High-order Approach Research Articles

Against Instantiation

ABSTRACT According to traditional universalism, properties are instantiated by objects, where instantiation is a ‘tie’ that binds objects and properties into facts. I offer two arguments against this view. I then develop an alternative higher-order account which holds that properties are primitively predicated of objects yet, unlike traditional nominalism, are nevertheless genuinely real. When it is a fact that Fo , it is not because object o instantiates F -ness, but just that Fo —where F still exists. Against orthodox higher-order approaches, however, my arguments against instantiation also serve to support a sparse conception of properties. In developing the view, I introduce an extension of ontological and ideological commitment in the form of syntactic commitment.

Contact detection between curved fibres: high order makes a difference

Computer Graphics has a long history in the design of effective algorithms for handling contact and friction between solid objects. For the sake of simplicity and versatility, most methods rely on low-order primitives such as line segments or triangles, both for the detection and the response stages. In this paper we carefully analyse, in the case of fibre systems, the impact of such choices on the retrieved contact forces. We highlight the presence of artifacts in the force response that are tightly related to the low-order geometry used for contact detection. Our analysis draws upon thorough comparisons between the high-order super-helix model and the low-order discrete elastic rod model. These reveal that when coupled to a low-order, segment-based detection scheme, both models yield spurious jumps in the contact force profile. Moreover, these artifacts are shown to be all the more visible as the geometry of fibres at contact is curved. In order to remove such artifacts we develop an accurate high-order detection scheme between two smooth curves, which relies on an efficient adaptive pruning strategy. We use this algorithm to detect contact between super-helices at high precision, allowing us to recover, in the range of wavy to highly curly fibres, much smoother force profiles during sliding motion than with a classical segment-based strategy. Furthermore, we show that our approach offers better scaling properties in terms of efficiency vs. precision compared to segment-based approaches, making it attractive for applications where accurate and reliable forces are desired. Finally, we demonstrate the robustness and accuracy of our fully high-order approach on a challenging hair combing scenario.

A unified higher-order unsplit CFS-PML technique for solving second-order seismic equations using discontinuous Galerkin method

The absorbing boundary conditions play a key role in numerical simulations. The complex frequency-shifted perfectly matched layer (CFS-PML), one of the absorbing boundary conditions, has attracted widespread attention because it can efficiently attenuate near-grazing incident waves and evanescent waves. In practical application, the distinct boundary reflections still exist using the CFS-PML in a thin PML region. To further enhance the absorbing performance, we have developed a novel unified high-order unsplit CFS-PML technique. The high-order CFS-PML combined with the discontinuous Galerkin (DG) method is applied to solve the second-order seismic wave equation on an unstructured mesh. In this work, we establish a unified framework for high-order unsplit CFS-PML formulations. The classical CFS-PML is the first-order form of our proposed unsplit high-order approach. By using auxiliary variables and auxiliary ordinary differential equations (AODEs), a higher-order CFS-PML formulation can be reduced to a first-order CFS-PML formula. For an Nth-order AODE CFS-PML, it will lead to (2N-1) additional variables and (2N-1) auxiliary differential equations. Taking second- and third-order as examples, we have derived the high-order unsplit AODE CFS-PML expressions in detail. The DG method can effectively deal with complex geological structures, such as caves, cracks, faults, etc., which yields more accurate numerical solutions. We incorporate the high-order unsplit AODE CFS-PML technique into the DG method to approximate seismic wave equations. Their strengths are combined to calculate the propagating wavefield in more complex finite models and obtain better results. In addition, the stability conditions of the second- and third-order CFS-PMLs are provided. We perform the high-order unsplit CFS-PML implementation for seismic wave modeling in several models. The isotropic and anisotropic examples prove that the high-order unsplit CFS-PML enjoys better absorbing performance than the classical CFS-PML. The numerical result for the graben model certifies the feasibility and flexibility of our proposed high-order CFS-PML combined with the DG method.

Why do project managers underuse Management Information Systems theories in their management of IT projects?

