Parabolic Method Research Articles

Modeling Soft X‐Ray Emissions at the Dayside Magnetopause

AbstractIn this study, we simulate the Solar Wind Charge Exchange (SWCX) soft X‐ray emissions at dayside magnetosheath and cusps by using magnetohydrodynamic (MHD) and LAtmos TEst Particle (LaTeP) models. MHD models are unable to resolve the particle kinetic effects, such as the different behaviors of ions with different q/m, or distinguish the magnetospheric plasma from the solar wind plasma. We investigate these effects with the LaTeP model. As the LaTeP model does not self‐compute magnetic and electric field, the magnetic and electric field data obtained from Open Geospace General Circulation Model (OpenGGCM) and Lagrangian version of the piecewise parabolic method (PPMLR) MHD model are used as the input to LaTeP model. The soft X‐ray emissivity maps simulated from pure OpenGGCM and PPMLR MHD approaches and from LaTeP‐OpenGGCM and LaTeP‐PPMLR approaches are presented and compared. The results indicate that the LaTeP model can well resolve the kinetic effects and can be used to investigate the individual spectral characteristics. Therefore, the LaTeP model is a complementary approach for simulating the X‐ray emissions near the dayside magnetopause. We also calculate the ratio of integrated OVII/OVIII line intensities, produced by charge exchange of O7+ ions and O8+ ions, respectively. We find a relatively higher ratio at the bow shock compared to the surrounding areas, suggesting that this ratio can be an effective parameter to identify the bow shock location.

An inverse Gauss curvature flow to the Lp-Gauss Minkowski problem

In this paper, we confirm the existence of asymmetric smooth solutions to the Lp-Gauss Minkowski problem for p>0 by a class of inverse Gauss curvature flows. Furthermore, asymmetric weak solution for p>0 is obtained by a parabolic approximation method.

Modelling and Impact Analysis of Combined Dam Failure of Small Tandem Reservoir Groups in Hilly Areas

Numerous small reservoirs in hilly areas play a significant role in flood control and profit-making in the basin, but there is also a risk of dam failure when encountering special circumstances such as excessive flooding, which may cause large losses downstream. In this paper, we take the small reservoirs in Shandong Province as the research object, analyze the hydraulic topology of three types of tandem reservoirs, generalize the shape of the breach by using the transient lateral local one-break to the end, calculate the dam-break flooding process by using the quadratic parabolic method, and simulate the dam-break by using the MIKE21 model based on the principle of the two-dimensional incompressible Reynolds mean stress equation for the incompressible fluid, and analyze the peak flow under various combinations of dam-break flow by setting various combinations of the number of dam-breaks and the timing of dam-break simulation. By setting various combinations of dam failure numbers and timing, we analyzed the changing rules of peak dam failure flow, inundation area and other elements under various combinations, and sought the most unfavorable combinations and parameters such as the timing of dam failure, and the results of the analyses can provide technical support for the assessment of the risk of dam failure in the tandem reservoirs in the hilly area and the risk correspondence.

Gradient Weakly Sensitive Multi-Source Sensor Image Registration Method

Aiming at the nonlinear radiometric differences between multi-source sensor images and coherent spot noise and other factors that lead to alignment difficulties, the registration method of gradient weakly sensitive multi-source sensor images is proposed, which does not need to extract the image gradient in the whole process and has rotational invariance. In the feature point detection stage, the maximum moment map is obtained by using the phase consistency transform to replace the gradient edge map for chunked Harris feature point detection, thus increasing the number of repeated feature points in the heterogeneous image. To have rotational invariance of the subsequent descriptors, a method to determine the main phase angle is proposed. The phase angle of the region near the feature point is counted, and the parabolic interpolation method is used to estimate the more accurate main phase angle under the determined interval. In the feature description stage, the Log-Gabor convolution sequence is used to construct the index map with the maximum phase amplitude, the heterogeneous image is converted to an isomorphic image, and the isomorphic image of the region around the feature point is rotated by using the main phase angle, which is in turn used to construct the feature vector with the feature point as the center by the quadratic interpolation method. In the feature matching stage, feature matching is performed by using the sum of squares of Euclidean distances as a similarity metric. Finally, after qualitative and quantitative experiments of six groups of five pairs of different multi-source sensor image alignment correct matching rates, root mean square errors, and the number of correctly matched points statistics, this algorithm is verified to have the advantage of robust accuracy compared with the current algorithms.

