Three-dimensional Grid Research Articles

Carbon-oxygen-neon mass nuclei in superstrong magnetic fields

The properties of $^{12}\mathrm{C},\phantom{\rule{0.16em}{0ex}}^{16}\mathrm{O}$, and $^{20}\mathrm{Ne}$ nuclei in strong magnetic fields $B\ensuremath{\simeq}{10}^{17}$ G are studied in the context of strongly magnetized neutron stars and white dwarfs. The sky3d code is extended to incorporate the interaction of nucleons with the magnetic field and is utilized to solve the time-independent Hartree-Fock equations with a Skyrme interaction on a Cartesian three-dimensional grid. The numerical solutions demonstrate a number of phenomena, which include a splitting of the energy levels of spin-up and -down nucleons, spontaneous rearrangement of energy levels in $^{16}\mathrm{O}$ at a critical field, which leads to jump-like increases of magnetization and proton current in this nucleus, and evolution of the intrinsically deformed $^{20}\mathrm{Ne}$ nucleus toward a more spherical shape under increasing field strength. Many of the numerical features can be understood within a simple analytical model based on the occupation by the nucleons of the lowest states of the harmonic oscillator in a magnetic field.

Selecting an Appropriate Upscaled Reservoir Model Based on Connectivity Analysis

Reservoir engineers aim to build reservoir models to investigate fluid flows within hydrocarbon reservoirs. These models consist of three-dimensional grids populated by petrophysical properties. In this paper, we focus on permeability that is known to significantly influence fluid flow. Reservoir models usually encompass a very large number of fine grid blocks to better represent heterogeneities. However, performing fluid flow simulations for such fine models is extensively CPU-time consuming. A common practice consists in converting the fine models into coarse models with less grid blocks: this is the upscaling process. Many upscaling methods have been proposed in the literature that all lead to distinct coarse models. The problem is how to choose the appropriate upscaling method. Various criteria have been established to evaluate the information loss due to upscaling, but none of them investigate connectivity. In this paper, we propose to first perform a connectivity analysis for the fine and candidate coarse models. This makes it possible to identify shortest paths connecting wells. Then, we introduce two indicators to quantify the length and trajectory mismatch between the paths for the fine and the coarse models. The upscaling technique to be recommended is the one that provides the coarse model for which the shortest paths are the closest to the shortest paths determined for the fine model, both in terms of length and trajectory. Last, the potential of this methodology is investigated from two test cases. We show that the two indicators help select suitable upscaling techniques as long as gravity is not a prominent factor that drives fluid flows.

Hierarchical Benders Decomposition for Open-Pit Mine Block Sequencing

The open-pit mine block sequencing problem (OPBS) models a deposit of ore and surrounding material near the Earth’s surface as a three-dimensional grid of blocks. A solution in discretized time identifies a profit-maximizing extraction (mining) schedule for the blocks. Our model variant, a mixed-integer program (MIP), presumes a predetermined destination for each extracted block, namely, processing plant or waste dump. The MIP incorporates standard constructs but also adds not-so-standard lower bounds on resource consumption in each time period and allows fractional block extraction in a novel fashion while still enforcing pit-wall slope restrictions. A new extension of nested Benders decomposition, “hierarchical” Benders decomposition (HBD), solves the MIP’s linear-programming relaxation. HBD exploits time-aggregated variables and can recursively decompose a model into a master problem and two subproblems rather than the usual single subproblem. A specialized branch-and-bound heuristic then produces high-quality, mixed-integer solutions. Medium-sized problems (e.g., 25,000 blocks and 20 time periods) solve to near optimality in minutes. To the best of our knowledge, these computational results are the best known for instances of OPBS that enforce lower bounds on resource consumption.

GenLocDip: A Generalized Program to Calculate and Visualize Local Electric Dipole Moments.

Local dipole moments (i.e., dipole moments of atomic or molecular subsystems) are essential for understanding various phenomena in nanoscience, such as solvent effects on the conductance of single molecules in break junctions or the interaction between the tip and the adsorbate in atomic force microscopy. We introduce GenLocDip, a program for calculating and visualizing local dipole moments of molecular subsystems. GenLocDip currently uses the Atoms-In-Molecules (AIM) partitioning scheme and is interfaced to various AIM programs. This enables postprocessing of a variety of electronic structure output formats including cube and wavefunction files, and, in general, output from any other code capable of writing the electron density on a three-dimensional grid. It uses a modified version of Bader's and Laidig's approach for achieving origin-independence of local dipoles by referring to internal reference points which can (but do not need to be) bond critical points (BCPs). Furthermore, the code allows the export of critical points and local dipole moments into a POVray readable input format. It is particularly designed for fragments of large systems, for which no BCPs have been calculated for computational efficiency reasons, because large interfragment distances prevent their identification, or because a local partitioning scheme different from AIM was used. The program requires only minimal user input and is written in the Fortran90 programming language. To demonstrate the capabilities of the program, examples are given for covalently and non-covalently bound systems, in particular molecular adsorbates. © 2016 Wiley Periodicals, Inc.

