Isovalue Surface Research Articles

Ab initio study of the biogenic amino acids.

Ten amino acids have been subjected to the quantum chemical calculations using the ab initio MO-LCAO-SCF calculations. When the geometry optimization started form the X-ray structure confirming the zwitterionic form, the ab initio calculations in vacuo result in the amino acid (canonical) form with the hydrogen atom attached not to the amine but to the carboxylate group. At the optimum geometry, a number of properties were evaluated: dipole moment, dipole polarizability, molecular surface, molecular volume, HOMO, LUMO, ionization energy, and electron affinity using the ΔSCF approach and their values corrected for electron correlation by the 2nd order perturbation theory (MP2). Also, the Mulliken electronegativity and Pearson hardness were evaluated. These properties have been mutually correlated by employing the statistical multivariate methods: the cluster analysis, the probabilistic neural network classifier, the principal component analysis, and the Pearson pair correlation. In addition, the molecular electrostatic potential mapped on the isovalue surface of charge density has been drawn. After the full vibrational analysis, thermodynamic properties at 300K were evaluated: internal energy, entropy, and the free energy.

Representation of a velocity model with implicitly embedded interface information

Accurately representing a velocity model for complex media still faces many challenges. The key issue involves the description of discontinuity surface with complicated shapes, such as pinch-out layers, salt domes with overhangs, and faulted interfaces. In this paper, a novel method for representing complex models is proposed. Each velocity discontinuity is described as an iso-value surface of a signed distance function, similar to an implicitly embedded interface. The implicit representation can construct the surfaces with non-manifold characteristics or multi-valued properties, e.g., fractured interfaces or mushroom models. For the velocity field within blocks, an approach involving the multiple copies of the computational mesh is used to bind a mesh to a block. This approach can faithfully describe the velocity distribution close to the block boundary without increasing the complexity of the computational mesh. A new data structure, termed stratigraphic binary tree, is also proposed to define the topological relationships between model elements (interfaces and blocks) and to efficiently manage the model data. A number of examples for different applications are given to evaluate the feasibility of the proposed representation scheme. The velocity model represented by the proposed method can serve as a good candidate for general ray-based forward and inverse applications.

Industrial computed tomography system for aerospace applications: development and characterisation

In this paper we report on the development and characterisation of an industrial computed tomography (ICT) system to image larger aerospace components and assemblies with sizes up to φ1000 mm, 10 m height and 2000 kg weight. The system consists of a 450 kV X-ray source, a linear detector array and a 6-axes computer numerical control (CNC) object manipulator. Mechanical as well as radiographic alignments were carried out to achieve 10 μm accuracy in mechanical motion of the objects under study. Rotate-only and translate-rotate scanning geometries were implemented for different sizes of object. Bi-directional scanning was implemented in translate-rotate geometry to reduce the scanning time by half. Corrections for centre of rotation error, ring artifacts, streak artifacts, unequal ray spacing error and cupping (beam-hardening) artifacts are implemented. A filtered back projection (FBP) algorithm is implemented for image reconstruction. The modulation transfer function (MTF) of the system is estimated using a 160 mm-diameter Perspex cylinder. The system resolution is found to be 350 μm. Details on the scanning of a few components are presented. 3D isovalue surface generation is implemented as an additional feature to aid better defect evaluation.

質量保存性に優れた気液２相流の数値解析手法の開発―液滴の相互衝突現象の数値解析への適用

In order to run a numerical analysis of gas-liquid two-phase flows accurately, a three-dimensional computational code has been developed with a new numerical method in consideration of superior mass conservation. In this code, which is based on the GTT code developed by the authors, the interface between two phases is discriminated by an interface tracking function, and the function is reconstructed according to its iso-value surface at appropriate intervals during its convection process so that the interface can be captured sharply and the mass can be absolutely conserved. By using this code with the original numerical method, the behavior of two water droplets, which impinge mutually in various manners, has been numerically analyzed and the calculated result compared with an experimental result. The results show that this code can reproduce well the phenomenon of coalescence or breakup after the mutual impingement of the droplets.

Quantitative structure–uptake relationship of metal-organic frameworks as hydrogen storage material

We have investigated the relationship between the molecular structures of metal-organic frameworks (MOFs) and their hydrogen uptake capabilities. Quantitative structure–property analysis was used to find out MOF structural factors important for hydrogen adsorption. To determine the quantitative interaction strength between hydrogen molecules and MOFs, the iso-value surface area of electrostatic potential was developed as a new descriptor. Quantitative analysis of structurally similar MOFs showed that the functionalization of aromatic organic linkers could induce noticeable polarization effect on the framework surface. We also found that the topology of MOFs plays an important role in determining the amount of ultimate hydrogen uptake. Through this quantitative structure–uptake relationship analysis, structural descriptors for the prediction of MOF hydrogen sorption capacity have been identified.

