Approximate 3D Research Articles

Assessing the Importance of the H2-H2O-H2O Three-Body Interaction on the Vibrational Frequency Shift of H2 in the sII Clathrate Hydrate and Comparison with Experiment.

The vibrational frequency shift of H2 in the 512 cage of the sII clathrate hydrate with and without surrounding water molecules is reported at 0 K, using diffusion Monte Carlo calculations for the ground and first excited vibrational states of H2. Approximate 1d calculations of the frequency shift are also reported with the H2 at the equilibrium position in the clathrate hydrate. These calculations make use of full-dimensional potential energy surfaces for the H2-H2O 2-body and H2-H2O-H2O 3-body interactions. The inclusion of the 3-body interaction is shown to make roughly a 33% contribution to the frequency shift and to bring the calculated value of -40 ± 4 cm-1 to within just 3 cm-1 of the experimental value at 20 K. This level of agreement with experiment may be somewhat fortuitous; however, the importance of the 3-body interaction is firmly established by these calculations. The frequency shift reported here with 2-body interactions does not agree with a previously reported calculation using just 2-body interactions from a different ab initio potential energy surface and with a different method to obtain the frequency shift. A similar 1d calculation of the frequency shift using that potential is reported and agrees to within roughly 10% of the one previously reported. Therefore, this suggests that the difference between the present calculations and the previous one using just 2-body interactions is mainly due to differences in the potential energy surfaces.

Filtration of Observations of Angular Distributions of Muon Fluxes from the URAGAN Hodoscope

The problem of noise filtering in observations of 2D functions of muon flux intensity distributions from the URAGAN hodoscope is considered. A filtering method based on the construction of sliding approximate local 2D models is proposed. A filtering algorithm based on sliding local piecewise linear 2D models is developed. The results of testing the algorithm on model and experimental observations for problems of Forbush decrease detection are presented. Errors of the algorithm are estimated on the basis of statistical modeling.

Analytical Solution of Functionally Graded Beam Having Longitudinal Stiffness Variation

The aim of the present paper is to developed analytical elasticity solution for a beam having longitudinal stiffness variation using recently developed multiterm extended Kantorovich (EKM) method. By applying the EKM method, the system of 4n first order ordinary differential equations (ODEs) and 1n algebraic equation are obtained along the in-plane (x) and thickness (z) directions. The system of the equations along the thickness direction (z) having constant coefficient but the set of equations along the x-direction have variable coefficients. In the thickness direction (z), exact closed-form solutions are obtained. And along the x-direction, the system of ODEs with variable coefficients are solved by employing the modified power series. In this paper, specific predefined variations are assumed in material property and their influence on the bending response of beam, subjected to mechanical loading, is investigated. Benchmark numerical results are presented for a different combination of boundary conditions. These numerical results can be used to validate approximate one-dimensional solutions and 2D numerical results.

On the Geometry of Nanowires and the Role of Torsion

A detailed analysis of the Schrödinger equation in curved coordinates, exact to all orders in the cross sectional dimension is presented, and we discuss the implications of the frame rotation for energies of both open and closed structures. For a circular cross‐section, the energy spectrum is independent of the frame orientation for an open structure. For a closed curve, the energies depend on the holonomy angle of a minimal rotating frame (MR) which is equal to the area enclosed by the tangent image on the unit sphere. In the case of a curve with a well‐defined torsion at all points this is up to a multiple of 2π equal to the total torsion, a result first found in 1992 by Takagi and Tanzawa. In both cases we find that the effect on the eigenstates is a phase shift. We validate our findings by accurate numerical solution of both the exact 3D equations and the approximate 1D equations for a helix structure and find that the error is proportional to the square of the diameter of the cross section. We discuss Dirichlet versus Neumann boundary conditions and show that care has to be taken in the latter case.

AUTOMATIC 3D LANE MARKING RECONSTRUCTION USING MULTI-VIEW AERIAL IMAGERY

Abstract. The 3D information of road infrastructures are gaining importance with the development of autonomous driving. The exact absolute position and height of lane markings, for example, support lane-accurate localization. Several approaches have been proposed for the 3D reconstruction of line features from multi-view airborne optical imagery. However, standard appearance-based matching approaches for 3D reconstruction are hardly applicable on lane markings due to the similar color profile of all lane markings and the lack of textures in their neighboring areas. We present a workflow for 3D lane markings reconstruction without explicit feature matching process using multi-view aerial imagery. The aim is to optimize the best 3D line location by minimizing the distance from its back projection to the detected 2D line in all the covering images. Firstly, the lane markings are automatically extracted from aerial images using standard line detection algorithms. By projecting these extracted lines onto the Semi-Global Matching (SGM) generated Digital Surface Model (DSM), the approximate 3D line segments are generated. Starting from these approximations, the 3D lines are iteratively refined based on the detected 2D lines in the original images and the viewing geometry. The proposed approach relies on precise detection of 2D lines in image space, a pre-knowledge of the approximate 3D line segments, and it heavily relies on image orientations. Nevertheless, it avoids the problem of non-textured neighborhood and is not limited to lines of finite length. The theoretical precision of 3D reconstruction with the proposed framework is evaluated.

