Three-dimensional Fourier Transformation Research Articles

A novel stochastic modeling framework for coal production and logistics through options pricing analysis

We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory. The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model. We derive a three-dimensional Fast Fourier Transform (“FFT”) lower bound approximation to value the inherent real optionality and for robustness check, we compare the semi-analytical pricing accuracy with the Monte Carlo simulation. Model parameters are estimated from the historical monthly data, and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross (“CIR”) model.

Hand character gesture recognition based on a single millimetre‐wave radar chip

In this work, a new method for hand character gesture recognition based on a single millimetre-wave radar chip is proposed. Most current radar-based gesture recognition approaches use Doppler spectrograms or the feature extraction of Doppler spectrograms. In contrast, the authors propose using the trajectory points of gesture movements. Compared with the previous methods, the variations in the gesture movement speed, distance and direction during data acquisition have relatively little impact on the generated trajectories. The character trajectories drawn by gestures in the air output a fixed shape, and this fixed output facilitates the classification of gestures at a later stage. In this work, a single millimetre-wave radar is used to collect data and a three-dimensional fast Fourier Transform (3D-FFT) algorithm is used to obtain the gesture trajectories. For the trajectory points, a trajectory conversion image method is proposed and finally the improved Xception network proposed in this work is used for image recognition. Compared with traditional methods, the proposed method does not require large-scale data acquisition to facilitate different users. This work is concluded by recognising hand character gestures and comparing them with other commonly used classification methods to verify the gesture recognition accuracy of the proposed method.

Direct numerical simulation of anisotropic turbulent flow for incompressible fluid

Equation for small-scale velocity or pulsation is a starting point to build almost all models of turbulence. Transport equation for Reynolds stresses, dissipation rate, kinetic energy are derived from this equation, adding some assumptions about structure of terms, including in these equations. Equation for small-scale velocity can be simplified, if we assume that large – scale velocity and its gradients are constants instead of linear profile for large-scale velocity. We implemented the direct numerical simulation of this equation under the simple shear, leading to anisotropy. The nonlinear helicity terms were computed in spectral space, using the three-dimensional Fast Fourier transformation, then, the inverse Fast Fourier transformation was used to return in physical space. Aliasing terms were not removed. Four – order Runge- Kutta method was used for integration in time. Evolution of Reynolds stresses in time were computed.

PROBLEMS OF BUILDING AND APPLICATION OF HYPERCOMPLEX NUMBERS

The article is dedicated to the problems of using multidimensional numbers for mathematical and computer modeling of complex physical processes and the design of knowledge-intensive devices, including digital image processing. The emphasis is on the issues of building the methods for processing three-dimensional signals. It is proposed to use three-dimensional variables presented in the form of hypercomplex numbers to formulate the three-dimensional Fourier transformation forms, which allows to analyze and process three-dimensional signals.

Nanovoids in uniaxially elongated polymer network filled with polydisperse nanoparticles via coarse-grained molecular dynamics simulation and two-dimensional scattering patterns

In order to investigate the relationship between nanovoids and two-dimensional scattering patterns (2DSPs) in elongated polymer nanocomposites (PNCs) filled with spherical nanoparticles (NPs), coarse-grained molecular dynamics simulations were performed with polydisperse NPs for Poisson's ratios of ν = 0.46 < 0.5. The polydispersity of NP diameter impacts on creation and early growth of nanovoids. Study of the growth of nanovoids under the attractive NP–polymer interactions showed that large NPs have a role of starting points of the growth. The 2DSP I(qx, qyz) is also calculated as the circular average of scattering intensity I(q), which is obtained by three-dimensional Fourier transformation of the density field weighted by contrasts of the NPs and polymers. It was confirmed that polydispersity of NPs causes disappearance of a ring pattern that was seen for uniform NPs. For the case with attractive NP–polymer interactions, the magnitudes of the central peaks of the 2DSPs was confirmed to become larger for larger elongation ratios. On the other hand, for the case with repulsive NP–polymer interactions, the central peak of the 2DSPs is much weaker than that for the case with attractive NP-polymer interaction, because of the occurrence of interfacial fractures and fine dispersal of nanovoids at the interface between NPs and polymers. In addition, creation and annihilation of a nanovoid during stretching process were observed for the cases with repulsive NP-polymer interactions. For the case with attractive NP–polymer interactions, a kink behavior on a plot of scattering invariant versus the elongation ratio was observed. From this behavior, it was confirmed that the detection of nanovoids through 2DSPs is effective for attractive NP–polymer interaction.

