Remote sensing data have been widely applied to extract minerals in geologic exploration, however, in areas covered by vegetation, extracted mineral information has mostly been small targets bearing little information...Remote sensing data have been widely applied to extract minerals in geologic exploration, however, in areas covered by vegetation, extracted mineral information has mostly been small targets bearing little information. In this paper, we present a new method for mineral extraction aimed at solving the difficulty of mineral identification in vegetation covered areas. The method selected six sets of spectral difference coupling between soil and plant(SVSCD). These sets have the same vegetation spectra reflectance and a maximum different reflectance of soil and mineral spectra from Hyperion image based on spectral reflectance characteristics of measured spectra. The central wavelengths of the six, selected band pairs were 2314 and 701 nm, 1699 and 721 nm, 1336 and 742 nm, 2203 and 681 nm, 2183 and 671 nm, and 2072 and 548 nm. Each data set's reflectance was used to calculate the difference value. After band difference calculation, vegetation information was suppressed and mineral abnormal information was enhanced compared to the scatter plot of original band. Six spectral difference couplings, after vegetation inhibition, were arranged in a new data set that requires two components that have the largest eigenvalue difference from principal component analysis(PCA). The spatial geometric structure features of PC1 and PC2 was used to identify altered minerals by spectral feature fitting(SFF). The collecting rocks from the 10 points that were selected in the concentration of mineral extraction were analyzed under a high-resolution microscope to identify metal minerals and nonmetallic minerals. Results indicated that the extracted minerals were well matched with the verified samples, especially with the sample 2, 4, 5 and 8. It demonstrated that the method can effectively detect altered minerals in vegetation covered area in Hyperion image.展开更多
The densification and the fractal dimensions of carbon-nickel films annealed at different temperatures 300, 500, 800, and 1000℃ with emphasis on porosity evaluation are investigated. For this purpose, the refractive...The densification and the fractal dimensions of carbon-nickel films annealed at different temperatures 300, 500, 800, and 1000℃ with emphasis on porosity evaluation are investigated. For this purpose, the refractive index of films is determined from transmittance spectra. Three different regimes are identified, T 〈 500℃, 500℃ 〈 T 〈 800℃ and T 〉 800℃. The Rutherford baekscattering spectra show that with increasing the annealing temperature, the concentration of nickel atoms into films decreases. It is shown that the effect of annealing temperatures for increasing films densification at T 〈 500℃ and T 〉 800℃ is greater than the effect of nickel concentrations. It is observed that the effect of decreasing nickel atoms into films at 500℃ 〈 T 〈 800℃ strongly causes improving porosity and decreasing densification. The fractal dimensions of carbon-nickel films annealed from 300 to 500℃ are increased, while from 500 to 1000℃ these characteristics are decreased. It can be seen that at 800℃, films have maximum values of porosity and roughness.展开更多
The exact short time propagator, in a form similar to the Crank-Nicholson method but in the spirit of spectrally transformed Hamiltonian, was proposed to solve the triatomic reactive time-dependent schrodinger equatio...The exact short time propagator, in a form similar to the Crank-Nicholson method but in the spirit of spectrally transformed Hamiltonian, was proposed to solve the triatomic reactive time-dependent schrodinger equation. This new propagator is exact and unconditionally convergent for calculating reactive scattering processes with large time step sizes. In order to improve the computational efficiency, the spectral difference method was applied. This resulted the Hamiltonian with elements confined in a narrow diagonal band. In contrast to our previous theoretical work, the discrete variable representation was applied and resulted in full Hamiltonian matrix. As examples, the collision energy-dependent probability of the triatomic H＋H2 and O＋O2 reaction are calculated. The numerical results demonstrate that this new propagator is numerically accurate and capable of propagating the wave packet with large time steps. However, the efficiency and accuracy of this new propagator strongly depend on the mathematical method for solving the involved linear equations and the choice of preconditioner.展开更多
Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ways.Here,we compare one important scheme to ordinary finite differences by a mixture of numerical experim...Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ways.Here,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the grid.For Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is tiny.However,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference weights.On a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors therein.We show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil width.The error of the infinite series(M=∞)decreases exponentially asα→0.However,truncated GARBF series have a second error(truncation error)that grows exponentially asα→0.Even forα∼O(1)where the sum of these two errors is minimized,it is shown that the finite difference formulas are always superior.We explain,less rigorously,why these arguments extend to more general species of RBFs and to an irregular grid.There are,however,a variety of alternative differentiation strategies which will be analyzed in future work,so it is far too soon to dismiss RBFs as a tool for solving differential equations.展开更多