Numerically Calculated 3D Space-Weighting Functions to Image Crustal Volcanic Structures Using Diffuse Coda Waves

Seismic coda measurements retrieve parameters linked to the physical characteristics of rock volumes illuminated by high frequency scattered waves. Space weighting functions (SWF) and kernels are different tools that model the spatial sensitivity of coda envelopes to scattering and absorption anomalies in these rock matrices, allowing coda-wave attenuation ( Q c o d a ) imaging. This note clarifies the difference between SWF and sensitivity kernels developed for coda wave imaging. It extends the SWF previously developed in 2D to the third dimension by using radiative transfer and the diffusion equation, based on the assumption that variations of Q c o d a depend solely on variations of the extinction length. When applied to active data (Deception Island, Antarctica), 3D SWF images strongly resemble 2D images, making this 3D extension redundant. On the other hand, diffusion does not efficiently model coda waveforms when using earthquake datasets spanning depths between 0 and 20 km, such as at Mount St. Helens volcano. In this setting, scattering attenuation and absorption suffer tradeoffs and cannot be separated by fitting a single seismogram energy envelope for SWF imaging. We propose that an approximate analytical 3D SWF, similar in shape to the common coda kernels used in literature, can still be used in a space weighted back-projection approach. While Q c o d a is not a physical parameter of the propagation medium, its spatially-dependent modeling allows improved reconstruction of crustal-scale tectonic and geological features. It is even more efficient as a velocity independent imaging tool for magma and fluid storage when applied to deep volcanism.

Packable Springs

AbstractLaser cutting is an appealing fabrication process due to the low cost of materials and extremely fast fabrication. However, the design space afforded by laser cutting is limited, since only flat panels can be cut. Previous methods for manufacturing from flat sheets usually roughly approximate 3D objects by polyhedrons or cross sections. Computational design methods for connecting, interlocking, or folding several laser cut panels have been introduced; to obtain a good approximation, these methods require numerous parts and long assembly times. In this paper, we propose a radically different approach: Our approximation is based on cutting thin, planar spirals out of flat panels. When such spirals are pulled apart, they take on the shape of a 3D spring whose contours are similar to the input object. We devise an optimization problem that aims to minimize the number of required parts, thus reducing costs and fabrication time, while at the same time ensuring that the resulting spring mimics the shape of the original object. In addition to rapid fabrication and assembly, our method enables compact packaging and storage as flat parts. We also demonstrate its use for creating armatures for sculptures and moulds for filling, with potential applications in architecture or construction.

Image-Based 2D Re-Projection for Attenuation Substitution in PET Neuroimaging.

In dual modality positron emission tomography (PET)/magnetic resonance imaging (MRI), attenuation correction (AC) methods are continually improving. Although a new AC can sometimes be generated from existing MR data, its application requires a new reconstruction. We evaluate an approximate 2D projection method that allows offline image-based reprocessing. 2-Deoxy-2-[18F]fluoro-D-glucose ([18F]FDG) brain scans were acquired (Siemens HR+) for six subjects. Attenuation data were obtained using the scanner's transmission source (SAC). Additional scanning was performed on a Siemens mMR including production of a Dixon-based MR AC (MRAC). The MRAC was imported to the HR+ and the PET data were reconstructed twice: once using native SAC (ground truth); once using the imported MRAC (imperfect AC). The re-projection method was implemented as follows. The MRAC PET was forward projected to approximately reproduce attenuation-corrected sinograms. The SAC and MRAC images were forward projected and converted to attenuation-correction factors (ACFs). The MRAC ACFs were removed from the MRAC PET sinograms by division; the SAC ACFs were applied by multiplication. The regenerated sinograms were reconstructed by filtered back projection to produce images (SUBAC PET) in which SAC has been substituted for MRAC. Ideally SUBAC PET should match SAC PET. Via coregistered T1 images, FreeSurfer (FS; MGH, Boston) was used to define a set of cortical gray matter regions of interest. Regional activity concentrations were extracted for SAC PET, MRAC PET, and SUBAC PET. SUBAC PET showed substantially smaller root mean square error than MRAC PET with averaged values of 1.5% versus 8.1%. Re-projection is a viable image-based method for the application of an alternate attenuation correction in neuroimaging.

