Diamond Scheme Research Articles

Application of the 2D diamond scheme to predict the macroscopic thermal conductivity of a three-phase composite with local anisotropy directions

In this contribution, we are interested in the prediction of the macroscopic thermal conductivity of three-phasic composite materials such as wood fibers. The main idea is to make use of up-scaling such as homogenization to link the pore scale and the sample scale. The studied wood species incorporates three phases: the air, the lumen or matrix and the fibers. Image processing is preformed on a tomographic acquisition with high resolution of some micrometers. It serves to identify the present phases and generates the morphology mesh. The 2D diamond scheme is employed to discretize Fourier's model posed on the segmented morphology. The resulting algorithm is validated using an exact solution. Optimal numerical convergence rates of second order are recorded. The thermal conductivity is therefore estimated following the 2D orthotropic directions. An emphasis is set on the impact of the orientation of fibers on this thermal property.

Implications Fraud Diamond in Fraudulent Financial Statements on Property, Real Estate and Building Construction Industries

Fraudulent financial statements involve intentional actions of manipulating or hiding information in financial reports to deceive users. Understanding the factors behind such fraud can be explored through the Diamond Scheme Theory, consists of four materials: opportunity, rationalization, ability, and pressure. The aim of this research analyze the impact of each component of the Fraud Diamond on fraudulent financial statements. The quantitative research methodology focuses on industries in the real estate, construction and property sectors listed on the Indonesia Stock Exchange starting 2020 to 2022. The sample includes 69 companies selected through purposive sampling. Utilizing multiple linear regression analysis using SPSS 26 is employed for analysis. The study results reveal that, individually, only the capability variable within the Fraud Diamond has a significant negative impact on fraudulent financial statements. Pressure, opportunity, and rationalization variables do not show a significant influence. Additionally, when considered collectively, there is no discernible impact of the Fraud Diamond components on fraudulent financial statements.

A linearity-preserving diamond scheme with extended least square interpolation for the heterogeneous and anisotropic diffusion problems on polyhedral meshes

A linearity-preserving diamond scheme with extended least square interpolation for the heterogeneous and anisotropic diffusion problems on polyhedral meshes

A nonlinear scheme preserving maximum principle for heterogeneous anisotropic diffusion equation

We present a new nonlinear method in order to preserve the maximum principle for the diffusion problem with heterogeneous anisotropic coefficient. It is well-known that for diffusion problems with general discontinuous coefficients, the existing cell-centered finite volume schemes on general meshes cannot unconditionally satisfy the discrete maximum principle (DMP), i.e., there are always certain severe restrictions on the mesh-cell geometry or locations of discontinuity in order to preserve DMP. To deal with the issue we propose a nonlinear method of modifying discrete flux of linear second-order schemes into a new conservative flux. Then the resulting scheme keeps conservation and accuracy, and has the structure preserving maximum principle without imposing those severe restrictions. Specifically, we will start with the diamond scheme whose flux is linear and has second-order accuracy, but has no the structure preserving maximum principle. Then the nonlinear correction method is applied to get a scheme satisfying the discrete maximum principle unconditionally. We give some theoretical analysis including the coercivity property and a prior estimation. Numerical results show that the accuracy of our new scheme is superior to the existing scheme preserving maximum principle, and in some cases the accuracy can even be improved by one order of magnitude.

Experimental and Numerical Evaluation of an Innovative Diamond-Scheme Bracing System Equipped with a Yielding Damper

