Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schr\"odinger equations

We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using Fast Fourier Transforms. To split the system into the quantum harmonic oscillator problem and the remaining part allows to get higher accuracies in many cases, but it requires to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build new methods which combine the advantages of using Fourier methods while solving the timedependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition).Comment: 12 pages of RevTex4-1, 8 figures; substantially revised and extended versio

Modélisation du ruissellement en relation avec l'évolution saisonnière de la végétation (mil, arachide, jachère) au centre Sénégal

Sous climat soudanien caractérisé par une unique saison des pluies, les sols sont dénudés en fin de saison sèche suite au pâturage et aux travaux préparatoires au semis. Le ruissellement intense en début d'hivernage diminue progressivement avec la mise en place des couverts végétaux.L'influence du développement de la végétation sur le ruissellement est étudié au moyen des données pluie-débit de 4 parcelles (50 m2) couvertes en mil, arachide, jachère ou maintenue dénudée du centre Sénégal au cours d'une saison des pluies (1994). Un modèle analogique de ruissellement ‡ stockage de surface (BADER, 1994), dans lequel l'infiltration est une fonction croissante de la lame d'eau en surface du sol est ajusté sur les données. Le modèle présente 3 paramètres: un paramètre de transfert n, un paramètre de ruissellement Hl et un paramètre d'infiltration S. Une analyse de sensibilité menée sur les données de la parcelle de sol nu montre que le paramètre n est le plus sensible des trois.Le calage numérique des paramètres sur chaque crue au cours de l'hivernage permet d'étudier leur évolution temporelle. Cette évolution est cohérente avec l'occupation de chaque parcelle. Les paramètres n et S de la parcelle de sol nu sont invariants sur la saison tandis que ceux des parcelles en végétation s'écartent progressivement des valeurs obtenues sur sol nu. Pour les parcelles en végétation, les valeurs de S divergent de celles du sol nu lorsque l'indice radiométrique de végétation (N.D.V.I.) servant à l'estimation du couvert dépasse 0.30 - 0.35 environ. L'évolution des paramètres n et S des parcelles en végétation peut être reliée au temps écoulé depuis le semis (mil, arachide) ou le sarclage initial (jachère) et à l'état d'humectation du sol (pour S). On montre également que le paramètre Hl peut être estimé linéairement à partir d'un indice de rugosité de surface descriptif de la microtopographie.The Sudanese climate is characterized by a rainy season and a dry season (mean annual rainfall between 400 and 900 mm). At the end of the dryseason (June in the northern hemisphere), the landscape is completely bare under the effect of animal grazing or soil tillage. During the first rainfalls this leads to high runoff coefficients. These runoff coefficients decrease gradually as the amount of vegetation increases during the growing season (RODIER (1984-1985); ALBERGEL (1988)).This is particularly true in the Groundnut basin of central Senegal where millet and groundnut are cultivated every other year. As the vegetative cover increases, a system of macropores develops in the soil and preferentially induces water infiltration through mesofauna burrows and along root systems. Hence, many authors have distinguished matrix infiltration governed by the generalized Darcy's law, from preferential infiltration through macropores characterized by a strongly heterogeneous spatial distribution (GERMAN, 1990). These macropores are thought to be responsible for the proportional increase in infiltration with increase in rainfall intensity observed on several experimental plots (BOUCHARDEAU and RODIER, 1960; VALENTIN, 1985; COLLINET,1985; ALBERGEL, 1988). A more complete surface ponding or a differential distribution of the macroporosity in relation with the microtopography can contribute to this phenomenon.A conceptual runoff model accounting for surface storage, which views infiltration as a function of water depth on the ground surface, is proposed to describe the aforementioned phenomenon under three characteristic vegetative canopies of central Senegal (millet, groundnut and fallow). The model (BADER, 1994) is a distributed, three parameter model that accounts for transfer between spatial elements (parameter n), runoff (parameter Hl) and infiltration (parameter S). The model solves the equation of continuity according to an explicit scheme (forward time). The discharge exiting a spatial element is defined by a power function based on the water depth on the element. The value of the transfer parameter n (dimensionless) depends on the roughness and slope of the soil surface. Parameter Hl (meters) is equivalent to the water depth from which runoff occurs and is found in the discharge expression. Infiltration is defined as the product of the squareroot of the depth of ponded water of a plot and a S parameter (dimensionless) representing surface porosity.The experimental work took place on 4 rectangular 50m2 plots (10 m by 5 m) that were initially bare and weedy. At the beginning of the rainy season, two plots were cultivated in millet and groundnut, one left fallow and the fourth stripped by a powerful herbicide. The runoff was measured by a capacitive gauging system with each tank being equipped with a pressure transducer connected to a datalogger. A tipping bucket raingauge was also connected to the datalogger and rainfall and runoff were recorded simultaneously. The measurements were made to a precision of 4 mm in the tanks (0.16 mm uncertainty for surface runoff depth). With a total seasonal rainfall of 711 mm in 1994, the cumulative surface runoff varied between 40mm for the fallow plot to 150 mm for the bare soil plot. The cultivated groundnut and millet plots had cumulative runoff depths of 55 and 60 mm, respectively. The fallow plot would have had less runoff if it had been more than one-year old. The microtopography of each plot was evaluated using a profile meter. The surface roughness was estimated by the standard-error of measured relative elevations (GUILLOBEZ and ZOUGMORE, 1994). Measurements were taken after each significant rainfall and following tillage operations. The index of roughness varied following vigorous weeding of the groundnut plot to 5 mm for the fallow plot whose microtopography remained constant throughout the season. The development of the vegetative cover was indirectly followed by the calculation of a vegetation index (NDVI) derived from red and near infrared reflectances measured with a field radiometer. Although this index tends to saturate with full ground cover, it nevertheless remains a good indicator at the start of vegetative growth.The proposed model was used to reproduce measured runoff during several storm events. Calculations were undertaken with a 10-s time step on a 1m-long spatial element with a uniform set of parameters for each plot. A sensitivity analysis was performed for all runoff events on the bare plot. Hydrograph characteristics (runoff volume, peak discharge and time-to-peak) were particularly sensitive to variations in the transfer parameter (n) and to a lesser extent to changes in the infiltration (S) and runoff (Hl) parameters. For the 42 measured runoff hydrographs for all fourplots, the results were excellent: 70% of the simulated hydrographs had a Nash's coefficient greater than or equal to 0.90.For each plot, the seasonal chronicle of each parameter is coherent with the plot cover. The parameters for the bare plot were invariant throughout the rainy season. However, for the other plots, they varied with the vegetative cover. At the beginning of the growing season, they were similar to those obtained on bare soil and, as the vegetative cover increased, they varied until the NDVI exceeded 0.35 (approximately 20 days after seeding). The evolution of the n and S parameters for the cultivated plots was linearly extrapolated from past events (seeding for the cultivated plots and chemical weeding for the fallow plot) and for S to an antecedent precipitation index. Farming practices that modified surface roughness needed to be accounted for as well. For the transfer parameter (n) of the groundnut plot, an increase of approximately 0.4 was observed when a rainfall event followed weeding. No significant increase was seen for the millet plot. A linear relationship between the index of roughness and the roughness parameter (Hl) was also derived

