Use Of Coordinates Research Articles

TICA-Metadynamics: Accelerating Metadynamics by Using Kinetically Selected Collective Variables.

Metadynamics is a powerful enhanced molecular dynamics sampling method that accelerates simulations by adding history-dependent multidimensional Gaussians along selective collective variables (CVs). In practice, choosing a small number of slow CVs remains challenging due to the inherent high dimensionality of biophysical systems. Here we show that time-structure based independent component analysis (tICA), a recent advance in Markov state model literature, can be used to identify a set of variationally optimal slow coordinates for use as CVs for Metadynamics. We show that linear and nonlinear tICA-Metadynamics can complement existing MD studies by explicitly sampling the system's slowest modes and can even drive transitions along the slowest modes even when no such transitions are observed in unbiased simulations.

Position Accuracy Improvement by Implementing the DGNSS-CP Algorithm in Smartphones

The position accuracy of Global Navigation Satellite System (GNSS) modules is one of the most significant factors in determining the feasibility of new location-based services for smartphones. Considering the structure of current smartphones, it is impossible to apply the ordinary range-domain Differential GNSS (DGNSS) method. Therefore, this paper describes and applies a DGNSS-correction projection method to a commercial smartphone. First, the local line-of-sight unit vector is calculated using the elevation and azimuth angle provided in the position-related output of Android’s LocationManager, and this is transformed to Earth-centered, Earth-fixed coordinates for use. To achieve position-domain correction for satellite systems other than GPS, such as GLONASS and BeiDou, the relevant line-of-sight unit vectors are used to construct an observation matrix suitable for multiple constellations. The results of static and dynamic tests show that the standalone GNSS accuracy is improved by about 30%–60%, thereby reducing the existing error of 3–4 m to just 1 m. The proposed algorithm enables the position error to be directly corrected via software, without the need to alter the hardware and infrastructure of the smartphone. This method of implementation and the subsequent improvement in performance are expected to be highly effective to portability and cost saving.

Analysis of the propagation dynamics and Gouy phase of Airy beams using the fast Fresnel transform algorithm.

There is great interest in Airy beams because they appear to propagate in a curved path. These beams are usually generated by inserting a cubic phase mask onto the input plane of a Fourier transform system. Here, we utilize a fast Fresnel diffraction algorithm to easily derive both the propagation dynamics and the Gouy phase shift for these beams. The trajectories of these beams can be modified by adding additional linear and quadratic phase terms onto the cubic phase mask. Finally, we have rewritten the equations regarding the propagating Airy beams completely in laboratory coordinates for use by experimentalists. Experimental results are included. We expect that these results will be of great importance in applications of Airy beams.

An efficient route to thermal rate constants in reduced dimensional quantum scattering simulations: Applications to the abstraction of hydrogen from alkanes

We present an efficient approach to the determination of two-dimensional potential energy surfaces for use in quantum reactive scattering simulations. Our method involves first determining the minimum energy path (MEP) for the reaction by means of an ab initio intrinsic reaction coordinate calculation. This one-dimensional potential is then corrected to take into account the zero point energies of the spectator modes. These are determined from Hessians in curvilinear coordinates after projecting out the modes to be explicitly treated in quantum scattering calculations. The final (1+1)-dimensional potential is constructed by harmonic expansion about each point along the MEP before transforming the whole surface to hyperspherical coordinates for use in the two-dimensional scattering simulations. This new method is applied to H-atom abstraction from methane, ethane and propane. For the latter, both reactive channels (producing i-C(3)H(7) or n-C(3)H(7)) are investigated. For all reactions, electronic structure calculations are performed using an efficient, explicitly correlated, coupled cluster methodology (CCSD(T)-F12). Calculated thermal rate constants are compared to experimental and previous theoretical results.