Usability as the Key Factor to the Design of a Web Server for the CReF Protein Structure Predictor: The wCReF

Protein structure prediction servers use various computational methods to predict the three-dimensional structure of proteins from their amino acid sequence. Predicted models are used to infer protein function and guide experimental efforts. This can contribute to solving the problem of predicting tertiary protein structures, one of the main unsolved problems in bioinformatics. The challenge is to understand the relationship between the amino acid sequence of a protein and its three-dimensional structure, which is related to the function of these macromolecules. This article is an extended version of the article wCReF: The Web Server for the Central Residue Fragment-based Method (CReF) Protein Structure Predictor, published in the 14th International Conference on Information Technology: New Generations. In the first version, we presented the wCReF, a protein structure prediction server for the central residue fragment-based method. The wCReF interface was developed with a focus on usability and user interaction. With this tool, users can enter the amino acid sequence of their target protein and obtain its approximate 3D structure without the need to install all the multitude of necessary tools. In this extended version, we present the design process of the prediction server in detail, which includes: (A) identification of user needs: aiming at understanding the features of a protein structure prediction server, the end user profiles and the commonly-performed tasks; (B) server usability inspection: in order to define wCReF’s requirements and features, we have used heuristic evaluation guided by experts in both the human-computer interaction and bioinformatics domain areas, applied to the protein structure prediction servers I-TASSER, QUARK and Robetta; as a result, changes were found in all heuristics resulting in 89 usability problems; (C) software requirements document and prototype: assessment results guiding the key features that wCReF must have compiled in a software requirements document; from this step, prototyping was carried out; (D) wCReF usability analysis: a glimpse at the detection of new usability problems with end users by adapting the Ssemugabi satisfaction questionnaire; users’ evaluation had 80% positive feedback; (E) finally, some specific guidelines for interface design are presented, which may contribute to the design of interactive computational resources for the field of bioinformatics. In addition to the results of the original article, we present the methodology used in wCReF’s design and evaluation process (sample, procedures, evaluation tools) and the results obtained.

A method for inversion of 1D vertical soundings of gravity anomalies

We have developed a method to interpret potential fields, which obtains 1D models by inverting vertical soundings of potential field data. The vertical soundings are built through upward continuation of potential field data, measured on either a profile or a surface. The method assumes a forward problem consisting of a volume partitioned in layers, each of them homogeneous and horizontally finite, but with the density changing versus depth. The continuation errors, increasing with the altitude, are automatically handled by determining the coefficients of a third-order polynomial function of the altitude. Due to the finite size of the source volume, we need a priori information about the total horizontal extent of the volume, which is estimated by boundary analysis and optimized by a Markov chain process. For each sounding, a 1D inverse problem is independently solved by a nonnegative least-squares algorithm. Merging of the several inverted models finally yields approximate 2D or 3D models that are, however, shown to generate a good fit to the measured data. The method is applied to synthetic models, producing good results for either perfect or continued data. Even for real data, i.e., the gravity data of a sedimentary basin in Nevada, the results are interesting, and they are consistent with previous interpretation, based on 3D gravity inversion constrained by two gamma-gamma density logs.

Almost constant-time 3D nearest-neighbor lookup using implicit octrees

A recurring problem in 3D applications is nearest-neighbor lookups in 3D point clouds. In this work, a novel method for exact and approximate 3D nearest-neighbor lookups is proposed that allows lookup times that are, contrary to previous approaches, nearly independent of the distribution of data and query points, allowing to use the method in real-time scenarios. The lookup times of the proposed method outperform prior art sometimes by several orders of magnitude. This speedup is bought at the price of increased costs for creating the indexing structure, which, however, can typically be done in an offline phase. Additionally, an approximate variant of the method is proposed that significantly reduces the time required for data structure creation and further improves lookup times, outperforming all other methods and yielding almost constant lookup times. The method is based on a recursive spatial subdivision using an octree that uses the underlying Voronoi tessellation as splitting criteria, thus avoiding potentially expensive backtracking. The resulting octree is represented implicitly using a hash table, which allows finding the leaf node a query point belongs to with a runtime that is logarithmic in the tree depth. The method is also trivially extendable to 2D nearest neighbor lookups.