در این مقاله به معرفی و بررسی عملکرد آزمایشگاهی سیستم نوین مهاربندی و ترکیب آن با میراگر تسلیم‌شونده پرداخته می شود. این سیستم که در راستای افزایش شکل پذیری، جذب انرژی بالاتر و پوشش ضعف های سیستم های موجود مورد پیشنهاد و بررسی قرار گرفته است، از یک عضو مهاربند لوزی شکل به همراه میراگر تسلیم شونده حلقوی در وسط آن تشکیل شده است. در ساخت نمونه ها 3 مدل مختلف با اتصالات صلب، نیمه صلب و مفصلی مدنظر قرار گرفته است که پس از ساخت، تحت بار چرخه ای قرار گرفته و نتایج آنها با یکدیگر مورد مقایسه شدند. نتایج این تحقیق در وهله اول بیانگر قابلیت اجرایی شدن سیستم و در ادامه نشان از قابلیت بالای هر سه سیستم در جذب انرژی و شکل پذیری را می دهد. همچنین با توجه به هندسه اعضای مهاربندی و میراگر، با ابعاد و ضخامت کوچکتر حلقه فولادی می توان به جذب انرژی بالاتر و نیروی وارد شده بیشتری برای تسلیم میراگرها نسبت به سایر سیستم های موجود دست یافت. در نهایت نیز در راستای امکان سنجی مدلسازی سیستم پیشنهادی در نرم افزارهای المان محدودی، مدل المان محدودی سیستم پیشنهادی در نرم‌افزار آباکوس مورد مدلسازی و صحت‌سنجی قرار گرفت که نتایج آن با نتایج آزمایشگاهی دارای هماهنگی مناسبی می باشد. همچنین ضریب شکل‌پذیری مدل مفصلی نسبت به مدل صلب و نیمه صلب به ترتیب 12/1 و 17/1 برابر می باشد. ظرفیت جذب انرژی مدل مفصلی نیز تا حدود 5/4 و 15/2 برابر مدل صلب و نیمه‌صلب می باشد.

A least squares based diamond scheme for 3D heterogeneous and anisotropic diffusion problems on polyhedral meshes

We propose a diamond scheme for 3D heterogeneous and anisotropic problem using piecewise linear approximation and least squares method. Since the continuity of the solution and flux is treated appropriately, the scheme and the vertex interpolation algorithm allow arbitrary diffusion tensors. In addition, we employ an adaptive weighted coefficient in the least squares problem of the vertex interpolation using a novel way to evaluate the magnitude of the diffusion anisotropy. Consequently our vertex interpolation has better performance than the least squares interpolation in most tested cases. The presented scheme and vertex interpolation algorithm do not need edge information, which leads to less topological searches and simplifies the programming compared with other edge-based ones. By means of unified calculations of the geometric quantities, this scheme is suitable for meshes with nonplanar faces. Numerical experiments show that our scheme is linearity-preserving and achieves nearly optimal accuracy for the solution on general meshes. Moreover, the new vertex interpolation algorithm has an ideal performance for heterogeneous and highly anisotropic diffusion problems which are tough for some existing algorithms.

A least squares based diamond scheme for anisotropic diffusion problems on polygonal meshes

AbstractWe present a new least squares based diamond scheme for anisotropic diffusion problems on polygonal meshes. This scheme introduces both cell‐centered unknowns and vertex unknowns. The vertex unknowns are intermediate ones and are expressed as linear combinations with the surrounding cell‐centered unknowns by a new vertex interpolation algorithm which is also derived in least squares approach. Both the new scheme and the vertex interpolation algorithm are applicable to diffusion problems with arbitrary diffusion tensors and do not depend on the location of discontinuity. Benefitting from the flexibility of least squares approach, the new scheme and vertex interpolation algorithm can also be extended to 3D cases naturally. The new scheme and vertex interpolation algorithm are linearity‐preserving under given assumptions and the numerical results show that they maintain nearly optimal convergence rates for both error and error in general cases. More interesting is that a very robust performance of the new vertex interpolation algorithm on random meshes compared with the algorithm LPEW2 is found from the numerical tests.

Parallelization, initialization, and boundary treatments for the diamond scheme

We study a class of general purpose linear multisymplectic integrators for Hamiltonian wave equations based on a diamond-shaped mesh. On each diamond, the PDE is discretized by a symplectic Runge–Kutta method. The scheme advances in time by filling in each diamond locally. We demonstrate that this leads to greater efficiency and parallelization and easier treatment of boundary conditions compared with methods based on rectangular meshes. We develop a variety of initial and boundary value treatments and present numerical evidence of their performance. In all cases, the observed order of convergence is equal to or greater than the number of stages of the underlying Runge–Kutta method.