Design of Parabolic Off-Axis Reflector Optical System for Large Aperture Single Star Simulators

This study proposes a parabolic off-axis reflective optical system design method to reduce the wave aberration of the optical system of a large aperture single star simulator and improve the optical system’s imaging quality. Firstly, we determined the design indexes of the optical system of the large aperture single star simulator by analyzing the technical indexes of the star sensitizer and the development status of the single star simulator; secondly, the initial structural parameters of the optical system were calculated based on the theory of primary aberration; then, we carried out the design optimization of the optical system, the image quality evaluation, and the tolerance analysis using Zemax software; finally, the study tested the wave aberration of the optical system by using the four-dimensional interferometer and the standard mirror together. The simulation results of the optical system are as follows: in the entire field of view, the aberration of the optical system is far less than 0.002%, the modulation transfer function (MTF) reaches the diffraction limit, and the maximum wave aberration is 0.0324 λ. The experimental results are as follows: the maximum wave aberration of the optical system is 0.0337 λ, which is less than 1/25 λ, and it meets the requirements of the index. The simulation and experimental results show that the optical system of the large aperture single star simulator designed by this method has good imaging quality and a simple system structure.

An improved version of the piecewise parabolic method advection scheme: description and performance assessment in a bidimensional test case with stiff chemistry in toyCTM v1.0.1

Abstract. This study presents a novel method to estimate the performance of advection schemes in numerical experiments along with a semi-realistic, non-linear, stiff chemical system. This method is based on the examination of the “signature function”, an invariant of the advection equation. Apart from exposing this concept in a particular numerical test case, we show that a new numerical scheme based on a combination of the piecewise parabolic method (PPM) with the flux adjustments of Walcek outperforms both the PPM and the Walcek schemes for inert tracer advection as well as for advection of chemically active species. From a fundamental point of view, we think that our evaluation method, based on the invariance of the signature function under the effect of advection, offers a new way to evaluate objectively the performance of advection schemes in the presence of active chemistry. More immediately, we show that the new PPM + W (“piecewise parabolic method + Walcek”) advection scheme offers chemistry-transport modellers an alternative, high-performance scheme designed for Cartesian-grid Eulerian chemistry-transport models, with improved performance over the classical PPM scheme. The computational cost of PPM + W is not higher than that of PPM. With improved accuracy and controlled computational cost, this new scheme may find applications in other fields such as ocean models or atmospheric circulation models.

TwoPhaseFlow: A Framework for Developing Two Phase Flow Solvers in OpenFOAM

We present a new OpenFOAM based open-source framework, TwoPhaseFlow, enabling fast implementation and testing of new phase change and surface tension force models for two-phase flows including interfacial heat and mass transfer. Capitalizing on the runtime-selection mechanism in OpenFOAM, the new models can easily be selected and benchmarked against analytical solutions and existing models. The framework currently includes the following three interface curvature calculation methods for surface tension: 1) the height function method, 2) the parabolic fit method and 3) the reconstructed distance function method. As for phase change, two models are available: 1) Interface heat resistance and 2) direct heat flux. These can be combined in three solvers: 1) InterFlow for isothermal, incompressible two-phase flow, 2) compressibleInterFlow for compressible, non-isothermal two-phase flow and 3) multiRegionPhaseChangeFlow for compressible, non-isothermal two-phase flow with conjugated heat transfer. By design, addition of new models and solvers is straightforward and users are encouraged to contribute their specific models, solvers, and validation cases to the library.

Development of the parabolic equation for calculation of sea waves diffraction in port area

Application method of parabolic equations is presented in this paper for calculating diffraction of sea waves behind converging breakwaters, which entrance is not parallel to front of approaching waves. For this, the method of linear superposition of results obtained separately for each breakwater was used. Based on a comparison of results obtained by this method with results of physical (obtained in a wave basin) and numerical (obtained using DHI MIKE 21 BW) model experiments with different settings (40 models in total), a conclusion about using allowability of the obtained equations was made. Results of the study make it possible to recommend the obtained equations for practical use in studies of seaports wave regimes, where diffraction phenomena are strong. Complexity of a function used in the parabolic method causes appearance of “petals” of diffraction coefficient isolines in protected water area. Approximate equations are presented for smoothing the oscillations of the complex amplitude function along lines parallel and perpendicular to axis of breakwaters. It is shown that associated error in obtaining diffraction coefficient varies on average within 2–5 %, and maximum error obtained was 12.5 %.

