On nonlinear time-dependent multivelocity transport equations

The aim of this paper is to show the existence and uniqueness of a solution for a class of nonlinear multivelocity neutron transport equations and to present a method for the determination of the solution. A recursion formula for the construction of a solution by the method of successive approximations and an error estimate for approximate solutions are given. Both global and local solutions are discussed. The conditions imposed on the nonlinear equation are directly applicable to the linear multivelocity transport problem, and a recursion formula for this system is also given. In the process of approximations, only successive integrations are involved. This fact indicates a promising possibility for the calculation of numerical results by using a computer. A brief discussion of this possibility and the applicability of the results on nonlinear problems are included.     

Nonlinear fourth-order elliptic equations with nonlocal boundary conditions

This paper is concerned with a class of fourth-order nonlinear elliptic equations with nonlocal boundary conditions, including a multi-point boundary condition in a bounded domain of Rn. Also considered is a second-order elliptic equation with nonlocal boundary condition, and the usual multi-point boundary problem in ordinary differential equations. The aim of the paper is to show the existence of maximal and minimal solutions, the uniqueness of a positive solution, and the method of construction for these solutions. Our approach to the above problems is by the method of upper and lower solutions and its associated monotone iterations. The monotone iterative schemes can be developed into computational algorithms for numerical solutions of the problem by either the finite difference method or the finite element method.     

On a coupled system of reaction–diffusion-transport equations arising from catalytic converter

This paper is concerned with two mathematical models which describe the transient behavior of a catalytic converter in automobile engineering. The first model consists of a coupled system of a heat-conduction equation and two integral equations while the second model involves only one integral equation. It is shown that for any nonnegative initial and boundary functions the three-equation model has a unique bounded global solution while the solution of the two-equation model blows up in finite time. The proof for the global existence and finite-time blow-up property of the solution is by the method of upper and lower solutions and its associated monotone iteration. This method can be used to develop computational algorithms for numerical solutions of the coupled systems.     

Development of an improved divergence‐free‐condition compensated coupled framework to solve flow problems with time‐varying geometries

In this article a coupled version of the improved divergence‐free‐condition compensated method will be proposed to simulate time‐varying geometries by direct forcing immersed boundary method. The proposed method can be seen as a quasi‐multi‐moment framework due to the fact that the momentum equations are discretized by both cell‐centered and cell‐face velocity. For simulating time‐varying geometries, a semi‐implicit iterative method is proposed for calculating the direct forcing terms. Treatments for suppressing spurious force oscillations, calculating drag/lift forces, and evaluating velocity and pressure for freshly cells will also be addressed. In order to show the applicability and accuracy, analytical as well as benchmark problems will be investigated by the present framework and compared with other numerical and experimental results.     

Single‐Electron Transfer between CuX2 and Thiols Determined by Extended X‐Ray Absorption Fine Structure Analysis: Application in Markovnikov‐Type Hydrothiolation of Styrenes

Transition‐metal mediated C?S bond formation using thiol compounds has been widely used in recent years. However, there has been less focus on the interaction between the metal and thiol compounds. In this work, we have successfully evidenced the single‐electron transfer between CuX₂ and thiophenol utilizing EXAFS. The fitting EXAFS results reveal that two halide anions are coordinated with the Cu^I center, whereas no sulfur atom is observed in the first coordination sphere. This Cu^I ate complex serves as the key intermediate for the proton transfer in the application of Markovnikov‐type hydrothiolation reactions.     

Evaluation of quantitative recovery methods for Listeria monocytogenes applied to stainless steel

The ability of Listeria monocytogenes to attach to various food contact surfaces, such as stainless steel, polypropylene, and rubber compounds, is well documented. The retention of these or other pathogenic bacteria on food contact surfaces increases the risk of transmission to food products. The objective of this study was to compare several methods for quantitative recovery of Listeria monocytogenes from stainless steel surfaces. A cocktail of 4 serotypes of Listeria monocytogenes mixed in equivalent concentrations was inoculated onto type 304 stainless steel coupons in a 2 x 2 cm area. After 1 h exposure, coupons were sampled by one of the following methods: (1) swabbing with a premoistened Dacron swab; (2) rinsing with phosphate-buffered saline; (3) direct contact onto tryptic soy agar containing 0.6% yeast extract (TSA + YE) plates for 10 s; (4) sonication in an ultrasonic water bath (40 kHz); (5) contact with the bristles of a sonicating brush head for 1 min; and (6) indirect contact (2-4 mm distance) with a sonicating brush head for 1 min. The 3 sonication methods yielded higher recovery than the other 3 methods (P < 0.05). Brushing the coupons with the sonicating brush head (contact or noncontact) yielded a recovery level of about 60%. The lowest cell recovery (about 20%) was observed with the swab and direct agar contact methods. After a 12 h exposure, recoveries ranged from 17.4 (brush contact method) to 2% (swab method).     

Asymptotic Behavior of Solutions for the Belousov-Zhabotinskii Reaction Diffusion System

The present paper characterizes the asymptotic behavior of the timedependenr solution of the coupled Belousov-Zhabotinskii reaction diffusion equations in relation to the steady-state solutions ot the corresponding boundary value problem. This characterization leads to an cxplicit reltionship among the various physical constants and the boundary and initial functions.     

Analysis of shallow spherical shell with circular base under eccentrically applied concentrated loads

In this paper,problems of a shallow sphericalshell with circular base under eccentrically appliedconcentrated loads are discussed.The solutions forsix cases of eccentrically applied concentrated loadsare given,namely:(1)Normal concentrated load,(2)Meridional tangential concentrated load,(3)Circumferential tangential concentrated load;(4)Concentrated moment in the tangential plane,(5)Concentrated moment in the meridional normalplane,(6)Concentrated moment in the circumferentialnormal plane.From the solutions of concentrated loads,thesolutions of distributed line loads in the form ofcosnθalong the circle are obtained.