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1
Izadi, Mohammad, and Hari Mohan Srivastava. "Applications of Modified Bessel Polynomials to Solve a Nonlinear Chaotic Fractional-Order System in the Financial Market: Domain-Splitting Collocation Techniques." Computation 11, no. 7 (July 3, 2023): 130. http://dx.doi.org/10.3390/computation11070130.
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We propose two accurate and efficient spectral collocation techniques based on a (novel) domain-splitting strategy to handle a nonlinear fractional system consisting of three ODEs arising in financial modeling and with chaotic behavior. One of the major numerical difficulties in designing traditional spectral methods is in the handling of model problems on a long computational domain, which usually yields to loss of accuracy. One remedy is to split the underlying domain and apply the spectral method locally in each subdomain rather than on the global domain of interest. To treat the chaotic financial system numerically, we use the generalized version of modified Bessel polynomials (GMBPs) in the collocation matrix approaches along with the domain-splitting strategy. Whereas the first matrix collocation scheme is directly applied to the financial model problem, the second one is a combination of the quasilinearization method and the direct first numerical matrix method. In the former approach, we arrive at nonlinear algebraic matrix equations while the resulting systems are linear in the latter method and can be solved more efficiently. A convergence theorem related to GMBPs is proved and an upper bound for the error is derived. Several simulation outcomes are provided to show the utility and applicability of the presented matrix collocation procedures.
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Khanduzi, Raheleh, Asyieh Ebrahimzadeh, and Samaneh Panjeh Ali Beik. "Optimal control of fractional integro-differential systems based on a spectral method and grey wolf optimizer." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 10, no. 1 (January 14, 2020): 55–65. http://dx.doi.org/10.11121/ijocta.01.2020.00753.
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This paper elaborated an effective and robust metaheuristic algorithm with acceptable performance based on solution accuracy. The algorithm applied in solution of the optimal control of fractional Volterra integro-differential (FVID) equation which be substituted by nonlinear programming (NLP). Subsequently the FIVD convert the problem to a NLP by using spectral collocation techniques and thereafter we execute the grey wolf optimizer (GWO) to improve the speed and accuracy and find the solutions of the optimal control and state as well as the optimal value of the cost function. It is mentioned that the utilization of the GWO is simple, due to the fact that the GWO is global search algorithm, the method can be applied to find optimal solution of the NLP. The efficiency of the proposed scheme is shown by the results obtained in comparison with the local methods. Further, some illustrative examples introduced with their approximate solutions and the results of the present approach compared with those achieved using other methods.
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Khader, M. M., and Mohammed M. Babatin. "On Approximate Solutions for Fractional Logistic Differential Equation." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/391901.
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A new approximate formula of the fractional derivatives is derived. The proposed formula is based on the generalized Laguerre polynomials. Global approximations to functions defined on a semi-infinite interval are constructed. The fractional derivatives are presented in terms of Caputo sense. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. The new spectral Laguerre collocation method is presented for solving fractional Logistic differential equation (FLDE). The properties of Laguerre polynomials approximation are used to reduce FLDE to solve a system of algebraic equations which is solved using a suitable numerical method. Numerical results are provided to confirm the theoretical results and the efficiency of the proposed method.
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Ibrahim, Yasser F., Sobhi E. Abd El-Bar, Mohamed M. Khader, and Mohamed Adel. "Studying and Simulating the Fractional COVID-19 Model Using an Efficient Spectral Collocation Approach." Fractal and Fractional 7, no. 4 (April 2, 2023): 307. http://dx.doi.org/10.3390/fractalfract7040307.
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We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). Initially, a rough approximation formula was created for the fractional derivative of tp. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a restricted optimization problem. To evaluate the effectiveness and accuracy of the suggested scheme, the residual error function was computed. The objective of this research was to halt the global spread of a disease. A susceptible person may be moved immediately into the confined class after being initially quarantined or an exposed person may be transferred to one of the infected classes. The researchers adopted this strategy and considered both asymptomatic and symptomatic infected patients. Results acquired with the achieved results were contrasted with those obtained using the generalized Runge-Kutta method.
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CHAKRABORTY, DEBANANDA, JAE-HUN JUNG, and GAURAV KHANNA. "A MULTI-DOMAIN HYBRID METHOD FOR HEAD-ON COLLISION OF BLACK HOLES IN PARTICLE LIMIT." International Journal of Modern Physics C 22, no. 05 (May 2011): 517–41. http://dx.doi.org/10.1142/s0129183111016415.
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A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method. The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-domain method composed of the spectral domain only does not yield the proper power-law decay unless the range of the computational domain is large. The finite-difference domain helps reduce boundary effects due to the truncation of the computational domain. The multi-domain approach with the finite-difference boundary domain method reduces the computational cost significantly and also yields the proper power-law decay. Stable and accurate interface conditions between the finite-difference and spectral domains and the spectral and spectral domains are derived. For the singular source term, we use both the Gaussian model with various values of full width at half-maximum and a localized discrete δ-function. The discrete δ-function was generalized to adopt the Gauss–Lobatto collocation points of the spectral domain. The gravitational waveforms are measured. Numerical results show that the developed hybrid method accurately yields the quasi-normal modes and the power-law decay profile. The numerical results also show that the power-law decay profile is less sensitive to the shape of the regularized δ-function for the Gaussian model than expected. The Gaussian model also yields better results than the localized discrete δ-function.
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Sánchez, José L. Carrión, Sílvio R. C. de Freitas, and Riccardo Barzaghi. "OFFSET EVALUATION OF THE ECUADORIAN VERTICAL DATUM RELATED TO THE IHRS." Boletim de Ciências Geodésicas 24, no. 4 (December 2018): 503–25. http://dx.doi.org/10.1590/s1982-21702018000400031.
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Abstract Considering the definition of the International Height Reference System (IHRS) in the geopotential space (Resolution 1/2015, International Association of Geodesy - IAG), among the present main objectives of the international geodetic community is the materialization of IHRS around the world. One fundamental task for this is the offset determination of each national vertical datum related to the IHRS. In this manuscript we establish the relationship between the Ecuadorian Vertical Datum (EVD) and the IHRS in the geopotential space following the foundations of the Resolution 1/2015 IAG. Gravity data, heights from the Ecuadorian Fundamental Vertical Network, Global Geopotential Models and Digital Elevation Models were used in the computations. Based on the Least Squares Collocation method, empirical covariance functions and spectral decomposition techniques, we realized the modelling of the geopotential in the study region (4° x 4° centered in the La Libertad tide gauge, Ecuador). Based on the referred approaches, we solved the free Geodetic Boundary Value Problem for determining the discrepancy of the EVD related to the IHRS. An offset of approximately 29 cm ± 3 cm was estimated for the W 0 - W 0 i relation when the GO_CONS_GCF_2_DIR_R5 model was used in the modeling of the medium and long wavelengths of the terrestrial gravity field, and approximately 43 cm ± 3 cm when the EIGEN6C4 model was used.
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Kim, Chang Ho, and U. Jin Choi. "Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 39, no. 3 (January 1998): 408–30. http://dx.doi.org/10.1017/s0334270000009474.
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AbstractWe propose and analyze the spectral collocation approximation for the partial integro-differential equations with a weakly singular kernel. The space discretization is based on the pseudo-spectral method, which is a collocation method at the Gauss-Lobatto quadrature points. We prove unconditional stability and obtain the optimal error bounds which depend on the time step, the degree of polynomial and the Sobolev regularity of the solution.
