Introduction to Axiomatic Geometry

This book presents Euclidean Geometry and was designed for a one-semester course preparing junior and senior level college students to teach high school Geometry. The book could also serve as a text for a junior level Introduction to Proofs course.https://ohioopen.library.ohio.edu/opentextbooks/1000/thumbnail.jp

Maximum Subarray Problem in 1D and 2D via Weighted Paths in Directed Acyclic Graphs

The Maximum Subarray Problem was encountered by Ulf Grenander for maximum likelihood estimation in pattern analysis. We are given a vector (or matrix) of numbers, and we have to find the contiguous sub-vector (or sub-matrix) which has the maximum sum of numbers in it. Apart from the original application, the problem also arises for example in biological sequence analysis.We present here a linear-time algorithm in one dimension which is different from the one known due to Kadane, and present a way of extending it to two dimensions. To achieve the latter, we provide a new technique, the red-blue graphs, which encodes all the contiguous sub-matrices of an m × n matrix in size O(m × n)

Investigation of Chain Extension Approaches for the Stereoselective Reagent-Controlled Synthesis of alpha-Heteroatom Substituted Alkyl Boronic Esters

Two distinct strategies were explored for the enantioselective synthesis of α-heteroatom substituted alkyl boronic esters by stereoselective reagent-controlled homologation using transient chiral carbenoid reagents CHYMX (Y = heteroatom, X = nucleofuge, M = electrofuge). In the first case, a stereospecific reagent-controlled homologation (sStReCH) approach to α-alkoxyalkylboronates using α-metalated S,O- and O,O-acetals was pursued that necessitated the development of methods to access these carbenoids in stereodefined form and study of their configurational and chemical stability (both classes of carbenoid are known to chain extend alkyl boronic esters). Sulfoxide-metal exchange from dithioorthoformate monooxides was evaluated as a means to access stereodefined α-metalated S,O-acetals. It was discovered that acyclic dithioorthoformate monooxides fragment spontaneously upon their oxidative generation from simple dithioorthoformates [(pTolS)₂CHOR, R = Me, Et]; however, two cyclic dithioorthoformate monooxides, trans and cis 2-isopentoxy-1,3-benzodithiolane-S-oxide (102), were obtained in 85% yield (trans:cis = 96:4) by 3-chloroperoxybenzoic acid mediated oxidation of 2-isopentoxy-1,3-benzodithiolane. Treatment of trans or cis-102 with EtMgCl (in THF at -78 °C) gave configurationally stable (≤ 2.5 h, at -78 °C) stereodefined α-magnesiated S,O-acetals 103 that incorporated D-atoms in a stereospecific manner upon reaction with CD3OD. Carbenoids 103 (M = MgCl) failed to react with all other electrophiles examined (allyl bromide, MeI, MeOTf), except benzaldehyde, and this low nucleophilicity precluded their use in boronic ester chain extension chemistry. α-Lithiated S,O-acetals 103 generated in the same fashion from 102 using PhLi were more reactive than their magnesiated congeners 103 but lacked sufficient configurational stability for applications in sStReCH (epimerization of 103 (M = Li) occurred within 1 min at -78 °C in THF). Direct metalation approaches to stereodefined lithiated S,O- and O,O-acetals were next explored, but ultimately, either acceptably high enantioselectivity was not realized or the organolithiums generated were found to be too chemically unstable for sStReCH applications. For example, kinetic enantioselective lithiation of methoxymethyl p-tolyl thioether (124) with s-butyllithium/(-)-sparteine (PhMe, -78 °C) followed by treatment of the resulting lithiated S,O-acetal [pTolSCH(Li)OMe] with benzaldehyde as a probe electrophile, led to addition products [pTolSCH(OMe)CH(OH)Ph] with low enantiomeric excess [55% yield, dr = 66:34, %ee (major isomer) = 24%, %ee (minor isomer) = 9%]. In another example, lithiation of a thiocarbamate of methoxymethyl mercaptan [i-Pr₂NC(=S)SCH₂OMe] with s-butyllithium and TMEDA (Et₂O, -110 °C) led to a chemically unstable carbenoid that spontaneously extruded methyl thioformate (MeOCHS) to yield putative a-lithio-N,N-diisopropylthioformamide [i-Pr₂NC(=S)Li]. The second strategy explored, and introduced here for the first time, ligand mediated stereoinductive reagent-controlled homologation (iStReCH), deliberately exploits the configurational lability of heteroatom substituted carbenoids and consequently it was more successful. In this case, dynamic kinetic resolution (DKR), or dynamic thermodynamic resolution (DTR), of a racemic configurationally labile carbenoid is effected by an exogenous chiral ligand as the carbenoid is trapped by the boronic ester electrophile. The iStReCH concept was demonstrated for an enantioselective synthesis of α-silylalkylboronates, as follows: (±)-lithio(dimethylphenylsilyl)methyl 2,4,6-triisopropylbenzoate [TIBOCH(Li)SiMe₂Ph], obtained by lithiation of the corresponding silylmethyl TIB ester with t-butyllithium (cumene, -78 °C), was incubated with the chiral BOX ligand 2,2-bis[(4S)-4,5-dihydro-4-isopropyloxazol-2-yl)propane (at -45 °C) before addition of B-phenethyl pinacol boronate at -95 °C. Warming to rt during 18 hours afforded the desired enantioenriched chain extended product (S)-2-[1-(dimethylphenylsilyl)-3-phenylpropyl]-4,4,5,5- tetramethyl-1,3,2-dioxaborolane (69% yield, 57% ee). Ligand mediated iStReCH of B-cyclohexyl (35% yield, 9% ee) and B-sec-butyl [43% yield, dr = 58:42, %ee (major) = 26%, %ee (minor) = 14%] pinacol boronates with the same silylated carbenoid was likewise demonstrated. Enantioselectivity was dependent on the temperature history of the organolithium/ligand complex indicating that the stereoinduction mechanism involves some aspect of DTR