GPU-HADVPPM V1.0: a high-efficiency parallel GPU design of the piecewise parabolic method (PPM) for horizontal advection in an air quality model (CAMx V6.10)

Abstract. With semiconductor technology gradually approaching its physical and thermal limits, graphics processing units (GPUs) are becoming an attractive solution for many scientific applications due to their high performance. This paper presents an application of GPU accelerators in an air quality model. We demonstrate an approach that runs a piecewise parabolic method (PPM) solver of horizontal advection (HADVPPM) for the air quality model CAMx on GPU clusters. Specifically, we first convert the HADVPPM to a new Compute Unified Device Architecture C (CUDA C) code to make it computable on the GPU (GPU-HADVPPM). Then, a series of optimization measures are taken, including reducing the CPU–GPU communication frequency, increasing the data size computation on the GPU, optimizing the GPU memory access, and using thread and block indices to improve the overall computing performance of the CAMx model coupled with GPU-HADVPPM (named the CAMx-CUDA model). Finally, a heterogeneous, hybrid programming paradigm is presented and utilized with GPU-HADVPPM on the GPU clusters with a message passing interface (MPI) and CUDA. The offline experimental results show that running GPU-HADVPPM on one NVIDIA Tesla K40m and an NVIDIA Tesla V100 GPU can achieve up to a 845.4× and 1113.6× acceleration. By implementing a series of optimization schemes, the CAMx-CUDA model results in a 29.0× and 128.4× improvement in computational efficiency by using a GPU accelerator card on a K40m and V100 cluster, respectively. In terms of the single-module computational efficiency of GPU-HADVPPM, it can achieve 1.3× and 18.8× speedup on an NVIDIA Tesla K40m GPU and NVIDIA Tesla V100 GPU, respectively. The multi-GPU acceleration algorithm enables a 4.5× speedup with eight CPU cores and eight GPU accelerators on a V100 cluster.

In-situ live jacking technology of corner transmission tower

Aiming at the current situation that the foundation of the corner transmission tower is corroded, sunken, or the height of the tower line is insufficient, innovative low-cost technology is proposed to upgrade the foundation in-situ based on no power outages, and the analysis of the whole process of the in-situ live jacking construction of the transmission tower is studied in this paper. Firstly, through elastic mechanical equilibrium relationship, two form-finding methods of numerical analysis are derived and the results of several form-finding methods are analyzed and compared by a project example, among which the result error of the finite element method and the catenary method is negligible, while the error of the parabolic method is about 2% compared with the first two methods, but it can meet the engineering requirements. Secondly, the relevant laws of internal force and deformation of the lifting process are summarized, and a comparative analysis of theoretical and measured results verified the reliability and safety of the technology. Through the calculation program of the self-compiled parabolic method, the laws of tower line changes during the lifting process of the transmission tower are summarized, providing technical support for engineering practice and reference for related research.

The Parables and Islamic Scriptures: An Analytical Study

Allah the exalted is the only Lord of all the worlds. He has sent Prophets and Messengers in all periods to guide the mankind. He has also revealed Divine Scriptures to edify mankind. Several Manuscripts and Books were revealed on different Prophets. The Qur’ān is the last and final word of Allah towards the humanity till the Day of Judgment. The Qur’ān teaches humanity about the Unity of Allah, love and obedience of Prophet Muhammad PBUH, methods of worship and many more. In the Qur’ān, different unique methods have been adopted for the purpose of guidance e.g. literary method, psychological, interrogative, method of telling a story of past times, etc. Parabolic method is one of these methods. In this article the significance and details of the parabolic method will be analyzed. It is the convention of Allah to teach through this method. The Apostles of Allah have also adopted this method to preach the word of Allah in an easier way.