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Lovetskiy, Konstantin P., Dmitry S. Kulyabov, and Ali Weddeye Hissein. "Multistage pseudo-spectral method (method of collocations) for the approximate solution of an ordinary differential equation of the first order." Discrete and Continuous Models and Applied Computational Science 30, no. 2 (May 3, 2022): 127–38. http://dx.doi.org/10.22363/2658-4670-2022-30-2-127-138.
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The classical pseudospectral collocation method based on the expansion of the solution in a basis of Chebyshev polynomials is considered. A new approach to constructing systems of linear algebraic equations for solving ordinary differential equations with variable coefficients and with initial (and/or boundary) conditions makes possible a significant simplification of the structure of matrices, reducing it to a diagonal form. The solution of the system is reduced to multiplying the matrix of values of the Chebyshev polynomials on the selected collocation grid by the vector of values of the function describing the given derivative at the collocation points. The subsequent multiplication of the obtained vector by the two-diagonal spectral matrix, inverse with respect to the Chebyshev differentiation matrix, yields all the expansion coefficients of the sought solution except for the first one. This first coefficient is determined at the second stage based on a given initial (and/or boundary) condition. The novelty of the approach is to first select a class (set) of functions that satisfy the differential equation, using a stable and computationally simple method of interpolation (collocation) of the derivative of the future solution. Then the coefficients (except for the first one) of the expansion of the future solution are determined in terms of the calculated expansion coefficients of the derivative using the integration matrix. Finally, from this set of solutions only those that correspond to the given initial conditions are selected.
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SEO, JEONG-KWEON, and BYEONG-CHUN SHIN. "NUMERICAL SOLUTIONS OF BURGERS EQUATION BY REDUCED-ORDER MODELING BASED ON PSEUDO-SPECTRAL COLLOCATION METHOD." Journal of the Korea Society for Industrial and Applied Mathematics 19, no. 2 (June 25, 2015): 123–35. http://dx.doi.org/10.12941/jksiam.2015.19.123.
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Bhrawy, A. H., M. A. Alghamdi, and D. Baleanu. "Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/513808.
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The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit and explicit forms of NFDEs to demonstrate the computation accuracy of the proposed method. We also compare the performance of the method with variational iteration method, one-legθ-method, continuous Runge-Kutta method, and reproducing kernel Hilbert space method.
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Bhrawy, A. H., and M. A. Alghamdi. "A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/306746.
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We extend the application of the Galerkin method for treating the multiterm fractional differential equations (FDEs) subject to initial conditions. A new shifted Legendre-Galerkin basis is constructed which satisfies exactly the homogeneous initial conditions by expanding the unknown variable using a new polynomial basis of functions which is built upon the shifted Legendre polynomials. A new spectral collocation approximation based on the Gauss-Lobatto quadrature nodes of shifted Legendre polynomials is investigated for solving the nonlinear multiterm FDEs. The main advantage of this approximation is that the solution is expanding by a truncated series of Legendre-Galerkin basis functions. Illustrative examples are presented to ensure the high accuracy and effectiveness of the proposed algorithms are discussed.
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Wang, Xiao, Juan Wang, Xin Wang, and Chujun Yu. "A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations." Mathematics 10, no. 3 (January 19, 2022): 296. http://dx.doi.org/10.3390/math10030296.
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Inhomogeneous elliptical inclusions with partial differential equations have aroused appreciable concern in many disciplines. In this paper, a pseudo-spectral collocation method, based on Fourier basis functions, is proposed for the numerical solutions of two- (2D) and three-dimensional (3D) inhomogeneous elliptic boundary value problems. We describe how one can improve the numerical accuracy by making some extra “reconstruction techniques” before applying the traditional Fourier series approximation. After the particular solutions have been obtained, the resulting homogeneous equation can then be calculated using various boundary-type methods, such as the method of fundamental solutions (MFS). Using Fourier basis functions, one does not need to use large matrices, making accrual computations relatively fast. Three benchmark numerical examples involving Poisson, Helmholtz, and modified-Helmholtz equations are presented to illustrate the applicability and accuracy of the proposed method.
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Zajkani, Asghar, Abolfazl Darvizeh, and Mansour Darvizeh. "Analytical modelling of high-rate elasto-viscoplastic deformation of circular plates subjected to impulsive loads using pseudo-spectral collocation method." Journal of Strain Analysis for Engineering Design 48, no. 2 (October 29, 2012): 126–49. http://dx.doi.org/10.1177/0309324712460359.
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An analytical methodology is developed to study dynamic elasto-viscoplastic behaviour of moderately thick circular plates subjected to high-intensity impulsive loads, comprehensively. First, incremental kinematic formulations are derived based on the first-order shear deformation theory to take into account viscous damping and rotary inertia. Geometrical and material non-linearities are applied by the complete von Kármán system and a mixed strain hardening law coupled with a physically based viscoplastic model, respectively. A semi-implicit scheme of return-mapping is employed by the cutting-plane algorithm to obtain effective plastic strains apart from satisfying the consistency condition. The subsequent part is devoted to the transformation of this boundary value problem into an initial value problem, to evaluate displacement fields. Spatial and temporal discretizations are carried out by the Chebyshev pseudo-spectral collocation method and Houbolt time-marching scheme, respectively. This transformation has been handled in the compact matrix forms to stabilize the solution and to make it more convenient. Influence of impulsive load and other parameters on plate deflections, effective strain and stress, temperature rise and stresses are considered. Ultimately, good accuracy is achieved through comparison between results and existing experimental data and finite element simulation from the literature. In addition, some challengeable aspects for the modelling are discussed.
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Wang, Jianing, Linhao Li, Yichen Liu, Jinyu Hu, Xiao Xiao, and Bo Liu. "AI-TFNet: Active Inference Transfer Convolutional Fusion Network for Hyperspectral Image Classification." Remote Sensing 15, no. 5 (February 26, 2023): 1292. http://dx.doi.org/10.3390/rs15051292.
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The realization of efficient classification with limited labeled samples is a critical task in hyperspectral image classification (HSIC). Convolutional neural networks (CNNs) have achieved remarkable advances while considering spectral–spatial features simultaneously, while conventional patch-wise-based CNNs usually lead to redundant computations. Therefore, in this paper, we established a novel active inference transfer convolutional fusion network (AI-TFNet) for HSI classification. First, in order to reveal and merge the local low-level and global high-level spectral–spatial contextual features at different stages of extraction, an end-to-end fully hybrid multi-stage transfer fusion network (TFNet) was designed to improve classification performance and efficiency. Meanwhile, an active inference (AI) pseudo-label propagation algorithm for spatially homogeneous samples was constructed using the homogeneous pre-segmentation of the proposed TFNet. In addition, a confidence-augmented pseudo-label loss (CapLoss) was proposed in order to define the confidence of a pseudo-label with an adaptive threshold in homogeneous regions for acquiring pseudo-label samples; this can adaptively infer a pseudo-label by actively augmenting the homogeneous training samples based on their spatial homogeneity and spectral continuity. Experiments on three real HSI datasets proved that the proposed method had competitive performance and efficiency compared to several related state-of-the-art methods.
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Sengupta, Tapan K., Vajjala K. Suman, Prasannabalaji Sundaram, and Aditi Sengupta. "Analysis of Pseudo-spectral Methods Used for Numerical Simulations of Turbulence." WSEAS TRANSACTIONS ON COMPUTER RESEARCH 10 (January 19, 2022): 9–24. http://dx.doi.org/10.37394/232018.2022.10.2.