Solvation thermodynamic mapping of molecular surfaces in AmberTools: GIST.

The expulsion of water from surfaces upon molecular recognition and nonspecific association makes a major contribution to the free energy changes of these processes. In order to facilitate the characterization of water structure and thermodynamics on surfaces, we have incorporated Grid Inhomogeneous Solvation Theory (GIST) into the CPPTRAJ toolset of AmberTools. GIST is a grid-based implementation of Inhomogeneous Fluid Solvation Theory, which analyzes the output from molecular dynamics simulations to map out solvation thermodynamic and structural properties on a high-resolution, three-dimensional grid. The CPPTRAJ implementation, called GIST-cpptraj, has a simple, easy-to-use command line interface, and is open source and freely distributed. We have also developed a set of open-source tools, called GISTPP, which facilitate the analysis of GIST output grids. Tutorials for both GIST-cpptraj and GISTPP can be found at ambermd.org. © 2016 Wiley Periodicals, Inc.

Cross Validation Through Two-Dimensional Solution Surface for Cost-Sensitive SVM.

Model selection plays an important role in cost-sensitive SVM (CS-SVM). It has been proven that the global minimum cross validation (CV) error can be efficiently computed based on the solution path for one parameter learning problems. However, it is a challenge to obtain the global minimum CV error for CS-SVM based on one-dimensional solution path and traditional grid search, because CS-SVM is with two regularization parameters. In this paper, we propose a solution and error surfaces based CV approach (CV-SES). More specifically, we first compute a two-dimensional solution surface for CS-SVM based on a bi-parameter space partition algorithm, which can fit solutions of CS-SVM for all values of both regularization parameters. Then, we compute a two-dimensional validation error surface for each CV fold, which can fit validation errors of CS-SVM for all values of both regularization parameters. Finally, we obtain the CV error surface by superposing K validation error surfaces, which can find the global minimum CV error of CS-SVM. Experiments are conducted on seven datasets for cost sensitive learning and on four datasets for imbalanced learning. Experimental results not only show that our proposed CV-SES has a better generalization ability than CS-SVM with various hybrids between grid search and solution path methods, and than recent proposed cost-sensitive hinge loss SVM with three-dimensional grid search, but also show that CV-SES uses less running time.

On the effect of rotation on populations of classical Cepheids

Classical Cepheid variable stars are high-sensitivity probes of stellar evolution and fundamental tracers of cosmic distances. While rotational mixing significantly affects the evolution of Cepheid progenitors (intermediate-mass stars), the impact of the resulting changes in stellar structure and composition on Cepheids on their pulsational properties is hitherto unknown. Here we present the first detailed pulsational instability analysis of stellar evolution models that include the effects of rotation, for both fundamental mode and first overtone pulsation. We employ Geneva evolution models spanning a three-dimensional grid in mass (1.7 - 15 $M_\odot$), metallicity (Z = 0.014, 0.006, 0.002), and rotation (non-rotating, average & fast rotation). We determine (1) hot and cool instability strip (IS) boundaries taking into account the coupling between convection and pulsation, (2) pulsation periods, and (3) rates of period change. We investigate relations between period and (a) luminosity, (b) age, (c) radius, (d) temperature, (e) rate of period change, (f) mass, (g) the flux-weighted gravity-luminosity relation (FWGLR). We confront all predictions aside from those for age with observations, finding generally excellent agreement. We tabulate period-luminosity relations (PLRs) for several photometric pass-bands and investigate how the finite IS width, different IS crossings, metallicity, and rotation affect PLRs. We show that a Wesenheit index based on H, V, and I photometry is expected to have the smallest intrinsic PLR dispersion. We confirm that rotation resolves the Cepheid mass discrepancy. Period-age relations depend significantly on rotation (rotation increases Cepheid ages), offering a straightforward explanation for evolved stars in binary systems that cannot be matched by conventional isochrones assuming a single age. Finally, we show that Cepheids obey a tight FWGLR.

