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The Explicit Fatunla’s Method for First-Order Stiff Systems of Scalar Ordinary Differential Equations: Application to Robertson Problem  [PDF]
Hippolyte Nyengeri, Eugène Ndenzako, Rénovat Nizigiyimana
Open Access Library Journal (OALib Journal) , 2019, DOI: 10.4236/oalib.1105291
Ordinary differential equations (ODEs) are among the most important mathe-matical tools used in producing models in the physical sciences, biosciences, chemical sciences, engineering and many more fields. This has motivated re-searchers to provide efficient numerical methods for solving such equations. Most of these types of differential models are stiff, and suitable numerical methods have to be used to simulate the solutions. This paper starts with a sur-vey on the basic properties of stiff differential equations. Thereafter, we present the explicit one-step algorithm proposed by Fatunla to solve stiff systems of first-order scalar ODEs. As an illustrative example, we consider the Robertson problem (RP) which is known to be stiff. The results obtained with the explicit Fatunla method (EFM) are compared with those computed by the solver RADAU which is based on implicit Runge-Kutta methods. Our results are in good agreement with the latter ones.
Frobenius Series Solutions of the Schrodinger Equation with Various Types of Symmetric Hyperbolic Potentials in One Dimension  [PDF]
Hippolyte Nyengeri, René Simbizi, Audace Girukwishaka, Rénovat Nizigiyimana, Eugène Ndenzako
Open Access Library Journal (OALib Journal) , 2018, DOI: 10.4236/oalib.1104728
The Schrodinger equation (SE) for a certain class of symmetric hyperbolic potentials is solved with the aid of the Frobenius method (FM). The bound state energies are given as zeros of a calculable function. The calculated bound state energies are successively substituted into the recurrence relations for the expanding coefficients of the Frobenius series representing even and odd solutions in order to obtain wave functions associated with even and odd bound states. As illustrative examples, we consider the hyperbolic Poschl-Teller potential (HPTP) which is an exactly solvable potential, the Manning potential (MP) and a model of the Gaussian potential well (GPW). In each example, the bound state energies obtained by means of the FM are presented and compared with the exact results or the literature ones. In the case of the HPTP, we also make a comparison between exact bound state wave functions and the eigenfunctions obtained by means of the present approach. We find that our results are in good agreement with those given by other methods considered in this work, and that our class of potentials can be a perfect candidate to model the GPW.
Application of the Frobenius Method to the Schrodinger Equation for a Spherically Symmetric Hyperbolic Potential  [PDF]
Hippolyte Nyengeri, Rénovat Nizigiyima, Eugène Ndenzako, Félix Bigirimana, Dieudonné Niyonkuru, Audace Girukwishaka
Open Access Library Journal (OALib Journal) , 2018, DOI: 10.4236/oalib.1104950
In this paper, an efficient technique for computing the bound state energies and wave functions of the Schrodinger Equation (SE) associated with a new class of spherically symmetric hyperbolic potentials is developed. This technique is based on a recent approximation scheme for the orbital centrifugal term and on the use of the Frobenius method (FM). The bound state eigenvalues are given as zeros of calculable functions. The corresponding eigenfunctions can be obtained by substituting the calculated energies into the recurrence relations for the expanding coefficients of the Frobenius series representing the solution. The excellent performance of this technique is illustrated through numerical results for some special cases like Poschl-Teller potential (PTP), Manning-Rosen potential (MRP) and Poschl-Teller polynomial potential (PTPP), with an application to the Gaussian potential well (GPW). Comparison with other methods is presented. Our results agree noticeably with the previously reported ones.
Bulk matter physics and its future at the Large Hadron Collider
B. Hippolyte
Physics , 2009, DOI: 10.1140/epjc/s10052-009-0910-9
Abstract: Measurements at low transverse momentum will be performed at the LHC for studying particle production mechanisms in $pp$ and heavy-ion collisions. Some of the experimental capabilities for bulk matter physics are presented, focusing on tracking elements and particle identification. In order to anticipate the study of baryon production for both colliding systems at multi-TeV energies, measurements for identified species and recent model extrapolations are discussed. Several mechanisms are expected to compete for hadro-production in the low momentum region. For this reason, experimental observables that could be used for investigating multi-parton interactions and help understanding the "underlying event" content in the first $pp$ collisions at the LHC are also mentioned.
