Angular Set Research Articles

Advanced quadratures for three-dimensional discrete ordinate transport simulations: A comparative study

Three-dimensional radiation transport simulations play a key role in a number of problems found in nuclear science and engineering. When considering deterministic methods for solving the three-dimensional radiation transport equation, the Sn method of Carlson and Lee is one of the most commonly found techniques. The Sn method relies on a given set of “discrete ordinates” or discrete directions in which radiation streams. This set of discrete ordinates also must form a quadrature (numerical integration) so that the angular flux moments can be estimated and the scattering source calculated. In this paper we review a number of recently developed angular quadrature sets and compare their performance on a number of reactor physics problems.

An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: tetrahedral molecules.

A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)(-2) type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated.

Greybody factors for rotating black holes in higher dimensions

We perform a thorough study of greybody factors for minimally-coupled scalar fields propagating on the background of rotating black holes (BHs) in higher (odd) dimensions with all angular momenta set equal. For this special case, the solution enjoys an enhanced symmetry, which translates into the advantageous feature of being cohomogeneity-1, i.e., these backgrounds depend on a single radial coordinate. Our analysis contemplates three distinct situations, with the cosmological constant being zero, positive or negative. Using the technique of matched asymptotic expansions we analytically compute the greybody factors in the low-frequency regime, restricting to s-wave scattering. Our formulas generalize those obtained previously in the literature for the static and spherically symmetric case, with corrections arising from the change in the horizon area due to rotation. It is also proven that, for this family of BHs, the horizon area is a decreasing function of the spin parameter, without regard to the dimensionality and cosmological constant. Through an improvement on a calculation specific to the class of small BHs in anti-de Sitter (AdS) and not restricted to the usual low-frequency regime, we uncover a rich structure of the greybody spectrum, more complex than previously reported but also enjoying a certain degree of universality. We complement our low-frequency analytic results with numerical computations valid over a wide range of frequencies and extend them to higher angular momentum quantum numbers, . This allows us to probe the superradiant regime that is observed for corotating wavefunctions. We point out that the maximum amplification factor for intermediate-size BHs in AdS can be surprisingly large.

Coherent and stochastic averaging in solid-state NMR

A new approach for calculating solid-state NMR lineshapes of uniaxially rotating membrane proteins under the magic-angle spinning conditions is presented. The use of stochastic Liouville equation (SLE) allows one to account for both coherent sample rotation and stochastic motional averaging of the spherical dipolar powder patterns by uniaxial diffusion of the spin-bearing molecules. The method is illustrated via simulations of the dipolar powder patterns of rigid samples under the MAS conditions, as well as the recent method of rotational alignment in the presence of both MAS and rotational diffusion under the conditions of dipolar recoupling. It has been found that it is computationally more advantageous to employ direct integration over a spherical grid rather than to use a full angular basis set for the SLE solution. Accuracy estimates for the bond angles measured from the recoupled amide 1H–15N dipolar powder patterns have been obtained at various rotational diffusion coefficients. It has been shown that the rotational alignment method is applicable to membrane proteins approximated as cylinders with radii of approximately 20Å, for which uniaxial rotational diffusion within the bilayer is sufficiently fast and exceeds the rate 2×105s−1.

Nuclear Data Library of High-Energy Nucleon Interactions with Heavy Nuclei

The nuclear data library of the interactions of 20 to 1000 MeV nucleons with the target nuclei 202Hg, 208Pb, 209Bi, 232Th, 235U, 238U,237Np, 239Pu,242Am, and 245Cm is examined. The library consists of complete files in the ENDF-6 format for each nucleus and contains the total, elastic scattering and fission cross sections, energy–angular distributions and sets of secondary neutrons as well as independent and cumulative yields of fission products. Up-to-date theoretical models verified on experimental data were used to build the library.

Controllability analysis and attitude path planning of underactuated spacecraft systems

The controllability analysis and attitude path planning are addressed for an underactuated spacecraft using two flywheels as actuators. Considering the spacecraft and flywheels as a whole system, we describe the dynamics of the system on an angular momentum level set such that the system is controllable with arbitrary initial momentum and direction of the torque singular vector. Moreover, an optimal performance index is proposed with the influence of friction torques in flywheels considered. With this index being optimized, Gauss Pseudospectral Method (GPM) is used to design the attitude path of the system, which satisfies the spacecraft maneuver requirement. Finally, simulation results show the effectiveness of the attitude path planning method.