Branch-pipe-routing approach for ships using improved genetic algorithm

Branch-pipe routing plays fundamental and critical roles in ship-pipe design. The branch-pipe-routing problem is a complex combinatorial optimization problem and is thus difficult to solve when depending only on human experts. A modified genetic-algorithm-based approach is proposed in this paper to solve this problem. The simplified layout space is first divided into threedimensional (3D) grids to build its mathematical model. Branch pipes in layout space are regarded as a combination of several two-point pipes, and the pipe route between two connection points is generated using an improved maze algorithm. The coding of branch pipes is then defined, and the genetic operators are devised, especially the complete crossover strategy that greatly accelerates the convergence speed. Finally, simulation tests demonstrate the performance of proposed method.

‘A University is a society’: an environmental history of the METU ‘campus’

The formation of a ‘society’ was the major goal of the founders of the Middle East Technical University (METU) in Turkey, which was established in 1956 and became a significant source of intellectual, ideological and architectural capital for its region. The university was designed as a total entity, a three-dimensional modern grid spread over the barren Anatolian prairie, and, in half a century, succeeded in transforming its immediate environment into an ‘ideal landscape’. There has been no publication to date documenting the formation processes of the institution, nor its impact as an environmental revolution. In opposition to the consensus that the development of this university was rooted in the United Nation's programmes for higher education in the developing world and the United States' post-war policy in the region, this paper suggests that the METU Project was rather indicative of the Turkish Republic's desire for modernisation in all of its social and ideological programmes. This paper examines the METU Project in a bid to understand how the Anatolian prairie was transformed into an urban environment, and the unique ways it is perceived in the surrounding political contexts of institutional and everyday life. By compiling an environmental historiography, the intention is to find answers to the questions of how, and to what extent, the ideal landscape was influential, and how it was presented with architecture through social and political practices.

Rapid approximate calculation of water binding free energies in the whole hydration domain of (bio)macromolecules.

The evaluation of water binding free energies around solute molecules is important for the thermodynamic characterization of hydration or association processes. Here, a rapid approximate method to estimate water binding free energies around (bio)macromolecules from a single molecular dynamics simulation is presented. The basic idea is that endpoint free-energy calculation methods are applied and the endpoint quantities are monitored on a three-dimensional grid around the solute. Thus, a gridded map of water binding free energies around the solute is obtained, that is, from a single short simulation, a map of favorable and unfavorable water binding sites can be constructed. Among the employed free-energy calculation methods, approaches involving endpoint information pertaining to actual thermodynamic integration calculations or endpoint information as exploited in the linear interaction energy method were examined. The accuracy of the approximate approaches was evaluated on the hydration of a cage-like molecule representing either a nonpolar, polar, or charged water binding site and on α- and β-cyclodextrin molecules. Among the tested approaches, the linear interaction energy method is considered the most viable approach. Applying the linear interaction energy method on the grid around the solute, a semi-quantitative thermodynamic characterization of hydration around the whole solute is obtained. Disadvantages are the approximate nature of the method and a limited flexibility of the solute. © 2016 Wiley Periodicals, Inc.

A numerical simulation method for the flow around floating bodies in regular waves using a three-dimensional rectilinear grid system

The motion of a floating body and the free surface flow are the most important design considerations for ships and offshore platforms. In the present research, a numerical method is developed to simulate the motion of a floating body and the free surface using a fixed rectilinear grid system. The governing equations are the continuity equation and Navier–Stokes equations. The boundary of a moving body is defined by the interaction points of the body surface and the centerline of a grid. To simulate the free surface the Modified Marker-Density method is implemented. Ships advancing in regular waves, the interaction of waves by a fixed circular cylinder array and the response amplitude operators of an offshore platform are simulated and the results are compared with published research data to check the applicability. The numerical method developed in this research gives results good enough for application to the initial design stage.

Wind direction field under the influence of topography, part I: A descriptive model

In both structural and environmental wind engineering, the vertical variation of wind direction is important as it impacts both the torsional response of the high-rise building and the pedestrian level wind environment. In order to systematically investigate the vertical variation of wind directions (i.e., the so-called \'twist effect\') induced by hills with idealized geometries, a series of wind-tunnel tests was conducted. The length-to-width aspect ratios of the hill models were 1⁄3, 1/2, 1, 2 and 3, and the measurements of both wind speeds and directions were taken on a three-dimensional grid system. From the wind-tunnel tests, it has been found that the direction changes and most prominent at the half height of the hill. On the other hand, the characteristic length of the direction change, has been found to increase when moving from the windward zone into the wake. Based on the wind-tunnel measurements, a descriptive model is proposed to calculate both the horizontal and vertical variations of wind directions. Preliminarily validated against the wind-tunnel measurements, the proposed model has been found to be acceptable to describe the direction changes induced by an idealized hill with an aspect ratio close to 1. For the hills with aspect ratios less than 1, while the description of the vertical variation is still valid, the horizontal description proposed by the model has been found unfit.