Approximate 3D model of electromagnetic modes in waveguide cross-shaped junctions with dielectric filling

A three-dimensional electrodynamic model of hybrid electromagnetic modes in a waveguide junction of cylindrical and rectangular waveguides with dielectric filling of a cylindrical waveguide is proposed in this study. To solve the vector problem, the mode matching technique (MMT) is applied with the separation of the common waveguide junction region and the representation of the field in this region in the form of superposition of the fields of the partial eigenwaves of waveguides. Classification of eigenmodes is carried out: intrinsic resonances of junction based on transcendental modes and resonances of a waveguide-dielectric type. The investigated structure can be used for measuring the electrical parameters of dielectric samples of both cylindrical and rectangular cross-section shape. Since the spectral characteristics of the junction are determined mainly by the size of the central coupling region of the waveguides and the electrical parameters of the dielectric in the junction, the measurements are of a local nature.

Evaluation of various analytical weight function methods base on exact K-solutions of an edge-cracked circular disc

Weight function method is a powerful tool for the determination of key parameters such as stress intensity factors and crack opening displacements for cracks in complicated stress fields. Accurate determination of the weight functions is of primary importance for successful applications of the method. This paper makes detailed accuracy evaluation of two kinds of widely used approximate (2D) weight function approaches, one being based on crack opening displacement for one reference stress, the other on two reference stresses coupled with a geometric condition. To eliminate possible sources of error, the edge-cracked circular disc with exactK-solutions is used for deriving the two kinds of weight functions and for benchmarking against the two weight function approaches. A highly accurate numerical weight function method using the complex Taylor series expansion and complex finite element computation is also used for assessing the related Green’s functions. Results from the evaluation will be instructive for accurate determination of weight functions for other finite edge-crack geometries.

Application of 1D Models to Particle Transport in a Duct of Rectangular Cross Section

ABSTRACTThe approximate 1D model for particle transport in ducts that is based on the use of two basis functions to represent the transverse and azimuthal-angle dependencies of the angular flux is applied to the case of a duct of rectangular cross section. Isotropic particle incidence is considered. Numerical results obtained for the reflection and transmission probabilities from the 1D models with one and two basis functions are compared with Monte Carlo results for the full 3D problem. It is shown that the 1D model with two basis functions performs very well for ducts of rectangular cross section, displaying deviations of less than 3% with respect to Monte Carlo, in general. Two exceptions in the general behavior of this model are very short ducts, for which deviations in the reflection probability of up to 9% in magnitude were encountered, and long ducts with strongly absorbing walls, for which the deviations in the transmission probability reached about 8% in magnitude.

Transient electromagnetic search engine for real-time imaging

To image the resistivity distribution of the subsurface, transient electromagnetic (TEM) surveying has been established as an effective geophysical method. Conventionally, an inversion method is applied to resolve the model parameters from the available measurements. However, significant time and effort are involved in preparing and executing an inversion and this prohibits its use as a real-time decision-making tool to optimize surveying in the field. We have developed a search engine method to find approximate 1D resistivity model solutions for circular central-loop configuration TEM data in real time. The search engine method is a concept used for query searches from large databases on the Internet. By extension, approximate solutions to any input TEM data can be found rapidly by searching a preestablished database. This database includes a large number of forward simulation results that represent the possible model solutions. The database size is optimized by the survey depth of investigation and the sensitivity analysis of the model layers. The fast-search speed is achieved by using the multiple randomized [Formula: see text]-dimensional tree method. In addition to its high speed in finding solutions, the search engine method provides a solution space that quantifies the resolutions and uncertainties of the results. We apply the search engine method to find 1D model solutions at different data points and then interpolate them to a pseudo-2D resistivity model. We tested the method with synthetic and real data.

Evaluating performance of lignite pillars with 2D approximation techniques and 3D numerical analyses

This paper attempts to investigate the use of approximate 2D numerical simulation techniques for the evaluation of lignite pillar geomechanical response, formed via the room and pillar mining method. Performance and applicability of the developing methodology are assessed through benchmarking with a more direct and accurate 3D numerical model. This analysis utilizes an underground lignite mine which is being developed in soft rock environment. Through the decisions made for the optimum room and pillar layout, the design process highlights the strong points and the weaknesses of 2D finite element analysis, and provides useful recommendations for future reference. The interpretations of results demonstrate that 2D approximation techniques come near quite well to the actual 3D problem. However, external load approximation technique seems to fit even better with the respective outcomes from the 3D analyses.

