Diffusive-Dispersive Traveling Waves and Kinetic Relations: Part I: Nonconvex Hyperbolic Conservation Laws

Motivated by the theory of phase transition dynamics, we consider one-dimensional, nonlinear hyperbolic conservation laws with nonconvex flux-function containing vanishing nonlinear diffusive-dispersive terms. Searching for traveling wave solutions, we establish general results of existence, uniqueness, monotonicity, and asymptotic behavior. In particular, we investigate the properties of the traveling waves in the limits of dominant diffusion, dominant dispersion, and asymptotically small or large shock strength. As the diffusion and dispersion parameters tend to 0, the traveling waves converge to shock wave solutions of the conservation law, which either satisfy the classical Oleinik entropy criterion or are nonclassical undercompressive shocks violating it.     

高速扫描相机时间测量不确定度分析

以国内普遍使用的SJZ-30型高速扫描相机为例,用精测转速方法的结果处理数据,转速测量相对合成不确定度小于0.1%,时间间隔测量的相对扩展不确定度为0.2%.扫描速度在像面上的位置误差,采用"中值扫描速度",可予以校正.同时讨论了进一步降低转速测量不确定度和位置误差的方法.     

Preparation and characterization of Pt-supported porous graphite nanofibers

In this work, porous graphite nanofibers (PGNFs) were manufactured as promising catalyst supporter by a physical activation method for direct methanol fuel cells, and Pt nanoparticles were loaded on the PGNFs in order to prepare electrode materials by a chemical reduction method. The pore structures of the Pt/PGNFs were analyzed by N₂ adsorption isotherms at 77 K. Electrocatalytic activities of final products were investigated by voltammetry and conductivity measurements in a 1.0 M CH₃OH/0.5 M H₂SO₄. As a result, electrocatalytic activities of Pt/PGNFs were increased in the presence of Pt particles on the PGNFs and with increasing the specific surface area of the carbons.     

Dynamic adhesive strength of fiber-polymer systems

A new device for studying the dynamic adhesive strength is created. A procedure for determining the dynamic adhesive strength in fiber—polymer systems under impact loading (pull-out technique) is developed. The adhesive strength of the interface of polymer—steel wire joints formed by polymers of different chemical nature (epoxy resin, polysulfone, and polypropylene) is examined. It is shown that the dynamic adhesive strength grows as the loading rate increases for all the systems under investigation and that the relationship between the adhesive strength and the loading rate, , over a wide range of rates can be described by two straight lines corresponding to the quasi-static and impact loading, respectively. When passing from the quasi-static to dynamic loading, the character of scale relations of the adhesive strength does not change.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 689–700, November–December, 1999.     

Gasdynamic characteristics of toroidal shock and detonation wave converging

Shock wave focusing is a fundamental problem in the shock wave research and the instantaneous impulse of high temperature and pressure generated at the focal points has been applied recently in industrial and medical researches[1]. There are several methods to create shock wave focusing, among which the more commonly-used one is to make a planar shock wave reflect from a concave surface, such as the elliptical or parabolic re- flector. Toroidal shock wave focusing has been proposed and investi…     

Riemann problem for kinematical conservation laws and geometrical features of nonlinear wavefronts

A pair of kinematical conservation laws (KCL) in a ray coordinatesystem (,t) are the basic equations governing the evolutionof a moving curve in two space dimensions. We first study elementarywave solutions and then the Riemann problem for KCL when themetric g, associated with the coordinate designating differentrays, is an arbitrary function of the velocity of propagationm of the moving curve. We assume that m>1 (m is appropriatelynormalized), for which the system of KCL becomes hyperbolic.We interpret the images of the elementary wave solutions inthe (,t)-plane to the (x,y)-plane as elementary shapes of themoving curve (or a nonlinear wavefront when interpreted in aphysical system) and then describe their geometrical properties.Solutions of the Riemann problem with different initial datagive the shapes of the nonlinear wavefront with different combinationsof elementary shapes. Finally, we study all possible interactionsof elementary shapes.     

A Global Solution to a Two-dimensional Riemann Problem Involving Shocks as Free Boundaries

We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values.     

Entropy Production and Admissibility of Shocks

In shock wave theory there are two considerations in selecting the physically relevant shock waves.There is the admissibility criterion for the well-posedness of hyperbolic conservation laws.Another consideraztion concerns the entropy production across the shochs.The latter is natural from the physical point of view,but is not sufficient in its straightforward formulation,if the system is not genuinely nonlinear.In this paper we propose the principles of increasing entropy production and that of the superposition of shocks.These principles arc shown to be equivalent to the admissibility criterion.     

Stress State of Multilayer Structural Elements Subjected to Static Loading and Optimization of Laminated Beams and Bars

The results of FEM investigation of the triaxial stress state in multilayer structural elements subjected to axial and bending loads are presented. The distribution regularities of the stiffness and stresses or strains depending on the geometric and mechanical characteristics of layers and their position in the cross section of beams and bars are examined. The optimization of these elements is carried out using the dependences of the Bareisis—Paulauskas method and the Optim-98 computer program created by the present authors. As the optimization criteria, the strength, stiffness, mass, and cost of the structural elements are considered.     

Changes in ADC caused by tensile loading of rabbit achilles tendon: evidence for water transport

Water diffusion measurements were performed on rabbit Achilles tendons during static tensile loading and tendons in an unloaded state. The apparent diffusion coefficient (ADC) was measured along two directions: parallel and perpendicular to the long axis of the tendon. Tendons were studied after being prepared in two ways: (a) after being stored frozen in phosphate-buffered saline (PBS) and (b) freshly isolated. Statistically significant directional anisotropy was observed in the ADC in all tendons. The ADC was significantly greater in the direction parallel to the long axis of the tendon than in the perpendicular direction. The anisotropy is attributed to the greater restrictions seen by the water molecules in the perpendicular direction and is consistent with the known geometry of the tendon. Storage in PBS caused tendons to swell. This increased the ADC measured along both directions and reduced the anisotropy. The existence of anisotropy in the ADC was not related to the orientation of the specimen in the magnet. The ADC increased along both directions following the application of a 5-N tensile load; the increase was greatest along the perpendicular axis of the tendon. In order to determine whether load-related changes in the ADC reflected changes in interfibrilar spacing, we used electron microscopy to measure load-related changes in fibril spacing. Load-related changes in fiber spacing could not account for the observed changes in the ADC. The increase in ADC caused by loading was attributed to the extrusion of tendon water into a bulk phase along the outside surface of the tendon. In PBS-stored samples, enough fluid was extruded that it could be visualized. The transient response of the ADC to a 5-N tensile load was also studied. The absolute ADC in both directions increased with loading and recovered to baseline upon unloading. The transient changes in ADC, for both loading and unloading, had a mean time constant of approximately 15 min. The magnitude of the load-induced transient ADC changes was comparable to that seen in the static-loading experiments.