Numerical simulation of burning front propagation

In the context of a numerical experiment, it is shown that the switching wave described by the reaction-diffusion equation can be delayed at a medium inhomogeneity with a thickness Δ and amplitude Δβ for a finite time τ = τ(Δβ, Δ) up to a complete stop at it (τ = ∞). Critical values Δβ _c and Δ _c corresponding to the autowave stop are found. The similarity laws \(\tau \sim (\Delta _c - \Delta )^{ - \gamma _\Delta } \) and \(\tau \sim (\Delta \beta _c - \Delta \beta )^{ - \gamma _\beta } \) are established, and the critical indices and are found. The similarity law is established for critical values of amplitude and width of the inhomogeneity corresponding to the autowave stop Δβ _c ～ Δ _c ^-δ where δ ≈ 1.     

声传播研究中拉格朗日法与欧拉法的区别

1　引　言在描述流体运动状态时有两种方法 :拉格朗日和欧拉描述。拉格朗日描述着眼于流体中某一体元 ,研究该体元在运动中的性质 ;欧拉描述着眼于空间某一固定点 ,研究某一时刻通过该固定点的流体的性质。在一维运动中 ,拉格朗日描述将初始位置为x0 的体元在时刻 t的位移 x、速度 u、密度ρ均写为 t和 x0 的函数 ;欧拉描述将表征流体性质的各量都写成固定点 x和时间 t函数。一般的研究流体力学问题采用欧拉描述 ,研究声学问题采用拉格朗日描述。在均匀流体中当体元速度及声压很小时 ,欧拉描述与拉格朗日描述之间的差别可以忽略 ,对于较大的…     

Estimation of the fracture front propagation time in structural components

We discuss special features of the fracture front propagation in structural components (variable-thickness disks and plates, internally pressurized thick-walled vessels). The upper and lower bounds of the relative time of the front propagation have been estimated. Some recommendations regarding the application of the results obtained are provided. __________ Translated from Problemy Prochnosti, No. 6, pp. 13–24, November–December, 2007.     

Coronal waves: propagation in the multi-fluid description

We study wave propagation in the low-beta coronal plasma using a collisionless multi-fluid model. Neglecting the electron inertia, this model allows us to take into account ion-cyclotron wave effects that are absent in the magnetohydrodynamics model. To accomplish this, we perform a Fourier plane-wave perturbation analysis. Solving numerically the dispersion relations obtained from a two- and three-fluid model, dispersion curves for representative parameters of the solar corona are presented. The results reveal the presence of resonance frequencies that might play a role in coronal heating.     

Effect of polymer additives on propagation of turbulence front

A study is made of the propagation of a turbulent region formed by vibrations of plates with holes in solutions of polyoxyethylene and guar resin. Polymer additives are found to appreciably affect the motion of a turbulence front.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 2, pp. 220–224, August, 1982.     

Diffusion-migration description of finely dispersed impurity propagation in a turbulent jet

Computations of the scattering of a finely dispersed impurity in a submerged jet are performed on the basis of a model taking account of turbulent diffusion and turbulent migration together.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 59, No. 4, pp. 609–614, October, 1990.     

Drying of porous building materials: hydraulic diffusivity and front propagation

One-dimensional drying of a porous building material is modelled as a nonlinear diffusion process. The most difficult case of strong surface drying when an internal drying front is created is treated in particular. Simple analytical formulae for the drying front and moisture profiles during second stage drying are obtained when the hydraulic diffusivity is known. The analysis demonstrates the origin of the constant drying front speed observed elsewhere experimentally. Application of the formulae is illustrated for an exponential diffusivity and applied to the drying of a fired clay brick.

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Résumé Le séchage d'un matériau poreux est décrit par l'équation de diffusion non linéaire. Pour un coefficient de diffusion donné, des formules analytiques simples sont obtenues pour les profils hydriques et pour le front de séchage. Le cas, difficile à traiter, où la surface du matériau est éventuellement sèche, est considéré en détail. L'analyse montre l'origine de la vitesse constante du front de séchage, qui a été observée dans des études expérimentales indépendantes. L'application des formules au séchage d'une brique d'argile est illustrée pour un coefficient de diffusion qui dépend exponentiellement du contenu hydrique.