Two-dimensional scattering patterns of coarse-grained molecular dynamics model of filled polymer gels during uniaxial expansion

In this study, coarse-grained molecular dynamics (CGMD) simulations of polymer network gels filled with spherical nanoparticles (NPs) were performed, and two-dimensional (2D) small-angle scattering patterns of the NPs during uniaxial elongation were examined. To create filled polymer network gels, mixtures of polymer chains, four-arm star chains, and NPs, and pseudo-reaction processes were considered. Active sites of the polymer chains, four-arm star chains, and surface particles of the NPs were reacted to create bonds. After this pseudo-reaction process, it was evaluated whether the obtained polymer network was a sol or gel. The gel polymer network obtained in this study was not percolated as a graph but was able to transmit force through catenane-like linkages. This paper named this gel as “topological-percolation.” Further, 2D scattering patterns (2DSPs) were calculated using three-dimensional fast Fourier transformation for efficient computing on a large-scale system. The obtained 2DSPs were quite different for the sol and gel, and depended on the properties of the crosslinked polymer networks. It is confirmed that changes in 2DSPs can be predicted by CGMD simulations because different patterns can be observed with different pre-polymer distributions, different chain lengths, and different chain densities.

Do We Need Three-Dimensional Fourier Transform Analysis to Evaluate High-Performance TEMs?

Abstract

Elastic fields caused by eigenstrains in two joined half-spaces with an interface of coupled imperfections: Dislocation-like and force-like conditions

This paper presents the derivation of a set of the novel closed-form solutions for the eigenstrain-induced elastic fields in two joined half-space solids with an interface of coupled dislocation-like and force-like imperfects. A model is proposed to characterize the interfacial discontinuity properties concerning displacements and stresses, which permits quantitative jumps of either the displacements or the stresses from one medium to the other. Basic Galerkin vectors in these two imperfectly joined half-spaces are derived based on the boundary conditions, and thus the elastic responses are obtained in explicit expressions. Taking advantage of the three-dimensional fast Fourier Transform algorithms for the convolution and correlation, the elastic fields subjected to one arbitrarily shaped inclusion or more can be efficiently and accurately evaluated. The influences of several types of interfaces, such as the perfectly bonded interface, the dislocation-like interface, and the force-like interface, on the stress and displacement transmissions are discussed. Cases for the elastic fields due to a cuboidal, a spherical, and an array of multiple cuboidal inclusions, are investigated.

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES). The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES) approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier–Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor–Green Vortex (TGV) test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS) data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT). All combinations of numerical methods produce a k − 4 spectrum at t * = 4 , and near the dissipation peak, all methods were capable of predicting the k − 5 / 3 slope accurately when refining the mesh.

Why Do We Need to Use Three-Dimensional (3D) Fourier Transform (FT) Analysis to Evaluate a High-Performance Transmission Electron Microscope (TEM)?

