Comparison results for nonlinear degenerate Dirichlet and Neumann problems with general growth in the gradient

This paper deals with both Dirichlet and Neumann problems for a class of nonlinear degenerate elliptic equations with general growth in the gradient. First, we give an existence result of a spherically symmetric solution to the “symmetrized” problems with data depending only on the radials. Second, we prove that the solutions of the original problems can be compared, under a rearrangement, with the solutions of the “symmetrized” problems.     

Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.     

Characterization of silver nanoparticles using flow-field flow fractionation interfaced to inductively coupled plasma mass spectrometry

The ability to detect and identify the physiochemical form of contaminants in the environment is important for degradation, fate and transport, and toxicity studies. This is particularly true of nanomaterials that exist as discrete particles rather than dissolved or sorbed contaminant molecules in the environment. Nanoparticles will tend to agglomerate or dissolve, based on solution chemistry, which will drastically affect their environmental properties. The current study investigates the use of field flow fractionation (FFF) interfaced to inductively coupled plasma-mass spectrometry (ICP-MS) as a sensitive and selective method for detection and characterization of silver nanoparticles. Transmission electron microscopy (TEM) is used to verify the morphology and primary particle size and size distribution of precisely engineered silver nanoparticles. Subsequently, the hydrodynamic size measurements by FFF are compared to dynamic light scattering (DLS) to verify the accuracy of the size determination. Additionally, the sensitivity of the ICP-MS detector is demonstrated by fractionation of μg/L concentrations of mixed silver nanoparticle standards. The technique has been applied to nanoparticle suspensions prior to use in toxicity studies, and post-exposure biological tissue analysis. Silver nanoparticles extracted from tissues of the sediment-dwelling, freshwater oligochaete Lumbriculus variegatus increased in size from approximately 31-46nm, indicating a significant change in the nanoparticle characteristics during exposure.     

Forensic examination of ink by high-performance thin layer chromatography--the United States Secret Service Digital Ink Library

Forensic examinations of ink have been performed since the beginning of the 20th century. Since the 1960s, the International Ink Library, maintained by the United States Secret Service, has supported those analyses. Until 2009, the search and identification of inks were essentially performed manually. This paper describes the results of a project designed to improve ink samples' analytical and search processes. The project focused on the development of improved standardization procedures to ensure the best possible reproducibility between analyses run on different HPTLC plates. The successful implementation of this new calibration method enabled the development of mathematical algorithms and of a software package to complement the existing ink library.     

Large deviations of Markov chains with multiple time-scales

For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a deterministic limit and a central limit theorem around it have already been proven in Kang and Kurtz (2013) and Kang et al. (2014). We present here a general approach to proving a large deviation principle in path space for such multi-scale Markov processes. Motivated by models arising in systems biology, we apply these large deviation results to general chemical reaction systems which exhibit multiple time-scales, and provide explicit calculations for several relevant examples.     

Automatized System for Measuring the Surface Density of Current Carriers and Electrical Permittivity of Conducting Materials

An automatised system for analyzing the electron topography of a conducting surface (semiconductors, metals, ferrites or conductor ceramics) is represented. The function of the system is based on the recently observed surface photo-charge effect. The investigation is express and contactless. The system allows visualisations of different formations on the surface such as defects, ion-implanted areas, etc. on a computer screen. The structure of the system is described. The results from investigations with GaP and Cu are reported.     

Analysis of Focal Depth of Remote Displacement Measuring System Based on Grating Doppler Effect

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Comparison of experimental data with the numerical simulation of planar entry flow: Role of the constitutive equation

The goal of this research was to determine whether there is any interaction between the type of constitutive equation used and the degree of mesh refinement, as well as how the type of constitutive equation might affect the convergence and quality of the solution, for a planar 4:1 contraction in the finite eiement method. Five constitutive equations were used in this work: the Phan-Thien–Tanner (PTT), Johnson–Segalman (JS), White–Metzner (WM), Leonov-like and upper convected Maxwell (UCM) models. A penalty Galerkin finite element technique was used to solve the system of non-linear differential equations. The constitutive equations were fitted to the steady shear viscosity and normal stress data for a polystyrene melt. In general it was found that the convergence limit based on the Deborah number De and the Weissenberg number We varied from model to model and from mesh to mesh. From a practical point of view it was observed that the wall shear stress in the downstream region should also be indicated at the point where convergence is lost, since this parameter reflects the throughput conditions. Because of the dependence of convergence on the combination of mesh size and constitutive equation, predictions of the computations were compared with birefringence data obtained for the same polystyrene melt flowing through a 4:1 planar contraction. Refinement in the mesh led to better agreement between the predictions using the PTT model and flow birefringence, but the oscillations became worse in the corner region as the mesh was further refined, eventually leading to the loss of convergence of the numerical algorithm. In comparing results using different models at the same wall shear stress conditions and on the same mesh, it was found that the PTT model gave less overshoot of the stresses at the re-entrant corner. Away from the corner there were very small differences between the quality of the solutions obtained using different models. All the models predicted solutions with oscillations. However, the values of the solutions oscillated around the experimental birefringence data, even when the numerical algorithm would not converge. Whereas the stresses are predicted to oscillate, the streamlines and velocity field remained smooth. Predictions for the existence of vortices as well as for the entrance pressure loss (ΔP_ent) varied from model to model. The UCM and WM models predicted negative values for ΔP_ent.     

g-期望关于凸(凹)函数的Jensen不等式

在文[8]的基础上和彭实戈提出的关于g-期望的最基本的条件下,证明了g-期望关于凸(凹)函数的Jensen不等式在一般意义下成立当且仅当g是关于(y,z)的超齐次(次齐次)生成元且不依赖于y．