Dynamics of solid-melt front migration from a reaction–diffusion model

Using physical experiments we investigated the evolution of thermally driven melt patterns in a semi-infinite solid crystalline phase subjected to uniform heating from one side, maintaining melting temperature. We treat the melt initiation phenomenon theoretically in the perspective of two-phase interactions on the microscopic level, and propose a new reaction–diffusion model based on the prey–predator dynamics. This model predicts the fractal behavior of melt fronts observed in the experiments.     

CH4-O2 混合气中爆燃爆震转捩的数值模拟

运用化学流体力学基本理论和两步燃烧反应模型原理，建立了一维封闭体系可燃气爆燃爆震转变现象的数学模型，利用拉格朗日质量坐标变换下的Ｌａｘ－Ｗｅｎｄｒｏｆ和Ｍｅｃｏｒｍｉｃ气动差分与Ａｄａｍｓ化学差分格式，求解基本方程，成功地完成了过程的数值模拟，清楚地说明了可燃气中ＤＤＴ现象由压缩波到激波达到稳态爆震的发生机制和火焰带引生爆震波的过程行为。     

Influence of Differential Diffusion on Super-Equilibrium Temperature in Turbulent Non-Premixed Hydrogen/Air Flames

In this paper we wish to investigate the occurrence of super-equilibrium temperature values, observed in many experimental configurations. We would like to understand the origin of this phenomenon. Previous authors have already shown that differential diffusion can lead to considerable changes in the temperature field and we would like to build on top of this observation. We investigate numerically super-equilibrium combustion by considering both laminar counter-flow and turbulent diluted hydrogen/air diffusion flames. These turbulent flames are computed using direct numerical simulations (DNS). A detailed reaction mechanism is employed and the transport properties are modeled using multicomponent diffusion velocities, including the Soret effect. Analyzing these results we introduce three complementary parameters (dilution-free mixture fraction, dilution excess and local enthalpy) to describe the local combustion conditions. Introducing a measure of dilution separately from the mixture fraction is necessary for a proper analysis. Using this set of parameters it becomes possible to explain super-equilibrium temperature levels as a consequence of differential diffusion.     

???????????????????????е????

``自燃'是燃料化学动力学控制的基本燃烧现象. 本文通过正庚 烷详细化学动力学机理和简化骨干机理相结合的研究方法,验证了Livengood-Wu ``爆震累积临界值'概念(knock integral approach). 证明当反应H$\cdot``自燃'是燃料化学动力学控制的基本燃烧现象. 本文通过正庚 烷详细化学动力学机理和简化骨干机理相结合的研究方法,验证了Livengood-Wu ``爆震累积临界值'概念(knock integral approach). 证明当反应H$\cdot ``自燃'是燃料化学动力学控制的基本燃烧现象. 本文通过正庚 烷详细化学动力学机理和简化骨干机理相结合的研究方法,验证了Livengood-Wu ``爆震累积临界值'概念(knock integral approach). 证明当反应H$\cdot ``自燃'是燃料化学动力学控制的基本燃烧现象. 本文通过正庚 烷详细化学动力学机理和简化骨干机理相结合的研究方法,验证了Livengood-Wu ``爆震累积临界值'概念(knock integral approach). 证明当反应H$\cdot"自燃"是燃料化学动力学控制的基本燃烧现象.本文通过正庚烷详细化学动力学机理和简化骨干机理相结合的研究方法,验证了Livengoodo-Wu"爆震累积临界值"概念(knock integral approach).证明当反应H·+O_2=O·+OH·的高活化能势垒被击穿,形成高浓度OH自由基,混合气释放出大量的热量,系统温度急剧升高,自燃发生.本文还介绍了"均质压燃、低温燃烧"技术的研究进展,燃料自燃过程的控制是现代内燃机技术的重要内容.     