Finite volume methods for numerical simulation of the discharge motion described by different physical models

This paper deals with the numerical solution of an ionization wave propagation in air, described by a coupled set of convection-diffusion-reaction equations and a Poisson equation. The standard three-species and more complex eleven-species models with simple chemistry are formulated. The PDEs are solved by a finite volume method that is theoretically second order in space and time on an unstructured adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convective and diffusive fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. The results of both models are compared in details for a test case. The influence of physically pertinent boundary conditions at electrodes is also presented. Finally, we deal with numerical accuracy study of implicit scheme in two variants for simplified standard model. It allows us in the future to compute simultaneously and efficiently a process consisting of short time discharge propagation and long-term after-discharge phase or repetitively pulsed discharge.

Formula omitted]- factor: A modified relaxation factor to accelerate the convergence rate of the radiative transfer equation with high-order resolution schemes using the Normalized Weighting-Factor method

In this paper the high computational cost problem by using high-order (HO) and high-resolution (HR) schemes is addressed and for that, we propose the incorporation of a modified relaxation factor to accelerate the numerical solution of the radiative transfer equation (RTE) using the Normalized Weighting-Factor (NWF) method to implement several high-order resolution schemes. The modified relaxation factor to accelerate the convergence rate is based on the artificial incorporation of a semi-implicit X-factor. This procedure is denoted as the X-factor method. The X-factor method is compared, in terms of computer time needed to obtain a converged solution, with the widely used deferred-correction (DC) method for the calculations of a two-dimensional cavity with emitting–absorbing–scattering gray media using the discrete ordinates method. Four parameters are considered to evaluate the purpose of this paper: the absorption coefficient, the emissivity of the boundary surface, the under-relaxation factor, and the scattering albedo. In general, the results showed that using the X-factor procedure there is superiority over the DC procedure for reducing the CPU time when the DIAMOND, QUICK, SMART and WACED schemes are used. Additionally, the results showed that the CPU time for the MUSCL scheme can be smaller than that obtained with the DC method. The absorption coefficient effect showed that the X-factor method provided a reduction of CPU time between 20 and 211%. The results of emissivity effect showed that the computational time decreases between 2 and 162% by using the X-factor procedure. Regarding the effect of the under-relaxation factor, the results showed that X-factor method provided reductions of the CPU time from 52 to 181%. Analogously, the results for the scattering albedo showed that the X-factor method reduced the CPU time by a factor ranging between 4 and 219%. Additionally, a second test case was presented and the results showed that our code produces the same solution considering the use of DC method, X-factor method and several high-order resolution schemes. Results clearly demonstrated the effectiveness of the X-factor method to reduce the CPU time and therefore, the X-factor method can potentially be used in commercial software and in-house codes due to the substantial reduction of the computational cost.

Evaluation of the CPU time for solving the radiative transfer equation with high-order resolution schemes applying the normalized weighting-factor method

In this paper, we evaluated the convergence rate (CPU time) of a new mathematical formulation for the numerical solution of the radiative transfer equation (RTE) with several High-Order (HO) and High-Resolution (HR) schemes. In computational fluid dynamics, this procedure is known as the Normalized Weighting-Factor (NWF) method and it is adopted here. The NWF method is used to incorporate the high-order resolution schemes in the discretized RTE. The NWF method is compared, in terms of computer time needed to obtain a converged solution, with the widely used deferred-correction (DC) technique for the calculations of a two-dimensional cavity with emitting–absorbing–scattering gray media using the discrete ordinates method. Six parameters, viz. the grid size, the order of quadrature, the absorption coefficient, the emissivity of the boundary surface, the under-relaxation factor, and the scattering albedo are considered to evaluate ten schemes. The results showed that using the DC method, in general, the scheme that had the lowest CPU time is the SOU. In contrast, with the results of theDC procedure the CPU time for DIAMOND and QUICK schemes using the NWF method is shown to be, between the 3.8 and 23.1% faster and 12.6 and 56.1% faster, respectively. However, the other schemes are more time consuming when theNWFis used instead of the DC method. Additionally, a second test case was presented and the results showed that depending on the problem under consideration, the NWF procedure may be computationally faster or slower that the DC method. As an example, the CPU time for QUICK and SMART schemes are 61.8 and 203.7%, respectively, slower when the NWF formulation is used for the second test case. Finally, future researches to explore the computational cost of the NWF method in more complex problems are required.