Monte Carlo and Deterministic Neutronics Analyses of YALINA Thermal Facility and Comparison with Experimental Results

This study compares Monte Carlo and deterministic neutronics analyses of the zero-power YALINA Thermal subcritical assembly, which is located in Minsk, Belarus. The YALINA Thermal facility consists of a subcritical core that can be driven by either a californium neutron source or a deuterium-deuterium (D-D) neutron source. The californium neutron source is generated by the natural decay of 252Cf; the D-D neutron source is generated by a deuteron accelerator. The MCNPX, MONK, NJOY, DRAGON, PARTISN, and TORT computer programs have been used for calculating the neutron spectrum, the neutron flux, and the 3He(n,p) reaction rate set by californium and D-D neutron sources. These parameters have been computed in different experimental channels of the assembly for different fuel loading configurations. The MCNPX and MONK computer programs modeled the facility without any major approximation; the PARTISN and TORT computer simulations used 69 energy groups, S16 angular quadrature set, linear anisotropic scattering, and approximately 60 homogenized material zones. The results calculated by different computer programs are in good agreement; in addition, they match the 3He(n,p) reaction rate from experimental measurements obtained by californium and D-D neutron sources.

Measuring Shape-Dependent Looping Probability of DNA

Recently, several studies have shown that short doubled-stranded DNA (dsDNA) loops more readily than the wormlike chain model predicts. In most of these experiments, the intrinsic bendedness of dsDNA, which in theory can dramatically influence looping dynamics, was either avoided or unaccounted for. To investigate the effect of the shape of dsDNA on looping dynamics, we characterized the shapes of several synthetic dsDNA molecules of equal length but different sequences using gel electrophoresis. We then measured their looping rates using a FRET (Förster resonance energy transfer)-based assay and extracted the looping probability density known as the J factor (jM). We also used, for comparison, several dinucleotide angular parameter sets derived from the observed electrophoretic mobility to compute the jM predicted by the wormlike chain model. Although we found a strong correlation between curvature and jM, the measured jM was higher than most dinucleotide model predictions. This result suggests that it is difficult to reconcile the looping probability with the observed gel mobility within the wormlike chain model and underscores the importance of determining the intrinsic shape of dsDNA for proper theoretical analysis.

Analytical methods for computational modeling of fixed-source slab-geometry discrete ordinates transport problems: Response matrix and hybrid SN

Presented here are two analytical methods for computational modeling of fixed-source slab-geometry discrete ordinates (SN) transport problems for shielding and nuclear reactor fuel-moderator lattice calculations. For shielding calculations a response matrix method is described, which generates numerical solutions completely free from spatial truncation errors. Therefore, the offered response matrix method with the one-region block inversion (RBI) iterative scheme converges numerical results for the region-edge angular fluxes, that coincide with the numerical values generated from the SN analytical solution, apart from computational finite arithmetic considerations. As with lattice cell calculations in nuclear reactor physics, we describe an analytical direct method for hybrid SN calculations. The basic idea is to use higher order angular quadrature set in the highly absorbing fuel region (SNF) and lower order angular quadrature set in the diffusive moderator region (SNM), i.e., NF > NM. Special continuity conditions for the fuel exiting fluxes that constitute the incoming fluxes for the moderation region, and conversely, for the moderator exiting fluxes that constitute the incoming fluxes for the fuel region are applied in the present hybrid numerical scheme. These special continuity conditions are based on the equivalence of the multigroup SN and PN − 1 equations in slab geometry. A spatial reconstruction scheme is added to yield detailed profile of the solution within each homogenized region of the slab, starting from the coarse-mesh results. Test problems are given to illustrate the methods' accuracy.

Isotropic and nematic phases of the hard spheroid fluid: A virial approach

We use a high level virial expansion to investigate the properties of the isotropic and nematic phases of the hard spheroid fluid. We use the Monte Carlo techniques described previously to calculate the virial coefficients up to seventh order and we represent the dependence of these coefficients on particle orientations via a spherical harmonic expansion. The expansion coefficients are determined using Lebedev quadrature which carries out the angular integration required exactly. For fairly spherical spheroids (1/3<a/b<3, where a and b are the semiaxes of the spheroid) the virial expansion appears to be convergent in both the isotropic and nematic phases up to high density. For more aspherical particles, the predictions varied in a more erratic fashion upon increasing the number of virials. The use of a finite angular basis set to represent the orientationally dependent virial coefficients could be a contributory cause to this.