Propane Dehydrogenation by Autothermal Reforming

The proposed design is for the the production of propene through propane dehydrogenation using Thyssen Krupp’s STAR technology and a hybrid membrane separation. The plant has a capacity of 700 kT/yr and will be located in the Middle East. At current propane/propene prices, the use of Thyssen Krupp’s STAR process and hybrid membrane separation is not economical and has a negative IRR. The NPV of this project at current market prices is -$865MM. However, economic feasibility depends on volatile market conditions. The process begins with the oxydehydrogenation section, consisting of four reformers connected to four oxyreactors that are cycled to allow for regeneration of the .2-.6%Pt- Sn/ZnAl2O5 catalyst. In order to produce polymer grade propene, a separation is needed following dehydrogenation. Separation operations include adsorption, MEA absorption system, distillation, and a hybrid distillation/membrane C3 splitter

A Space and Bandwidth Efficient Multicore Algorithm for the Particle-in-Cell Method

International audienceThe Particle-in-Cell (PIC) method allows solving partial differential equation through simulations, with important applications in plasma physics. To simulate thousands of billions of particles on clusters of multicore machines, prior work has proposed hybrid algorithms that combine domain decomposition and particle decomposition with carefully optimized algorithms for handling particles processed on each multicore socket. Regarding the multicore processing, existing algorithms either suffer from suboptimal execution time, due to sorting operations or use of atomic instructions, or suffer from suboptimal space usage. In this paper, we propose a novel parallel algorithm for two-dimensional PIC simulations on multicore hardware that features asymptotically-optimal memory consumption, and does not perform unnecessary accesses to the main memory. In practice, our algorithm reaches 65% of the maximum bandwidth, and shows excellent scalability on the classical Landau damping and two-stream instability test cases

Efficient Data Layouts for a Three-Dimensional Electrostatic Particle-in-Cell Code

International audienceThe Particle-in-Cell (PIC) method is a widely used tool in plasma physics. To accurately solve realistic problems, the method requires to use trillions of particles and therefore, there is a strong demand for high performance code on modern architectures. The present work describes performance results of Pic-Vert, a hybrid OpenMP/MPI and vectorized three-dimensional electrostatic PIC code.The code simulates 3d3v Vlasov-Poisson systems on Cartesian grids with periodic boundary conditions. Overall, it processes 590 million particles/second on a 24-core Intel Skylake architecture, without hyper-threading (25 million particles per second per core).The paper presents extensions in 3d of our preliminary 2d results, with highlights on the difficulties andsolutions proposed for these extensions. Specifically, our main contributions consist in proposing a new space-filling curve in 3d (called L6D) to improve the cache reuse and an adapted loop transformation (strip-mining) to achieve efficient vectorization. The analysis of these optimization strategies is performed in two-stages, first on a 24-core socket and second on a super-computer, from 1 to 3,072 cores, demonstrating significant performance gains and very satisfactory weak scaling results of the code

Efficient Data Structures for a Hybrid Parallel and Vectorized Particle-in-Cell Code