A model instability issue in the National Centers for Environmental Prediction Global Forecast System version 16 and potential solutions

Abstract. The National Centers for Environmental Prediction (NCEP) Global Forecast System version 16 (GFSv16) encountered a few model instability failures during the pre-operational real-time parallel runs. The model forecasts failed when an extremely small thickness depth appeared at the model's lowest layer during the landfall of strong tropical cyclones. A quick solution was to increase the value of minimum thickness depth, an arbitrary parameter introduced to prevent numerical instability. This modification solved the model's numerical instability with a small impact on forecast skills. It was adopted in GFSv16 to implement this version of the operational system as planned. Upon further investigation, it was determined that the extremely thin depth was a result of the advection of geopotential heights at the interfaces of model layers. In the Finite-Volume Cubed-Sphere (FV3) dynamical core, the horizontal winds at interfaces for advection are calculated from the layer-mean values by solving a tridiagonal system of equations in the entire vertical column based on the parabolic spline method (PSM) with high-order boundary conditions (BCs). We replaced the high-order BCs with zero-gradient BCs for the interface-wind reconstruction. The impact of the zero-gradient BCs was investigated by performing sensitivity experiments with GFSv16, idealized mountain ridge tests and the Rapid Refresh Forecast System (RRFS). The results showed that zero-gradient BCs can fundamentally solve the instability and have little impact on the forecast performances and the numerical solutions of idealized mountain tests. This option has been added to FV3 and will be utilized in the GFS (GFSv17/Global Ensemble Forecast System version 13 – GEFSv13) and RRFS for operations.

Through Joyce's Looking Glass: Dubliners and the Parable Form

Abstract: This essay explores James Joyce's engagement with Biblical parables in Dubliners . Like parables, Joyce's stories employ realistic situations, vivid imagery, and puzzling endings to prompt readers into moral reflection. Joyce's stories also draw upon specific Biblical parables. In "The Boarding House," Joyce inverts the Parable of the Ten Virgins to illuminate the disconnect between love and duty in Irish society. In "A Painful Case," he draws upon the Parable of the Great Banquet to highlight the implications of individual and societal inhospitality. Examining Joyce's parabolic method adds to the growing conversation about Joyce's sustained interest in Scripture and Christian thought.

Existence and Uniqueness of Local Regular Solution to the Schrödinger Flow from a Bounded Domain in $${\mathbb {R}}^3$$ into $${\mathbb {S}}^2$$

In this paper, we show the existence and uniqueness of local regular solutions to the initial-Neumann boundary value problem of the Schrödinger flow from a smooth bounded domain $$\Omega \subset \mathbb {R}^3$$ into $$\mathbb {S}^2$$ (namely Landau–Lifshitz equation without dissipation). The proof is built on a parabolic perturbation method, an intrinsic geometric energy argument, the symmetric (algebraic) properties of $${\mathbb {S}}^2$$ and some observations on the behaviors of some geometric quantities on the boundary of the domain manifold.It is based on methods from Ding and Wang (one of the authors of this paper) for the Schrödinger flows of maps from a closed Riemannian manifold into a Kähler manifold as well as on methods by Carbou and Jizzini for solutions of the Landau–Lifshitz equation.

The dataset of the manuscript "GPU-HADVPPM V1.0: high-efficient parallel GPU design of the Piecewise Parabolic Method (PPM) for horizontal advection in air quality model (CAMx V6.10)"

The dataset of the manuscript "GPU-HADVPPM V1.0: high-efficient parallel GPU design of the Piecewise Parabolic Method (PPM) for horizontal advection in air quality model (CAMx V6.10)"

An improved meta-heuristic algorithm for developing high-quality ReaxFF force fields of Fe/Ni transition metals and alloys

A reliable and transferable reactive force field (ReaxFF) is necessary for ReaxFF molecular dynamic simulations to study physical and chemical interactions of interest. The determination of ReaxFF force fields is a particularly challenging global optimization problem with multiple local minima. Here, an improved meta-heuristic algorithm (IMHA) based on particle swarm optimization (PSO) is proposed to accelerate the convergence of the optimization solution and improve the quality of ReaxFF parameterization. Firstly, a Latin hypercube design (LHD) algorithm is used to generate a uniform distribution of initial swarm, improving the exploration of whole parameter space. Secondly, the strategies for generating trial individuals in backtracking search optimization are modified and applied into PSO to enhance the search capacities and evade from local optimum. Thirdly, the sequential one parameter parabolic extrapolation method is utilized to obtain a rapid convergence in local region by optimizing global best particle. Consequently, the IMHA algorithm is demonstrated its capabilities by optimizing ReaxFF force field parameters of Fe/Ni transition metals and alloys. MD simulations show that the developed force fields accurately reproduce the fundamental properties of bcc Fe and fcc Ni transition metals and their alloys compared to experimental and QM values.

