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91.
Dia Zeidan Chi Kin Chau Tzon-Tzer Lu Wei-Quan Zheng 《Mathematical Methods in the Applied Sciences》2020,43(5):2171-2188
In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers. 相似文献
92.
93.
H. F. Chau H. Y. Chan F. K. Chow 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,72(4):641-655
Recently, Yin et al. [Eur. Phys. J. B 49, 205 (2006)] introduced an
efficient small-world network traffic model using preferential next-nearest
neighbor routing strategy with the so-called path iteration avoidance (PIA)
rule to study the jamming transition of internet.
Here we study their model without PIA rule by a mean-field analysis which
carefully divides the message packets into two types. Then, we argue that
our mean-field analysis is also applicable in the presence of PIA rule
in the limit of a large number of nodes in the network.
Our analysis gives an explicit expression of the critical packet injection
rate Rc as a function of a bias parameter of the routing strategy
α in their model with or without PIA rule. In particular, we predict
a sudden change in Rc at a certain value of α. These predictions
agree quite well with our extensive computer simulations. 相似文献
94.
Geometry optimization and harmonic vibrational frequency calculations have been carried out on the low-lying doublet electronic states of antimony dioxide (SbO(2)) employing a variety of ab initio methods, including the complete active space self-consistent field/multireference configuration interaction and the RCCSD(T) methods. Both large and small core relativistic effective core potentials were used for Sb in these calculations, together with valence basis sets of up to aug-cc-pV5Z quality. Contributions from outer core correlation and off-diagonal spin-orbit interaction to relative electronic energies have been calculated. The ground electronic state of SbO(2) is determined to be the X (2)A(1) state, as is the case for dioxides of other lighter group 15 p-block (or group VA) elements. However, the A (2)B(2) and B (2)A(2) states are estimated to be only 4.1 and 10.7 kcalmole above the X (2)A(1) state, respectively, at the complete basis set limit. Reliable vertical excitation energies from the X (2)A(1) state to low-lying excited states of SbO(2) have been computed with a view to assist future spectral assignments of the absorption and/or laser-induced fluorescence spectra of SbO(2), when they become available. 相似文献
95.
Geometry optimization calculations were carried out on the (approximate)X (1)A(1) state of SCl(2) and the (approximate)X(2)B(1), (approximate)A(2)B(2), (approximate)B(2)A(1), (approximate)C(2)A(1), (approximate)D(2)A(2), and (approximate)E (2)B(2) states of SCl(2) (+) at the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] level with basis sets of up to the augmented correlation-consistent polarized quintuple-zeta [aug-cc-pV(5+d)Z] quality. Effects of core electron correlation, basis set extension to the complete basis set limit, and relativistic contributions on computed minimum-energy geometrical parameters and/or relative electronic energies were also investigated. RCCSD(T) potential energy functions (PEFs) were calculated for the (approximate)X (1)A(1) state of SCl(2) and the low-lying states of SCl(2)(+) listed above employing the aug-cc-pV(5+d)Z basis set. Anharmonic vibrational wave functions of these neutral and cationic states of SCl(2), and Franck-Condon (FC) factors of the lowest four one-electron allowed neutral photoionizations were computed employing the RCCSD(T)aug-cc-pV(5+d)Z PEFs. Calculated FC factors with allowance for the Duschinsky rotation and anharmonicity were used to simulate the first four photoelectron (PE) bands of SCl(2). The agreement between simulated and observed He I PE spectra reported by Colton et al. [J. Electron Spectrosc. Relat. Phenom. 3, 345 (1974)] and Solouki et al. [Chem. Phys. Lett. 26, 20 (1974)] is excellent. However, our FC spectral simulations indicate that the first observed vibrational component in the first PE band of SCl(2) is a "hot" band arising from the SCl(2)(+)(approximate)X(2)B(1)(0,0,0)<--SCl(2)(approximate)X (1)A(1)(1,0,0) ionization. Consequently, the experimental adiabatic ionization energy of SCl(2) is revised to 9.55+/-0.01 eV, in excellent agreement with results obtained from state-of-the-art ab initio calculations in this work. 相似文献
96.
97.
Chau Le Tyler E. Bruns Daniel A. Tortorelli 《Journal of the mechanics and physics of solids》2012,60(2):351-378
We describe a systematic approach to design material microstructures to achieve desired energy propagation in a two-phase composite plate. To generate a well-posed topology optimization problem we use the relaxation approach which requires homogenization theory to relate the macroscopic material properties to the microstructure, here a sequentially ranked laminate. We introduce an algorithm whereby the laminate layer volume fractions and orientations are optimized at each material point. To resolve numerical instabilities associated with the dynamic simulation and constrained optimization problem, we filter the laminate parameters. This also has the effect of generating smoothly varying microstructures which are easier to manufacture. To demonstrate our algorithm we design microstructure layouts for tailored energy propagation, i.e. energy focus, energy redirection, energy dispersion and energy spread. 相似文献
98.
Yuan-Fong Chou Chau Chung-Ting Chou Chao Hai-Pang Chiang Chee Ming Lim Nyuk Yoong Voo Abdul Hanif Mahadi 《Journal of nanoparticle research》2018,20(7):190
We have investigated numerically the plasmonic effect on a two-dimensional periodic array of metallic nanostructures. The unit cell of the array has an Ag nanosphere and nanorod pair formed in a single structure. Three-dimensional finite element method is used for the study on the sensing performance within the optical spectra. The study takes into account the influences of the structural and material parameters, the rotational angle of the metal nanostructure, the number of metal nanostructure per unit cell, and the localized surface plasmon resonances. The proposed nanostructures function as a refractive index sensor with a sensitivity of 400 nm/RIU (RIU is the refractive index unit), showing the characteristics of low transmittance (T?=?3.90%), high absorptance (A?=?94.5%), and near-zero reflectance (R?=?0.15%), could be achieved by a triangular arrangement of nanostructures within a unit cell. We also show how the tailoring of the structural parameters relates to the specific sensing schematics of the sensor. 相似文献
99.
Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics. 相似文献
100.
Ultrasound-assisted extraction of ginseng saponins from ginseng roots and cultured ginseng cells 总被引:11,自引:0,他引:11
Ultrasound-assisted extraction was evaluated as a simpler and more effective alternative to conventional extraction methods for the isolation of ginsenosides (saponins) from various types of ginseng. The ginseng samples were extracted with different solvents, under either direct sonication by an ultrasound probe horn or indirect sonication in an ultrasound cleaning bath. The ultrasonic extraction was compared with the conventional method of refluxing boiling solvents in a soxhlet extractor, on the yields of both the total saponin isolated by thin-layer chromatography and the individual ginsenosides by high performance liquid chromatography. It was found that the sonication-assisted extraction of ginseng saponins was about three times faster than the traditional extraction method. The ultrasonic extraction was not only more efficient but also convenient for the recovery and purification of the active ingredients of plant materials. In addition, the sonication-assisted extraction can be carried out at lower temperatures which are favorable for the thermally unstable compounds. 相似文献