Aten—An application for the creation, editing, and visualization of coordinates for glasses, liquids, crystals, and molecules

Aten is a tool for Linux, Mac, and Windows platforms to ease the creation, editing, and visualization of coordinates for use in, for example, molecular dynamics simulations. The code handles gas-phase molecules in addition to crystals, surfaces, and liquids, providing standard tools to edit "by the atom" along with specific "by the box" methods suited to periodic systems, including full crystallographic spacegroup packing definitions. Visualization of systems encompasses the standard drawing styles and may be mixed with an arbitrary number of other basic objects, such as arrows and geometric objects allowing creation of scenes involving vector fields, coarse-grained particles, etc. Standard molecular mechanics forcefields can be read in, edited, applied to molecules using the built-in chemical typing language, and subsequently used to calculate energies and forces, minimize energies with respect to coordinates, decompose energies into contribution by molecule type, etc. Monte Carlo methods are available with which to generate random configurations of N-component systems, or solvate around molecules or in specific regions within existing configurations. Supported file formats are governed by user-defined "filters," which provide flexibility of input/output as well as the ability to define custom or extended formats of traditional files. Forcefield descriptions for loaded systems can be output and formatted for use as input to common codes. All features can be accessed by a comprehensive GUI and scripting language based on the C syntax.

An adaptive density-guided approach for the generation of potential energy surfaces of polyatomic molecules

We present an adaptive density-guided approach for the construction of Born–Oppenheimer potential energy surfaces (PES) in rectilinear normal coordinates for use in vibrational structure calculations. The procedure uses one-mode densities from vibrational structure calculations for a dynamic sampling of PESs. The implementation of the procedure is described and the accuracy and versatility of the method is tested for a selection of model potentials, water, difluoromethane and pyrimidine. The test calculations illustrate the advantage of local basis sets over harmonic oscillator basis sets in some important aspects of our procedure.

Can Principal Components Yield a Dimension Reduced Description of Protein Dynamics on Long Time Scales?

The suitability of principal component analysis (PCA) to yield slow collective coordinates for use within a dimension reduced description of conformational motions in proteins is evaluated. Two proteins are considered, T4 lysozyme and crambin. We present a quantitative evaluation of the convergence of conformational coordinates obtained with principal component analysis. Detailed analyses of (>200 ns) molecular dynamics trajectories and crystallographic data suggests that simulations of a few nanoseconds should generally provide a stable and statistically reliable definition of the essential and near constraints subspaces. Moreover, a systematic assessment of the density of states of the dynamics of all principal components showed that for an optimal separation of time scales it is crucial to include also side chain atoms in the PCA.

Seeing the Sky through Hubble’s Eye: The COSMOS SkyWalker

ABSTRACTLarge, high‐resolution space‐based imaging surveys produce a volume of data that is difficult to present to the public in a comprehensible way. While megapixel‐sized images can still be printed out or downloaded via the World Wide Web, this is no longer feasible for images with 109 pixels (e.g., the Hubble Space Telescope Advanced Camera for Surveys [ACS] images of the Galaxy Evolution from Morphology and SEDs [GEMS] project) or even 1010 pixels (for the ACS Cosmic Evolution Survey [COSMOS]). We present a Web‐based utility called the COSMOS SkyWalker that allows viewing of the huge ACS image data set, even through slow Internet connections. Using standard HTML and JavaScript, the application successively loads only those portions of the image at a time that are currently being viewed on the screen. The user can move within the image by using the mouse or interacting with an overview image. Using an astrometrically registered image for the COSMOS SkyWalker allows the display of calibrated world coordinates for use in science. The SkyWalker “technique” can be applied to other data sets. This requires some customization, notably the slicing up of a data set into small (e.g., 2562 pixel) subimages. An advantage of the SkyWalker is the use of standard Web browser components; thus, it requires no installation of any software and can therefore be viewed by anyone across many operating systems.

Vibration-rotation coordinates and kinetic energy operators for polyatomic molecules

In molecular vibration-rotation calculations it is frequently desirable to work in a nuclear coordinate system tailored to the nuclear potential energy surface. It is now possible to derive the kinetic energy operator for virtually any coordinate system by using computer algebra programs. We discuss how to choose coordinates for use in practical calculations, in particular variational energy level calculations, with special consideration of the vibration-rotation separation. As an example we present a kinetic energy operator suitable for calculating the rovibrational spectrum of sequentially bonded four-atomic molecules, using valence coordinates. We carry out a rigorous symmetry classification using the MS group, and also consider how the problem of singularities affects the choice of basis set.

