Mathematical Sciences: "Wave Motion in Single-Phase and Multi-Phase Reactive Media

小行星9623235 拟议的工作旨在模拟和分析波浪运动所造成的，援助，或激发的化学能的解放， 反应媒体。 最终的目标是对燃烧波的起源、相互作用、对扰动的反应和过渡的方式进行数学描述。 建议在四个具体领域开展工作：其中两个领域的介质是单相材料，即，气态混合物，和 其中介质是两相材料，即，固体的混合物 粒子和气体。 在单相的情况下，该计划是研究（一）火焰如何传播通过分层的混合物中的分层的规模是可比的火焰的自然长度，以及（二）如何爆炸的发展和传播（或未能做到这一点）的温度，速度和浓度梯度的区域，特别是在非平面配置。 在研究的两个阶段部分，目标是（i）渐近 减少复杂的模型，利用某些自然和现实的限制，快速平衡，及（ii）探索正规化问题所产生的数值实现减少模型。 在所有情况下，努力将主要集中在非定常过程。 预计该 这些问题大体上将由非线性偏微分方程系统来模拟。 其目的是明确的解决方案的建设，只要可行，与分析技术（特别是渐近性和奇异摄动）和准确，良好解决的数值之间的相互作用的强烈强调。 %%% 安全有效地使用、无危险地储存和运输 易燃易爆材料要求精确了解燃烧的基本过程。 该提案旨在实现这一目标。 通过数学建模，分析和计算，了解某些特定的燃烧问题。 研究中的一类问题涉及分层混合物中火焰和爆炸的传播。 这是一个在包括消防安全在内的几种情况下具有实际意义的领域 分层可能是由意外溢出造成的，以及 可能已经产生分层进气的内燃机 故意的 第二类问题是关于 在损坏的爆炸物中，爆炸可能非常容易受到低速冲击或相对温和的热损伤。 ***

9623235 Kapila The proposed work is aimed at the modelling and analysis of wave motion that is caused, aided, or provoked by the liberation of chemical energy in exothermically reacting media. The ultimate goal is a mathematical description of the manner in which waves of combustion originate, interact, respond to disturbances, and undergo transitions. Work is proposed in four specific areas: two in which the medium is a single-phase material, i.e., a gaseous mixture, and two in which the medium is a two-phase material, i.e., a mixture of solid particles and gas. In the single-phase context the plan is to study (i) how flames propagate through a stratified mixture in which the scale of stratification is comparable to the natural length of the flame, and (ii) how detonations evolve and propagate (or fail to do so) in regions of temperature, velocity and concentration gradients, especially in nonplanar configurations. In the two-phase portion of the study the objectives are (i) asymptotic reduction of complex models by exploitation of certain natural and realistic limits of rapid equilibration, and (ii) exploration of regularization issues arising in the numerical implementation of reduced models. In all cases the effort will focus largely on unsteady processes. It is anticipated that the problems will be modelled, by and large, by systems of nonlinear partial differential equations. The aim is the construction of explicit solutions, wherever feasible, with strong emphasis on the interplay between analytical techniques (especially asymptotics and singular perturbations) and accurate, well-resolved numerics. %%% Safe and efficient usage, and hazard-free storage and transportation, of combustible and explosive materials demands that the fundamental processes of combustion be precisely understood. This proposal is aimed at achieving such an understanding of certain specific combustion problems, via mathematical modelling, analysis and computation. One c lass of problems under study deals with propagation of flames and detonations in stratified mixtures. This is an area of practical interest in several contexts, including fire safety where stratification may have been caused by an accidental spill, and internal combustion engines where a stratified charge may have been produced intentionally. The second class of problems is concerned with the occurence of explosions in damaged explosives, which can be highly susceptible to low-velocity impacts or relatively mild thermal insults. ***