Lubos Mitas

Interpolation by regularized spline with tension: I. Theory and implementation

Bivariate and trivariate functions for interpolation from scattered data are derived. They are constructed by explicit minimization of a general smoothness functional, and they include a tension parameter that controls the character of the interpolation function (e.g., for bivariate case the surface can be tuned from a “membrane” to a “thin steel plate”), Tension can be applied also in a chosen direction, for modeling of phenomena with a simple type of anisotropy. The functions have regular derivatives of all orders everywhere. This makes them suitable for analysis of surface geometry and for direct application in models where derivatives are necessary. For processing of large datasets (thousands of data points), which are now common in geosciences, a segmentation algorithm with a flexible size of overlapping neighborhood is presented. Simple examples demonstrating flexibility and accuracy of the functions are presented.

Observation of a magic discrete family of ultrabright Si nanoparticles

We demonstrate that electrochemically etched, hydrogen capped SinHx clusters with n larger than 20 are obtained within a family of discrete sizes. These sizes are 1.0 (Si29), 1.67 (Si123), 2.15, 2.9, and 3.7 nm in diameter. We characterize the particles via direct electron imaging, excitation and emission optical spectroscopy, and colloidal crystallization. The band gaps and emission bands are measured. The smallest four are ultrabright blue, green, yellow and red luminescent particles. The availability of discrete sizes and distinct emission in the red, green and blue (RGB) range is useful for biomedical tagging, RGB displays, and flash memories.

Nonlocal pseudopotentials and diffusion Monte Carlo

We have applied the technique of evaluating a nonlocal pseudopotential with a trial function to give an approximate, local many‐body pseudopotential which was used in a valence‐only diffusion Monte Carlo (DMC) calculation. The pair and triple correlation terms in the trial function have been carefully optimized to minimize the effect of the locality approximation. We discuss the accuracy and computational demands of the nonlocal pseudopotential evaluation for the DMC method. Calculations of Si, Sc, and Cu ionic and atomic states and the Si2 dimer are reported. In most cases ∼90% of the correlation energy was recovered at the variational level and excellent estimations of the ground state energies were obtained by the DMC simulations. The small statistical error allowed us to determine the quality of the assumed pseudopotentials by comparison of the DMC results with experimental values.

Distributed soil erosion simulation for effective erosion prevention

We present a bivariate model of erosion, sediment transport, and deposition by overland flow, designed for complex terrain, soil, and cover conditions. We use a Greens function Monte Carlo method to solve the underlying continuity equations, leading to improved robustness and implementation efficiency. By deriving the relationship between the terrain shape and erosion/deposition pattern, we clarify the physical interpretation of terrain curvatures and overall importance of the bivariate formulation. We explain the impact of various soil and cover properties by simulating the detachment and transport capacity limited erosion for uniform land use and by predicting the erosion/deposition distribution for a conventional, spatially variable land use at an experimental farm. We compare the results with the observed colluvial deposits and linear erosion features and illustrate the application of the model for improving the effectiveness of erosion prevention measures.

High accuracy many-body calculational approaches for excitations in molecules

Two state-of-the-art computational approaches: quantum Monte Carlo and GW with exciton effects [GW-BSE (Bethe-Salpeter equation)] are employed to calculate ionization potentials, electron affinities, and first excited singlet and triplet energies for the silane and methane molecules. Results are in excellent agreement between these dramatically different approaches and with available experiment. The optically forbidden triplet excitation in silane is predicted to lie roughly 1 eV higher than previously reported. In the GW-BSE method, we demonstrate that inclusion of off-diagonal matrix elements in the self-energy operator is crucial for an accurate picture.

Multivariate Interpolation of Precipitation Using Regularized Spline with Tension

Regularized Spline with Tension (RST) is an accurate, flexible and efficient method for multivariate interpolation of scattered data. This study evaluates its capabilities to interpolate daily and annual mean precipitation in regions with complex terrain. Tension, smoothing and anisotropy parameters are optimized using the cross-validation technique. In addition, smoothing and rescaling of the third variable (elevation) is used to minimize the predictive error. The approach is applied to data sets from Switzerland and Slovakia and interpolation accuracy is compared to the results obtained by several other methods, expert-drawn maps and measured runoff. The results demonstrate that RST performs as well or better than the methods tested in the literature. The incorporation of terrain improves the spatial model of precipitation in terms of its predictive error, spatial pattern and water balance.

Applications of quantum Monte Carlo methods in condensed systems

Quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schrequation for atoms, molecules, solids and a variety of model systems. The algorithms are intrinsically parallel and are able to take full advantage of present-day high-performance computing systems. This review paper concentrates on the fixed-node/fixed-phase diffusion Monte Carlo method with emphasis on its applications to the electronic structure of solids and other extended many-particle systems. (Some figures in this article are in colour only in the electronic version) This article was invited by M-Y Chou.

Modelling spatially and temporally distributed phenomena: new methods and tools for GRASS GIS

Abstract The concept of GRASS (Geographic Resources Analysis Support System) as an open system has created a favourable environment for integration of process based modelling and GIS. To support this integration a new generation of tools is being developed in the following areas: (a) interpolation from multidimensional scattered point data, (b) analysis of surfaces and hypersurfaces, (c) modelling of spatial processes and, (d) 3D dynamic visualization. Examples of two applications are given-spatial and temporal modelling of erosion and deposition, and multivariate interpolation and visualization of nitrogen concentrations in the Chesapeake Bay.

Effect of surface reconstruction on the structural prototypes of ultrasmall ultrabright Si29 nanoparticles

We propose, using density functional, configuration interaction, and quantum Monte Carlo calculations, structural prototypes of ultrasmall ultrabright particles prepared by dispersion from bulk. We constructed near spherical structures (Td point group symmetry) that contain 29 Si atoms, five of which constitute a tetrahedral core and the remaining 24 constitute a hydrogen terminated reconstructed Si surface. The surface is a highly wrinkled or puckered system of hexagons and pentagons (as in a filled fullerene). We calculated, for several surface reconstruction models, the coordinates of atoms, the absorption spectrum, the absorption edge, polarizability, and the electron diffraction pattern. The Si29H24 (six reconstructed surface dimers) gives a size of 0.9 nm, an absorption spectrum and bandgap (3.5±0.3 eV), in fair agreement with measurement. The structure yields a polarizability of 830 a.u. with an effective “dielectric” constant of ∼6.0. The calculated electron diffraction of single particles shows r...

QWalk: A quantum Monte Carlo program for electronic structure

We describe QWalk, a new computational package capable of performing quantum Monte Carlo electronic structure calculations for molecules and solids with many electrons. We describe the structure of the program and its implementation of quantum Monte Carlo methods. It is open-source, licensed under the GPL, and available at the web site http://www.qwalk.org.