The Impact of ARM on Climate Modeling

Climate models are among humanity's most ambitious and elaborate creations. They are designed to simulate the interactions of the atmosphere, ocean, land surface, and cryosphere on time scales far beyond the limits of deterministic predictability, and including the effects of time-dependent external forcings. The processes involved include radiative transfer, fluid dynamics, microphysics, and some aspects of geochemistry, biology, and ecology. The models explicitly simulate processes on spatial scales ranging from the circumference of the Earth down to one hundred kilometers or smaller, and implicitly include the effects of processes on even smaller scales down to a micron or so. The atmospheric component of a climate model can be called an atmospheric global circulation model (AGCM). In an AGCM, calculations are done on a three-dimensional grid, which in some of today's climate models consists of several million grid cells. For each grid cell, about a dozen variables are time-stepped as the model integrates forward from its initial conditions. These so-called prognostic variables have special importance because they are the only things that a model remembers from one time step to the next; everything else is recreated on each time step by starting from the prognostic variables and the boundary conditions. The prognostic variables typically include information about the mass of dry air, the temperature, the wind components, water vapor, various condensed-water species, and at least a few chemical species such as ozone. A good way to understand how climate models work is to consider the lengthy and complex process used to develop one. Lets imagine that a new AGCM is to be created, starting from a blank piece of paper. The model may be intended for a particular class of applications, e.g., high-resolution simulations on time scales of a few decades. Before a single line of code is written, the conceptual foundation of the model must be designed through a creative envisioning that starts from the intended application and is based on current understanding of how the atmosphere works and the inventory of mathematical methods available.

Steel gratings as an innovative temporary roads pavement

The needs related to reduction of lead time and quality of construction determines implementation of the new technologies. An example of such an activity is a development of pavements used to build temporary roads, carried out mainly for the needs of equipment and materials delivery to a construction site. This is especially important in civil engineering, where location is dictated by a number of local conditions, which often is associated with the occurrence of adverse groundwater conditions. Commonly used traditional design solutions of temporary roads such as unpaved roads or roads made by concrete slabs require good ground conditions or proper stabilized subsoil,which may ultimately result in a significant increase of the cost of the construction. Modern temporary paving structures not only transmit the exploitation load on the subsoil. They use subsoil, as a an structure cooperating in load distribution, so it is possible to use such a construction of road on a low-bearing soil. An innovative solution in this case are three-dimensional steel grids cooperating with a subsoil. The paper describes the preliminary modeling studies of this type of pavement structures.

On graphene melting

Dynamics of disordering of graphene upon heating has been studied by computer simulation. The mechanism governing the formation of seeds for a three-dimensional grid of entangled carbon chains into which graphene is transformed upon melting has been analyzed in detail. It has been shown that the emergence of these seeds is preceded by the disruption of several interatomic bonds, accompanied with the formation of large rings or groups of adjacent rings and the formation of penta- and heptagons of their C–C bonds. The results of this work on the whole agree with the Lindemann–Lozovik criterion. The melting temperature is estimated as Tm ~ 5100 K.

Incorporation of deformation band fault damage zones in reservoir models

Fault damage zones in porous sandstones commonly exhibit networks of deformation bands reflecting crushing and reorganization of grains associated with small-scale, localized displacement. Deformation bands introduce anisotropic, order-of-magnitude reduction of effective permeability, which will affect fluid flow in reservoir rocks. We here present a method for incorporating these features in industrial-type reservoir models. The method involves the use of a three-dimensional fault zone grid generation technique that allows property modeling on a discrete high-resolution fault zone grid without refining the entire reservoir model. Deformation band data from 106 outcrop scan lines of fault damage zones were classified into discrete fault facies defined according to deformation band density. The distributional pattern of fault facies in the data exhibits recurrent spatial relationships, which could be reproduced using truncated Gaussian simulation in the modeling process. The frequency distribution of deformation band density for each facies was analyzed, and average density values were assigned to each facies for calculating cell permeability. Permeability anisotropy was handled by approximating the relationship between deformation band densities in different directions based on published high-resolution fault zone maps and cross sections. Fluid-flow simulations were carried out on several damage zones models, and results were benchmarked against models with conventional fault rendering without damage zones. Simulation results show that flow paths, remaining oil distribution, and reservoir responses in models incorporating damage zones deviate from models employing conventional fault representation without damage zones, and these differences increase as deformation band permeability decreases.