Geometric analysis and optimization of a parabolic concentrator for production at both thermal receivers at its focal point

The exploitation of solar energy for the production of electricity through a thermodynamic cycle is done according to several methods. The parabolic concentration method remains the best because of its high thermal efficiency (about 68%) but the least used because of difficulties related to the storage of its energy. Our work concerns a parabolic reflector with two receivers at its focal point. These two receivers are a boiler and a Stirling engine. The boiler and the Stirling engine receive the energy concentrated by the reflector. In the presence of the Sun it is the Stirling engine that produces the electricity. During the periods when the solar energy is insufficient or absent it is the thermal tank that will send the heat to the fluid that will turn the blades of a turbine to produce electricity. To meet the thermal needs of these two receivers, the efficiency of the reflector's heat production must be improved. To this end, we have studied the possibilities of optimizing the geometric parameters of the parabolic concentrator. For a surface of 12.56 m2 of the reflector, the use of standard geometric parameters allowed us to obtain a daily energy of 824.474 kWh when the solar power is 1104.938 kWh. For the same surface, using the optimized parameters, the production increased to 975.937kWh; a gain of 13.7%. This study allowed us to discover that the geometric and optical parameters strongly influence the thermal production of a reflector.

A Method for Threshold Setting and False Alarm Probability Evaluation for Radar Detectors

A threshold setting and false alarm probability evaluation method is proposed for radar detectors for which an analytical relationship between thresholds and false alarm probabilities is impossible or difficult to obtain due to complicated detection schemes or non-Gaussian noise and clutter. Importance sampling is performed to increase the sampling efficiency of low-probability samples. Then, the weighted piecewise parabolic (P2) interpolation method is used to rapidly plot the relationship curve between the threshold and the false alarm of the detector, with a low storage requirement and high accuracy. The proposed method effectively enhances the detector threshold computing scale and addresses the statistical verification of the false alarm probability for radar detectors with a low false alarm rate.

Numerical solutions to two-dimensional fourth order parabolic thin film equations using the Parabolic Monge-Ampere method

<abstract><p>This article presents the Parabolic-Monge-Ampere (PMA) method for numerical solutions of two-dimensional fourth-order parabolic thin film equations with constant flux boundary conditions. We track the PMA technique, which employs special functions to acclimate and force the mesh moving associated with the physical PDE representing the thin liquid film equation. The accuracy and convergence of the PMA approach are investigated numerically using a one two-dimensional problem. Comparing the results of this method to the uniform mesh finite difference scheme, the computing effort is reduced.</p></abstract>

Crack propagation and arrests in gelatin hydrogels are linked to tip curvatures.

Gelatin hydrogels are attractive scaffold materials for tissue engineering applications as they provide motifs for cell attachment, undergo large deformations, and are tunable. Low toughness and brittle fractures however limit their use in load bearing applications. An investigation of crack tip processes and mechanisms of crack propagation is warranted to link fracture properties with material microstructure. We cross-linked gelatin using glutaraldehyde to obtain low cross-linked control hydrogels and used an additional cross-linker, methylglyoxal, to fabricate MGO hydrogels with higher cross-links. We quantified fractures in the gelatin hydrogels from both groups using pure shear notch tests and characterized strain fields near the crack tip using 2-D digital image correlation. We used a numerical method based on Taylor's series expansion to measure the crack tip curvatures in the hydrogels. This method captures tip curvatures better than the parabolic method routinely used in studies. Results from our study show that cracks in gelatin hydrogels underwent frequent arrests during propagation through the specimen width in both groups. MGO hydrogels had 85% enhanced fracture toughness and a significantly higher number of stalls compared to the control group. Crack initiations following stalls in the sample correlated with low tip curvatures in both hydrogel groups. We also show that mechanical stretching blunts the crack tip before crack propagation; the degree of blunting was independent of the cross-link density and elastic modulus of the gelatin hydrogels. These results show a link between crack growth and the tip curvature in cross-linked gelatin hydrogels, and offer potential insights for the development of tougher hydrogels.