depressed more than 15 K below the triple point temperatures of pure ethane (90.4 K) and pure methane (90.7 K). Experimental effervescence measurements will be used to compare directly with effervescence modeling to determine if changes are required in the design of the thermal management system as well as the propellers

Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

Sparse matrix‐vector and matrix‐multivector products for the truncated SVD on graphics processors

Many practical algorithms for numerical rank computations implement an iterative procedure that involves repeated multiplications of a vector, or a collection of vectors, with both a sparse matrix $A$ and its transpose. Unfortunately, the realization of these sparse products on current high performance libraries often deliver much lower arithmetic throughput when the matrix involved in the product is transposed. In this work, we propose a hybrid sparse matrix layout, named CSRC, that combines the flexibility of some well-known sparse formats to offer a number of appealing properties: (1) CSRC can be obtained at low cost from the popular CSR (compressed sparse row) format; (2) CSRC has similar storage requirements as CSR; and especially, (3) the implementation of the sparse product kernels delivers high performance for both the direct product and its transposed variant on modern graphics accelerators thanks to a significant reduction of atomic operations compared to a conventional implementation based on CSR. This solution thus renders considerably higher performance when integrated into an iterative algorithm for the truncated singular value decomposition (SVD), such as the randomized SVD or, as demonstrated in the experimental results, the block Golub–Kahan–Lanczos algorithm

Heterogeneity in the Effect of Common Shocks on Healthcare Expenditure Growth

Health care expenditure growth is affected by important unobserved common shocks such as technological innovation, changes in sociological factors, shifts in preferences and the epidemiology of diseases. While common factors impact in principle all countries, their effect is likely to differ across countries. To allow for unobserved heterogeneity in the effects of common shocks, we estimate a panel data model of health care expenditure growth in 34 OECD countries over the years 1980 to 2012 where the usual fixed or random effects are replaced by a multifactor error structure. We address model uncertainty with Bayesian Model Averaging, to identify a small set of important expenditure drivers from 43 potential candidates. We establish 16 significant drivers of healthcare expenditure growth, including growth in GDP per capita and in insurance premiums, changes in financing arrangements and some institutional characteristics, expenditures on pharmaceuticals, population aging, costs of health administration, and inpatient care. Our approach allows us to derive estimates that are less subject to bias than in previous analyses, and provide robust evidence to policy makers on the drivers that were most strongly associated with the growth in health care expenditures over the past 32 years

The Equitable Basis for sl_2

This article contains an investigation of the equitable basis for the Lie algebra sl_2. Denoting this basis by {x,y,z}, we have [x,y] = 2x + 2y, [y,z] = 2y + 2z, [z, x] = 2z + 2x. One focus of our study is the group of automorphisms G generated by exp(ad x*), exp(ad y*), exp(ad z*), where {x*,y*,z*} is the basis for sl_2 dual to {x,y,z} with respect to the trace form (u,v) = tr(uv). We show that G is isomorphic to the modular group PSL_2(Z). Another focus of our investigation is the lattice L=Zx+Zy+Zz. We prove that the orbit G(x) equals {u in L |(u,u)=2}. We determine the precise relationship between (i) the group G, (ii) the group of automorphisms for sl_2 that preserve L, (iii) the group of automorphisms and antiautomorphisms for sl_2 that preserve L, and (iv) the group of isometries for (,) that preserve L. We obtain analogous results for the lattice L* =Zx*+Zy*+Zz*. Relative to the equitable basis, the matrix of the trace form is a Cartan matrix of hyperbolic type; consequently,we identify the equitable basis with the set of simple roots of the corresponding Kac-Moody Lie algebra g. Then L is the root lattice for g and 1/2L* is the weight lattice, and G(x) coincides with the set of real roots for g. Using L, L*, and G, we give several descriptions of the isotropic roots for g and show that each isotropic root has multiplicity 1. We describe the finite-dimensional sl_2-modules from the point of view of the equitable basis. In the final section, we establish a connection between the Weyl group orbit of the fundamental weights of g and Pythagorean triples.Comment: Minor changes made to the introductory material, and a few typos corrected. The final publication is available at http://www.springerlink.co

Compressed basis GMRES on high-performance graphics processing units

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. We develop a high-performance implementation of the “compressed basis GMRES” solver in the Ginkgo sparse linear algebra library using a large set of test problems from the SuiteSparse Matrix Collection. We demonstrate robustness and performance advantages on a modern NVIDIA V100 graphics processing unit (GPU) of up to 50% over the standard GMRES solver that stores all data in IEEE double-precision

Compression and load balancing for efficient sparse matrix-vector product on multicore processors and graphics processing units

[EN] We contribute to the optimization of the sparse matrix-vector product by introducing a variant of the coordinate sparse matrix format that balances the workload distribution and compresses both the indexing arrays and the numerical information. Our approach is multi-platform, in the sense that the realizations for (general-purpose) multicore processors as well as graphics accelerators (GPUs) are built upon common principles, but differ in the implementation details, which are adapted to avoid thread divergence in the GPU case or maximize compression element-wise (i.e., for each matrix entry) for multicore architectures. Our evaluation on the two last generations of NVIDIA GPUs as well as Intel and AMD processors demonstrate the benefits of the new kernels when compared with the optimized implementations of the sparse matrix-vector product in NVIDIA's cuSPARSE and Intel's MKL, respectively.J. I. Aliaga, E. S. Quintana-Ortí, and A. E. Tomás were supported by TIN2017-82972-R of the Spanish MINECO. H. Anzt and T. Grützmacher were supported by the Impuls und Vernetzungsfond of the Helmholtz Association under grant VH-NG-1241 and by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. The authors would like to thank the Steinbuch Centre for Computing (SCC) of the Karlsruhe Institute of Technology for providing access to an NVIDIA A100 GPU.Aliaga, JI.; Anzt, H.; Grützmacher, T.; Quintana-Ortí, ES.; Tomás Domínguez, AE. (2022). Compression and load balancing for efficient sparse matrix-vector product on multicore processors and graphics processing units. Concurrency and Computation: Practice and Experience. 34(14):1-13. https://doi.org/10.1002/cpe.6515113341