Compression behavior and energy absorption of carbon fiber reinforced composite sandwich panels made of three-dimensional honeycomb grid cores

Carbon fiber reinforced three dimensional egg and pyramidal honeycomb grids cores with interconnected void spaces were fabricated using an interlocking method. The out-of-plane compression properties, failure modes, and energy absorption capacity of all-composite sandwich panels made of the new 3D grid cores were investigated. The analytical models for predicting the compressive stiffness and strength of both egg and pyramidal honeycomb grids cores were derived. The results showed that the fabricated sandwich panels have higher specific energy absorbing abilities compared to lightweight square honeycombs of same density (10–100 Kg/m3). The new core design promises novel applications for lightweight multifunctional structures due to increased flow in the inner spaces of the core construction, embedding of electrical lines, enhanced heat transfer, fuel storage and higher energy absorption compared to traditional cores.

Developing Calibrating Curves for a Trilinear Interpolation Model During Display Characterization

Trilinear interpolation is a method of multivariate interpolation on a three-dimensional regular grid. It approximates the value of an intermediate point using data on the lattice points, and thus is frequently used for display characterization with 3D lookup tables (3D LUTs). However, large color errors are usually caused by the nonlinear relationship between the source RGB space and the destination CIELAB space. In this article the display characterization is improved by modifying the traditional trilinear interpolation model. First, the Yule–Nielsen n-factor is applied to the destination functions, for the purpose of reducing the nonlinearity between the source and destination color spaces. Afterward, different calibrating curves are developed to calculate the effective values of the source RGB values. The input/source RGB values are usually called nominal values, and the effective values can be regarded as the optimized RGB values which improve the matching degree of the predicted and measured destination CIELAB values. In experiment, a Toshiba M5 liquid crystal display is characterized by using the modified trilinear interpolation model, and the forward and inverse characterization errors of different methods are calculated and compared. The evaluation results demonstrate that both the average and the maximum color errors have significantly decreased when calibrating curve III (one of the three types of curves developed) is employed in combination with the optimal n-factor. Thus, the method of developing effective calibrating curves and finding optimal n-factors proposed in this article can be adopted during display characterization. © 2016 Society for Imaging Science and Technology.

Discrete fracture model for coupled flow and geomechanics

We present a fully implicit formulation of coupled flow and geomechanics for fractured three-dimensional subsurface formations. The Reservoir Characterization Model (RCM) consists of a computational grid, in which the fractures are represented explicitly. The Discrete Fracture Model (DFM) has been widely used to model the flow and transport in natural geological porous formations. Here, we extend the DFM approach to model deformation. The flow equations are discretized using a finite-volume method, and the poroelasticity equations are discretized using a Galerkin finite-element approximation. The two discretizations—flow and mechanics—share the same three-dimensional unstructured grid. The mechanical behavior of the fractures is modeled as a contact problem between two computational planes. The set of fully coupled nonlinear equations is solved implicitly. The implementation is validated for two problems with analytical solutions. The methodology is then applied to a shale-gas production scenario where a synthetic reservoir with 100 natural fractures is produced using a hydraulically fractured horizontal well.

Finite-difference time-domain method for three-dimensional grid of hexagonal prisms

The finite-difference time-domain (FDTD) method was applied in a grid of hexagonal prisms, having as objective to yield less numerical anisotropy of phase velocity than the Yee FDTD method (with hexahedral cells). Comparisons of wave propagation are made between the FDTD method with grid of hexagonal prisms and the Yee FDTD method. The theoretical analyses of the numerical anisotropy, dispersion and stability condition are obtained using the Fourier analysis in the FDTD method with grid of hexagonal prisms. Measurements of numerical anisotropy are also accomplished in this FDTD method, and then ones are compared with the results of the Fourier analysis. As a result, the grid of hexagonal prisms yielded somewhat less numerical anisotropy and dispersion than the Yee grid. Additionally, a simplification in compensation of numerical dispersion in the grid of hexagonal prisms may improve on the accuracy and density of mesh for indoor buildings that are large, mainly in the xy-plane.