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Events in turbulent flows computed by direct numerical simulation (DNS) are often calibrated with properties based on homogeneous isotropic turbulence, advanced by Kolmogorov, and given in Turbulence, U. Frisch, Cambridge Univ. Press, UK (1995). However, these computational procedures are not calibrated using numerical analyses in order to assess their strengths and weaknesses for DNS. This is with the exception in "A critical assessment of simulations for transitional and turbulence flows- Sengupta, T.K., In Proc. of IUTAM Symp. on Advances in Computation, Modeling and Control of Transitional and Turbulent Flows, 491-532, (eds. Sengupta, Lele, Sreenivasan, Davidson), WSPC, Singapore (2016)", where such a calibration has been advocated for numerical schemes using global spectral analysis (GSA) for the convection equation. In recent times, due to growing computing power, simulations have been reported using pseudo-spectral methods, with spatial discretization performed in Fourier spectral space and time-integration by multi-stage Runge-Kutta (RK) methods. Here, we perform GSA of Fourier spectral methods for the first time with RK2 and other multistage Runge-Kutta methods using the model linear convection and convection-diffusion equations. With the help of GSA, various sources of numerical errors are quantified. The major limitations of the RK2-Fourier spectral method are demonstrated for DNS and alternate choices are presented. We specify optimal parameters to achieve the best possible accuracy for simulations. There is a one-to-one correspondence of numerical solutions obtained by linear convection-diffusion equation and nonlinear Navier-Stokes equation with respect to numerical parameters. This enables us to investigate the capabilities of the numerical methods for DNS.
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Gil, Jorge, Juan Fernando Rodrigo, Pablo Salvador, Diego Gómez, Julia Sanz, and Jose Luis Casanova. "An Empirical Radiometric Intercomparison Methodology Based on Global Simultaneous Nadir Overpasses Applied to Landsat 8 and Sentinel-2." Remote Sensing 12, no. 17 (August 24, 2020): 2736. http://dx.doi.org/10.3390/rs12172736.
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The Simultaneous Nadir Overpass (SNO) method was developed by the NOAA/NESDIS to improve the consistency and quality of climate data acquired by different meteorological satellites. Taking advantage of the reduced impact induced by the Bidirectional Reflectance Distribution Function (BRDF), atmospheric effects, illumination and viewing geometries during an SNO, we created a sensor comparison methodology for all spectral targets. The method is illustrated by applying it to the assessment of data acquired by the Landsat 8 (L8), Sentinel-2A (S2A), and Sentinel-2B (S2B) optical sensors. Multiple SNOs were identified and selected without the need for orbit propagators. Then, by locating spatially homogeneous areas, it was possible to assess, for a wide range of Top-of-Atmosphere reflectance values, the relationship between the L8 bands and the corresponding ones of S2A and S2B. The results yield high coefficients of determination for S2 A/B with respect to L8. All are higher than 0.980 for S2A and 0.984 for S2B. If the S2 band 8 (wide near-infrared, NIR) is excluded then the lowest coefficients of determination become 0.997 and 0.999 from S2A and S2B, respectively. This methodology can be complementary to those based on Pseudo-Invariant Calibration Sites (PICS) due to its simplicity, highly correlated results and the wide range of compared reflectances and spectral targets.
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DE STEFANO, G., and O. V. VASILYEV. "Stochastic coherent adaptive large eddy simulation of forced isotropic turbulence." Journal of Fluid Mechanics 646 (March 8, 2010): 453–70. http://dx.doi.org/10.1017/s002211200999303x.
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The stochastic coherent adaptive large eddy simulation (SCALES) methodology is a novel approach to the numerical simulation of turbulence, where a dynamic grid adaptation strategy based on wavelet threshold filtering is utilized to solve for the most ‘energetic’ eddies. The effect of the less energetic unresolved motions is simulated by a model. Previous studies have demonstrated excellent predictive properties of the SCALES approach for decaying homogeneous turbulence. In this paper the applicability of the method is further explored for statistically steady turbulent flows by considering linearly forced homogeneous turbulence at moderate Reynolds number. A local dynamic subgrid-scale eddy viscosity model based on the definition of the kinetic energy associated with the unresolved motions is used as closure model. The governing equations for the wavelet filtered velocity field, along with the additional evolution equation for the subgrid-scale kinetic energy, are numerically solved by means of a dynamically adaptive wavelet collocation method. It is demonstrated that adaptive simulations closely match results from a reference pseudo-spectral fully de-aliased direct numerical simulation, by using only about 1% of the corresponding computational nodes. In contrast to classical non-adaptive large eddy simulation, the agreement with direct solution holds for the mean flow statistics as well as in terms of energy and enstrophy spectra up to the dissipative wavenumbers range.
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Zhang, Jun, Hao Wu, and Shu Peng. "A KNOWLEDGE-BASED APPROACH ON GLOBELAND30 INCREMENTAL UPDATING: A CASE STUDY OF BUILT-UP AREA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B8 (June 24, 2016): 1335–39. http://dx.doi.org/10.5194/isprs-archives-xli-b8-1335-2016.
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Global land cover/land use product in multiple periods is pivotal to understand the complex drivers and mechanisms in global climate change, and to forecast future land use trends in sustainable development. GlobeLand30, as the world’s first high spatial resolution land cover product (83% accuracy), needs to be continually updated to meet various needs. However, many challenges - such as removing pseudo change to keep consistency of updating - remain unsolved. To deal with high temporal and spatial variability happened within built-up area class and between it and other classes, this paper presents an alternative approach that exploits domain knowledge and object-based change detection technique. The central premise of the approach is that one-class segmentation is first proceeded on both former image and current image. Then, segments of former image are labeled by using corresponding Globeland30 product. Segments of built-up area in current image are finally recognized through correlation which is established based on domain knowledge. Knowledge used in this study mainly includes area index, shape index, perimeter index, spectral similarity, 'from to' types and spatial relation. The proposed method and classification method were tested for their ability for built-up area updating in Shandong area. Results showed that the proposed method proved particularly effective for maintaining consistency of unchanged areas from former product to current one, and more than 80% changes could be identified correctly. The proposed method also provided a practical way for an economic and accurate updating of Globeland30 product.
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Zhang, Jun, Hao Wu, and Shu Peng. "A KNOWLEDGE-BASED APPROACH ON GLOBELAND30 INCREMENTAL UPDATING: A CASE STUDY OF BUILT-UP AREA." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B8 (June 24, 2016): 1335–39. http://dx.doi.org/10.5194/isprsarchives-xli-b8-1335-2016.
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Global land cover/land use product in multiple periods is pivotal to understand the complex drivers and mechanisms in global climate change, and to forecast future land use trends in sustainable development. GlobeLand30, as the world’s first high spatial resolution land cover product (83% accuracy), needs to be continually updated to meet various needs. However, many challenges - such as removing pseudo change to keep consistency of updating - remain unsolved. To deal with high temporal and spatial variability happened within built-up area class and between it and other classes, this paper presents an alternative approach that exploits domain knowledge and object-based change detection technique. The central premise of the approach is that one-class segmentation is first proceeded on both former image and current image. Then, segments of former image are labeled by using corresponding Globeland30 product. Segments of built-up area in current image are finally recognized through correlation which is established based on domain knowledge. Knowledge used in this study mainly includes area index, shape index, perimeter index, spectral similarity, 'from to' types and spatial relation. The proposed method and classification method were tested for their ability for built-up area updating in Shandong area. Results showed that the proposed method proved particularly effective for maintaining consistency of unchanged areas from former product to current one, and more than 80% changes could be identified correctly. The proposed method also provided a practical way for an economic and accurate updating of Globeland30 product.