Structure and binding in crystals of cage-like molecules: hexamine and platonic hydrocarbons

In this paper, we show that first-principle calculations using a van der Waals density functional (vdW-DF), [Phys. Rev. Lett. $\mathbf{92}$, 246401 (2004)] permits determination of molecular crystal structure. We study the crystal structures of hexamine and the platonic hydrocarbons (cubane and dodecahedrane). The calculated lattice parameters and cohesion energy agree well with experiments. Further, we examine the asymptotic accounts of the van der Waals forces by comparing full vdW-DF with asymptotic atom-based pair potentials extracted from vdW-DF. The character of the binding differ in the two cases, with vdW-DF giving a significant enhancement at intermediate and relevant binding separations. We analyze consequences of this result for methods such as DFT-D, and question DFT-D's transferability over the full range of separations

Polarization forces in water deduced from single molecule data

Intermolecular polarization interactions in water are determined using a minimal atomic multipole model constructed with distributed polarizabilities. Hydrogen bonding and other properties of water-water interactions are reproduced to fine detail by only three multipoles $\mu_H$, $\mu_O$, and $\theta_O$ and two polarizabilities $\alpha_O$ and $\alpha_H$, which characterize a single water molecule and are deduced from single molecule data.Comment: 4 revtex pages, 3 embedded color PS figure

Beyond the local approximation to exchange and correlation: the role of the Laplacian of the density in the energy density of Si

We model the exchange-correlation (XC) energy density of the Si crystal and atom as calculated by variational Monte Carlo (VMC) methods with a gradient analysis beyond the local density approximation (LDA). We find the Laplacian of the density to be an excellent predictor of the discrepancy between VMC and LDA energy densities in each system. A simple Laplacian-based correction to the LDA energy density is developed by means of a least square fit to the VMC XC energy density for the crystal, which fits the homogeneous electron gas and Si atom without further effort.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

The local electronic structure of alpha-Li3N

New theoretical and experimental investigation of the occupied and unoccupied local electronic density of states (DOS) are reported for alpha-Li3N. Band structure and density functional theory calculations confirm the absence of covalent bonding character. However, real-space full-multiple-scattering (RSFMS) calculations of the occupied local DOS finds less extreme nominal valences than have previously been proposed. Nonresonant inelastic x-ray scattering (NRIXS), RSFMS calculations, and calculations based on the Bethe-Salpeter equation are used to characterize the unoccupied electronic final states local to both the Li and N sites. There is good agreement between experiment and theory. Throughout the Li 1s near-edge region, both experiment and theory find strong similarities in the s- and p-type components of the unoccupied local final density of states projected onto an orbital angular momentum basis (l-DOS). An unexpected, significant correspondence exists between the near-edge spectra for the Li 1s and N 1s initial states. We argue that both spectra are sampling essentially the same final density of states due to the combination of long core-hole lifetimes, long photoelectron lifetimes, and the fact that orbital angular momentum is the same for all relevant initial states. Such considerations may be generically applicable for low atomic number compounds.Comment: 34 pages, 7 figures, 1 tabl

Poly(ADP-ribose)glycohydrolase is an upstream regulator of Ca2+ fluxes in oxidative cell death

Oxidative DNA damage to cells activates poly(ADP-ribose)polymerase-1 (PARP-1) and the poly(ADP-ribose) formed is rapidly degraded to ADP-ribose by poly(ADP-ribose)glycohydrolase (PARG). Here we show that PARP-1 and PARG control extracellular Ca2+ fluxes through melastatin-like transient receptor potential 2 channels (TRPM2) in a cell death signaling pathway. TRPM2 activation accounts for essentially the entire Ca2+ influx into the cytosol, activating caspases and causing the translocation of apoptosis inducing factor (AIF) from the inner mitochondrial membrane to the nucleus followed by cell death. Abrogation of PARP-1 or PARG function disrupts these signals and reduces cell death. ADP-ribose-loading of cells induces Ca2+ fluxes in the absence of oxidative damage, suggesting that ADP-ribose is the key metabolite of the PARP-1/PARG system regulating TRPM2. We conclude that PARP-1/PARG control a cell death signal pathway that operates between five different cell compartments and communicates via three types of chemical messengers: a nucleotide, a cation, and protein

Pressure formulas for liquid metals and plasmas based on the density-functional theory

At first, pressure formulas for the electrons under the external potential produced by fixed nuclei are derived both in the surface integral and volume integral forms concerning an arbitrary volume chosen in the system; the surface integral form is described by a pressure tensor consisting of a sum of the kinetic and exchange-correlation parts in the density-functional theory, and the volume integral form represents the virial theorem with subtraction of the nuclear virial. Secondly on the basis of these formulas, the thermodynamical pressure of liquid metals and plasmas is represented in the forms of the surface integral and the volume integral including the nuclear contribution. From these results, we obtain a virial pressure formula for liquid metals, which is more accurate and simpler than the standard representation. From the view point of our formulation, some comments are made on pressure formulas derived previously and on a definition of pressure widely used.Comment: 18 pages, no figur