The resolution of high-resolution transmission electron microscopes (TEM) has been improved down to subangstrom levels by correcting the spherical aberration (Cs) of the objective lens, and the information limit is thus determined mainly by partial temporal coherence. As a traditional Young's fringe test does not reveal the true information limit for an ultra-high-resolution electron microscope, new methods to evaluate temporal coherence have been proposed based on a tilted-beam diffractogram. However, the diffractogram analysis cannot be applied when the nonlinear contribution becomes significant. Therefore, we have proposed a method based on the three-dimensional (3D) Fourier transform (FT) of through-focus TEM images, and evaluated the performance of some Cs-corrected TEMs at lower voltages. In this report, we generalize the 3D FT analysis and derive the 3D transmission cross-coefficient. The profound difference of the 3D FT analysis from the diffractogram analysis is its capability to extract linear image information from the image intensity, and further to evaluate two linear image contributions separately on the Ewald sphere envelopes. Therefore, contrary to the diffractogram analysis the 3D FT analysis can work with a strong scattering object. This is the necessary condition if we want to directly observe the linear image transfer down to a few tens of picometer.

Effect of local stress fields on twin characteristics in HCP metals

We study the effect of nearest neighboring grains on the propensity for {1012} twin growth in Mg and Zr. Twin lamellae lying within one grain flanked by two neighboring grains with several orientations are considered. The fields of resolved shear stress on the twin system are calculated in the multicrystal using a three-dimensional full-field crystal plasticity Fast Fourier Transform approach. The calculations were carried out for Mg and Zr using slip threshold stresses corresponding to 300 K and 76 K, respectively, where twin activity is important. We show that the neighboring grain constraint tends to oppose further growth and that the critical applied stress needed to overcome this resistance depends on neighboring grain orientation, more strongly in Zr than in Mg. We also present results for a pair of adjacent and parallel twins at various spacings. It is found that their paired interaction increases the resistive forces for twin growth above that for an isolated twin. The critical spacing above which this enhanced resistance is removed is smaller for Zr than Mg. Our analysis reveals that these two disparate responses of Zr and Mg are both a consequence of the fact that Zr is elastically and plastically more anisotropic than Mg. Additional calculations carried out on Ti support this conclusion. These findings can help explain why, for the same grain size, more twins per grain form in Zr than in Mg, twins in Zr tend to be thinner than those in Mg, and the relationship between the thickness of the twin and its Schmid factor in Zr is not as strong as in Mg.

Effect of electrolyte temperature on the formation of highly ordered nanoporous alumina template

In this work, we present a systematic influence of electrolyte temperature along with anodizing potential on the pore parameters during two-step anodization of Al in H2SO4 electrolyte. Top surface morphology of the nanoporous templates was examined with the help of field emission scanning electron microscope and atomic force microscope. Three-dimensional (3D) Fast Fourier Transform (FFT) image analysis was then employed to quantify pore regularity and pore periodicity as a function of both the bath temperature (1–15 °C) and the anodic potential (15–25 V). A highest pore regularity ratio of 5 × 108 was obtained at 3 °C and 25 V with a pore diameter of 32 ± 3 nm and inter-pore distance of 65 nm. With further increase in temperature, the pore regularity ratio was found to decrease drastically. It was found that higher temperature favored the dissolution of compact aluminum oxide layer isotropically along the pore length. This process in effect enhanced the pore size, growth rate, and template top surface roughness without affecting much inter-pore distance. Self-ordering of the pores was found to improve with increasing anodizing potential with a critical influence of the current density along with inter-pore distance. The mechanism of pore growth was discussed in terms of temperature-dependent activation energy controlled dissolution of aluminum. The typical activation energy evaluated at 25 V was 72.8 kJ/mol at 3 °C.

Parallel implementation of 3D FFT with volumetric decomposition schemes for efficient molecular dynamics simulations