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Ducasse, Etienne, Karine Adeline, Xavier Briottet, Audrey Hohmann, Anne Bourguignon, and Gilles Grandjean. "Montmorillonite Estimation in Clay–Quartz–Calcite Samples from Laboratory SWIR Imaging Spectroscopy: A Comparative Study of Spectral Preprocessings and Unmixing Methods." Remote Sensing 12, no. 11 (May 27, 2020): 1723. http://dx.doi.org/10.3390/rs12111723.
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Clay minerals play an important role in shrinking–swelling of soils and off–road vehicle mobility mainly due to the presence of smectites including montmorillonites. Since soils are composed of different minerals intimately mixed, an accurate estimation of its abundance is challenging. Imaging spectroscopy in the short wave infrared spectral region (SWIR) combined with unmixing methods is a good candidate to estimate clay mineral abundance. However, the performance of unmixing methods is mineral-dependent and may be enhanced by using appropriate spectral preprocessings. The objective of this paper is to carry out a comparative study in order to determine the best couple spectral preprocessing/unmixing method to quantify montmorillonite in intimate mixtures with clays, such as montmorillonite, kaolinite and illite, and no-clay minerals, such as calcite and quartz. To this end, a spectral database is built with laboratory hyperspectral imagery from 51 dry pure mineral samples and intimate mineral mixtures of controlled abundances. Six spectral preprocessings, standard normal variate (SNV), continuum removal (CR), continuous wavelet transform (CWT), Hapke model, first derivative (1st SGD) and pseudo–absorbance (Log(1/R)), are applied and compared with reflectance spectra. Two linear unmixing methods, fully constrained least square method (FCLS) and multiple endmember spectral mixture analysis (MESMA), and two non-linear unmixing methods, generalized bilinear method (GBM) and multi-linear model (MLM), are compared. Global results showed that the benefit of spectral preprocessings occurs when spectral absorption features of minerals overlap for SNV, CR, CWT and 1st SGD, whereas the use of reflectance spectra performs the best when no overlap is present. With one mineral having no spectral feature (quartz), montmorillonite abundance estimation is difficult and gives RMSE higher than 50%. For the other mixtures, performances of linear and non-linear unmixing methods are similar. Consequently, the recommended couple spectral preprocessing/unmixing method based on the trade-off between its simplicity and performance is 1st SGD/FCLS for clay binary and ternary mixtures (RMSE of 9.2% for montmorillonite–illite mixtures, 13.9% for montmorillonite–kaolinite mixtures and 10.8% for montmorillonite–illite–kaolinite mixtures) and reflectance/FCLS for binary mixtures with calcite (RMSE of 8.8% for montmorillonite–calcite mixtures). These performances open the way to improve the classification of expansive soils.
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Fesenko, O. D., R. O. Bieliakov, H. D. Radzivilov, S. A. Sasin, O. V. Borysov, I. V. Borysov, T. M. Derkach, and O. O. Kovalchuk. "METHOD OF IMPROVING THE ACCURACY OF NAVIGATION MEMS DATA PROCESSING OF UAV INERTIAL NAVIGATION SYSTEM." Radio Electronics, Computer Science, Control, no. 3 (October 18, 2022): 196. http://dx.doi.org/10.15588/1607-3274-2022-3-18.
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Context. Modern theory and practice of preparation and conduct of hostilities on land, at sea, in the air, and recently in cyberspace dictates the relentless modernization of military equipment. The development of fundamentally new weapons is carried out considering one of the main requirements – maximum automation of operational processes, which allows combatants to distance themselves from each other as much as possible.
Among the newest models of armaments on the battlefield, due to the predominantly positional nature of the armed confrontation, unmanned aerial vehicles (UAVs) have become virtually indispensable due to their own multitasking. One of the ways to increase the efficiency of UAVs on the battlefield is to increase the level of technical perfection of flight control systems.
Creating new approaches to the design of unmanned aerial vehicle navigation systems, in particular, based on a platformless inertial navigation system is an urgent task that will provide automatic control of the UAV flight route in the absence of corrective signals from the global satellite navigation system.
Objective. The purpose of this work is to develop a method for improving the accuracy of MEMC navigation data processing of an inertial navigation system of an unmanned aerial vehicle based on an advanced Madgwik filter.
This method will increase the speed of data processing of navigation parameters and the accuracy of determining the positioning parameters in the space of the UAV through the use of an advanced Madgwik filter.
The paper shows the developed block diagram of MEMS PINS filtration on the basis of the improved Madgwik filter, the detailed mathematical description of filtration processes is carried out.
This method was tested experimentally in the MATLAB software environment using a real set of data collected during the flight of the UAV.
Method. To achieve this goal, the following methods were used: intelligent systems, theory of automatic control, pseudo-spectral method; methods based on genetic algorithm and fuzzy neural network apparatus.
Results. A method for improving the accuracy of MEMC navigation data processing of an inertial navigation system of an unmanned aerial vehicle based on an advanced Madgwik filter has been developed. The possibility of practical application of the obtained results and in comparison, with traditional methods is investigated. An experiment was performed in the MatLab software environment, and a comparison was made with the method of processing navigation data based on the Madgwik filter and the Kalman filter.
Conclusions. The developed method of increasing the accuracy of MEMC navigation data processing of an inertial navigation system of an unmanned aerial vehicle based on an advanced Madgwik filter shows an advantage over known methods in the absence of corrective signals from the global satellite navigation system for accuracy and speed of navigation data processing.
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Yu, Qixin, and Dieter Horns. "Searching for photon-ALPs mixing effects in AGN gamma-ray energy spectra." Journal of Cosmology and Astroparticle Physics 2023, no. 05 (May 1, 2023): 029. http://dx.doi.org/10.1088/1475-7516/2023/05/029.
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Abstract High energy gamma-rays propagating in external magnetic fields may convert into axion-like particles (ALPs). In this case, the observed gamma-ray spectra are modified by the resulting energy-dependent conversion probability. In this study, we use the energy spectra of 20 extra-galactic gamma-ray sources recorded during 10 years of Fermi-LAT observations. We define a test statistics based upon the likelihood ratio to test the hypothesis for a spectral model without vs. a model with photon-ALPs coupling. The conversion probability is calculated for fixed values of the mass and two-photon coupling of the pseudo-scalar particle while the external magnetic field is characterized by the additional free parameters length scale s and average field strength B. As a consistency check and in order to extend the analysis to include very high energy gamma-ray data, another test statistics is defined with the χ2 method. We find for 18 of the 20 sources a favorable fit, particularly for Markarian 421 and NGC 1275 a significant improvement, with the hypothesis of photon-ALPs coupling in likelihood analysis. The test statistics of the sources are combined and the significance has been estimated 5.3σ (test statistics summed in local maxima of all sources) and 6.0σ (global maxima). The significance is estimated from dedicated simulations under the null hypotheses. The locally best-fitting values of B and s fall into the range that is expected for large scale magnetic fields present in relevant astrophysical environments.
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Tabata, Tasuku, Viju O. John, Rob A. Roebeling, Tim Hewison, and Jörg Schulz. "Recalibration of over 35 Years of Infrared and Water Vapor Channel Radiances of the JMA Geostationary Satellites." Remote Sensing 11, no. 10 (May 18, 2019): 1189. http://dx.doi.org/10.3390/rs11101189.