Pattern analysis of viscous oscillation in a shear flow induced by an exothermic reaction

An investigation is made of oscillatory phenomenon induced by an exothermic reaction. This oscillatory phenomenon occurs in a very thin mixing layer between two miscible and reacting fluids. A qualitative model based on the interaction among reaction, molecular momentum transfer, molecular heat transfer, molecular mass transfer and forced convective transfer was proposed by Kuroda and Ogawa [1994. Nonlinear waves in a shear flow with a diffusive exothermic reaction and its qualitative reasoning. Chem. Eng. Sci. 49(16), 2699-2708]. It is experimentally shown in the present study that the oscillatory patterns change in the flow direction. In the upstream area where oscillatory patterns are nearly straight stripes, effects of viscosity on those stripes are investigated. In the downstream area where stripes are wavy and disordered, fractal analysis is introduced to investigate the relationship between the transition of oscillatory flow patterns and process factors, i.e. the viscosity ratio, the entire viscosity, flow rate and the flow rate ratio. Fractal analysis is also applied to temperature oscillation, and it is confirmed that the characteristic patterns of oscillation become obscure as the entire viscosity increases. The entire viscosity is an important factor for controlling both oscillatory patterns of flow and temperature in this reactive flow system.     

Shock tube investigation of hydrodynamic issues related to inertial confinement fusion

A shock tube investigation of two hydrodynamic issues related to inertial confinement fusion (ICF) is undertaken. ICF is a promising source of energy for the future. There has been a considerable increase in the interest in ICF with the development of the National Ignition Facility (NIF). However, much remains to be investigated before a useful yield is obtained from a fusion reaction for power generation. The physics involved in carrying out a fusion reaction combines hydrodynamics, plasma physics and radiation effects superimposed on each other, at extremely small scales, making the problem very complex. One such phenomenon occurring in the deuterium-tritium pellet implosion is the Richtmyer-Meshkov instability occuring at each layer of the fuel which results in the mixing of the ablator with the fuel. This causes dilution of the fuel and reduces the yield of the reaction. Another issue is the impulsive loading of ICF reactor cooling tubes due to the shock wave produced as a result of the fusion reaction. These tubes must withstand the impulse of the shock wave. A shock tube provides an ideal environment to study these issues at large geometric scales with the isolation of hydrodynamics from other effects. A new vertical, square shock tube has been designed specifically for the purpose of studying these fluid flow phenomena from a fundamental point of view. The shock tube is vertical, with a large square inner cross-section and is designed to allow for the release of a shock into air at atmospheric pressure. In this paper, we describe the new shock tube and related instrumentation in detail and present a few preliminary results on the Richtmyer-Meshkov instability and shock-cylinder interactions. Received 5 January 1999 / Accepted 10 July 2000     

Universality of Crystallographic Pinning

We study traveling waves for reaction diffusion equations on the spatially discrete domain \mathbb Z²{\mathbb Z^2}. The phenomenon of crystallographic pinning occurs when traveling waves become pinned in certain directions despite moving with non-zero wave speed in nearby directions. In [19] it was shown that crystallographic pinning occurs for all rational directions, so long as the nonlinearity is close to the sawtooth, which itself was considered in [6]. In this paper we show that crystallographic pinning holds in the horizontal and vertical directions for bistable nonlinearities which satisfy a specific computable generic condition. The proof is based on dynamical systems. In particular, it relies on an examination of the heteroclinic chains which occur as singular limits of wave profiles on the boundary of the pinning region.     

Surface geometry of a liquid explosive burning beyond the stability limit

After L. D. Landau's work [1] on the stability of normal burning of liquid explosives, many experimental studies of this phenomenon, e. g., [2, 3], were published. In this paper, on the basis of Landau's theory, we investigate the geometry of the perturbations which develop on the surface of the liquid explosive in a vessel of circular cross section and consider the influence of vessel diameter on burning stability. Results of an experimental observation of the geometry of the liquid surface are also presented for developed turbulent combustion in a circular cylindrical tube. The calculation was based on the usual assumptions that the chemical reaction of combustion proceeds in a thin layer of vapor over the plane (meniscus neglected) surface of the inviscid liquid explosive.     