On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part I: Formulation and Comparison of Exact Solutions

Motivated by the general objective of pursuing oceanographic process and data assimilation studies of the complex, nonlinear eddy and jet current fields observed over the continental shelf and slope off the west coast of the United States, we investigate the use of intermediate models for that purpose. Intermediate models contain physics between that in the primitive equations and that in the quasigeostrophic equations and are capable of representing subinertial frequency motion over the O(1) topographic variations typical of the continental slope, while filtering out high-frequency gravity-inertial waves. As an initial step, we compare and evaluate several intermediate models applied to the f-plane shallow-water equations for flows over topography. The accuracy and utility of the intermediate models are assessed by a comparison of exact analytical and numerical solutions with those of the primitive shallow-water equations (SWE) and with those of the quasi-geostrophic equations (QG). The intermediate models that we consider are based on the geostrophic momentum (GM) approximation, the derivation of Salmon (1983) utilizing Hamilton's principle (HP), a geostrophic vorticity (GV) approximation, the quasi-geostrophic momentum and full continuity equations (IM), the linear balance equations (LBE), the balance equations (BE), the related balance-type (HBE, BEM, NBE) and modified linear balance equations (LQBE), the slow equations (SE) of Lynch (1989), and the modified slow equations (MSE). In Part I, we discuss the intermediate models and develop formulations that are suitable for numerical solution in physical coordinates for use in Parts II and III. We investigate the capability of the intermediate models to represent linear ageostrophic coastally trapped waves, i.e., Kelvin and continental shelf waves, and demonstrate that they do so with accuracy consistent with standard linear low-frequency approximations. We also assess the accuracy of the models by a comparison of exact nonlinear analytical solutions to the SWE for steady flow in an elliptic paraboloid and for unsteady motion of elliptical vortices in a circular paraboloid with corresponding analytical solutions to the intermediate models and to QG. General results from the exact solution comparisons include the following. Many of the intermediate models are capable of producing more accurate solutions than QG over a range of Rossby numbers 0 < ε < 1. In some cases, the intermediate models provide accurate approximate solutions where QG is not applicable and fails to give a relevant solution. Considerable parameter-dependent variation in quality exists, however, among the different intermediate models. For the particular problems considered here, BE, HBE, BEM, NBE, and MSE reproduce the exact results of the SWE while LBE and LQBE give the same approximation as QG. The accuracy of the models is typically in the order GV, GM, IM, HP, and QG, with GV most accurate and IM and HP sometimes less accurate than QG.

Investigations of transformed mass-scaled Jacobi coordinates for vibrations of polyatomic molecules with application to H2O

We present an investigation of orthogonal transformations of Delves coordinates, i.e., mass-scaled Jacobi coordinates, in applications to polyatomic molecule vibrations. First, we show for triatomic molecules with a stationary point of C2v symmetry that these coordinates can be transformed exactly to yield normal coordinates in the small displacement limit. A partial transformation to normal coordinates is also given for tetraatomic molecules with C2v symmetry. Second, we show that this transformation can be used to optimize a set of coordinates for use in variational calculations of vibrations of polyatomic molecules, and demonstrate its utility in variational calculations of vibrational energies for H2O.

Weather Radar Signal Processing and Recording at the National Severe Storms Laboratory

The radar data system at the National Severe Storms Laboratory presents weather radar return power data with a significant reduction in the variations that arise from the relative motion of discrete precipitation elements. The system provides intensity-contoured plan position indicator (PPI) displays for visual inspection and photographic archival, and digital records in azimuth-range coordinates for use in computers and for narrow-band transmission to remote locations. Digital records can also be reproduced in the PPI format. The spatial distribution of echo power perceived during each two degrees of antenna azimuthal revolution, is represented as ten levels of return power intensity at intervals of 2°×1 nmi. Spatial reticulation is of the same order as limits of resolution inherent in the radar beamwidth and pulse length, and the system output thus retains most of the information on precipitation rate distributions contained in the unprocessed video signals. Averaging over two pulse lengths and the equivalence of ten pulse periods provides approximately Gaussian-distributed estimates of mean intensity with a standard error of 1 dB, less than one-fifth of the uncertainty of point-sampled unprocessed video. The system is used routinely at NSSL with a 10-cm WSR-57 radar, a type widely used by the Weather Bureau, and could be adapted to any weather radar system.

(1) Elements of Plane and Spherical Trigonometry (2) Homogeneous Coordinates for Use in Colleges and Schools (3) A Geometry for Schools (4) Analytic Geometry

(1) Elements of Plane and Spherical Trigonometry (2) Homogeneous Coordinates for Use in Colleges and Schools (3) A Geometry for Schools (4) Analytic Geometry