High performance BLAS formulation of the multipole-to-local operator in the fast multipole method

The multipole-to-local (M2L) operator is the most time-consuming part of the far field computation in the fast multipole method for Laplace equation. Its natural expression, though commonly used, does not respect a sharp error bound: we here first prove the correctness of a second expression. We then propose a matrix formulation implemented with basic linear algebra subprograms (BLAS) routines in order to speed up its computation for these two expressions. We also introduce special data storages in memory to gain greater computational efficiency. This BLAS scheme is finally compared, for uniform distributions, to other M2L improvements such as block FFT, FFT with polynomial scaling, rotations and plane wave expansions. When considering runtime, extra memory storage, numerical stability and common precisions for Laplace equation, the BLAS version appears as the best one.     

Linear and nonlinear optical properties of cationic bipyridyl iridium(III) complexes: tunable and photoswitchable?

A series of cationic Ir(III) substituted bipyridyl ()(N(∧)N (N(∧)N-bpy) complexes incorporating electron-donor and -acceptor substituents, [Ir(C(∧)N-ppy-R')(2)(N(∧)N-bpy-CH═CH-C(6)H(4)-R)][X] (X(-) = PF(6)(-) or C(12)H(25)SO(3)(-)), 2 (a, R = NEt(2) and R' = Me; b, R = O-Oct and R' = Me; c, R = NO(2) and R' = C(6)H(13); C(∧)N-ppy = cyclometalated 2-phenylpyridine, [Ir(C(∧)N-ppy-Me)(2)(N(∧)N-bpy-CH═CH-thienyl-Me)][PF(6)], 2d, and the dithienylethene (DTE)-containing complex 2e have been synthesized and characterized, and their absorption, luminescence, and quadratic nonlinear optical (NLO) properties are reported. Density functional theory (DFT) and time-dependent-DFT (TD-DFT) calculations on the complexes facilitate a detailed assignment of the excited states involved in the absorption and emission processes. All five complexes are luminescent in a rigid glass at 77 K, displaying vibronically structured spectra with long lifetimes (14-90 μs), attributed to triplet states localized on the styryl-appended bipyridines. The second-order NLO properties of 2a-d and related complexes 1a-d with 1,10-phenanthrolines have been investigated by both electric field induced second harmonic generation (EFISH) and harmonic light scattering (HLS) techniques. They are characterized by high negative EFISH μβ values which decrease when the ion pair strength between the cation and the counterion (PF(6)(-), C(12)H(25)SO(3)(-)) increases. The EFISH response is mainly controlled by metal-to-ligand charge-transfer/ligand-to-ligand charge-transfer (MLCT/L'LCT) processes. A combination of HLS and EFISH techniques is used to evaluate both the dipolar and octupolar contributions to the total quadratic hyperpolarizability, demonstrating that the major contribution is controlled by the octupolar part. The incorporation of a photochromic DTE unit into the N(∧)N-bpy ligand (complex 2e) allows the luminescence to be switched ON or OFF. The photocyclisation of the DTE unit can be triggered by using either UV (365 nm) or visible light (430 nm), leading to an efficient quenching of the ligand-based 77 K luminescence, which can be restored upon irradiation of the closed form at 715 nm. In contrast, no significant modification of the EFISH μβ value is observed upon photocyclization, suggesting that the quadratic NLO response is dominated by the MLCT/L'LCT processes, rather than by the intraligand excited states localized on the substituted bipyridine ligand.     

Stark broadening of the overlapping 4471.48 Å HeI line in a plasma. II. Nonmarkovian and ion dynamic effects

The inclusion of a frequency-dependent collision operator in the line shape expression is investigated quantitatively for the 4471 Å overlapping HeI line. We compare at several electron densities frequency-independent (markovian) profiles with frequency-dependent (nonmarkovian) profiles taking into account incomplete electron-atom collisions. No significant discrepancies appear in the domain of validity of the impact approximations (|Δω| ? ωp_e), whereas for the far wings important differences may be found. At the extrema (two peaks, one dip) the nonmarkovian intensities prove to be the higher ones. For a modest electron density, the inclusion of ion dynamic shielding introduces more modifications then nonmarkovian effects. In the blue wing, the frequency-dependent profile lies below the frequency-independant profile in accord with the hydrogenic behavior for that part of the line shape in the presence of a large perturber density.     