An implicit non-linear lower-upper symmetric Gauss-Seidel(LU-SGS)solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral grids.The non-linear LU-SGS s...An implicit non-linear lower-upper symmetric Gauss-Seidel(LU-SGS)solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral grids.The non-linear LU-SGS solver is preconditioned by a block element matrix,and the system of equations is then solved with the LU decomposition approach.The large sparse Jacobian matrix is computed numerically,resulting in extremely simple operations for arbitrarily complex residual operators.Several inviscid and viscous test cases were performed to evaluate the performance.The implicit solver has shown speedup of 1 to 2 orders of magnitude over the multi-stage Runge-Kutta time integration scheme.展开更多
A high order multidomain spectral difference method has been developed for the three dimensional Navier-Stokes equations on unstructured hexahedral grids.The method is easy to implement since it involves one-dimension...A high order multidomain spectral difference method has been developed for the three dimensional Navier-Stokes equations on unstructured hexahedral grids.The method is easy to implement since it involves one-dimensional operations only,and does not involve surface or volume integrals.Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit cube.The concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order accuracy.In this paper,accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions.High order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and Couette flow.The capability of the method for both inviscid and viscous flow problems with curved boundaries is also demonstrated.展开更多
Hyperspectral imaging,with many narrow bands of spectra,is strongly capable to detect or classify objects.It has been become one research hotspot in the field of near-ground remote sensing.However,the higher demands f...Hyperspectral imaging,with many narrow bands of spectra,is strongly capable to detect or classify objects.It has been become one research hotspot in the field of near-ground remote sensing.However,the higher demands for computing and complex operating of instrument are still the bottleneck for hyperspectral imaging technology applied in field.Band selection is a common way to reduce the dimensionality of hyperspectral imaging cube and simplify the design of spectral imaging instrument.In this research,hyperspectral images of blueberry fruit were collected both in the laboratory and in field.A set of spectral bands were selected by analyzing the differences among blueberry fruits at different growth stages and backgrounds.Furthermore,a normalized spectral index was set up using the bands selected to identify the three growth stages of blueberry fruits,aiming to eliminate the impact of background included leaf,branch,soil,illumination variation and so on.Two classifiers of spectral angle mapping(SAM),multinomial logistic regression(MLR)and classification tree were used to verify the results of identification of blueberry fruit.The detection accuracy was 82.1%for SAM classifier using all spectral bands,88.5%for MLR classifier using selected bands and 89.8%for decision tree using the spectral index.The results indicated that the normalization spectral index can both lower the complexity of computing and reduce the impact of noisy background in field.展开更多
Large eddy simulation of the flow over a circular cylinder at Reynolds number ReD=2580 has been studied with a high-order unstructured spectral difference method.Grid and polynomial refinement studies were carried out...Large eddy simulation of the flow over a circular cylinder at Reynolds number ReD=2580 has been studied with a high-order unstructured spectral difference method.Grid and polynomial refinement studies were carried out to assess numerical errors.The mean and fluctuating velocity fields in the wake of a circular cylinder were compared with PIV experimental measurements.The numerical results are in excellent agreement with the experimental data for both the mean velocity and Reynolds stresses using the high-order SD scheme.Other wake characteristics such as the recirculation bubble length,vortex formation length and maximum intensity of the velocity fluctuations have also been predicted accurately.The numerical simulations demonstrated the potential of the high-order SD method in accurate large eddy simulation of physically complex problems.展开更多
In this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin(DG)discretization of a nonlinear conservation law.This allows interpretation of the Spectral Difference Scheme...In this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin(DG)discretization of a nonlinear conservation law.This allows interpretation of the Spectral Difference Scheme as a particular discretization under the quadrature-free nodal DG paradigm.Moreover,it enables identification of the key differences between the Spectral Difference Scheme and standard nodal DG schemes.展开更多