A Combined Experimental and Theoretical Electron Density Study of Intra‐ and Intermolecular Interactions in ThioureaS,S‐Dioxide

AbstractThe thioureaS,S‐dioxide molecule is recognized as a zwitterion with a high dipole moment and an unusually long CS bond. The molecule has a most interesting set of intermolecular interactions in the crystalline state—a relatively strong O⋅⋅⋅HN hydrogen bond and very weak intermolecular C⋅⋅⋅S and N⋅⋅⋅O interactions. The molecule hasCssymmetry, and each oxygen atom is hydrogen‐bonded to two hydrogen atoms with O⋅⋅⋅HN distances of 2.837 and 2.826 Å and angles of 176.61 and 158.38°. The electron density distribution is obtained both from Xray diffraction data at 110 K and from a periodic density functional theory (DFT) calculation. Bond characterization is made in terms of the analysis of topological properties. The covalent characters of the CN, NH, CS, and SO bonds are apparent, and the agreement on the topological properties between experiment and theory is adequate. The features of the Laplacian distributions, bond paths, and atomic domains are comparable. In a systematic approach, DFT calculations are performed based on a monomer, a dimer, a heptamer, and a crystal to see the effect on the electron density distribution due to the intermolecular interactions. The dipole moment of the molecule is enhanced in the solid state. The typical values ofρbandHbof the hydrogen bonds and weak intermolecular C⋅⋅⋅S and N⋅⋅⋅O interactions are given. All the interactions are verified by the location of the bond critical point and its associated topological properties. The isovalue surface of Laplacian charge density and the detailed atomic graph around each atomic site reveal the shape of the valence‐shell charge concentration and provide a reasonable interpretation of the bonding of each atom.

Cerebellar isolation, parcellation, and conformal surface mapping

The topographic organization of motor, sensory and cognitive functions in the human cerebellum is poorly understood, and, owing to its anatomical organization, most of the folial surface is hidden from view. In order to facilitate surface-based analysis of functional activation within the cerebellar cortex, we constructed a “pipeline” for extracting, labelling and conformally mapping the cortical surface. Methods The pipeline utilizes a cerebellar template volume isolated from a high-resolution, high-contrast-to-noise Tl-weighted MRI brain volume [l] and parcellated according to Schmahmann et al. [2]. See Figure 1. Isolation of a cerebellar subvolume was landmark driven; the posterior commissure, obex and apex of the fourth ventricle defined a standard orientation [3]. A template-to-source warp facilitiated removal of the cerebrum. The brainstem was then removed from the cerebellum by a computerized cut-plane that stepped though the volume until it reached the lingula, sparing wrap-around cerebellar tissue. The final perimeter of the cut surface served as the boundary for flatmapping to a plane. Parcellation was effected by warping the template cerebellum to a source subvolume, applying the resulting transform to the template parcellation, and editing the labels to correct errors due to poorly resolved fissures and/or variable fissuration. Marching Cubes was used to extract an isovalue surface from individual cerebellar subvolumes; however, these surfaces commonly exhibited undesirable Figure 1. Cerebellar template with fissure

DIFFUSIVE CUT-OFF SCALE OF FRACTAL SURFACES IN CHAOTIC MIXING

Results concerning the fractal properties of isovalue surfaces of a passive, diffusive scalar field being advected by a three-dimensional, steady flow exhibiting chaotic streamlines are presented. For all the Péclet numbers and the flow fields studied, the mixing efficiency is shown to be related to the extent of the so-called advective zone for which the similarity dimension Ds is optimal in the sense of mixing (Ds=3). For global chaos, the effective mixing time can be related to the diffusive cut-off scale which bounds this zone. For partial chaos, this cut-off scale corresponds to the size of the regular region which limits asymptotically the mixing.

An algorithm for construction of iso-valued surfaces for finite elements

Finite element analysis of 3D phenomena gives as a result a set of function values specified on the nodes of the mesh. Various modes of graphical representation of such results are possible, including contour plots on cross-sections and surfaces of constant field values. In this paper, we propose an algorithm for the generation of such models. The continuous surfaces representing constant field values are obtained element-by-element by linear interpolation of nodal values. The normalized gradient of computed values is used for surface smoothing and shading. The method uses shaded polygon and shaded triangle strip primitives to meet with industry standards for graphical equipment.

