Regional Quadratic Problem for Distributed Bilinear Systems With Bounded Controls

Sidi, M. Oluld; Beinane, Sid Ahmed Ould

doi:10.12732/ijpam.v89i5.10

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…The next few paragraphs recap a breakthrough in two‐electron integral calculations, based on Coulomb operator resolutions. It is particularly significant, eliminating the arduous orbital translations which were necessary for exponential type orbitals 6, 7. ETO translations can be avoided by expanding them as Gaussians,8 without fully retaining their desirable physical properties.…”

Section: Atomic Basis Functionsmentioning

confidence: 99%

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Hoggan

2012

Int J of Quantum Chemistry

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Review publications show the advantages of using quantum Monte Carlo (QMC) methods when bonding interactions are modified and consequently, where the electron correlation energy varies and needs to be evaluated accurately. This article considers a model efficient metal catalyst for reactions of carbon monoxide. The ultimate aim is to help design industrially useful catalysts, since the reaction with water produces hydrogen gas selectively, that is, a clean fuel and a sustainable energy source. To narrow the gap between the industrial process and calculation, a model of platinum/oxide is studied. It is mimicked here by copper with and without adsorbed oxygen. Periodicity as well as a validated pseudo-potential are used to limit the number of active electrons considered. A suitable code to carry out this task is CASINO. Furthermore, this code scales linearly to 100,000 processors and possesses a shared memory facility so that it is well-suited to runs on the Blugene/P. It has been in production on such computers since early in 2011. A mixed plane-wave/exponential type orbitals (ETO) basis is used for the systems studied. Plane waves are well-suited to periodic solid substrates and a linear combination of ETOs for molecules. The atomic orbitals have direct physical interpretation, i.e., Coulomb Sturmians and hydrogen-like orbitals. Their radial nodes are shown to be essential in obtaining the vitally important accurate QMC trial wave-functions. Until 2008,ETO products on different atoms were difficult to manipulate for the evaluation of two-electron integrals. Coulomb resolutions provide an excellent approximation that reduces these integrals to a sum of one-electron overlap-like integral products that each involve orbitals on at most two centers. They are thus readily evaluated. Only these integrals need to be re-evaluated to change basis functions. In this article, QMC-VMC variational optimisation is used with a quasi analytic two-electron and nucleus correlation factor. The QMC diffusion Monte Carlo methodology is applied to adsorbed carbon monoxide and some of its reactions.

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Section: Atomic Basis Functionsmentioning

confidence: 99%

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Hoggan

2012

Int J of Quantum Chemistry

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“…Table II lists the results for p = 0 whilst the corresponding values for p = 8 are given in Table III. A more detailed comparison reveals that larger values of p are connected with slower convergence of the series (47), but the range of applicability remains roughly the same.…”

Section: E Numerical Tests and Examplesmentioning

confidence: 91%

“…Hoggan 47,48 where an elegant formulation has been given. For convenience of the readers we list the relevant formulae of Sidi and Hoggan in the Appendix B, utilising our notation.…”

Section: B Alternative Integral Representations Of L µ (α)mentioning

confidence: 99%

“…According to the work of Sidi et al 47,48 the modified spherical Bessel functions posses the following large-order expansions…”

Section: Appendix A: Auxiliary Integralsmentioning

confidence: 99%

“…This is advantageous, as the large-order expansions of i µ (α) and k µ (α) are more compact and straightforward. In particular, we rely on the recent works of Sidi and Hoggan47,48 where an elegant formulation has been given. For convenience of the readers we list the relevant formulae of Sidi and Hoggan in the Appendix B, utilising our notation.C.…”

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confidence: 99%

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Calculation of STOs electron repulsion integrals by ellipsoidal expansion and large-order approximations

Lesiuk

2015

J Math Chem

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For general two-electron two-centre integrals over Slater-type orbitals (STOs), the use of the Neumann expansion for the Coulomb interaction potential yields infinite series in terms of few basic functions. In many important cases the number of terms necessary to achieve convergence by a straightforward summation is large and one is forced to calculate the basic integrals of high order. We present a systematic approach to calculation of the higher-order terms in the Neumann series by large-order expansions of the basic integrals. The final expressions are shown to be transparent and straightforward to implement, and all auxiliary quantities can be calculated analytically. Moreover, numerical stability and computational efficiency are also discussed. Results of the present work can be used to speed up calculations of the STOs integral files, but also to study convergence of the Neumann expansion and develop appropriate convergence accelerators.

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Nonlinear state feedback control of bilinear systems

Hamdi

Kardous

Braïek

2015

2015 4th International Conference on Systems and Control (ICSC)

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Regional Quadratic Problem for Distributed Bilinear Systems With Bounded Controls

Cited by 3 publications

References 8 publications

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

Calculation of STOs electron repulsion integrals by ellipsoidal expansion and large-order approximations

Nonlinear state feedback control of bilinear systems

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