Three-dimensional Fast Fourier Transform (3D FFT) plays an important role in a wide variety of computer simulations and data analyses, including molecular dynamics (MD) simulations. In this study, we develop hybrid (MPI+OpenMP) parallelization schemes of 3D FFT based on two new volumetric decompositions, mainly for the particle mesh Ewald (PME) calculation in MD simulations. In one scheme, (1d_Alltoall), five all-to-all communications in one dimension are carried out, and in the other, (2d_Alltoall), one two-dimensional all-to-all communication is combined with two all-to-all communications in one dimension. 2d_Alltoall is similar to the conventional volumetric decomposition scheme. We performed benchmark tests of 3D FFT for the systems with different grid sizes using a large number of processors on the K computer in RIKEN AICS. The two schemes show comparable performances, and are better than existing 3D FFTs. The performances of 1d_Alltoall and 2d_Alltoall depend on the supercomputer network system and number of processors in each dimension. There is enough leeway for users to optimize performance for their conditions. In the PME method, short-range real-space interactions as well as long-range reciprocal-space interactions are calculated. Our volumetric decomposition schemes are particularly useful when used in conjunction with the recently developed midpoint cell method for short-range interactions, due to the same decompositions of real and reciprocal spaces. The 1d_Alltoall scheme of 3D FFT takes 4.7 ms to simulate one MD cycle for a virus system containing more than 1 million atoms using 32,768 cores on the K computer.

GENESIS: a hybrid-parallel and multi-scale molecular dynamics simulator with enhanced sampling algorithms for biomolecular and cellular simulations.

GENESIS (Generalized-Ensemble Simulation System) is a new software package for molecular dynamics (MD) simulations of macromolecules. It has two MD simulators, called ATDYN and SPDYN. ATDYN is parallelized based on an atomic decomposition algorithm for the simulations of all-atom force-field models as well as coarse-grained Go-like models. SPDYN is highly parallelized based on a domain decomposition scheme, allowing large-scale MD simulations on supercomputers. Hybrid schemes combining OpenMP and MPI are used in both simulators to target modern multicore computer architectures. Key advantages of GENESIS are (1) the highly parallel performance of SPDYN for very large biological systems consisting of more than one million atoms and (2) the availability of various REMD algorithms (T-REMD, REUS, multi-dimensional REMD for both all-atom and Go-like models under the NVT, NPT, NPAT, and NPγT ensembles). The former is achieved by a combination of the midpoint cell method and the efficient three-dimensional Fast Fourier Transform algorithm, where the domain decomposition space is shared in real-space and reciprocal-space calculations. Other features in SPDYN, such as avoiding concurrent memory access, reducing communication times, and usage of parallel input/output files, also contribute to the performance. We show the REMD simulation results of a mixed (POPC/DMPC) lipid bilayer as a real application using GENESIS. GENESIS is released as free software under the GPLv2 licence and can be easily modified for the development of new algorithms and molecular models. WIREs Comput Mol Sci 2015, 5:310–323. doi: 10.1002/wcms.1220

Automated Design Space Exploration with Aspen

Architects and applications scientists often use performance models to explore a multidimensional design space of architectural characteristics, algorithm designs, and application parameters. With traditional performance modeling tools, these explorations forced users to first develop a performance model and then repeatedly evaluate and analyze the model manually. These manual investigations proved laborious and error prone. More importantly, the complexity of this traditional process often forced users to simplify their investigations. To address this challenge of design space exploration, we extend our Aspen (Abstract Scalable Performance Engineering Notation) language with three new language constructs: user-defined resources, parameter ranges, and a collection of costs in the abstract machine model. Then, we use these constructs to enable automated design space exploration via a nonlinear optimization solver. We show how four interesting classes of design space exploration scenarios can be derived from Aspen models and formulated as pure nonlinear programs. The analysis tools are demonstrated using examples based on Aspen models for a three-dimensional Fast Fourier Transform, the CoMD molecular dynamics proxy application, and the DARPA Streaming Sensor Challenge Problem. Our results show that this approach can compose and solve arbitrary performance modeling questions quickly and rigorously when compared to the traditional manual approach.