Many of the challenges in management of IT projects belong to a class of problems for which a higher-order approach to a solution already exists in the form of a MIS theory. Management Information Systems (MIS) theories can be used as guidance for answering many of the important questions that occur for IT project managers. Despite this, many IT project managers underuse such theories in their management of projects. In this paper, we identify and explain the underlying reasons for the underuse of MIS theories by project managers in their management of IT projects. The underlying reasons that we identified include: (a) confusion around personal (specific-implicit) theory and scientific (general-explicit) MIS theory, (b) misunderstandings about the position of MIS theories among scientific theories, (c) the difficulty of gathering evidence and facts about the outcomes of using MIS theories in IT projects, (d) difficulties managers experience in choosing the right type of MIS theory for a particular challenge in an IT project, and (e) the ability or otherwise of current MIS theories to respond to evolving challenges of managing IT projects. The main audience of our paper is IT project managers and IT and MIS researchers.

Real-time measurement-driven reinforcement learning control approach for uncertain nonlinear systems

The paper introduces an interactive machine learning mechanism to process the measurements of an uncertain, nonlinear dynamic process and hence advise an actuation strategy in real-time. For concept demonstration, a trajectory-following optimization problem of a Kinova robotic arm is solved using an integral reinforcement learning approach with guaranteed stability for slowly varying dynamics. The solution is implemented using a model-free value iteration process to solve the integral temporal difference equations of the problem. The performance of the proposed technique is benchmarked against that of another model-free high-order approach and is validated for dynamic payload and disturbances. Unlike its benchmark, the proposed adaptive strategy is capable of handling extreme process variations. This is experimentally demonstrated by introducing static and time-varying payloads close to the rated maximum payload capacity of the manipulator arm. The comparison algorithm exhibited up to a seven-fold percent overshoot compared to the proposed integral reinforcement learning solution. The robustness of the algorithm is further validated by disturbing the real-time adapted strategy gains with a white noise of a standard deviation as high as 5%.

A HIGHER-ORDER APPROACH FOR TIME-FRACTIONAL GENERALIZED BURGERS’ EQUATION

A fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers’ equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann’s method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the [Formula: see text]-norm. The scheme’s proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.

Free vibration analysis of a nanoscale FG-CNTRCs sandwich beam with flexible core: Implementing an extended high order approach

The present work uses an extended high-order technique to examine free vibration analysis of Nanoscale CNTRCs sandwich beams. In this study, face sheets are made of PMMA reinforced with single-wall carbon nanotubes, and the honeycomb structure is selected for the flexible core. First-order shear deformation theory is utilized for the skins. The so-called high-order sandwich panel theory (HSAPT) is used for the core to consider the transverse shear strains in theoretical formulations. Then, skins and cores are subjected to the modified couple stress theory (MCST). For obtaining equations and related boundary conditions, the Hamilton principle is used. Additionally, three forms of beam support are examined: simply supported on both sides (SS), simply supported on one side and clamped supported on the other (SC), and clamped supported on both sides (CC). The material properties in skins are simulated to be graded in the thickness direction. The shooting method, as the numerical solution, is adopted to solve the governing differential equations to determine the natural frequencies of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams in which boundary conditions are converted into initial conditions. Compared to other techniques, this method is a reliable way to solve complicated equations and boundary conditions; therefore, its applicability, convergence, and accuracy are verified by comparing obtained results with those existing ones in the literature. Furthermore, the influences of distribution pattern and volume fraction of carbon nanotubes, boundary conditions, the size dependency parameter, core thickness, and slenderness ratio on vibration responses are discussed. It is concluded that natural frequencies rise with an increase in skin thicknesses and length scale parameter values while decreasing when beams’ length and core thicknesses increase.

Higher Order Trust Ranking of LinkedIn Accounts with Iterative Matrix Methods

Trust is a fundamental sociotechnological mainstay of the Web today. There is substantial evidence about this since netizens implicitly or explicitly agree to trust virtually every Web service they use ranging from Web-based mail to e-commerce portals. Moreover the methodological framework for trusting individual netizens, primarily their identity and communications, has considerably progressed. Nevertheless, the core of fact checking for human generated content is still far from being substantially automated as most proposed smart algorithms capture inadequately fundamental human traits. One such case is the evaluation of the profile trustworthiness of LinkedIn members based on publicly available attributes available from the platform itself. A trusted profile may indirectly indicate a more suitable candidate since its contents can be easily verified. In this article a first order graph search mechanism for discovering LinkedIn trusted profiles based on a random walker is extended to higher order ranking based on a combination of functional and connectivity patterns. Results are derived for the same benchmark dataset and the first- and higher-order approaches are compared in terms of accuracy.