The static and dynamic behavior of MEMS arch resonators near veering and the impact of initial shapes

We investigate experimentally and analytically the effect of initial shapes, arc and cosine wave, on the static and dynamic behavior of microelectromechanical systems (MEMS) arch resonators. We show that by carefully choosing the geometrical parameters and the initial shape of the arch, the veering phenomenon (avoided-crossing) among the first two symmetric modes can be strongly activated. To demonstrate this, we study electrothermally tuned and electrostatically driven initially curved MEMS resonators. Upon changing the electrothermal voltage, we demonstrate high frequency tunability of arc resonators compared to the cosine-configuration resonators for the first and third resonance frequencies. For arc beams, we show that the first resonance frequency increases up to twice its fundamental value and the third resonance frequency decreases until getting very close to the first resonance frequency triggering the veering phenomenon. Around the veering regime, we study experimentally and analytically the dynamic behavior of the arc beam for different electrostatic loads. The analytical study is based on a reduced order model of a nonlinear Euler–Bernoulli shallow arch beam model. The veering phenomenon is also confirmed through a finite-element multi-physics and nonlinear model.     

低冲击下固体推进剂延迟起爆现象

为了研究固体推进剂在低强度冲击作用下的延迟爆轰现象（XDT）,设计了2次冲击波加载的双隔板实验。用X光摄像技术观测了推进剂在低强度冲击作用下的延迟起爆现象。建立了推进剂双隔板实验计算模型,运用非线性动力学有限元方法对推进剂的双隔板实验进行了数值模拟,得到推进剂在2次独立冲击波加载作用下的压力历史,分析了推进剂发生延迟爆轰的受力过程。结果表明,在强度较低的冲击波作用下,该推进剂会发生XDT现象,对推进剂重复冲击加载作用和推进剂在加载作用下的敏化程度是控制XDT现象发生的主要因素。     

The Lavrentiev Gap Phenomenon in Nonlinear Elasticity

The main objective of this paper is to present examples of the Lavrentiev phenomenon within the framework of two-dimensional nonlinear elasticity. Loosely speaking, this phenomenon is associated with the sensitivity of the infimum in a variational problem to the regularity required of the competing mappings. We provide a physically natural stored energy density and reasonable, though nontraditional, boundary conditions such that the energy functional exhibits the Lavrentiev phenomenon with admissible classes that are subsets of the continuous deformations. The stored-energy density W that we produce is smooth, materially homogeneous, frame-indifferent, isotropic and polyconvex. Furthermore, the corresponding minimization problem is such that existence of a continuous minimizer follows from known results. The basis for our examples is a convex integrand W ₀ for which the Euler-Lagrange equations have a very special form. We show that the functional associated with this W ₀ exhibits the Lavrentiev phenomenon for certain problems; by making a perturbation to W ₀ , we create the stored-energy density W described in the previous paragraph. With other perturbations to the integrand W ₀ and modifications of the boundary conditions, we are able to produce additional examples of the Lavrentiev phenomenon. Finally, we note that the integrand we use is just one of a family of integrands that can be used to produce examples of the phenomenon. (Accepted October 18, 2002) Published online March 12, 2003 Communicated by J. M. Ball     

Singularities in Three-Dimensional Compressible Euler Flows with Vorticity

It is known from earlier work that three-dimensional incompressible Euler flows with vorticity can develop a singularity in a finite time, at least if the initial conditions are of a certain class. Here we discuss corresponding possibilities for flows with compressibility. Naturally, it is known that the shock-wave phenomenon represents an important singular field in compressible fluid dynamics especially in the irrotational case. However, here we are concerned not with that phenomenon but rather with compressible flows where any singularity is associated with the presence of vorticity. In particular we expose the role played by the ratio of specific heats in an adiabatic flow field. Received 9 December 1996 and accepted 4 April 1997     

Investigation of Jet-Flame Blowout with Lean-Limit Considerations

The current study utilizes digital image sequences of flames to better understand the blowout phenomenon. Methane flames are studied near blowout conditions to determine if the disappearance of the diffusion flame prior to extinguishment signifies the leading edge of the reaction zone reaching the lean-limit. Various concentrations of nitrogen are used to dilute methane flames. The axial position of the flames is compared with the calculated position of the lean flammability limit to determine the role of the diffusion flame. The blowout limits of these flames are established and a blowout parameter is empirically determined from the data. Results from flames in co-flow show agreement with the blowout parameter previously published; however, the analysis shows that, the disappearance of the bulk diffusive reaction zone occurs at the lean flammability limit and is an accurate predictor of blowout for diluted and non-diluted methane flames.     