基金Under the auspices of National Science and Technology Major Project of China(No.04-Y20A35-9001-15/17)the Program for JLU Science and Technology Innovative Research Team(No.JLUSTIRT,2017TD-26)the Changbai Mountain Scholars Program,Jilin Province,China
文摘Remote sensing data have been widely applied to extract minerals in geologic exploration, however, in areas covered by vegetation, extracted mineral information has mostly been small targets bearing little information. In this paper, we present a new method for mineral extraction aimed at solving the difficulty of mineral identification in vegetation covered areas. The method selected six sets of spectral difference coupling between soil and plant(SVSCD). These sets have the same vegetation spectra reflectance and a maximum different reflectance of soil and mineral spectra from Hyperion image based on spectral reflectance characteristics of measured spectra. The central wavelengths of the six, selected band pairs were 2314 and 701 nm, 1699 and 721 nm, 1336 and 742 nm, 2203 and 681 nm, 2183 and 671 nm, and 2072 and 548 nm. Each data set's reflectance was used to calculate the difference value. After band difference calculation, vegetation information was suppressed and mineral abnormal information was enhanced compared to the scatter plot of original band. Six spectral difference couplings, after vegetation inhibition, were arranged in a new data set that requires two components that have the largest eigenvalue difference from principal component analysis(PCA). The spatial geometric structure features of PC1 and PC2 was used to identify altered minerals by spectral feature fitting(SFF). The collecting rocks from the 10 points that were selected in the concentration of mineral extraction were analyzed under a high-resolution microscope to identify metal minerals and nonmetallic minerals. Results indicated that the extracted minerals were well matched with the verified samples, especially with the sample 2, 4, 5 and 8. It demonstrated that the method can effectively detect altered minerals in vegetation covered area in Hyperion image.
文摘The densification and the fractal dimensions of carbon-nickel films annealed at different temperatures 300, 500, 800, and 1000℃ with emphasis on porosity evaluation are investigated. For this purpose, the refractive index of films is determined from transmittance spectra. Three different regimes are identified, T 〈 500℃, 500℃ 〈 T 〈 800℃ and T 〉 800℃. The Rutherford baekscattering spectra show that with increasing the annealing temperature, the concentration of nickel atoms into films decreases. It is shown that the effect of annealing temperatures for increasing films densification at T 〈 500℃ and T 〉 800℃ is greater than the effect of nickel concentrations. It is observed that the effect of decreasing nickel atoms into films at 500℃ 〈 T 〈 800℃ strongly causes improving porosity and decreasing densification. The fractal dimensions of carbon-nickel films annealed from 300 to 500℃ are increased, while from 500 to 1000℃ these characteristics are decreased. It can be seen that at 800℃, films have maximum values of porosity and roughness.
文摘The exact short time propagator, in a form similar to the Crank-Nicholson method but in the spirit of spectrally transformed Hamiltonian, was proposed to solve the triatomic reactive time-dependent schrodinger equation. This new propagator is exact and unconditionally convergent for calculating reactive scattering processes with large time step sizes. In order to improve the computational efficiency, the spectral difference method was applied. This resulted the Hamiltonian with elements confined in a narrow diagonal band. In contrast to our previous theoretical work, the discrete variable representation was applied and resulted in full Hamiltonian matrix. As examples, the collision energy-dependent probability of the triatomic H＋H2 and O＋O2 reaction are calculated. The numerical results demonstrate that this new propagator is numerically accurate and capable of propagating the wave packet with large time steps. However, the efficiency and accuracy of this new propagator strongly depend on the mathematical method for solving the involved linear equations and the choice of preconditioner.
文摘Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ways.Here,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the grid.For Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is tiny.However,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference weights.On a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors therein.We show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil width.The error of the infinite series(M=∞)decreases exponentially asα→0.However,truncated GARBF series have a second error(truncation error)that grows exponentially asα→0.Even forα∼O(1)where the sum of these two errors is minimized,it is shown that the finite difference formulas are always superior.We explain,less rigorously,why these arguments extend to more general species of RBFs and to an irregular grid.There are,however,a variety of alternative differentiation strategies which will be analyzed in future work,so it is far too soon to dismiss RBFs as a tool for solving differential equations.
基金The study was partially funded by Rockwell Scientific/DARPA contract W911NF-04-C-0102,AFOSR grant FA9550-06-1-0146,and DOE grant DE-FG02-05ER25677The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements,either expressed or im-plied,of DARPA,AFOSR,DOE,or the U.S.Government.