Full textAbstract:
Infrared sounding measurements of the Infrared Atmospheric Sounding Interferometer (IASI), Atmospheric Infrared Sounder (AIRS), and High-resolution Infrared Radiation Sounder/2 (HIRS/2) instruments are used to recalibrate infrared (IR; ~11 µm) channels and water vapor (WV; ~6 µm) channels of the Visible and Infrared Spin Scan Radiometer (VISSR), Japanese Advanced Meteorological Imager (JAMI), and IMAGER instruments onboard the historical geostationary satellites of the Japan Meteorological Agency (JMA). The recalibration was performed using a common recalibration method developed by European Organization for the Exploitation of Meteorological Satellites (EUMETSAT), which can be applied to the historical geostationary satellites to produce Fundamental Climate Data Records (FCDR). Pseudo geostationary imager radiances were computed from the infrared sounding measurements and regressed against the radiances from the geostationary satellites. Recalibration factors were computed from these pseudo imager radiance pairs. This paper presents and evaluates the result of recalibration of longtime-series of IR (1978–2016) and WV (1995–2016) measurements from JMA’s historical geostationary satellites. For the IR data of the earlier satellites (Geostationary Metrological Satellite (GMS) to GMS-4) significant seasonal variations in radiometric biases were observed. This suggests that the sensors on GMS to GMS-4 were strongly affected by seasonal variations in solar illumination. The amplitudes of these seasonal variations range from 3 K for the earlier satellites to <0.4 K for the recent satellites (GMS-5, Geostationary Operational Environmental Satellite-9 (GOES-9), Multi-functional Transport Satellite-1R (MTSAT-1R) and MTSAT-2). For the WV data of GOES-9, MTSAT-1R and MTSAT-2, no seasonal variations in radiometric biases were observed. However, for GMS-5, the amplitude of seasonal variation in bias was about 0.5 K. Overall, the magnitude of the biases for GMS-5, MTSAT-1R and MTSAT-2 were smaller than 0.3 K. Finally, our analysis confirms the existence of errors due to atmospheric absorption contamination in the operational Spectral Response Function (SRF) of the WV channel of GMS-5. The method used in this study is based on the principles developed within Global Space-based Inter-calibration System (GSICS). Moreover, presented results contribute to the Inter-calibration of imager observations from time-series of geostationary satellites (IOGEO) project under the umbrella of the World Meteorological Organization (WMO) initiative Sustained and Coordinated Processing of Environmental Satellite data for Climate Monitoring (SCOPE-CM).
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Cortesi, U., J. C. Lambert, C. De Clercq, G. Bianchini, T. Blumenstock, A. Bracher, E. Castelli, et al. "Geophysical validation of MIPAS-ENVISAT operational ozone data." Atmospheric Chemistry and Physics Discussions 7, no. 3 (May 7, 2007): 5805–939. http://dx.doi.org/10.5194/acpd-7-5805-2007.
Full textAbstract:
Abstract. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), on-board the European ENVIronmental SATellite (ENVISAT) launched on 1 March 2002, is a middle infrared Fourier Transform spectrometer measuring the atmospheric emission spectrum in limb sounding geometry. The instrument is capable to retrieve the vertical distribution of temperature and trace gases, aiming at the study of climate and atmospheric chemistry and dynamics, and at applications to data assimilation and weather forecasting. MIPAS operated in its standard observation mode for approximately two years, from July 2002 to March 2004, with scans performed at nominal spectral resolution of 0.025 cm−1 and covering the altitude range from the mesosphere to the upper troposphere with relatively high vertical resolution (about 3 km in the stratosphere). Only reduced spectral resolution measurements have been performed subsequently. MIPAS data were re-processed by ESA using updated versions of the Instrument Processing Facility (IPF v4.61 and v4.62) and provided a complete set of level-2 operational products (geo-located vertical profiles of temperature and volume mixing ratio of H2O,O3, HNO3, CH4, N2O and NO2) with quasi continuous and global coverage in the period of MIPAS full spectral resolution mission. In this paper, we report a detailed description of the validation of MIPAS-ENVISAT operational ozone data, that was based on the comparison between MIPAS v4.61 (and, to a lesser extent, v4.62) O3 VMR profiles and a comprehensive set of correlative data, including observations from ozone sondes,ground-based lidar, FTIR and microwave radiometers, remote-sensing and in situ instruments on-board stratospheric aircraft and balloons, concurrent satellite sensors and ozone fields assimilated by the European Center for Medium-range Weather Forecasting. A coordinated effort was carried out, using common criteria for the selection of individual validation data sets, and similar methods for the comparisons. This enabled merging the individual results from a variety of independent reference measurements of proven quality (i.e., well characterised error budget) into an overall evaluation of MIPAS O3 data quality, having both statistical strength and the widest spatial and temporal coverage. Collocated measurements from ozone sondes and ground-based lidar and microwave radiometers of the Network for Detection Atmospheric Composition Change (NDACC) were selected to carry out comparisons with time series of MIPAS O3 partial columns and to identify groups of stations and time periods with a uniform pattern of ozone differences, that were subsequently used for a vertically resolved statistical analysis. The results of the comparison are classified according to synoptic and regional systems and to altitude intervals, showing a generally good agreement within the comparison error bars in the upper and middle stratosphere. Significant differences emerge in the lower stratosphere and are only partly explained by the larger contributions of horizontal and vertical smoothing differences and of collocation errors to the total uncertainty. Further results obtained from a purely statistical analysis of the same data set from NDACC ground-based lidar stations, as well as from additional ozone soundings at middle latitudes and from NDACC ground-based FTIR measurements, confirm the validity of MIPAS O3 profiles down to the lower stratosphere, with evidence of larger discrepancies at the lowest altitudes. The validation against O3 VMR profiles using collocated observations performed by other satellite sensors (SAGE II, POAM III, ODIN-SMR, ACE-FTS, HALOE, GOME) and ECMWF assimilated ozone fields leads to consistent results, that are to a great extent compatible with those obtained from the comparison with ground-based measurements. Excellent agreement in the full vertical range of the comparison is shown with respect to collocated ozone data from stratospheric aircraft and balloon instruments, that was mostly obtained in very good spatial and temporal coincidence with MIPAS scans. This might suggest that the larger differences observed in the upper troposphere and lowermost stratosphere with respect to collocated ground-based and satellite O3 data are only partly due to a degradation of MIPAS data quality. They should be rather largely ascribed to the natural variability of these altitude regions and to other components of the comparison errors. By combining the results of this large number of validation data sets we derived a general assessment of MIPAS v4.61 and v4.62 ozone data quality. A clear indication of the validity of MIPAS O3 vertical profiles is obtained for most of the stratosphere, where the mean relative difference with the individual correlative data sets is always lower than 10%. Furthermore, these differences always fall within the combined systematic error (from 1 hPa to 50 hPa) and the standard deviation is fully consistent with the random error of the comparison (from 1 hPa to ~30–40 hPa). A degradation in the quality of the agreement is generally observed in the lower stratosphere and upper troposphere, with biases up to 25% at 100 hPa and standard deviation of the global mean differences up to three times larger than the combined random error in the range 50–100 hPa. The larger differences observed at the bottom end of MIPAS retrieved profiles can be associated, as already noticed, to the effects of stronger atmospheric gradients in the UTLS that are perceived differently by the various measurement techniques. However, further components that may degrade the results of the comparison at lower altitudes can be identified as potentially including cloud contamination, which is likely not to have been fully filtered using the current settings of the MIPAS cloud detection algorithm, and in the linear approximation of the forward model that was used for the climatological estimate of systematic error components. The latter, when affecting systematic contributions with a random variability over the spatial and temporal scales of global averages, might result in an underestimation of the random error of the comparison and add up to other error sources, such as the possible underestimates of the p and T error propagation based on the assumption of a 1 K and 2% uncertainties, respectively, on MIPAS temperature and pressure retrievals. At pressure lower than 1 hPa, only a small fraction of the selected validation data set provides correlative ozone data of adequate quality and it is difficult to derive quantitative conclusions about the performance of MIPAS O3 retrieval for the topmost layers.
