Complex dynamics of a simple distributed self-oscillatory model system with delay

A simple model for a distributed self-oscillatory system with cubic nonlinearity and delay is presented. Conditions for oscillation self-excitation and stationary oscillation conditions, as well as the stability of the oscillations, are analyzed. Nonstationary self-modulation regimes (including conditions of complex dynamics and chaos) are simulated numerically over a wide range of control parameters. As the factor of nonequilibrium grows, regular and chaotic regimes alternate in a complex manner. The transitions to chaos may follow all scenarios known for finite-dimensional systems. The model suggested is somewhat akin to a number of earlier finite-dimensional models aimed at studying mode competition in resonance electron masers.     

一类非线性方程解的存在和唯一性及在图像中的应用

本文我们给出一个修正的非线性扩散方程模型，与Cotte Lions和Morel的模型相比该模型有许多实质上的优点。主要的想法是把原来去噪声部分：卷积Gauss过程替代为解一个有界区域上的线性抛物方程问题，因此避开了对初始数值如何全平面延拓的问题。我们从数学上的证明该问题解的存在性和适定性，同时给出对矩形域情况的解的级数形式。最后我们给基于本模型的数值计算差分模型，并且给出几个具体图像在该模型下处理结果。     

Numerical simulation and experimental validation of heat transfer within rotating flows for three‐dimensional non‐axisymmetric,turbulent conditions

A control volume type numerical methodology for the analysis of steady three‐dimensional rotating flows with heat transfer, in both laminar and turbulent conditions, is implemented and experimentally tested. Non‐axisymmetric momentum and heat transfer phenomena are allowed for. Turbulent transport is alternatively represented through three existing versions of the k–ε model that were adjusted to take into account the turbulence anisotropy promoted by rotation, streamline curvature and thermal buoyancy. Their relative performance is evaluated by comparison of calculated local and global heat balances with those obtained through measurements in a laboratory device. A modified version of the Lam and Bremhorst, low Reynolds number model is seen to give the best results. A preliminary analysis focused on the flow structure and the transfer of heat is reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Growth of K(DxH1 − x )2PO4 single crystals from solutions in the K2O-P2O5-(D, H)2O system

Based on the analysis of the K₂O-P₂O₅-D₂O solubility phase diagram, the optimum conditions of KD₂PO₄ crystallization—the compositions of mother solutions and the temperature range of crystallization—in the KH₂PO₄-D₂O system have been determined. The technique of K(D_xH_{1 ? x} )₂PO₄ growth is developed. The DKDP single crystals with deuterium concentration up to 88 wt % are grown on DKDP seeds from KH₂PO₄ solutions in D₂O by the method of temperature decrease.     

Assigning patients to nurses in neonatal intensive care

An intensive care nursery provides health care for critically ill newborn infants. During a typical shift, infants range from those needing only occasional care to those requiring constant attention. At the beginning of each shift, the head nurse groups the patients for assignment to staff nurses. Typically each nurse cares for one group of infants throughout the shift. The large variation in infant conditions along with several complicating side constraints makes it difficult to develop balanced nurse work loads. We develop a mathematical programming approach for achieving better workload balance. We first develop a detailed neonatal acuity system that quantifies the nursing workload of each patient. We then develop an integer linear program that assigns patients to nurses while balancing nurse workloads. Because this model is computationally intractable, we develop a heuristic that exploits the fact that most nurseries are divided into a number of physical zones. We use ten case studies taken from a major university hospital to benchmark the performance of this heuristic. We also perform a designed experiment using randomly generated problems that examines the effect of nursery parameters on heuristic performance.     

Fleet configuration subject to stochastic demand: an application in the distribution of liquefied petroleum gas

We study the problem of configuring a fleet, in which vehicles receive information on-line about the demand that they should fulfil while they are on the road. In each district it must be decided the number of vehicles and their capacity. The objective function is to minimise the operational cost subject to constraints for the minimum delivery capacity, the maximum vehicle size and the average waiting time for customers. The last constraint is modelled as a queuing system that is adjusted according to the simulation of the delivery process of a Chilean company that distributes liquefied petroleum gas in portable cylinders. We provide the analytical form of all the components of the model, so it can be solved using a standard non-linear programming package. We show that the fleet may increase its sales by 3% and reduce the waiting time of customers 10% by allowing a set of vehicles to share the buffer of orders rather than having vehicles to exclusively serve smaller sectors.     

The role of water vapour on the oxidation of two Ln-Si-Al-O-N glasses (Ln=Y, La)

The oxidation behaviour of LnSiAlON (Ln=Y, La) glasses was studied at different temperatures (990-1150 °C) and under different water vapour pressures (360-2690 Pa). These results were also compared with those obtained under O₂, N₂/H₂O or O₂/H₂O mixtures. When glasses are treated under a N₂/H₂O mixture, optical and SEM observations show porous scales. Transformations of the reaction rate data and a kinetic model show that there is only one limiting process occurring during oxidation. This rate limiting step is the progress of the chemical reaction at the internal interface. Determination of the pressure law dependence and thermodynamics calculations of water vapour molecules dissociation at the investigated temperatures allow us to suggest that the mechanism of oxidation corresponds to decomposition of water molecules on the oxynitride glass surface.     

Disintegration of a drop in an external electrostatic field

Regular features of the disintegration of both a drop of a perfectly conducting liquid and a drop of a dielectric liquid into two or three parts in an external uniform electric field are studied using the principle of minimizing the potential energy of the final state of a closed system with spontaneous processes.     

Mode-locking dynamics of a laser coupled to an empty external cavity

The effect of incorporating an empty external cavity into the feedback loop of a mode-locked laser is investigated. Particular attention is paid to the response of the mode-locking as the external cavity is detuned by a fraction of a wavelength from the round trip transit time associated with the laser. The results for two regimes of operation are presented. In the first case a series of short lived transients develop whereas the other case leads to a persistent intermittent Q-switching scenario, where mode-locking fails. The role of coupling between the cavities and the laser's memory time in relation to the results is discussed. A mechanism for the improved mode-locking observed with non-linear external cavities is suggested.     

Asymptotic stability of the numerical solution for an integrodifferential reaction-diffusion system

This paper presents the study of the numerical solution of a reaction-diffusion system involving a reaction term of integral type arising from biological models. By means of a monotone approach we introduce upper and lower solutions and then we show the existence and the asymptotic behavior of nonnegative numerical solutions. To this end, we require the positivity of the numerical scheme and so we can use some properties of positive and M-matrices. Finally we give some sufficient conditions to verify the asymptotic stability of the numerical solution.