文摘An implicit non-linear lower-upper symmetric Gauss-Seidel(LU-SGS)solution algorithm has been developed for a high-order spectral difference Navier-Stokes solver on unstructured hexahedral grids.The non-linear LU-SGS solver is preconditioned by a block element matrix,and the system of equations is then solved with the LU decomposition approach.The large sparse Jacobian matrix is computed numerically,resulting in extremely simple operations for arbitrarily complex residual operators.Several inviscid and viscous test cases were performed to evaluate the performance.The implicit solver has shown speedup of 1 to 2 orders of magnitude over the multi-stage Runge-Kutta time integration scheme.
基金funded by Rockwell Scientific/DARPA under contractW911NF-04-C-0102,by DOE grant DE-FG02-05ER25677 and AFOSR grant FA9550-06-1-0146.
文摘A high order multidomain spectral difference method has been developed for the three dimensional Navier-Stokes equations on unstructured hexahedral grids.The method is easy to implement since it involves one-dimensional operations only,and does not involve surface or volume integrals.Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner in a unit cube.The concepts of the Riemann solver and high-order local representations are applied to achieve conservation and high order accuracy.In this paper,accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions.High order of accuracy and spectral convergence are obtained for the propagation of an isotropic vortex and Couette flow.The capability of the method for both inviscid and viscous flow problems with curved boundaries is also demonstrated.
基金The work was financially supported by the National Key Research and Development Program of China Sub-project(No.2016YFD0700103)the National Natural Science Foundation of China(No.61805073)+1 种基金Innovation Scientists and Technicians Talent Projects of Henan Provincial Department of Education(No.19HASTIT021)Henan provincial science and technology project(No.182102110201&No.192102110204).
文摘Hyperspectral imaging,with many narrow bands of spectra,is strongly capable to detect or classify objects.It has been become one research hotspot in the field of near-ground remote sensing.However,the higher demands for computing and complex operating of instrument are still the bottleneck for hyperspectral imaging technology applied in field.Band selection is a common way to reduce the dimensionality of hyperspectral imaging cube and simplify the design of spectral imaging instrument.In this research,hyperspectral images of blueberry fruit were collected both in the laboratory and in field.A set of spectral bands were selected by analyzing the differences among blueberry fruits at different growth stages and backgrounds.Furthermore,a normalized spectral index was set up using the bands selected to identify the three growth stages of blueberry fruits,aiming to eliminate the impact of background included leaf,branch,soil,illumination variation and so on.Two classifiers of spectral angle mapping(SAM),multinomial logistic regression(MLR)and classification tree were used to verify the results of identification of blueberry fruit.The detection accuracy was 82.1%for SAM classifier using all spectral bands,88.5%for MLR classifier using selected bands and 89.8%for decision tree using the spectral index.The results indicated that the normalization spectral index can both lower the complexity of computing and reduce the impact of noisy background in field.
基金supported by the Air Force Office of Scientific Research(AFOSR)grant FA9550-06-1-0146the Department of Energy(DOE)grant DE-FG02-05ER25677。
文摘Large eddy simulation of the flow over a circular cylinder at Reynolds number ReD=2580 has been studied with a high-order unstructured spectral difference method.Grid and polynomial refinement studies were carried out to assess numerical errors.The mean and fluctuating velocity fields in the wake of a circular cylinder were compared with PIV experimental measurements.The numerical results are in excellent agreement with the experimental data for both the mean velocity and Reynolds stresses using the high-order SD scheme.Other wake characteristics such as the recirculation bubble length,vortex formation length and maximum intensity of the velocity fluctuations have also been predicted accurately.The numerical simulations demonstrated the potential of the high-order SD method in accurate large eddy simulation of physically complex problems.
基金Financial support from the Deutsche Forschungsgemeinschaft(German Research Association)through grant GSC 111the Air Force Office of Scientific Research,Air Force Materiel Command,USAF,under grant number FA8655-08-1-3060,is gratefully acknowledged。
文摘In this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin(DG)discretization of a nonlinear conservation law.This allows interpretation of the Spectral Difference Scheme as a particular discretization under the quadrature-free nodal DG paradigm.Moreover,it enables identification of the key differences between the Spectral Difference Scheme and standard nodal DG schemes.