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Cortesi, U., J. C. Lambert, C. De Clercq, G. Bianchini, T. Blumenstock, A. Bracher, E. Castelli, et al. "Geophysical validation of MIPAS-ENVISAT operational ozone data." Atmospheric Chemistry and Physics 7, no. 18 (September 21, 2007): 4807–67. http://dx.doi.org/10.5194/acp-7-4807-2007.
Full textAbstract:
Abstract. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), on-board the European ENVIronmental SATellite (ENVISAT) launched on 1 March 2002, is a middle infrared Fourier Transform spectrometer measuring the atmospheric emission spectrum in limb sounding geometry. The instrument is capable to retrieve the vertical distribution of temperature and trace gases, aiming at the study of climate and atmospheric chemistry and dynamics, and at applications to data assimilation and weather forecasting. MIPAS operated in its standard observation mode for approximately two years, from July 2002 to March 2004, with scans performed at nominal spectral resolution of 0.025 cm−1 and covering the altitude range from the mesosphere to the upper troposphere with relatively high vertical resolution (about 3 km in the stratosphere). Only reduced spectral resolution measurements have been performed subsequently. MIPAS data were re-processed by ESA using updated versions of the Instrument Processing Facility (IPF v4.61 and v4.62) and provided a complete set of level-2 operational products (geo-located vertical profiles of temperature and volume mixing ratio of H2O, O3, HNO3, CH4, N2O and NO2) with quasi continuous and global coverage in the period of MIPAS full spectral resolution mission. In this paper, we report a detailed description of the validation of MIPAS-ENVISAT operational ozone data, that was based on the comparison between MIPAS v4.61 (and, to a lesser extent, v4.62) O3 VMR profiles and a comprehensive set of correlative data, including observations from ozone sondes, ground-based lidar, FTIR and microwave radiometers, remote-sensing and in situ instruments on-board stratospheric aircraft and balloons, concurrent satellite sensors and ozone fields assimilated by the European Center for Medium-range Weather Forecasting. A coordinated effort was carried out, using common criteria for the selection of individual validation data sets, and similar methods for the comparisons. This enabled merging the individual results from a variety of independent reference measurements of proven quality (i.e. well characterized error budget) into an overall evaluation of MIPAS O3 data quality, having both statistical strength and the widest spatial and temporal coverage. Collocated measurements from ozone sondes and ground-based lidar and microwave radiometers of the Network for the Detection Atmospheric Composition Change (NDACC) were selected to carry out comparisons with time series of MIPAS O3 partial columns and to identify groups of stations and time periods with a uniform pattern of ozone differences, that were subsequently used for a vertically resolved statistical analysis. The results of the comparison are classified according to synoptic and regional systems and to altitude intervals, showing a generally good agreement within the comparison error bars in the upper and middle stratosphere. Significant differences emerge in the lower stratosphere and are only partly explained by the larger contributions of horizontal and vertical smoothing differences and of collocation errors to the total uncertainty. Further results obtained from a purely statistical analysis of the same data set from NDACC ground-based lidar stations, as well as from additional ozone soundings at middle latitudes and from NDACC ground-based FTIR measurements, confirm the validity of MIPAS O3 profiles down to the lower stratosphere, with evidence of larger discrepancies at the lowest altitudes. The validation against O3 VMR profiles using collocated observations performed by other satellite sensors (SAGE II, POAM III, ODIN-SMR, ACE-FTS, HALOE, GOME) and ECMWF assimilated ozone fields leads to consistent results, that are to a great extent compatible with those obtained from the comparison with ground-based measurements. Excellent agreement in the full vertical range of the comparison is shown with respect to collocated ozone data from stratospheric aircraft and balloon instruments, that was mostly obtained in very good spatial and temporal coincidence with MIPAS scans. This might suggest that the larger differences observed in the upper troposphere and lowermost stratosphere with respect to collocated ground-based and satellite O3 data are only partly due to a degradation of MIPAS data quality. They should be rather largely ascribed to the natural variability of these altitude regions and to other components of the comparison errors. By combining the results of this large number of validation data sets we derived a general assessment of MIPAS v4.61 and v4.62 ozone data quality. A clear indication of the validity of MIPAS O3 vertical profiles is obtained for most of the stratosphere, where the mean relative difference with the individual correlative data sets is always lower than ±10%. Furthermore, these differences always fall within the combined systematic error (from 1 hPa to 50 hPa) and the standard deviation is fully consistent with the random error of the comparison (from 1 hPa to ~30–40 hPa). A degradation in the quality of the agreement is generally observed in the lower stratosphere and upper troposphere, with biases up to 25% at 100 hPa and standard deviation of the global mean differences up to three times larger than the combined random error in the range 50–100 hPa. The larger differences observed at the bottom end of MIPAS retrieved profiles can be associated, as already noticed, to the effects of stronger atmospheric gradients in the UTLS that are perceived differently by the various measurement techniques. However, further components that may degrade the results of the comparison at lower altitudes can be identified as potentially including cloud contamination, which is likely not to have been fully filtered using the current settings of the MIPAS cloud detection algorithm, and in the linear approximation of the forward model that was used for the a priori estimate of systematic error components. The latter, when affecting systematic contributions with a random variability over the spatial and temporal scales of global averages, might result in an underestimation of the random error of the comparison and add up to other error sources, such as the possible underestimates of the p and T error propagation based on the assumption of a 1 K and 2% uncertainties, respectively, on MIPAS temperature and pressure retrievals. At pressure lower than 1 hPa, only a small fraction of the selected validation data set provides correlative ozone data of adequate quality and it is difficult to derive quantitative conclusions about the performance of MIPAS O3 retrieval for the topmost layers.
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Han, Holly Kyeore, Natalya Gomez, and Jeannette Xiu Wen Wan. "Capturing the interactions between ice sheets, sea level and the solid Earth on a range of timescales: a new “time window” algorithm." Geoscientific Model Development 15, no. 3 (February 16, 2022): 1355–73. http://dx.doi.org/10.5194/gmd-15-1355-2022.