International audienceThe contribution of the present work relies on an innovative and judicious combination of several optimization techniques for achieving high performance when using automatic vectorization and hybrid MPI/OpenMP parallelism in a Particle-in-Cell (PIC) code. The domain of application is plasma physics: the code simulates 2d2v Vlasov-Poisson systems on Cartesian grids with periodic boundary conditions. Overall, our code processes 65 million particles/second per core on Intel Haswell (without hyper-threading) and achieves a good weak scaling up to 0.4 trillion particles on 8,192 cores. The optimizations mainly consist in using (i) a structure of arrays for the particles, (ii) an efficient data structure for the electric field and the charge density, and (iii) an appropriate code for automatic vectorization of the charge accumulation and of the positions' update. In particular, we use space-filling curves to enhance data locality while enabling vectorization: starting from a redundant cell-based data structure for the electric field and for the charge density, we compare several space-filling curves for an efficient ordering of these data and we obtain a gain of 36% in the number of L2 and L3 cache misses when using a Morton curve instead of the classical row-major one. In addition, by proposing a specific writing of the updating positions code we achieve a 31% time improvement in that step. The optimizations bring an overall gain in the execution time of 42% with respect to a standard code. The parallelization of the particle loops is simply performed by means of both distributed and shared memory paradigms, without domain decomposition. We explain the weak and the strong scalings of the code bounded as expected by the overhead of the MPI communications

OptiTrust: an Interactive Framework for Source-to-Source Transformations

This paper presents an interactive framework for developing high-performance C code via series of source-to-source transformations. Optimization steps are described in transformation scripts, expressed as OCaml programs. The programmer can interactively visualize the textual differences associated with any step of the script. We demonstrate the effectiveness of OptiTrust by reproducing a manually optimized Particle-In-Cell numerical simulation, starting from a direct, unoptimized version of the algorithm. This case study covers many state-of-the-art optimization patterns that appear in numerical simulation codes. We argue that, compared with optimizing code by hand, deriving high performance code using a transformation script makes the code easier to review, easier to debug, and easier to maintain as the intended program or as the target hardware evolves

Space Environment Factors Affecting the Performance of International Space Station Materials: The First Two Years of Flight Operations

In this paper, the natural and induced space environment factors affecting materials performance on ISS are described in some detail. The emphasis will be on ISS flight experience and the more significant design and development issues of the last two years. The intent is to identify and document the set of space environment factors, affecting materials, that are producing the largest impacts on the ISS flight hardware verification and acceptance process and on ISS flight operations. Orbital inclination (S1.6 ) and altitude (nominal3S0 km to 400 km altitude) determine the set of natural environment factors affecting the functional life of materials and subsystems on ISS. ISS operates in the F2 region of Earth's ionosphere in well-defined fluxes of atomic oxygen, other ionospheric plasma species, and solar UV, VUV, and x-ray radiation, as well as galactic cosmic rays, trapped radiation, and solar cosmic rays (1,2). The high latitude orbital environment also exposes external surfaces to significantly less well-defined or predictable fluxes of higher energy trapped electrons and auroral electrons (3 ,4). The micrometeoroid and orbital debris environment is an important determinant of spacecraft design and operations in any orbital inclination. Environment factors induced by ISS flight operations include ram-wake effects, magnetic induction voltages arising from flight through Earth's magnetic field, hypergolic thruster plume impingement from proximity operations of visiting vehicles, materials outgassing, venting and dumping of fluids, ISS thruster operations, as well as specific electrical power system interactions with the ionospheric plasma (S-7). ISS must fly in a very limited number of approved flight attitudes leading to location specific environmental exposures and extreme local thermal environments (8). ISS is a large vehicle and produces a deep wake structure from which both ionospheric plasma and neutrals (atomic oxygen) are largely excluded (9-11). At high latitude, the ISS wake may produce a spacecraft charging environment similar to that experienced by the DMSP and Freja satellites (800 to 100 km altitude polar orbits), especially during geo-magnetic disturbances (12-14). ISS is also subject to magnetic induction voltages (VxB L) on conducting structure, a result of high velocity flight through Earth's magnetic field. The magnitude of the magnetic induction voltage varies with location on ISS, as well as the relative orientation of the vehicle velocity vector and planetary magnetic field vector, leading to maximum induction voltages at high latitude (15). The space environment factors, natural and induced, that have had the largest impact on pre-launch ISS flight hardware verification and flight operations during the first two years of ISS flight operations are listed below and grouped according to the physical and chemical processes driving their interaction with ISS materials

High order numerical methods for Vlasov-Poisson models of plasma sheaths

This article is a report of the CEMRACS 2022 project, called HIVLASHEA, standing for "High order methods for Vlasov-Poisson models for sheaths". A two-species Vlasov-Poisson model is described together with some numerical simulations, permitting to exhibit the formation of a plasma sheath. The numerical simulations are performed with two different methods: a first order classical finite difference (FD) scheme and a high order semi-Lagrangian (SL) scheme with Strang splitting; for the latter one, the implementation of (non-periodic) boundary conditions is discussed. The codes are first evaluated on a one-species case, where an analytical solution is known. For the two-species case, cross comparisons and the influence of the numerical parameters for the SL method are performed in order to have an idea of a reference numerical simulation. Aknowledgements Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high performance computing resources