Efficacy of line-based explicit and compact high-order finite difference schemes for hybrid unstructured grids

This study enables the use of explicit and compact high-order finite-difference schemes with a line-based solver to solve conservation laws on unstructured grids. A quadrilateral subdivision process is used to identify unique line structures (also known as Hamiltonian loops) before formulating stencil-based discretizations. To demonstrate the methodology for canonical flows represented by the Navier–Stokes equations, up to sixth-order spatial discretization and a maximum of tenth-order low-pass filters are implemented along with the Hamiltonian loops. The filter restores the benefits of the high-order approach even in the presence of abrupt grid discontinuities that cause abrupt changes in loop curvature. Isentropic vortex convection, lid-driven cavity, double periodic shear layer, and inviscid and viscous flow past a cylinder and NACA 0012 airfoil are all used to demonstrate the formulation. The ability of some schemes, particularly the fourth-order explicit, to nearly achieve the formal order of accuracy and successfully predict the flow following available results in the literature is one of the key findings. Compact schemes have been found to be more sensitive to loop curvature than explicit schemes.

Quadratic approximation manifold for mitigating the Kolmogorov barrier in nonlinear projection-based model order reduction

A quadratic approximation manifold is presented for performing nonlinear, projection-based, model order reduction (PMOR). It constitutes a departure from the traditional affine subspace approximation that is aimed at mitigating the Kolmogorov barrier for nonlinear PMOR, particularly for convection-dominated transport problems. It builds on the data-driven approach underlying the traditional construction of projection-based reduced-order models (PROMs); is application-independent; is linearization-free; and therefore is robust for highly nonlinear problems. Most importantly, this approximation leads to quadratic PROMs that deliver the same accuracy as their traditional counterparts using however a much smaller dimension – typically, n2∼n1, where n2 and n1 denote the dimensions of the quadratic and traditional PROMs, respectively. The computational advantages of the proposed high-order approach to nonlinear PMOR over the traditional approach are highlighted for the detached-eddy simulation-based prediction of the Ahmed body turbulent wake flow, which is a popular CFD benchmark problem in the automotive industry. For a fixed accuracy level, these advantages include: a reduction of the total offline computational cost by a factor greater than five; a reduction of its online wall clock time by a factor greater than 32; and a reduction of the wall clock time of the underlying high-dimensional model by a factor greater than two orders of magnitude.

Multifrequency Spaceborne Synthetic Aperture Radar Data for Backscatter-Based Characterization of Land Use and Land Cover

Polarimetric synthetic aperture radar remote sensing extracts the information about the target using decomposition models to separate the polarimetric information into single-bounce (contributed by smooth surfaces), double-bounce (contributed by urban structure), and volume (mainly due to vegetation cover) scattering components. The penetration capacity of the electromagnetic wave into the surface increases with the decrease in its frequency. This study explores and compares the polarimetric decomposition models for scattering-based characterization of land use and cover using multifrequency spaceborne synthetic aperture radar sensor datasets that were acquired over San Francisco, CA, USA. The present work compares the scattering parameters of coherent (Pauli), roll-invariant (Barnes), eigenvalue–eigenvector (Cloude), and compact-polarimetric (Raney) decomposition modeling approaches for scattering-based characterization of urban structures, waterbody, and vegetation cover. The land use/cover classification was performed based on the scattering response of the scatterers using a support vector machine classifier. The outputs of the classification approach on multisensor, multifrequency, and multi-polarization polarimetric synthetic aperture radar data have shown reasonable accuracy in classifying the land use and land cover. The decomposition models fail to characterize the oriented urban structures that cause misclassification of urban structures as vegetation. The higher-order roll-invariant decomposition modeling approaches could improve the interpretation of different targets and accuracy in land use and land cover classification.