Full textAbstract:
Abstract. Retreat and advance of ice sheets perturb the gravitational field, solid surface and rotation of the Earth, leading to spatially variable sea-level changes over a range of timescales O(100−6 years), which in turn feed back onto ice-sheet dynamics. Coupled ice-sheet–sea-level models have been developed to capture the interactive processes between ice sheets, sea level and the solid Earth, but it is computationally challenging to capture short-term interactions O(100−2 years) precisely within longer O(103−6 years) simulations. The standard forward sea-level modelling algorithm assigns a uniform temporal resolution in the sea-level model, causing a quadratic increase in total CPU time with the total number of input ice history steps, which increases with either the length or temporal resolution of the simulation. In this study, we introduce a new “time window” algorithm for 1D pseudo-spectral sea-level models based on the normal mode method that enables users to define the temporal resolution at which the ice loading history is captured during different time intervals before the current simulation time. Utilizing the time window, we assign a fine temporal resolution O(100−2 years) for the period of ongoing and recent history of surface ice and ocean loading changes and a coarser temporal resolution O(103−6 years) for earlier periods in the simulation. This reduces the total CPU time and memory required per model time step while maintaining the precision of the model results. We explore the sensitivity of sea-level model results to the model temporal resolution and show how this sensitivity feeds back onto ice-sheet dynamics in coupled modelling. We apply the new algorithm to simulate sea-level changes in response to global ice-sheet evolution over two glacial cycles and the rapid collapse of marine sectors of the West Antarctic Ice Sheet in the coming centuries and provide appropriate time window profiles for each application. The time window algorithm reduces the total CPU time by ∼ 50 % in each of these examples and changes the trend of the total CPU time increase from quadratic to linear. This improvement would increase with longer simulations than those considered here. Our algorithm also allows for coupling time intervals of annual temporal scale for coupled ice-sheet–sea-level modelling of regions such as West Antarctica that are characterized by rapid solid Earth response to ice changes due to the thin lithosphere and low mantle viscosities.
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He, Chen, Dakun Sun, and Xiaofeng Sun. "Stall Inception Analysis of Transonic Compressors With Chordwise and Axial Sweep." Journal of Turbomachinery 140, no. 4 (February 21, 2018). http://dx.doi.org/10.1115/1.4038873.
Full textAbstract:
This paper concentrates on the stall inception analysis of transonic compressors with chordwise and axial sweep. A new prediction approach of stall inception is developed based on global stability analysis and immersed boundary theory, which makes it possible to take both the concrete blade geometry and the complicated base flow into consideration. The prediction of stall inception boils down to an eigenvalue problem. Spectral collocation method is adopted to discretize the eigenvalue equations and the eigenvalues are solved by using singular value decomposition method. The developed prediction approach is validated on two different typical transonic compressors, a single stage compressor and an isolated-rotor compressor, which shows a good agreement with the experimental data. The latter is adopted as a baseline rotor for the investigation of chordwise and axial sweep. By adjusting the stacking line of the baseline rotor, a series of swept rotors are modeled and the stall inception behavior of them is predicted by using the developed approach. The comparison of stall inception behaviors between these rotors is presented, and in combination with steady flow analyses, the effects of sweep features on the stall inception in transonic compressors are discussed.
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Herrada, M. A., S. Blanco-Trejo, J. Eggers, and P. S. Stewart. "Global stability analysis of flexible channel flow with a hyperelastic wall." Journal of Fluid Mechanics 934 (January 18, 2022). http://dx.doi.org/10.1017/jfm.2021.1131.
Full textAbstract:
We consider the stability of flux-driven flow through a long planar rigid channel, where a segment of one wall is replaced by a pre-tensioned hyperelastic (neo-Hookean) solid of finite thickness and subject to a uniform external pressure. We construct the steady configuration of the nonlinear system using Newton's method with spectral collocation and high-order finite differences. In agreement with previous studies, which use an asymptotically thin wall, we show that the thick-walled system always has at least one stable steady configuration, while for large Reynolds numbers the system exhibits three co-existing steady states for a range of external pressures. Two of these steady configurations are stable to non-oscillatory perturbations, one where the flexible wall is inflated (the upper branch) and one where the flexible wall is collapsed (the lower branch), connected by an unstable intermediate branch. We test the stability of these steady configurations to oscillatory perturbations using both a global eigensolver (constructed based on an analytical domain mapping technique) and also fully nonlinear simulations. We find that both the lower and upper branches of steady solutions can become unstable to self-excited oscillations, where the oscillating wall profile has two extrema. In the absence of wall inertia, increasing wall thickness partially stabilises the onset of oscillations, but the effect remains weak until the wall thickness becomes comparable to the width of the undeformed channel. However, with finite wall inertia and a relatively thick wall, higher-frequency modes of oscillation dominate the primary global instability for large Reynolds numbers.
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Abdelhakem, Mohamed, Doha Mahmoud, Dumitru Baleanu, and Mamdouh El-kady. "Shifted ultraspherical pseudo-Galerkin method for approximating the solutions of some types of ordinary fractional problems." Advances in Difference Equations 2021, no. 1 (February 17, 2021). http://dx.doi.org/10.1186/s13662-021-03247-6.
Full textAbstract:
AbstractIn this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods. Also, this method can be extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The spatial approximations with their derivatives are based on shifted ultraspherical polynomials (SUPs). Modified Galerkin spectral method has been used to create direct approximate solutions of linear/nonlinear ordinary fractional differential equations, a system of ordinary fraction differential equations, fractional integro-differential equations, or fractional optimal control problems. The aim is to transform those problems into a system of algebraic equations. That system will be efficiently solved by any solver. Three spaces of collocation nodes have been used through that transformation. Finally, numerical examples show the accuracy and efficiency of the investigated method.
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Wei, Yi, Xing-Qiu Zhang, Zhu-Yan Shao, Jian-Qiang Gao, and Xiao-Feng Yang. "Multi-symplectic integrator of the generalized KdV-type equation based on the variational principle." Scientific Reports 9, no. 1 (November 4, 2019). http://dx.doi.org/10.1038/s41598-019-52419-8.
Full textAbstract:
Abstract The variational principle is used to construct a multi-symplectic structure of the generalized KdV-type equation. Accordingly, the local energy conservation law, the local momentum conservation law, and the Cartan form of the generalized KdV-type equation are given. An explicit multi-symplectic scheme for the generalized KdV equation based on the Fourier pseudo-spectral method and the symplectic Euler scheme is constructed. Through a numerical examination, the explicit multi-symplectic Fourier pseudo-spectral scheme for the generalized KdV equation not only preserve the discrete global energy conservation law and the global momentum conservation law with high accuracy, but show long-time numerical stability as well.
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Sun, Yunhao, Zhengxing Dai, Gulou Shen, Xiaohua Lu, Xiang Ling, and Xiaoyan Ji. "Accelerate the Electrolyte Perturbed-Chain Statistical Associating Fluid Theory–Density Functional Theory Calculation With the Chebyshev Pseudo-Spectral Collocation Method. Part II. Spherical Geometry and Anderson Mixing." Frontiers in Chemistry 9 (January 24, 2022). http://dx.doi.org/10.3389/fchem.2021.801551.
Full textAbstract:
To improve the efficiency of electrolyte perturbed-chain statistical associating fluid theory–density functional theory (ePC-SAFT-DFT) calculation of the confined system, in this work, first, the Chebyshev pseudo-spectral collocation method was extended to the spherical pores. Second, it was combined with the Anderson mixing algorithm to accelerate the iterative process. The results show that the Anderson mixing algorithm can reduce the computation time significantly. Finally, based on the accelerated ePC-SAFT-DFT program, a systematic study of the effects of the temperature, pressure, pore size, and pore shape on the CO2 solubilities in the ionic liquids (ILs) confined inside the silica nanopores was conducted. Based on the simulation results, to obtain high CO2 solubilities in the ILs confined in silica, a better option is to use the silica material with a narrow spherical pore, and the IL-anion should be selected specifically considering that it has a more significant impact on the absorption enhancement effect.
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Gao, Haiyang, Xinglin Guo, Huajiang Ouyang, and Fang Han. "Crack Identification of Cantilever Plates Based on a Kriging Surrogate Model." Journal of Vibration and Acoustics 135, no. 5 (June 18, 2013). http://dx.doi.org/10.1115/1.4023813.