Inductive electromagnetic data interpretation using a 3D distribution of 3D magnetic or electric dipoles

In inductive electromagnetics, the magnetic field measured in the air at any instant can be considered to be a potential field. As such, we can invert measured magnetic fields (at a fixed time or frequency) for the causative subsurface current system. These currents can be approximated with a 3D subsurface grid of 3D magnetic (closed-loop current) or electric (line current) dipoles whose location and orientation can be solved for using a potential-field-style smooth-model inversion. Because the problem is linear, both inversions can be solved quickly even for large subsurface volumes; and both can be run on a single data set for complementary information. Synthetic studies suggest that for discrete induction dominated targets, the magnetic and electric dipole inversions can be used to determine the center and top edge of the target, respectively. Furthermore, the orientation of plate targets can be estimated from visual examination of the orientations of the 3D vector dipoles and/or using the interpreted location of the center and top edge of the target. In the first field example, ground data from a deep massive sulfide body (mineral exploration target) was inverted and the results were consistent with the conclusions drawn from the synthetic examples and with the existing interpretation of the body (shallow dipping conductor at a depth of approximately 400 m). A second example over a near-surface mine tailing (a near-surface environmental/engineering study) highlighted the strength of being able to invert data using either magnetic or electric dipoles. Although both models were able to fit the data, the electric dipole model was considerably simpler and revealed a southwest−northeast-trending conductive zone. This fast approximate 3D inversion can be used as a starting point for more rigorous interpretation and/or, in some cases, as a stand-alone interpretation tool.

Low-Complexity Multidimensional DCT Approximations for High-Order Tensor Data Decorrelation.

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. 3D DCT approximations are formalized in terms of high-order tensor theory. The formulation is extended to higher dimensions with arbitrary lengths. Several multiplierless 8×8 ×8 approximate methods are proposed and the computational complexity is discussed for the general multidimensional case. The proposed methods complexity cost was assessed, presenting considerably lower arithmetic operations when compared with the exact 3D DCT. The proposed approximations were embedded into 3D DCT-based video coding scheme and a modified quantization step was introduced. The simulation results showed that the approximate 3D DCT coding methods offer almost identical output visual quality when compared with exact 3D DCT scheme. The proposed 3D approximations were also employed as a tool for visual tracking. The approximate 3D DCT-based proposed system performs similarly to the original exact 3D DCT-based method. In general, the suggested methods showed competitive performance at a considerably lower computational cost.

Fast 3D inversion of “total field” resistive limit TEM data

Rapid interpretation of transient electromagnetic (TEM) data sets is highly desirable for timely decision-making in exploration. However, full solution 3D inversion of TEM data sets is often unpractically slow. Therefore, a fast approximate 3D TEM inversion scheme has been developed for time-integrated (resistive limit) data. The resistive limits are amenable to linear 3D magnetic inversion, which is up to 100 times faster than “rigorous” 3D TEM inversion. The resistive limit inversion scheme is suitable for airborne, ground, and downhole TEM, both dB/dt and B-field. Its efficacy is illustrated here via application to a heli-borne sub-audio magnetic (HeliSAM) data set recorded over the Lalor Zn-Cu-Au VMS deposit in Manitoba, Canada. The response from the deposit is clear in the “total field” EM (TFEM) data even though the mineralisation is very deep, extending from depth 575m to over 1100m. A three-stage inversion of resistive limits derived from the TFEM rapidly defined a 3D conductor below the uppermost pyrite-sphalerite lenses, enclosing a volume containing mainly pyrrhotite-chalcopyrite stringer sulphides. Total inversion time was less than one minute on a notebook PC.

Area and Power Efficient VLSI Architecture for Two Dimensional 16-point Modified Gate Diffusion Input Discrete Cosine Transform

The two-dimensional (2D) Discrete Cosine Transform (DCT) is used widely in image and video processing systems. The perception of human visualization permits us to design approximate rather than exact DCT. In this paper, we propose a digital implementation of 16-point approximate 2D DCT architecture based on one-dimensional (1D) DCT and Modified Gate Diffusion Input (MGDI) technique. The 8-point 1D Approximate DCT architecture requires only 12 additions for realization in digital VLSI. Additions can be performed using the proposed 8 transistor (8T) MGDI Full Adder which reduces 2 transistors than the existing 10 transistor (10T) MGDI Full Adder. The Approximate MGDI 2D DCT using 8T MGDI Full adders is simulated in Tanner SPICE for 0.18㎛ CMOS process technology at 100MHZ.The simulation result shows that 13.9% of area and 15.08 % of power is reduced in the 8-point approximate 2D DCT, 10.63 % of area and 15.48% of power is reduced in case of 16-point approximate 2D DCT using 8 Transistor MGDI Full Adder than 10 Transistor MGDI Full Adder. The proposed architecture enhances results in terms of hardware complexity, regularity and modularity with a little compromise in accuracy.