Preface: artificial intelligence in operations management

Annals of Operations Research -     

Thermal stability for a reactive viscous flow in a slab

The paper deals with the effect of dimensionless non-Newtonian coefficient on the thermal stability of a reactive viscous liquid in steady flow between parallel heated plates. It is assumed that the liquid is symmetrically heated and the flow fully developed. Approximate analytical solution is obtained for the velocity of the flow and the criterion for which this solution is valid is determined. After the velocity distribution is known, the temperature distribution may be calculated. Disappearance of criticality (transition values) are obtained in the following cases: (i) bimolecular (ii) Arrhenius and (iii) sensitized temperature dependence. We have observed that non-linear effect from velocity and temperature fields introduced decaying for the transitional values of the dimensionless central temperature. Other effects of this non-linearity are reported. The results help to enhance understanding of the interplay between Newtonian and non-Newtonian thermal explosions.     

A correction of the 2D KdV equation of Djordjevic ＆ Redekopp in exponentially stratified fluid＊

To further study the fission laws of initial internal solitons on the continental shelf/slope, we rederive and correct the 2D KdV equation of Djordjevic & Redekopp for exponentially stratified fluid (or ocean) and with two-dimensional topography. Through a combination of theoretical study and numerical experiments, we show that solitons in the odd vertical modes can fission. However, because of the corrections, the fission conditions are different from those of Djordjevic & Redekopp. The even modes cannot fission unless the initial internal solitons propagate from shallow sea to deep sea. This conclusion is entirely opposite to that of Djordjevic & Redekopp.The project supported by the National Natural Science Foundation of China (40276008) and the Grant of Key Laboratory of Marine Science and Numerical Modeling, SOA (0201(2003))The English text was polished by Keren Wang.     

Reactive-diffusive equation with variable pre-exponential factor

We consider the steady-state solutions for the exothermic chemical reaction, taking the diffusion of the reactant in a slab into account and assuming an Arrhenius temperature dependence with variable pre-exponential factor. We solve the resulting nonlinear boundary value problem using both numerical and analytical methods. This new analytical solution for the Frank-Kamenetskii parameter δ, as it is in terms of Bernoulli’s numbers, is in accordance with the numerical integration provided the activation energy parameter ε (1) is very small and for ε→0 it goes to the well-known Frank-Kamenetskii case. We determine numerically the transitional values of δ, ε and the dimensionless central temperature θ_m.     

The Structure of Precipitation Fronts for Finite Relaxation Time

When convection is parameterized in an atmospheric circulation model, what types of waves are supported by the parameterization? Several studies have addressed this question by finding the linear waves of simplified tropical climate models with convective parameterizations. In this paper’s simplified tropical climate model, convection is parameterized by a nonlinear precipitation term, and the nonlinearity gives rise to precipitation front solutions. Precipitation fronts are solutions where the spatial domain is divided into two regions, and the precipitation (and other model variables) changes abruptly at the boundary of the two regions. In one region the water vapor is below saturation and there is no precipitation, and in the other region the water vapor is above saturation level and precipitation is nonzero. The boundary between the two regions is a free boundary that moves at a constant speed. It is shown that only certain front speeds are allowed. The three types of fronts that exist for this model are drying fronts, slow moistening fronts, and fast moistening fronts. Both types of moistening fronts violate Lax’s stability criterion, but they are robustly realizable in numerical experiments that use finite relaxation times. Remarkably, here it is shown that all three types of fronts are robustly realizable analytically for finite relaxation time. All three types of fronts may be physically unreasonable if the front spans an unrealistically large physical distance; this depends on various model parameters, which are investigated below. From the viewpoint of applied mathematics, these model equations exhibit novel phenomena as well as features in common with the established applied mathematical theories of relaxation limits for conservation laws and waves in reacting gas flows.     

Fourier transform spectroscopy around 3 μm with a broad difference frequency comb

We characterize a new mid-infrared frequency comb generator based on difference frequency generation around 3.1 μm. High power per comb mode (>10^?7 W/mode) is obtained over a broad spectral span (>750 nm, >790 cm^?1). The source is used for direct absorption spectroscopy with a Michelson-based Fourier transform interferometer.     

The Anomaly Line Bundle of the Self-Dual Field Theory

In this work, we determine explicitly the anomaly line bundle of the abelian self-dual field theory over the space of metrics modulo diffeomorphisms, including its torsion part. Inspired by the work of Belov and Moore, we propose a non-covariant action principle for a pair of Euclidean self-dual fields on a generic oriented Riemannian manifold. The corresponding path integral allows one to study the global properties of the partition function over the space of metrics modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual fields differs from the determinant bundle of the Dirac operator coupled to chiral spinors by a flat bundle that is not trivial if the underlying manifold has middle-degree cohomology, and whose holonomies are determined explicitly. We briefly sketch the relevance of this result for the computation of the global gravitational anomaly of the self-dual field theory, that will appear in another paper.     

Rate of Convergence for Cardy’s Formula

We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy–Smirnov formula. We use this result to obtain new upper and lower bounds of ${e^{O(\sqrt{{\rm log}\,{\rm log} R})}\, R^{-1/3}}$ for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R ^?1/3+o(1).