     

Link between alginate reaction front propagation and general reaction diffusion theory

We provide a common theoretical framework reuniting specific models for the Ca(2+)-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differential equations that are traditionally solved numerically: the Mikkelsen-Elgsaeter model. Applying the traveling-wave hypothesis as a major simplification, we obtain an analytical solution. The solution indicates that the fundamental properties of the alginate reaction front are governed by a single dimensionless parameter λ. For small λ values, a large depletion zone accompanies the reaction front. For large λ values, the alginate reacts before having the time to diffuse significantly. We show that the λ parameter is of general importance beyond the alginate model system, as it can be used to classify known solutions for second-order reaction diffusion schemes, along with the novel solution presented here. For experimental validation, we develop a microchip model system, in which the alginate gel formation can be carried out in a highly controlled, essentially 1D environment. The use of a filter barrier enables us to rapidly renew the CaCl(2) solution, while maintaining flow speeds lower than 1 μm/s for the alginate compartment. This allows one to impose an exactly known bulk CaCl(2) concentration and diffusion resistance. This experimental model system, taken together with the theoretical development, enables the determination of the entire set of physicochemical parameters governing the alginate reaction front in a single experiment.     

Eikonal equation‐based front propagation for arbitrary complex configurations

This paper presents a front propagation method using the Eikonal equation, ?? ? ?? = 1, in which, ? represents the smallest Euclidean distance field to the front to be propagated. The offset capturing approach consists in first calculating the ? field over a uniform Cartesian grid fully covering the front to be propagated, and then constructing the iso‐? curves or surfaces as the propagated result. The calculation of ? uses a 3D numerical scheme, the Fast Sweeping Scheme. Validation for accuracy of the method is presented using academic test cases. A real 3D industry application, draft tube with two piers, is successfully propagated and demonstrated using special boundary conditions to cope with inlet and outlet planes during front propagtion. This application involves the propagation of a front that exhibits both concave and convex shape regions, sharp corners, and local tangent plane surface discontinuities as well as a multi‐connected domain. Copyright © 2007 John Wiley & Sons, Ltd.     

Shock front analysis for axial shear wave propagation in a hyperelastic incompressible solid

Summary A wavefront analysis is employed to study the propagation of axial shear waves in an incompressible hyperelastic solid, whose strain energy function is expressible as a truncated power series in terms of the basic invariants of the left Cauchy-Green tensor. Waves are generated by the application of an axial shear stress at the surface of a cylindrical cavity in an unbounded medium. Depending on the nature of the boundary condition, an acceleration front or a shock front propagates from the boundary of the cavity. For an acceleration front, the coefficients in the wavefront expansion satisfy a sequence of transport equations which can be solved analytically. For a shock front, a wavefront analysis gives approximate formulas for the wave speed, shock front and intensity of the various field variables at the front. As well, our shock front analysis is used to devise a method of estimating the breaking distance of a shock front. In order to test the validity of the results of our wavefront analysis, numerical solutions are obtained for waves initiated by a step function or by a finite duration pulse at the boundary. Our numerical solutions are found by using a recently proposed relaxation scheme for systems of conservation laws.     

On the propagation of a weak shock front: Theory and application

Summary In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of shock-rays, which play the same role as the rays in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.With 7 Figures     

Transient effects in fatigue crack propagation

The transient fatigue crack propagation resulting from the sudden change of the stress intensity factor amplitude or from the change of the stress cycle asymmetry or from the application of the single overload cycle was measured on carbon steel specimens. To simplify the conditions and to increase the accuracy the shape of the specimens was chosen in such a way, that the stress intensity factor was independent of the crack length. It was shown that the transient effects can be qualitatively understood and quantitatively in the first approximation described solely on the basis of the steady state fatigue crack propagation data, provided that the threshold conditions of non-propagation are taken into account.     

Bloch's oscillations in quantum circuits with charge discreteness

We consider the effect of charge discreteness in a quantum circuit with inductance L. The inductance is pierced by a time-depending external magnetic field, which creates a time-dependent magnetic flux /spl phi//sub ext/(t). When the external magnetic flux varies linearly with time, the induced current in the inductance oscillates with a frequency proportional to the flux variation and charge discreteness. This phenomenon is equivalent to well-known Bloch's oscillation in crystal or periodic superlattices heterostructures. In fact, formally, the charge discreteness plays the role of a lattice constant. The same phenomenon occurs when the flux variations are replaced by a (constant) electromotive force. We expect this phenomena to be realized in micrometer sized solid-state systems.