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In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results. 相似文献
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Kai Cheng Xiao-Shuai Zhang Jie An Cheng Li Ruo-Yun Zhang Run Ye Prof. Dr. Bang-Jiao Ye Prof. Dr. Bo Liu Prof. Dr. Yuan-Di Zhao 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(31):7553-7560
Given their superior penetration depths, photosensitizers with longer absorption wavelengths present broader application prospects in photodynamic therapy (PDT). Herein, Ag2S quantum dots were discovered, for the first time, to be capable of killing tumor cells through the photodynamic route by near-infrared light irradiation, which means relatively less excitation of the probe compared with traditional photosensitizers absorbing short wavelengths. On modification with polydopamine (PDA), PDA-Ag2S was obtained, which showed outstanding capacity for inducing reactive oxygen species (increased by 1.69 times). With the addition of PDA, Ag2S had more opportunities to react with surrounding O2, which was demonstrated by typical triplet electron spin resonance (ESR) analysis. Furthermore, the PDT effects of Ag2S and PDA-Ag2S achieved at longer wavelengths were almost identical to the effects produced at 660 nm, which was proved by studies in vitro. PDA-Ag2S showed distinctly better therapeutic effects than Ag2S in experiments in vivo, which further validated the enhanced regulatory effect of PDA. Altogether, a new photosensitizer with longer absorption wavelength was developed by using the hitherto-unexplored photodynamic function of Ag2S quantum dots, which extended and enhanced the regulatory effect originating from PDA. 相似文献
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The influence of different referencing methods on the accuracy of δ13C value measurement of ethanol fuel by gas chromatography/combustion/isotope ratio mass spectrometry 下载免费PDF全文
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ABSTRACTThe Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle. 相似文献
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Cavitation erosion is caused in solids exposed to strong pressure waves developing in an adjacent fluid field. The knowledge of the transient distribution of stresses in the solid is important to understand the cause of damaging by comparisons with breaking points of the material. The modeling of this problem requires the coupling of the models for the fluid and the solid. For this purpose, we use a strategy based on the solution of coupled Riemann problems that has been originally developed for the coupling of 2 fluids. This concept is exemplified for the coupling of a linear elastic structure with an ideal gas. The coupling procedure relies on the solution of a nonlinear equation. Existence and uniqueness of the solution is proven. The coupling conditions are validated by means of quasi‐1D problems for which an explicit solution can be determined. For a more realistic scenario, a 2D application is considered where in a compressible single fluid, a hot gas bubble at low pressure collapses in a cold gas at high pressure near an adjacent structure. 相似文献
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