Parallel constrained molecular dynamics

A block version of the Shake method for heavy atom simulation in biological systems is presented in this paper. The method solves successively, independent blocks of constraints of small size by a Newton method. This algorithm is implemented in TAKAKAW, an efficient parallel molecular dynamics code. This method has been tested on a small system and on an ionic canal of 67671 atoms. This revised version was published online in June 2006 with corrections to the Cover Date.     

Study of propagation of ultraintense electromagnetic wave throughplasma using semi-Lagrangian Vlasov codes

Interaction of relativistically strong laser pulses with underdense and overdense plasmas is investigated by a semi-Lagrangian Vlasov code. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by the electromagnetic wave as electron trapping, particle acceleration, and electron plasma wavebreaking. To describe the distribution of accelerated particle momenta and energy will require a very detailed analysis of the kinetic and time history of the plasma wave evolution. The semi-Lagrangian Vlasov code allows us to handle the interaction of ultrashort electromagnetic pulse with plasma at strongly relativistic intensities with a great deal of resolution in phase space     

Magnetic exchange coupling in bis-nitroxides: a theoretical analysis of the solvent effects

Magnetic properties of nitroxide radicals can be greatly affected by solvent effects. In this study, the change of the magnetic exchange interaction J, coupling the two unpaired electrons of a model solvated antiferromagnetic bis-iminyl-nitroxide molecule (2IN), is rationalized thanks to different geometric and electronic criteria provided by density functional theory calculations. It is shown that for a given geometry, simple tools can be used to analyze with good accuracy the dependence of J with the solvent polarity. Estimates of two important magnetic parameters are given: the magnetic orbitals exchange and the in-site energy gap between ionic and neutral configurations. 2IN can be engaged in different hydrogen-bonds with first shell water molecules, modifying both the 2IN geometry and the electrostatic potential felt by the molecule. In all, the additivity of electrostatic and hydrogen-bond solvent effects is found to be responsible for J variations as large as 50%.     

Integrales radiales d'un atome hydrogenoide a potentiel Coulombien a ecran

The Schrödinger equation for a hydrogenic atom with a screened Coulomb potential has been solved using both the variation method and the Numerov numerical method. The atomic parameters, such as the eigenvalues, the mean electron radii, the radial integrals and the number of bound states are calculated and compared with the values for the unperturbed atom.

It is found that for a few of the atomic states with positive eigenvalues (metastable states), the preionisation probability is definitely larger than the spontaneous probability of transition toward the lower bound atomic states.

The effect of the screening parameter on the eigenvalues, the mean radii and the radial integrals is illustrated with a few tables and figures.     

Stark broadening of sodium lines emitted by a sodium argon mixture plasma

Stark-broadened sodium line have been observed from a sodium-argon mixture plasma. Comparison between measured and theoretical$\text{3}{}^2\text{P}{}^0\text{? n}{}^2\text{D}\text{(n = 4, 5, 6)}$ line profiles indicates agreement within 10%. The temperature and electron density in the sodium emission region are 4500 K and 4.2 × 10¹⁵cm^-3 respectively.     

Nonlinear mapping and distance geometry

Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: DGP is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear Mapping is a weighted Least Square Scaling (LSS) method. We show how all these methods (LSS, NLM, DGP) can be assembled in a common framework, being each identified as an instance of an optimization problem with a choice of a weight matrix. We study the continuity between the solutions (which are point clouds) when the weight matrix varies, and the compactness of the set of solutions (after centering). We finally study a numerical example, showing that solving the optimization problem is far from being simple and that the numerical solution for a given procedure may be trapped in a local minimum.