Strange prospects for LHC energies
B. Hippolyte
Physics , 2006, DOI: 10.1140/epjc/s10052-006-0120-7
Abstract: Strange quark and hadron production will be studied at the Large Hadron Collider (LHC) energies in order to explore the properties of both pp and heavy-ion collisions. The ALICE experiment will be specifically efficient in the strange sector with the identification of baryons and mesons over a wide range of transverse momentum. Dedicated measurements are proposed for investigating chemical equilibration and bulk properties. Strange particles can also help to probe kinematical regions where hard processes and pQCD dominate. We try to anticipate here several ALICE analyses to be performed as the first Pb--Pb and pp data will be available.
Global variables and correlations: Summary of the results presented at the Quark Matter 2012 conference
Boris Hippolyte,Dirk Rischke
Physics , 2012, DOI: 10.1016/j.nuclphysa.2013.01.078
Abstract: In these proceedings, we highlight recent developments from both theory and experiment related to the global description of matter produced in ultra-relativistic heavy-ion collisions as presented during the Quark Matter 2012 conference.
Strange and multi-strange particle production at the LHC energies with ALICE
Boris Hippolyte,for the ALICE Collaboration
Physics , 2011,
Abstract: Strange quark and particle production is studied at the LHC with unprecedented high beam energies in both heavy-ion and proton-proton collisions: on the one hand, strangeness is used for investigating chemical equilibration and bulk properties; on the other hand, strange particles contribute to probe different kinematical domains, from the one where collective phenomena are at play up to the region dominated by pQCD-calculable processes. We highlight the suitability of the ALICE experiment for this topic, presenting our latest measurements and comparing them to models.
Strange Content of Baryons at RHIC
B. Hippolyte,for the STAR Collaboration
Physics , 2003,
Abstract: Via the study of strange particle production within the STAR experiment, we try to address the surprising amount of baryon transport at the Relativistic Heavy Ion Collider (RHIC). We report here preliminary results showing that, at mid-rapidity and for the top energy of RHIC, the number of created baryons exceeds the number transported from the colliding nuclei. However, thanks to the large acceptance of the experimental setup, one could expect to observe the transition between the ``soft'' regime (low transverse momentum -$\pt$- region corresponding to a bulk of hot and dense matter hadronizing) and the perturbative one (higher $\pt$ region) where the fragmentation of incoming partons is supposed to dominate hadron production.}
Tensile effective stresses in hydrocarbon storage caverns
Hippolyte Djizanne,Pierre Berest,Beno?t Brouard
Physics , 2013,
Abstract: The "no-tensile effective stress" criterion is discussed. It is proven that effective tensile stresses can be generated at a cavern wall after a rapid increase or decrease in pressure. The Etzel K-102 test, performed in Germany more than 20 years ago, is revisited using the notion of effective tensile stresses.
High Blood Pressure and Its Correlates among Assistant Physical Education Teachers in Republic of Benin (West Africa)  [PDF]
Polycarpe Gouthon, Barnabe Akplogan, Jean-Marie Falola, Houndjovi Pierre Dansou, Hippolyte Agboton, Solange Adegnika, Issiako Bio Nigan
Advances in Physical Education (APE) , 2012, DOI: 10.4236/ape.2012.22011
Abstract: Objective: This cross-sectional study carried out in Republic of Benin, aimed at assessing the relation between high blood pressure (HBP) and its correlates in an exhaustive sample of 123 Assistant physical education teachers (APE teachers), enrolled in a two-year in-service training. Methods: These teachers have been interviewed and clinically tested. The lifestyle, blood pressure, three indexes of adiposity, blood lipids, white blood cells and neutrophils counts and plasma C-reactive protein were the main study variables. Results: HBP was present in 34.1% of the teachers. The three main factors associated to HBP, that had the higher rates were neck circumference (78.3%), the biological index of atherogenicity (72.2%), and waist circumference (44.2%). Neck circumference was the most relevant modifiable variable to explaining HBP in this group (OR = 3.14; 95% IC: 1.09 - 9.00; p = 0.033). Conclusions: The teachers studied must keep on exercising as early as their primary training comes to an end. Doing so, they could avoid overweight and reduce the risk of hypertension.
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