The Radiation Problem from a Vertical Hertzian Dipole Antenna above Flat and Lossy Ground: Novel Formulation in the Spectral Domain with Closed-Form Analytical Solution in the High Frequency Regime

We consider the problem of radiation from a vertical short (Hertzian) dipole above flat lossy ground, which represents the well-known “Sommerfeld radiation problem” in the literature. The problem is formulated in a novel spectral domain approach, and by inverse three-dimensional Fourier transformation the expressions for the received electric and magnetic (EM) field in the physical space are derived as one-dimensional integrals over the radial component of wavevector, in cylindrical coordinates. This formulation appears to have inherent advantages over the classical formulation by Sommerfeld, performed in the spatial domain, since it avoids the use of the so-called Hertz potential and its subsequent differentiation for the calculation of the received EM field. Subsequent use of the stationary phase method in the high frequency regime yields closed-form analytical solutions for the received EM field vectors, which coincide with the corresponding reflected EM field originating from the image point. In this way, we conclude that the so-called “space wave” in the literature represents the total solution of the Sommerfeld problem in the high frequency regime, in which case the surface wave can be ignored. Finally, numerical results are presented, in comparison with corresponding numerical results based on Norton’s solution of the problem.

Real‐time 3D magnetic resonance imaging of the pharyngeal airway in sleep apnea

To investigate the feasibility of real-time 3D magnetic resonance imaging (MRI) with simultaneous recording of physiological signals for identifying sites of airway obstruction during natural sleep in pediatric patients with sleep-disordered breathing. Experiments were performed using a three-dimensional Fourier transformation (3DFT) gradient echo sequence with prospective undersampling based on golden-angle radial spokes, and L1-norm regularized iterative self-consistent parallel imaging (L1-SPIRiT) reconstruction. This technique was demonstrated in three healthy adult volunteers and five pediatric patients with sleep-disordered breathing. External airway occlusion was used to induce partial collapse of the upper airway on inspiration and test the effectiveness of the proposed imaging method. Apneic events were identified using information available from synchronized recording of mask pressure and respiratory effort. Acceptable image quality was obtained in seven of eight subjects. Temporary airway collapse induced via inspiratory loading was successfully imaged in all three volunteers, with average airway volume reductions of 63.3%, 52.5%, and 33.7%. Central apneic events and associated airway narrowing/closure were identified in two pediatric patients. During central apneic events, airway obstruction was observed in the retropalatal region in one pediatric patient. Real-time 3D MRI of the pharyngeal airway with synchronized recording of physiological signals is feasible and may provide valuable information about the sites and nature of airway narrowing/collapse during natural sleep.

NMR Fourier zeugmatography

A new technique of forming two- or three-dimensional images of a macroscopic sample by means of NMR is described. It is based on the application of a sequence of pulsed magnetic field gradients during a series of free induction decays. The image formation can be achieved by a straightforward two- or three-dimensional Fourier transformation. The method has the advantage of high sensitivity combined with experimental and computational simplicity.

Response to: Prognostic indicators of hearing after complete resection of cholesteatoma causing a labyrinthine fistula by Stephenson MF and saliba I. Eur Arch Otorhinolaryngol 2011 Mar 9 [epub ahead of print