Single-Photon Interference due to Motion in an Atomic Collective Excitation.

We experimentally demonstrate the heralded generation of bichromatic single photons from an atomic collective spin excitation (CSE). The photon arrival times display collective quantum beats, a novel interference effect resulting from the relative motion of atoms in the CSE. A combination of velocity-selective excitation with strong laser dressing and the addition of a magnetic field allows for exquisite control of this collective beat phenomenon. The present experiment uses a diamond scheme with near-IR photons that can be extended to include telecommunications wavelengths or modified to allow storage and retrieval in an inverted-Y scheme.

The performances of the discrete ordinates-collocation spectral method for the three-dimensional radiative transfer equation

ABSTRACTThe discrete ordinates-collocation spectral method (DO-CSM) is successfully applied to solve the three-dimensional radiative transfer equation (RTE). The RTE is angular discretized by the DOM first and then solved by the CSM. Two examples are adopted to identify the performances of the DO-CSM for 3D RTE. The results that are obtained from the DO-CSM and the discrete ordinates method with a diamond scheme (DOM-DS), respectively, are compared with those of the exact solutions or benchmarks. These comparisons indicate that the DO-CSM can give more accurate intensity distribution in both space and direction than the DOM-DS. The false scattering of the DO-CSM is much less than that of the DOM-DS. The errors of the DO-CSM are primarily due to the “ray-effect” and the errors caused by the false scattering can even be ignored when the resolutions are fine enough. The errors due to the ray-effect are significant especially for an optical thin medium and the ray-effects are largely suppressed by the finer angular discretization. The results of the DO-CSM improved more quickly than those of the DOM-DS with the increase in the number of directions because the errors caused by the false scattering of the DO-CSM are much less than those of the DOM-DS.

Numerical modeling of subsidence in saturated porous media: A mass conservative method

In this paper, a second order accurate cell-centered finite volume method (FVM) is coupled with a finite element method (FEM) to solve the deformation of a saturated porous layer based on Biot’s consolidation model. The proposed numerical technique is applied to the fully unstructured triangular grids to simulate actual geological formations. To reconstruct the pressure gradient at control volume faces, the diamond scheme is implemented as a multipoint flux approximation method. Also the least square algorithm is used to interpolate pressure at the vertices from the cell-center values. The stability of this numerical model is studied in comparison to the different FEMs through various examples. It is shown that, although the Taylor-Hood FEM has been introduced as a remedy for violation of the inf-sup condition, it does not entirely remove the non-physical oscillations. Contrary to the linear and Taylor-Hood FEMs, the proposed discretization model provides monotonic solution without imposing any restriction on the mesh or time step size. Compared to the mixed FEM, the method achieves local mass balance with fewer degrees of freedom. To couple the flow and mechanical sub-problems, the fixed-stress operator split is implemented as an iterative sequential method, due to its unconditional stability, accuracy and high rate of convergence. The accuracy of the proposed model is verified via a range of examples including analytical and numerical solutions. The performance of this methodology is assessed through modeling of subsidence in an aquifer-interbed system. This problem illustrates the capability of the model in providing stable solution in heterogeneous domains with complicated shapes.

