A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

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.     

A volatolomic approach using cerumen as biofluid to diagnose bovine intoxication by Stryphnodendron rotundifolium

An innovative volatolomic approach employs the detection of biomarkers present in cerumen (earwax) to identify cattle intoxication by Stryphnodendron rotundifolium Mart., Fabaceae (popularly known as barbatimão). S. rotundifolium is a poisonous plant with the toxic compound undefined and widely distributed throughout the Brazilian territory. Cerumen samples from cattle of two local Brazilian breeds (‘Curraleiro Pé-Duro’ and ‘Pantaneiro’) were collected during an experimental intoxication protocol and analyzed using headspace (HS)/GC–MS followed by multivariate analysis (genetic algorithm for a partial least squares, cluster analysis, and classification and regression trees). A total of 106 volatile organic metabolites were identified in the cerumen samples of bovines. The intoxication by S. rotundifolium influenced the cerumen volatolomic profile of the bovines throughout the intoxication protocol. In this way, it was possible to detect biomarkers for cattle intoxication. Among the biomarkers, 2-octyldecanol and 9-tetradecen-1-ol were able to discriminate all samples between intoxicated and nonintoxicated bovines. The cattle intoxication diagnosis by S. rotundifolium was accomplished by applying the cerumen analysis using HS/GC–MS, in an easy, accurate, and noninvasive way. Thus, the proposed bioanalytical chromatography protocol is a useful tool in veterinary applications to determine this kind of intoxication.     

Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

Analogue Models of and for Gravity

Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide experimentally accessible models of curved-space quantum field theory. As such they mimic kinematic aspects of general relativity, though typically they do not mimic the dynamics. Although these analogue models are thereby limited in their ability to duplicate all the effects of Einstein gravity they nevertheless are extremely important—they provide black hole analogues (some of which have already been seen experimentally) and lead to tests of basic principles of curved-space quantum field theory. Currently these tests are still in the realm of gedanken-experiments, but there are plausible candidate models that should lead to laboratory experiments in the not too distant future.     

Pseudo-epitaxial C60 films prepared by a hot-wall method

We have used both reflection-geometry and grazing-incidence-geometry X-ray scattering to study thin films of C₆₀ evaporated onto mica substrates via a hot-wall technique. The growth mode yields close-packed C₆₀ planes, which are parallel to the substrate surface and which exhibit out-of-plane correlation lengths of 850 Å. In the film plane the C₆₀ is at best pseudo-epitaxial, with a 0.9° distribution of crystallite orientations, a 450 Å in-plane correlation length, and a 3.7% lattice mismatch, better than obtained by other thin film techniques but far from the accepted definition of single crystal thin film epitaxy.     

Diamagnetic susceptibility of hydrogenic donor impurity in low-dimensional semiconducting systems

The binding energies of a hydrogenic donor both in the parabolic and non-parabolic conduction band model within the effective mass approximation have been computed for the low-dimensional semiconducting systems (LDSS) like quantum well, quantum well wire and quantum dot taking GaAs/Al_xGa_1−xAs systems as an example. It is observed that the effect of non-parabolicity is not effective when the system goes to lower dimensionality. The diamagnetic susceptibility of a hydrogenic donor impurity has also been computed in these LDSS in the infinite barrier model. Since no theoretical or experimental works on the diamagnetic susceptibility of LDSS are available in the literature, as a realistic case the diamagnetic susceptibility has been computed in the finite barrier model (x=0.3) for a quantum well and the results are discussed in the light of semiconductor-metal transition.     

A possible counterexample to well posedness of entropy solutions and to Godunov scheme convergence

A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.

     

采用多元化的教学手段,提高物理人才的综合素质——南开大学物理学基础科学人才培养基地建设经验介绍

介绍了南开大学国家物理学基础科学研究人才培养基地在十多年的建设中,通过多元化的教学手段提高学生的学习自主性,通过加强科研训练提高物理人才综合素质的经验和取得的成果.