Recently, Stephenson and Saliba [1] reported their data on preoperative CT-scanning in cholesteatoma patients with labyrinthine fistula in the article ‘‘Prognostic indicators of hearing after complete resection of cholesteatoma causing a labyrinthine fistula’’. The authors state that high-resolution preoperative CT-scan is very precise in diagnosing labyrinthine fistulas and that its radiologic size helps to predict the type of the fistula. This study is generally well designed and well reported, but we have several comments. The authors mention: ‘‘a further study is needed to identify if a diffusion-weighted sequence for magnetic resonance imaging of labyrinthine cholesteatomatous fistula can predict the effect of the depth on the postoperative hearing outcome after a complete removal of the cholesteatoma’’. Although we consider non-echo-planar diffusion-weighted MRI as an essential tool in the preoperative work-up (and postoperative follow-up) of the cholesteatoma patient, its usefulness for the work-up of labyrinthine fistula in the cholesteatoma patient is limited [2]. Indeed, this sequence does not allow for discrimination of both cholesteatoma and other tissues, such as bone. However, other MRI sequences can be useful. Earlier studies on T1and T2-weighted imaging, gadolinium-enhanced spin-echo, three-dimensional Fourier transformation constructive interference in steady state (3DFT-CISS), and fluid-attenuated inversion recovery (FLAIR) were reported, respectively by Casselman et al. [3], Smadja et al. [4], and Sone et al [5]. In our department, we routinely perform preoperative temporal bone cone-beam CT-scans combined with a full MRI protocol (including non-echo-planar diffusion-weighted MRI) in the cholesteatoma patient [2]. In case of a lateral canal fistula, as diagnosed on CT, we use T2-weighted imaging to evaluate the presence of the labyrinthine fluid. If the labyrinthine fluid in the part of the lateral semicircular canal adjacent to the cholesteatoma is absent (no signal on T2 MRI), this will probably be due to reactive fibrosis. In such cases, the risk for perioperative sensorineural hearing loss is lower because the matrix and perimatrix of the cholesteatoma are not directly in contact with the membranous labyrinth. In case the fluid is still present (high signal on T2 MRI), the risk for a perioperative sensorineural hearing loss is higher because the matrix and perimatrix of the cholesteatoma can be in direct contact with the fluid contents of the membranous labyrinth, depending on the extent of the fistula. Our preoperative counseling of the patient is based on this policy [6]. A further study on the use of preoperative MRI in lateral canal fistula is definitely feasible and should, in our opinion, focus on T2-weighted imaging instead of diffusionweighted imaging. Additionally, the role of the cone-beam CT-scan should be further studied because of the increased spatial resolution and the significant decrease in radiation dosage. V. Van Rompaey E. Offeciers (&) University Department of Otorhinolaryngology and Head and Neck Surgery, Sint Augustinus Hospital, Oosterveldlaan 24, Wilrijk, 2610 Antwerp, Belgium e-mail: erwin.offeciers@gza.be

Visual Grading Characteristics (VGC) Analysis of Diagnostic Image Quality for High Resolution 3 Tesla MRI Volumetry of the Olfactory Bulb

The aim of this study was to evaluate the suitability of 3-T magnetic resonance imaging (MRI) for olfactory bulb volumetry, comparing image quality obtained using different sequences on the basis of physical characteristics in combination with observer performance. Twenty-two healthy volunteers (11 men, 11 women; mean age, 25 years) underwent 3-T MRI of the frontal skull base in this prospective study. Imaging was performed using a constructive interference in steady state (CISS) three-dimensional Fourier transformation sequence, a three-dimensional T2-weighted (3D-T2w) sequence, and a two-dimensional T2-weighted (2D-T2w) sequence. The relative performance of sequences was assessed using visual grading characteristic analysis. Interobserver agreement was assessed using κ statistics. For evaluation of physical image quality characteristics, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) were calculated and compared using Wilcoxon's test. SNR and CNR measurements were correlated with visual grading results. Visual grading characteristic analysis showed significantly better image quality ratings for the CISS sequence compared to the 3D-T2w and 2D-T2w sequence, and the 2D-T2w sequence performed significantly better compared to the 3D-T2w sequence (P < .001). Interobserver agreement was substantial (κ = 0.66-0.73). Wilcoxon's test revealed significantly higher SNR and CNR values for the 2D-T2w sequence compared to the 3D-T2w and CISS sequences, and SNR and CNR values for the 3D-T2w sequence were significantly higher compared to those for the CISS sequence (P < .001 for each). Significant correlation between SNR and CNR and visual grading was found for the 3D-T2w sequence (SNR: ρ = 0.510, P = .015; CNR: ρ = 0.546, P = .009). High-resolution 3-T MRI resulted in excellent values for SNR and CNR, suggesting the appropriateness of the sequences for olfactory bulb MRI volumetry. Visual grading characteristic analysis revealed the CISS sequence to be the most suitable for olfactory bulb volumetry.