Collective state synthesis in an optical cavity using Rydberg atom dipole blockade

We investigate the coherent manipulation of interacting Rydberg atoms placed inside a high-finesse optical cavity for the deterministic preparation of strongly coupled light-matter systems. We consider a four-level diamond scheme with one common Rydberg level for N interacting atoms. One side of the diamond is used to excite the atoms into a collective ‘superatom’ Rydberg state using either π-pulses or stimulated Raman adiabatic passage (STIRAP) pulses. The upper transition on the other side of the diamond is used to transfer the collective state to one that is coupled to a field mode of an optical cavity. Due to the strong interaction between the atoms in the Rydberg level, the Rydberg blockade mechanism plays a key role in the deterministic quantum state synthesis of the atoms in the cavity. We use numerical simulation to show that non-classical states of light can be generated and that the state that is coupled to the cavity field is a collective one. We also investigate how different decay mechanisms affect this interacting many-body system. We also analyze our system in the case of two Rydberg excitations within the blockade volume. The simulations are carried out with parameters corresponding to realizable high-finesse optical cavities and alkali atoms like rubidium.

Nodal SN-method for HEX-Z geometry

The problem of spatial approximation becomes very important in the solution of neutronics problems with coarse spatial grids, in particular, in the calculations of fuel assemblies of fast reactors (for instance, BN-800 and BN-1200 reactors) with computational cell in the form of hexagonal prism.“Weighted diamond difference” (WDD) schemes are the most widely used among the finite difference schemes for the neutron and gamma-ray transport equation solution. They are efficient from the viewpoint of ease of their implementation and associated CPU time expenditures. However, some drawbacks of these schemes are manifested when they are applied to solve the above described problems. Diamond difference scheme (DD) having second-order approximation (the best for this class of schemes) does not possess the properties of positivity and monotonicity. This is the reason why negative values and non-physical oscillations are often present in the solutions obtained. “Step” scheme (St), which is free from the disadvantages of the diamond difference scheme, has accuracy of only the first order. In connection with the need in high-accuracy calculations its use appears to be inefficient.There exist algorithms for correction of negative values, as well as adaptive (AWDD) schemes aimed both at the reduction of the level of oscillations and at the obtaining positive solutions. However, these algorithms negatively affect the order of approximation, and schemes of the first – second order of accuracy are discussed in such cases. Besides that, for adaptive schemes there exists the problem of correct selection of parameters of the scheme.The evident way to escape such situation with simultaneously enhancing quality and accuracy of the calculation is to select a fine mesh. In case of calculation of fuel assemblies of fast reactors spatial grid represents an arrangement of rectangular prisms with regular hexagons forming their bases (in such cases reference is made to HEX-Z-geometry). Therefore, hexagonal cells can be divided into rhomb-shaped cells (three rhombs per one hexagon; 12 rhombs per one hexagon, etc.). Diamond scheme is applied for the grids consisting of rhombs thus obtained. Because of the smaller cell size as compared with original cell size, the drawbacks inherent to this scheme will not be pronounced. Triangular grid can also be used.A different approach for the solution of the above indicated problem is to develop computational methods with enhanced order of accuracy without increasing the number of computational points. Nodal method is one of such methods. Expansion of unknown function inside the node (elementary volume with constant properties) in basis functions with subsequent calculation of expansion moments constitutes the basis of any nodal method.Nodal SN-method in HEX-Z geometry will be discussed in the present paper.

A Finite Volume Scheme for Three-Dimensional Diffusion Equations

AbstractThe extension of diamond scheme for diffusion equation to three dimensions is presented. The discrete normal flux is constructed by a linear combination of the directional flux along the line connecting cell-centers and the tangent flux along the cell-faces. In addition, it treats material discontinuities by a new iterative method. The stability and first-order convergence of the method is proved on distorted meshes. The numerical results illustrate that the method appears to be approximate second-order accuracy for solution.

