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81.
Xiaopeng Zhao Changchun Liu 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6348-6357
This paper is concerned with the viscous Cahn-Hilliard equation, which arises in the dynamics of viscous first order phase transitions in cooling binary solutions. The optimal control under boundary condition is given and the existence of optimal solution to the equation is proved. 相似文献
82.
J. Javier Ibáñez 《Journal of Computational and Applied Mathematics》2011,235(7):1798-1804
Numerical methods for solving Ordinary Differential Equations (ODEs) have received considerable attention in recent years. In this paper a piecewise-linearized algorithm based on Krylov subspaces for solving Initial Value Problems (IVPs) is proposed. MATLAB versions for autonomous and non-autonomous ODEs of this algorithm have been implemented. These implementations have been compared with other piecewise-linearized algorithms based on Padé approximants, recently developed by the authors of this paper, comparing both precisions and computational costs in equal conditions. Four case studies have been used in the tests that come from stiff biology and chemical kinetics problems. Experimental results show the advantages of the proposed algorithms, especially when the dimension is increased in stiff problems. 相似文献
83.
一阶线性模糊微分方程的解 总被引:4,自引:0,他引:4
利用文[8]中的扩展原理求解了一阶线性模糊微分方程,给出了解可表示的条件,讨论了同其他求解方法之间的关系,最后给出了具体算例。 相似文献
84.
李振邦 《纯粹数学与应用数学》2019,35(1):15-33
研究一类对流非局部Cahn-Hilliard方程的Neumann问题.通过一致Schauder估计和Leray-Schauder不动点定理,得到了该问题经典解的存在唯一性.进而,利用弱收敛方法得到了该问题弱解的存在唯一性. 相似文献
85.
We consider a diffuse interface model describing flow and phase separation of a binary isothermal mixture of (partially) immiscible viscous incompressible Newtonian fluids having different densities. The model is the nonlocal version of the one derived by Abels, Garcke and Grün and consists in a inhomogeneous Navier-Stokes type system coupled with a convective nonlocal Cahn-Hilliard equation. This model was already analyzed in a paper by the same author, for the case of singular potential and non-degenerate mobility. Here, we address the physically more relevant situation of degenerate mobility and we prove existence of global weak solutions satisfying an energy inequality. The proof relies on a regularization technique based on a careful approximation of the singular potential. Existence and regularity of the pressure field is also discussed. Moreover, in two dimensions and for slightly more regular solutions, we establish the validity of the energy identity. We point out that in none of the existing contributions dealing with the original (local) Abels, Garcke Grün model, an energy identity in two dimensions is derived (only existence of weak solutions has been proven so far). 相似文献
86.
The absorbance signal in electrothermal atomic absorption spectrometry is a result of the processes of atom formation and dissipation and first of all depends on the initial generation of atoms from the surface. The rising part of the absorbance time profiles can be used for characterization of the release of the metals like Pd, Ag, Au etc. The method is applied to investigate the palladium release from a pyrocoated graphite support at different initial masses of the Pd. The kinetic parameters are evaluated and conclusions about the distribution of palladium on the graphite surface are made. The estimated values of apparent activation energies depend on the initial mass of analyte. The advantages and limitations of the present approach are discussed. 相似文献
87.
The high-pressure and high-temperature behaviors of LiF and NaF have been studied up to 37 GPa and 1000 K. No phase transformations have been observed for LiF up to the maximum pressure reached. The B1 to B2 transition of NaF at room temperature was observed at ~28 GPa, this transition pressure decreases with temperature. Unit-cell volumes of LiF and NaF B1 phase measured at various pressures and temperatures were fitted using a P–V–T Birch–Murnaghan equation of state. For LiF, the determined parameters are: α0 = 1.05 (3)×10?4 K?1, dK/dT = ?0.025 (2) GPa/K, V 0 = 65.7 (1) Å3, K 0 = 73 (2) GPa, and K′ = 3.9 (2). For NaF, α0 = 1.34 (4)×10?4 K?1, dK/dT = ?0.020 (1) GPa/K, V 0 = 100.2 (2) Å3, K 0 = 46 (1) GPa, and K′ = 4.5 (1). 相似文献
88.
A theoretical investigation of the MgAl 2 O 4 crystal response to high-pressure conditions has been carried out to determine its stability against decomposition towards MgO and f -Al 2 O 3 , and towards recently observed orthorhombic phases. We have evaluated total energy versus volume curves using the density functional formalism under the non-local B3LYP approximation, as implemented in the CRYSTAL package. Numerical and analytical fittings have been carried out to determine the equilibrium unit cell geometry and equation of state parameters for all the structures and compounds involved in the phase diagram. The macroscopic compressibility of the spinel phase is interpreted considering the compressibility of its elementary MgO 4 and AlO 6 coordination polyhedra, and implications to understand the phase stability are suggested. 相似文献
89.
Kaleb C. Burrage Christopher S. Perreault Eric K. Moss Jeffrey S. Pigott Blake T. Sturtevant Jesse S. Smith 《高压研究》2013,33(3):489-498
ABSTRACTThe isothermal compression of transition metal tantalum (Ta) was studied in a diamond anvil cell by X-ray diffraction utilizing rhenium (Re) and gold (Au) as internal X-ray pressure standards. The Re pressure marker was employed during non-hydrostatic compression to pressures up to 310?GPa while the Au pressure marker was used during quasi-hydrostatic compression in a neon pressure-transmitting medium to 80?GPa. Two ultra-high pressure experiments were conducted on Ta and Re mixtures utilizing focused-ion beam machined toroidal diamond anvils with central flats varying from 8 microns to 16 microns in diameter. The Ta metal was observed to be stable in the body-centered-cubic phase to a volume compression V/V0?=?0.581. The measured equations of state (EOS) of Ta using two different calibrations of the Re pressure marker are compared with the ambient temperature isotherm derived from shock compression data. We provide a detailed analysis of EOS fit parameters for Ta under quasi-hydrostatic and non-hydrostatic conditions. 相似文献
90.