A scalar three‐dimensional spectral model with variable anisotropy

This paper introduces a simple three‐dimensional (3‐D) spectral model for scalar fluctuations with variable anisotropy. This heuristic model is useful in the study of statistical properties of stably stratified flows. It goes a step further than existing analogues by explicitly taking into account variation of anisotropy with the size of the fluctuations. The spectral model is specified by its isovalue surfaces and by its generalized energy spectrum. These surfaces are ellipsoids, (variably) elongated in the vertical direction. The model depends on two arbitrary functions of the spectral parameter. The possibilities of such variable anisotropy models are demonstrated by choosing specific functions. The choice was guided by maximal simplicity requirement and by the “tradition” of turbulent studies which heavily uses “power law” functions. These examples show how quantitative predictions are obtained using such 3‐D spectral models. They were selected in order to display characteristics that depend explicitly on the variable anisotropy and that could not have been obtained with previous models. The first example is the calculation of the one‐dimensional spectrum of temperature for arbitrary direction of measurement and the natural prediction of a change in slope for quasi‐horizontal spectra, while the oblique and vertical spectra retain the same slope. The second example is to account for radar echo aspect sensitivity, with angular contrast depending on the radar wavelength. The main advantages of the present model are its great flexibility provided by the use of two arbitrary functions and also the (relative) simplicity of its mathematical formulation.

Structure-activity relationship between the 3D distribution of the electrophilicity of sugar derivatives and their cytotoxic and antiviral properties.

The cytotoxic activities of a series of sugar derivatives bearing electrophilic groups (1-cyanovinyl, 4-cyanochromen-2-yl and 3-nitrochromen-2-yl) have been correlated with their electrophilic properties. To this end, an electrophilic index was defined as an isovalue surface where the interaction energy with an incoming model nucleophile (H-) was equal to a predefined value. This index, calculated from extended Hückel wave functions, allows one to quantify the electrophilic character of the substrates and to describe its spatial localization within the molecular volume (at Michael acceptor sites or on other parts of the molecules). Only sugars for which Michael acceptor reactivity was predicted were retained, and they were subdivided into two groups: those showing antiviral activity against a retrovirus and those devoid of such activity. Under these conditions, good correlations between cytotoxic activity and electrophilic reactivity--positive for the first group, negative for the second--were found. In addition, the ratio electrophilicity/sum of the absolute value of the dipole plus its projection along the principal axis of inertia, Z, of the molecule allows one to predict to which of these groups a sugar derivative belongs.

On the use of isovalued surfaces to determine molecule shape and reaction pathways

Novel insights into local molecule structure and reactivity can be gained from viewing isovalued surfaces of the molecular electron density, electrostatic potential and molecular orbitals rendered as colored, 3-D objects. For example, drawing positive and negative electrostatic isopotential surfaces partitions the molecule into regions subject to nucleophilic or electrophilic attack. Similarly, coloring isodensity surfaces to indicate the magnitude of the gradient of the electron density maps the molecule surface into regions of high and low electronegativity. A basic understanding of reaction mechanisms can also come from viewing and manipulating isovalued surfaces. A theory of molecular interactions, based upon second-order perturbation theory, provides for the decomposition of the intermolecular interaction energy into steric, electrostatic and orbital interactions. Color figures illustrate the docking of reactant molecular densities, electrostatic potentials and orbitals on low-energy pathways. The figures are used to visualize the steric, electrostatic and orbital contributions to molecular interaction energy. The visualization not only identifies low-energy reaction pathways, but it frequently reveals local interactions which determine the magnitude of the total interaction energy. Similar insight is not easily obtained by simple evaluation of the total interaction energy. Approximate transition states, built from structures along low-energy approach pathways, are excellent starting points for transition state searches.

B106 バイオ分子のポテンシャル分布のソリッドモデル化

A method to visualize iso-value surfaces of bio-molecular properties using 3-D solid models is proposed. The marching cube algorithm is improved to construct a 3-D solid model for this purpose. A program that generates iso-value surfaces of molecular properties such as non-bond interaction energy is developed. Boolean operation on solid models is efficient to analyze shapes of active sites of bio-molecules. For example a fundamental study of molecular design for Trypsin - Trypsin inhibitor complex is demonstrated. This method allows more comprehensive analysis of bio-molecular structure.

ISOSRF—an algorithm for plotting Iso-valued surfaces of a function of three variables

Given a three-dimensional array containing values of a function of three variables, the algorithm presented here draws an approximation of the surface or surfaces where the function attains a specified value. This is done by contouring two-dimensional subsets of the three-dimensional array and suppressing the invisible parts of the contours. The union of all the contour line parts approximates the desired surface. The suppression of the invisible lines is the most complicated part of the algorithm and is done by forming a silhouette of the processed subset of the array and testing lines against this structure.