SU-E-T-270: Diffusion Synthetic Acceleration for Linear Boltzmann Transport Equation

Purpose: Linear Boltzmann transport equation (LBTE) is as accurate as the Monte Carlo method (MC) for dose calculation in photon/particle therapy (LBTE is a deterministic and Eulerian formulation and MC is a statistical and Lagrangian description). An advantage of LBTE is that numerous acceleration techniques can be utilized for acceleration. This work is to explore the acceleration of LBTE via diffusion synthetic acceleration (DSA). Methods: For simplicity, two-dimensional, steady-state, and within-group LBTE is considered with two angular dimensions and two spatial dimensions. The discrete ordinate method is developed for solving this integro-differential equation. The angular variables are discretized using a level-symmetric quadrature set on the unit sphere. The spatial variables are discretized on the structured grid based on the diamond scheme. The source-iteration method (SI) is used to solve the discretized system.Since SI is slow in optically thick and highly scattering regime. DSA is developed to accelerate SI. The motivation for DSA is that diffusion equation (DE) is a good approximation of LBTE in the above regime. However, DE is much cheaper than LBTE computationally since DE only involves spatial variables. Thus, in each DSA iteration, DSA adds to the SI step a computationally-negligible DE step, i.e., to first solve DE with the SI residual as source term, and then compensate the SI solution with DE solution. Results: DSA was benchmarked and compared with SI. The difference between two methods was within 0.12% which verifies the accuracy of DSA, while DSA demonstrated the great advantage in speed, e.g., the reduction of iteration number to 6% and 4% respectively for cases with 100 and 1,000 scattering-absorption ratio that commonly occur in clinical dose calculation. Conclusion: DSA has been developed as one of many possible means for accelerating the numerical solver of LBTE for dose calculation. The authors were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500).

SU‐E‐T‐22: A Deterministic Solver of the Boltzmann‐Fokker‐Planck Equation for Dose Calculation

Purpose:The Boltzmann‐Fokker‐Planck equation (BFPE) accurately models the migration of photons/charged particles in tissues. While the Monte Carlo (MC) method is popular for solving BFPE in a statistical manner, we aim to develop a deterministic BFPE solver based on various state‐of‐art numerical acceleration techniques for rapid and accurate dose calculation.Methods:Our BFPE solver is based on the structured grid that is maximally parallelizable, with the discretization in energy, angle and space, and its cross section coefficients are derived or directly imported from the Geant4 database. The physical processes that are taken into account are Compton scattering, photoelectric effect, pair production for photons, and elastic scattering, ionization and bremsstrahlung for charged particles.While the spatial discretization is based on the diamond scheme, the angular discretization synergizes finite element method (FEM) and spherical harmonics (SH). Thus, SH is used to globally expand the scattering kernel and FFM is used to locally discretize the angular sphere. As a Result, this hybrid method (FEM‐SH) is both accurate in dealing with forward‐peaking scattering via FEM, and efficient for multi‐energy‐group computation via SH. In addition, FEM‐SH enables the analytical integration in energy variable of delta scattering kernel for elastic scattering with reduced truncation error from the numerical integration based on the classic SH‐based multi‐energy‐group method.Results:The accuracy of the proposed BFPE solver was benchmarked against Geant4 for photon dose calculation. In particular, FEM‐SH had improved accuracy compared to FEM, while both were within 2% of the results obtained with Geant4.Conclusion:A deterministic solver of the Boltzmann‐Fokker‐Planck equation is developed for dose calculation, and benchmarked against Geant4.Xiang Hong and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500).

High performance wafer-fused semiconductor disk lasers emitting in the 1300 nm waveband

We report for the first time on the performance of 1300 nm waveband semiconductor disc lasers (SDLs) with wafer fused gain mirrors that implement intracavity diamond and flip-chip heat dissipation schemes based on the same gain material. With a new type of gain mirror structure, maximum output power values reach 7.1 W with intracavity diamond gain mirrors and 5.6 W with flip-chip gain mirrors, using a pump spot diameter of 300 µm, exhibiting a beam quality factor M(2)< 1.25 in the full operation range. These results confirm previously published theoretical modeling of these types of SDLs.