Higher-Order Accurate and Conservative Hybrid Numerical Scheme for Relativistic Time-Fractional Vlasov-Maxwell System

The historical analysis demonstrates that plasma scientists produced a variety of numerical methods for solving “kinetic” models, i.e., the Vlasov-Maxwell (VM) system. Still, on the other hand, a significant fact or drawback of most algorithms is that they do not preserve conservation philosophies. This is a crucial fact that cannot be disregarded since the Vlasov Maxwell system is associated with conservation rules and is capable of assessing after the accomplishment of certain helpful mathematical actions. To examine the fractional-order routine of charged particles, we constructed a fractional-order plasma model and proposed a higher-order conservative numerical approach based on operational matrices theory and Shifted Gegenbauer estimations. Numerical convergence is investigated to confirm its competence and compatibility. This concept may be used in problems involving variable order and multidimensionality, such as those involving Vlasov and Boltzmann systems.

On the convective wave equation for the investigation of combustor stability using FEM-methods

Solving the Helmholtz equation with spatially resolved finite element method (FEM) approaches is a well-established and cost-efficient methodology to numerically predict thermoacoustic instabilities. With the implied zero Mach number assumption all interaction mechanisms between acoustics and the mean flow velocity including the advection of acoustic waves are neglected. Incorporating these mechanisms requires higher-order approaches that come at massively increased computational cost. A tradeoff might be the convective wave equation in frequency domain, which covers the advection of waves and comes at equivalent cost as the Helmholtz equation. However, with this equation only being valid for uniform mean flow velocities it is normally not applicable to combustion processes. The present paper strives for analyzing the introduced errors when applying the convective wave equation to thermoacoustic stability analyses. Therefore, an acoustically consistent, inhomogeneous convective wave equation is derived first. Similar to Lighthill’s analogy, terms describing the interaction between acoustics and non-uniform mean flows are considered as sources. For the use with FEM approaches, a complete framework of the equation in weak formulation is provided. This includes suitable impedance boundary conditions and a transfer matrix coupling procedure. In a modal stability analysis of an industrial gas turbine combustion chamber, the homogeneous wave equation in frequency domain is subsequently compared to the Helmholtz equation and the consistent Acoustic Perturbation Equations (APE). The impact of selected source terms on the solution is investigated. Finally, a methodology using the convective wave equation in frequency domain with vanishing source terms in arbitrary mean flow fields is presented.

High order approach for solving chaotic and hyperchaotic problems

In this work, the method of Taylor's decomposition on two points is suggested in order to find approximate solutions of chaotic and hyperchaotic initial value problems and to analyze the behaviors of these solutions. Unlike to the classical Taylor's method, the proposed numerical scheme is based on the application of the Taylor's decomposition on two points to the system of nonlinear initial value problems, and as a result an implicit method is obtained. Stability and error analysis of the method are presented, and its high-order accuracy and A-stability are proven. One of the advantages of the proposed method is that it is a stable and very efficient method for chaotic problems as it is an implicit one-step method. The most important advantage of the Taylor's decomposition method is that it has high order accuracy for large step sizes with a simple algorithm compared to other methods. The applicability of the proposed method has been examined in some famous chaotic systems; the Lorenz and Chen systems, and hyperchaotic systems; the Chua and Rabinovich-Fabrikant systems, to emphasize both its accuracy and effectiveness. The accuracy of the proposed method is checked by comparing the calculated results with semi-explicit Adams-Bashforth-Moulton method and ninth order Runge-Kutta method. The calculated results are also compared with multi-stage spectral relaxation method and multi-domain compact finite difference relaxation method. Comparisons have shown that the method is more accurate and efficient than the other mentioned methods for large step sizes. The obtained results are also compared with the theoretical findings and it is shown that the theoretical and numerical results are consistent.

Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method

The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function is perfectly shifted to the neighbor node on the uniform mesh arrangement. This advantage may curtail the applicability of the method to problems with complex geometries. To overcome this issue, a high-order meshless interpolation-based approach is proposed to handle the streaming step. Owing to its high accuracy, the radial basis function (RBF) is one of the popular methods used for interpolation. In general, RBF-based approaches suffer from some stability issues, where their stability strongly depends on the shape parameter of the RBF. In the current work, a stabilized RBF approach is used to handle the streaming. The stabilized RBF approach has a weak dependency on the shape parameter, which improves the stability of the method and reduces the dependency of the shape parameter. Both the stabilized RBF method and the streaming of the LBM are used for solving three benchmark problems. The results of the stabilized method and the perfect streaming LBM are compared with analytical solutions or published results. Excellent agreements are observed, with a little advantage for the stabilized approach. Additionally, the computational cost is compared, where a marginal difference is observed in the favor of the streaming of the LBM. In conclusion, one could report that the stabilized method is a viable alternative to the streaming of the LBM in handling both simple and complex geometries.