Local electron tomography using angular variations of surface tangents: Stomo version 2

Local electron tomography using angular variations of surface tangents: Stomo version 2

On the Construction of Galerkin Angular Quadratures

An angular approximation of the transport equation based on a collocation technique results as an intermediary step in the search for a set of modified discrete ordinates (DO) equations, which eliminates ray effects. The collocation equations are similar to the DO ones with the only difference being that the scattering term is evaluated with a full Galerkin matrix instead of with the DO quadrature formula. The Galerkin quadrature offers the advantage of a better treatment of scattering anisotropy and a correct evaluation of the singular scattering associated to multigroup transport correction. However, the construction of the Galerkin matrix requires the existence of two equivalent bases in a final-dimensional representation space: an interpolatory basis to retain the collocative nature of the DO approximation and a spherical harmonic basis to represent scattering terms accurately. Up to now, the relationship between these two bases was heuristic, stemming from trial and errors. In this work we analyze the symmetries of the angular direction set and also use the factorized form of the spherical harmonics to derive a set of necessary conditions for the construction of the spherical harmonic basis. These conditions give an analytical explanation to previous heuristic techniques and fully extend them to three-dimensional geometries. We have adopted an assembling method for which extensive numerical tests show that the necessary conditions permit the construction of the Galerkin quadrature from level-symmetric, triangular, and product direction sets up to a high number of polar cosines. Our results can also be generalized to calculate Galerkin matrices for nonregular quadrature formulas. However, these necessary conditions are not sufficient, and we give numerical proof of this fact using different assembling techniques. Our assembling technique allows for the construction of Galerkin matrices from triangular direction sets (for which the DO quadrature is notoriously poor), which have positive weights for up to 44 polar cosines. In three dimensions this quadrature has 2024 angular directions and is able to exactly integrate scattering of anisotropy order 24.

Ultraspinning instability: the missing link

We study linearized perturbations of Myers-Perry black holes in d=7, with two of the three angular momenta set to be equal, and show that instabilities always appear before extremality. Analogous results are expected for all higher odd d. We determine numerically the stationary perturbations that mark the onset of instability for the modes that preserve the isometries of the background. The onset is continuously connected between the previously studied sectors of solutions with a single angular momentum and solutions with all angular momenta equal. This shows that the near-extremality instabilities are of the same nature as the ultraspinning instability of d>5 singly-spinning solutions, for which the angular momentum is unbounded. Our results raise the question of whether there are any extremal Myers-Perry black holes which are stable in d>5.

Effect of Complex Training on Lower Body Strength, Speed and Power in Basketball Players

The purpose of this study was to investigate the effect of 6 weeks complex training with different training order on the maximum lower body strength (half-squat, peak torque of knee extension and flexion measured in isokinetic test with angular velocity set at 60°•S^(-1)), power (static jump, counter movement jump & drop jump) and speed (28 meter sprint) among collegiate basketball athletes. Twenty Division-I male basketball players (aged: 19 ± 1.5 yr, height: 181.1 ± 9.18cm, weight: 80.0 ± 12.97kg, VO2max: 57.0 ± 6.27ml•min^(-1)•kg^(-1)) were randomly assigned into WP (weight training followed by plyometric training) and PW (plyometric training followed by weight training) groups. Both groups received two 60-min training sessions per week for 6 weeks. Pre and post test were carried out before and after 6 weeks complex training. Data were analyzed by using one-way ANCOVA with α level set at .05. The results indicated that after 6 weeks complex training, both groups revealed significant improvement in 1RM half-squat (195.3 ± 24.16 vs. 235.3 ± 18.47kg), knee flexor at 60°•S^(-1) peak torque (171.4 ± 46.4 vs. 205.7 ± 20.46 N•m), 28 m dash (4.13 ± .20 vs. 4.07 ± .19 sec), static jump (44.6 ± 4.53 vs. 47.7 ± 6.14 cm), counter movement jump (51.4 ± 4.39 vs. 54.7 ± 6.09 cm) and drop jump (44.7 ± 5.28 vs. 47.9 ± 6.09 cm) (p ＜ .05). No significant difference was found between WP and PW. In conclusion, regardless of training order, complex training improved lower body strength, speed and power in basketball players.

New efficient algorithm for the calculation of energy levels of AB3 type molecules

This paper illustrates a method for the construction of a symmetry-adapted contracted angular basis set for AB3 molecules. Simple formulas that use this basis set for calculations of the angular matrix elements of the kinetic energy (KE) operator and angular matrix elements of potential energy surface (PES) are reported. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. The symmetric form of vibration KE operators without the sin(q)−2 type singularity is applied. A good basis set convergence for the calculations of vibrational levels of the PH3 molecule is demonstrated.