Full textAbstract:
This work presents an effective method to identify the tip locations of an internal crack in cantilever plates based on a Kriging surrogate model. Samples of varying crack parameters (tip locations) and their corresponding root mean square (RMS) of random responses are used to construct the initial Kriging surrogate model. Moreover, the pseudo excitation method (PEM) is employed to speed up the spectral analysis. For identifying crack parameters based on the constructed Kriging model, a robust stochastic particle swarm optimization (SPSO) algorithm is adopted for enhancing the global searching ability. To improve the accuracy of the surrogate model without using extensive samples, a small number of samples are first used. Then an optimal point-adding process is carried out to reduce computational cost. Numerical studies of a cantilever plate with an internal crack are performed. The effectiveness and efficiency of this method are demonstrated by the identified results. The effect of initial sampling size on the precision of the identified results is also investigated.
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M S, Basavaraj, and Shivaraj Kumar D L. "Optimal Transient Energy Growth Of 2D Perturbation In A Magnetohydrodynamic Plane Poiseuille Flow Of Casson Fluid." Journal of Fluids Engineering, August 5, 2023, 1–55. http://dx.doi.org/10.1115/1.4063117.
Full textAbstract:
Abstract The study investigates the influence of the Casson fluid parameter and the spanwise uniform magnetic field on the onset of instability against infinitesimal disturbances in an electrically conducting fluid flow between two parallel non-conducting rigid plates. The 4th-order linearized disturbance equation governing stability is solved using the spectral collocation method with Chebyshev-based polynomials. The aim is to analyze in detail the effect of the parameters involved in the problem using both modal and non-modal linear stability analysis. The modal analysis provides accurate values of the critical Reynolds number, critical wave number, and critical wave speed, denoted as critical triplets (αc, Rc, cc). Additionally, it examines the eigen-spectrum, growth rate curves, and neutral stability curves. On the other hand, the non-modal analysis investigates the transient energy growth G(t) of two-dimensional optimal perturbations, the pseudo-spectrum of the non-normal Orr-Sommerfeld (O-S) operator (L), and the regions of stability, instability, and potential instability of the fluid flow system. The extensive examination of both long-term behavior through modal analysis and short-term behavior through nonmodal analysis reveals that the Hartmann number acts as a stabilizing agent, delaying the onset of instability. Conversely, the Casson parameter acts as a destabilizing agent, advancing the onset of instability. The results obtained here are verified to be in good agreement with the existing literature in the absence of the Casson fluid flow parameter.
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Hosseinverdi, Shirzad, and Hermann F. Fasel. "High-Order-Accurate Incompressible Flow Solver for High-Fidelity Numerical Simulations and Linear Stability Analysis." AIAA Journal, February 1, 2023, 1–18. http://dx.doi.org/10.2514/1.j062110.
Full textAbstract:
The development of high-fidelity versatile incompressible Navier–Stokes solver that is applicable for both direct numerical simulations (DNSs) and linear global stability investigations is presented and discussed. The solver is based on a vorticity–velocity formulation of the Navier–Stokes equations for orthogonal curvilinear grids. A rigorous and efficient approach is proposed that guarantees the divergence-free condition for the velocity and vorticity fields. The code incorporates advanced numerical algorithms including compact finite differences in combination with a pseudo-spectral method, together with an efficient and high-order-accurate Poisson solver. Linear stability modules based on the linearized Navier–Stokes equations (LNSEs) tailored for primary and secondary instability analyses are developed and incorporated into the code, such that the solver can switch from DNS to LNSE in a consistent manner by turning off the nonlinear terms and vice versa. The linear framework includes all the nonparallel effects with respect to the steady/unsteady baseflow and the form of disturbances, and because it is formulated as an initial value problem, both convective and absolute/global instability mechanisms can be investigated. An additional significant advantage of the linear module is that, for the secondary stability analysis, time-periodic assumption is not required and/or the unsteady baseflow does not have to be computed a priori. In the present paper, results obtained with the new Navier–Stokes solver are compared with benchmark solutions for the flow past a static and oscillating circular cylinder. The new code then was employed for a three-dimensional DNS of the flow for a wing section with a modified NACA 6 series airfoil at a chord Reynolds number of [Formula: see text]. Furthermore, the capability of the linear stability modules was demonstrated by investigating the primary and secondary (convective and absolute) instability mechanisms for boundary layers and the flow past a circular cylinder.
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Li Xiang, Liu Yun, Zhu Tian-Xin, and Duan Chuan-Xi. "New rovibrational subbands of Ar-D<sub>2</sub>O complex in the D<sub>2</sub>O bending mode region." Acta Physica Sinica, 2023, 0. http://dx.doi.org/10.7498/aps.72.20221728.
Full textAbstract:
The intermolecular interactions involving the water molecule play important roles in many fields of physics, chemistry, and biology. High-resolution spectroscopy of Van der Waals complexes formed by a rare gas atom and a water molecule could provide a wealth of information on these intermolecular interactions. The precise experimental data can be used to test the accuracy and efficiency of various theoretical methods for constructing the intermolecular potential energy surfaces and calculating the bound states. In this work, the high-resolution infrared absorption spectrum of the Ar-D<sub>2</sub>O complex in the <em>v</em><sub>2</sub> bending region of D<sub>2</sub>O was measured using an external cavity quantum cascade laser. A segmented rapid-scan data acquisition method was employed. The Ar-D<sub>2</sub>O compex was generated in a slit supersonic jet expansion by passing Ar gas through a vessel containing liquid D<sub>2</sub>O. Four new rovibrational subbands are assigned in the spectral range of 1150-1190 cm<sup>-1</sup>, namely <img src="20221728_O_editing.files/image059.png" alt="" />，<img src="20221728_O_editing.files/image094.png" alt="" />，<img src="20221728_O_editing.files/image090.png" alt="" /> and <img src="20221728_O_editing.files/image091.png" alt="" />. The first two subbands belong to the <em>otho</em>- species of Ar-D<sub>2</sub>O, while the latter two belong to the <em>para</em>- species. The observed rovibrational transitions together with the previously reported pure rotational spectra having the common lower vibrational sub-states are analyzed by a weighted least-squares fitting using a pseudo-diatomic effective Hamiltonian. An experimental error of 10 kHz for the far-infrared transitions and 0.001 cm<sup>-1</sup> for the infrared transitions was set in the global fitting when using Pickett’s program SPFIT, respectively. Molecular constants including vibrational substate energies, rotational and centrifugal distortion constants, and Coriolis coupling constant, are determined accurately. The previous results for the <img alt="" /> substate are found to be likely wrong. The energies of the <img src="20221728_O_editing.files/image081.png" alt="" />和<img alt="" />substates are determined experimentally for the first time. The band origin of Ar-D<sub>2</sub>O in the D<sub>2</sub>O <em>v</em><sub>2</sub> bending mode region is determined to be 1177.92144(13) cm<sup>-1</sup>, which is red-shifted from that of D<sub>2</sub>O monomer by about 0.458 cm<sup>-1</sup>. The experimental vibrational substate energies are compared with their theoretical values based on a four-dimensional intermolecular potential energy surface which includes the normal coordinate of the D<sub>2</sub>O <em>v</em><sub>2</sub> bending mode. The experimental and theoretical results are in good agreement with each other. But the calculated energy levels are generally higher than the experimental values so the theoretical calculations still have the space to be improved.