A multi-scale high-order recursive filter approach for the sea ice concentration analysis

A multi-scale high-order recursive filter approach for the sea ice concentration analysis

Solution of a One-Dimension Heat Equation Using Higher-Order Finite Difference Methods and Their Stability

One-dimensional heat equation was solved for different higher-order finite difference schemes, namely, forward time and fourth-order centered space explicit method, backward time and fourth-order centered space implicit method, and fourth-order implicit Crank-Nicolson finite difference method. Higher-order schemes have complexity in computing values at the neighboring points to the boundaries. It is required there a specification of the values of field variables at some points exterior to the domain. The complexity was incorporated using Hicks approximation. The convergence and stability analysis was also computed for those higher-order finite difference explicit and implicit methods in case of solving a one dimensional heat equation. The obtained numerical results were compared with exact solutions. It is found that backward time and fourth-order centered space implicit scheme along with Hicks approximation performed well over the other mentioned higher-order approaches.

A Higher-Order Approach to Diachronic Continence

We often form intentions to resist anticipated future temptations. But when confronted with the temptations our resolutions were designed to withstand, we tend to revise our previous evaluative judgments and conclude that we should now succumb—only to then revert to our initial evaluations, once temptation has subsided. Some evaluative judgments made under the sway of temptation are mistaken. But not all of them are. When the belief that one should now succumb is a proper response to relevant considerations that have newly emerged, can acting in line with one’s previous intention nonetheless be practically rational? To answer this question, I draw on recent debates on the nature of higher-order evidence and on what rationally responding to such evidence involves. I propose that agents facing temptation often have evidence of “deliberative unreliability”, which they ought to heed even when it is “misleading” (that is, even when their evaluative judgments are in fact proper responses to the relevant considerations then available). Because evidence of deliberative unreliability can “dispossess” agents of normative reasons for evaluative judgments and actions that they would otherwise have, being continent despite judging that one should now succumb can often be more rational than giving in.

A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives

In this paper, we present a high-order approach for solving one- and two-dimensional time-space fractional diffusion equations (FDEs) with Caputo-Riesz derivatives. To design the scheme, the Caputo temporal derivative is approximated using a high-order method, and the spatial Riesz derivative is discretized by the second-order weighted and shifted Grünwald difference (WSGD) method. It is proved that the scheme is unconditionally stable and convergent with the order of O(ταh2+τ4), where τ and h are time and space step sizes, respectively. We illustrate the accuracy and effectiveness of the method by providing several numerical examples.

Gas Transport across Carbon Nitride Nanopores: A Comparison of van der Waals Functionals against the Random-Phase Approximation

C2N is an ordered two-dimensional carbon nitride with a high density (1.7 × 1014 cm–2) of 3.1 Å-sized nanopores, making it promising for high-flux gas sieving for energy-efficient He and H2 purification. Herein, we discuss the accurate calculation of potential energy surfaces for He, H2, N2, and CO2 across C2N nanopores, to characterize the gas-sieving potential of C2N. We compare the potential energy surface derived from density-functional theory calculations using five commonly used van der Waals (vdW) approximations. While all five functionals point that the C2N nanopore yields He/N2 and H2/N2 selectivities over 1000, adsorption energies and energy barriers vary remarkably depending on the approximation chosen. To make progress, we compare the calculations against the results from the adiabatic connection fluctuation dissipation theory, with random-phase approximation, known to be accurate in capturing vdW interactions. The comparison indicates that the interaction energy is less accurate with vdW density functional theory. On the other hand, more empirical corrections work reasonably well, a finding that we also confirm for another carbon nitride lattice, poly(triazine imide). Overall, we recommend these for screening carbon nitride materials for gas separation, but also comparing functionals with higher-order approaches when dealing with different materials.