Unraveling the spectroscopy of coupled intramolecular tunneling modes: A study of double proton transfer in the formic-acetic acid complex

The rotational spectrum of the hetero dimer comprising doubly hydrogen-bonded formic acid and acetic acid has been recorded between 4 and 18 GHz using a pulsed-nozzle Fourier transform microwave spectrometer. Each rigid-molecule rotational transition is split into four as a result of two concurrently ongoing tunneling motions, one being proton transfer between the two acid molecules, and the other the torsion/rotation of the methyl group within the acetyl part. We present a full assignment of the spectrum J = 1 to J = 6 for the ground vibronic states. The transitions are fitted to within a few kilohertz of the observed frequencies using a molecule-fixed effective rotational Hamiltonian for the separate A and E vibrational species of the G(12) permutation-inversion symmetry group. Interpretation of the motion problem uses an internal-vibration and overall-rotation angular momentum coupling scheme and full sets of rotational and centrifugal distortion constants are determined. The tunneling frequencies of the proton-transfer motion are measured for the ground A and E methyl rotation states as 250.4442(12) and -136.1673(30) MHz, respectively. The slight deviation of the latter tunneling frequency from being one half of the former, as simple theory otherwise predicts, is due to different degrees of mixing in wavefunctions between the ground and excited states.

Improved Discrete Ordinates Method for Ray Effects Mitigation

A new and improved method based on the concept of discrete ordinates scheme with infinitely small weights (DOS+ISW) is developed for modeling radiative heat transfer in three-dimensional participating media. To demonstrate the effectiveness of the method in mitigating ray effects, the ray effects caused by (1) abrupt step changes in the boundary conditions and (2) the stepwise variation of the medium emissive power are considered. In this work, angular quadrature sets with large number of discrete ordinate directions are chosen to mitigate ray effects while at the same time keeping the computational time increase to a minimum. Comparing with the conventional discrete ordinates method, the difference is that intensities in these directions are calculated by DOS+ISW method. Intensity with fine directional resolution calculated by this method is validated by comparing with that of reverse Monte Carlo method. The large number of discrete ordinate directions used in the new method becomes computationally prohibitive in the conventional discrete ordinates method due to the increased computer memory and computation time requirements.

Performance Optimization of Tomlinson-Harashima Precoder with Tilted Constellation

An algorithm is proposed to optimize performance of a novel technique providing a great performance improvement over Tomlinson-Harashima precoder (THP), referred to as THP with tilted constellation (THP-TC). Proposed algorithm deals with a problem that THP-TC has faced with, the optimization of size of angular candidate set under a constant noise power condition, which is valid for the most applications of THP-TC including multiuser MIMO applications. As a result, proposed algorithm facilitates THP-TC to reach its best compromise between the transmit power reduction and the symbol error increase caused by the estimation process of tilted angle at the receiver.

Analytical reconstruction scheme for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates transport model in slab geometry

Coarse-mesh numerical methods are very efficient in the sense that they generate accurate results in short computational time, as the number of floating point operations generally decrease, as a result of the reduced number of mesh points. On the other hand, they generate numerical solutions that do not give detailed information on the problem solution profile, as the grid points can be located considerably away from each other. In this paper we describe two steps for the analytical reconstruction of the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates ( S N ) transport model in slab geometry. The first step of the algorithm is based on the analytical reconstruction of the coarse-mesh solution within each discretization cell of the grid set up on the spatial domain. The second step is based on the angular reconstruction of the discrete ordinates solution between two contiguous ordinates of the angular quadrature set used in the S N model. Numerical results are given so we can illustrate the accuracy of the two reconstruction techniques, as described in this paper.

Evaluation of digital breast tomosynthesis reconstruction algorithms using synchrotron radiation in standard geometry

In this article, the image quality of reconstructed volumes by four algorithms for digital tomosynthesis, applied in the case of breast, is investigated using synchrotron radiation. An angular data set of 21 images of a complex phantom with heterogeneous tissue-mimicking background was obtained using the SYRMEP beamline at ELETTRA Synchrotron Light Laboratory, Trieste, Italy. The irradiated part was reconstructed using the multiple projection algorithm (MPA) and the filtered backprojection with ramp followed by hamming windows (FBR-RH) and filtered backprojection with ramp (FBP-R). Additionally, an algorithm for reducing the noise in reconstructed planes based on noise mask subtraction from the planes of the originally reconstructed volume using MPA (MPA-NM) has been further developed. The reconstruction techniques were evaluated in terms of calculations and comparison of the contrast-to-noise ratio (CNR) and artifact spread function. It was found that the MPA-NM resulted in higher CNR, comparable with the CNR of FBP-RH for high contrast details. Low contrast objects are well visualized and characterized by high CNR using the simple MPA and the MPA-NM. In addition, the image quality of the reconstructed features in terms of CNR and visual appearance as a function of the initial number of projection images and the reconstruction arc was carried out. Slices reconstructed with more input projection images result in less reconstruction artifacts and higher detail CNR, while those reconstructed from projection images acquired in reduced angular range causes pronounced streak artifacts. Of the reconstruction algorithms implemented, the MPA-NM and MPA are a good choice for detecting low contrast objects, while the FBP-RH, FBP-R, and MPA-NM provide high CNR and well outlined edges in case of microcalcifications.