Phase-field model for the two-phase lithiation of silicon

As an ideal anode material, silicon has the highest lithium-ion capacity in theory, but the broader application is limited by the huge volumetric strain caused by lithium insertion and extraction. To better understand the physical process and to resolve the related reliability issue, enormous efforts have been made. Recent experiments observed sharp reaction fronts in both crystalline and amorphous silicon during the first lithiation half-cycle. Such a concentration profile indicates that the process is likely to be reaction limited. Based on this postulation, a phase-field model is developed and implemented into a finite-element code to simulate the coupled large inelastic deformation and motion of the reaction front in a silicon electrode. In contrast to most existing models, the model treats both volumetric and deviatoric inelastic deformation in silicon as a direct consequence of the lithiation at the reaction front. The amount of deviatoric deformation is determined by using the recently developed kinetic model of stress-induced anisotropic reaction. By considering the role of stress in the lithiation process, this model successfully recovers the self-limiting phenomenon of silicon electrodes, and relates it to the local geometry of electrodes. The model is also used to evaluate the energy-release rate of the surface crack on a spherical electrode, and the result suggests a critical size of silicon nanoparticles to avert fracture. As examples, the morphology evolution of a silicon disk and a Si nanowire during lithiation are also investigated.     

Curvature relation of wave front and wave changing in external field

Introduction ThestudiesofexcitablemediaconcernwithBZreaction,slimemoldaggregationand cardiactissue[1].Thepropertiesofthesemediaare:forsmallperturbationsthemediaquickly recovertotheirreststates,whileforstimuliexceedingathresholdthemediawillbeactivated andr…     

爆轰等离子体非平衡区的双流体模型

在爆轰等离子体中存在一个由化学反应放热非平衡导致的非平衡电离区。由于电子质量远小于重粒子质量,使得在电离区中电子与重粒子的能量与动量交换效率较低,这也加剧了这种非平衡特性。建立了爆轰等离子体非平衡电离区中的电子和重粒子的双流体模型,并通过该模型研究爆轰等离子体中的非平衡现象。以氢氧爆轰为例计算不同氢氧摩尔比和初始压力条件下,爆轰非平衡区中重粒子参数和电子参数的变化情况。     

Singularly perturbed semilinear elliptic equation with boundary-interior layer interaction

In this paper, we consider the phenomenon of the boundary and interior layer interactions for a class of semilinear elliptic equation. Under some appropriate conditions,we get the existence of the exact solution for the problem and its high order uniformly valid expansion.     

Projectile Impact on a Thin. Flexible Structure: A Singular Dynamic Contact Phenomenon

ABSTRACT

In this paper we demonstrate an unexpected type of dynamic contact phenomenon which arises when a large object impacts a thin flexible structure. It is shown that the contact pressure distribution is singular at the edges of the contact region when the region is expanding with a speed which is higher than the wave speed in the structure. This type of phenomenon will occur in a number of structural collision problems in which one of the objects such as a cable or a thin plate is much more flexible than the other. Head injury problems represent a typical example

The solution for a very simple model of such a system, namely that of a rigid cylindrical impaclor striking an infinitely long string, is given in detail to illustrate the phenomenon.     

Exact Statics and Approximate Dynamics of Adhering Lipid Tubules

In this paper we are concerned with the adhesion of lipid tubules to a plane wall: we treat both the statics and the dynamics of this phenomenon. Though we provide an exact solution to the equilibrium problem, our treatment of the dynamical problem is approximate, as it is based on a simplified model, which, nevertheless allows us to obtain quantitative information about the detachment dynamics of tubules. Received September 1, 1997