Traveling waves in trimer granular lattice I: Bifurcation structure of traveling waves in the unit-cell model

Present paper is the first one in the series devoted to the dynamics of traveling waves emerging in the uncompressed, tri-atomic granular crystals. This work is primarily concerned with the dynamics of one-dimensional periodic granular trimer (tri-atomic) chains in the state of acoustic vacuum. Each unit cell consists of three spherical particles of different masses subject to periodic boundary conditions. Hertzian interaction law governs the mutual interaction of these particles. Under the assumption of zero pre-compression, this interaction is modeled as purely nonlinear, which means the absence of linear force component. The dynamics of such chains is governed by the two system parameters that scale the mass ratios between the particles of the unit cell. Such a system supports two different classes of periodic solutions namely the traveling and standing waves. The primary objective of the present study is the numerical analysis of the bifurcation structure of these solutions with emphasis on the dynamics of traveling waves. In fact, understanding of the bifurcation structure of the traveling wave solutions emerging in the unit-cell granular trimer is rather important and can shed light on the more complex nonlinear wave phenomena emerging in semi-infinite trimer chains. (c) 2016 Elsevier B.V. All rights reserved.

Dynamic Characteristics of Spherically Converging Detonation Waves

The spherically converging detonation wave was numerically investigated by solving the one-dimensional multi-component Euler equations in spherical coordinates with a dispersion-controlled dissipative scheme. Finite rate and detailed chemical reaction models were used and numerical solutions were obtained for both a spherical by converging detonation in a stoichiometric hydrogen-oxygen mixture and a spherically focusing shock in air. The results showed that the post-shock pressure approximately arises to the same amplitude in vicinity of the focal point for the two cases, but the post-shock temperature level mainly depends on chemical reactions and molecular dissociations of a gas mixture. While the chemical reaction heat plays an important role in the early stage of detonation wave propagation, gas dissociations dramatically affect the post-shock flow states near the focal point. The maximum pressure and temperature, non-dimensionalized by their initial value, are approximately scaled to the propagation radius over the initial detonation diameter. The post-shock pressure is proportional to the initial pressure of the detonable mixture, and the post-shock temperature is also increased with the initial pressure, but in a much lower rate than that of the post-shock pressure.

Kramers Escape Rate in Nonlinear Diffusive Media

In this paper, we study nonlinear Kramers problem by investigating overdamped systems ruled by the one-dimensional nonlinear Fokker-Planck equation. We obtain an analytic expression for the Kramers escape rate under quasistationary conditions by employing

Influences of Hydration Force and Elastic Strain Energy on the Stability of Solid Film in a Very Thin Solid-on-Liquid Structure

Since hydration forces become very strong at short range and are particularly important for determining the magnitude of the adhesion between two surfaces or interaction energy, the influences of the hydration force and elastic strain energy due to hydration-induced layering of liquid molecules close to a solid film surface on the stability of a solid film in a solid-on-liquid (SOL) nanostructure are studied in this paper. The liquid of this thin SOL structure is a kind of water solution. Since the surface forces play an important role in the structure, the total free energy change of SOL structures consists of the changes in the bulk elastic energy within the solid film, the surface energy at the solid-liquid interface and the solid-air interface, and highly nonlinear volumetric component associated with interfacial forces. The critical wavelength of one-dimensional undulation, the critical thickness of the solid film, and the critical thickness of the liquid layer are studied, and the stability regions of the solid film have been determined. Emphasis is placed on calculation of critical values, which are the basis of analyzing the stability of the very thin solid film.

Simulating shock to detonation transition: Algorithm and results

An algorithm based on flux-corrected transport and the Lagrangian finite element method is presented for solving the problem of shock dynamics. It is verified through the model problem of one-dimensional strain elastoplastic shock wave propagation that the algorithm leads to stable, non-oscillatory results. Shock initiation and detonation wave propagation is simulated using the algorithm, and some interesting results are obtained. (C) 1999 Academic Press.

The Mach reflection of a detonation based on soot track measurements

This paper presents a series of soot tracks formed by gaseous detonation waves diffracting around wedges with different wedge angles. These cellular structure patterns describe the Mach-reflection processes of a detonation and reveal some unique characteristics. They can be used to analyze the relationship between the trajectory angle of the triple point, wedge angle, and initial pressure in Mach reflection. Compared to the Mach-reflected one-dimensional shock wave in nonreactive air, all these unique characteristics for a Mach-reflected detonation should be attributed to the transverse-wave structure of the detonation front; meanwhile, the precursor shock wave and transverse wave influence the Mach-reflected detonation, respectively. The experimental results support the recently published numerical simulation of this complex phenomenon.

Spatiotemporal chaos control with pinning signals in distributed systems

We suggest a local pinning feedback control for stabilizing periodic pattern in spatially extended systems. Analytical and numerical investigations of this method for a system described by the one-dimensional complex Ginzburg-Landau equation are carried out. We found that it is possible to suppress spatiotemporal chaos by using a few pinning signals in the presence of a large gradient force. Our analytical predictions well coincide with numerical observations.

The application of B-P constitutive equations in finite element analysis of high velocity impact

We present in this paper the application of B-P constitutive equations in finite element analysis of high velocity impact. The impact process carries out in so quick time that the heat-conducting can be neglected and meanwhile, the functions of temperature in equations need to be replaced by functions of plastic work. The material constants in the revised equations can be determined by comparison of the one-dimensional calculations with the experiments of Hopkinson bar. It can be seen from the comparison of the calculation with the experiment of a tungsten alloy projectile impacting a three-layer plate that the B-P constitutive equations in that the functions of temperature were replaced by the functions of plastic work can be used to analysis of high velocity impact.

Martensitic transformation under impact with high strain rate

This paper deals with the quantitative prediction of the volume fraction of martensitic transformation in a austenitic steel that undergoes impact with high strain rate. The coupling relations between strain, stress, strain rate, transformation rate and transformed fraction were derived from the OTC model and modified Bodner-Partom equations, where the impact process was considered as an adiabatic and no entropy-increased process (pressure less than or equal to 20GPa). The one-dimensional results were found to model and predict various experimental results obtained on 304 stainless steel under impact with high strain rate.

High Frequency Acousto-electric Single Photon Source

We propose a single optical photon source for quantum cryptography based on the acousto-electric effect. Surface acoustic waves (SAWs) propagating through a quasi-one-dimensional channel have been shown to produce packets of electrons which reside in the SAW minima and travel at the velocity of sound. In our scheme these electron packets are injected into a p-type region, resulting in photon emission. Since the number of electrons in each packet can be controlled down to a single electron, a stream of single (or N) photon states, with a creation time strongly correlated with the driving acoustic field, should be generated.

超燃燃烧室一维流场分析模型的研究

对公开发表的用于超声速燃烧流场分析的几种一维模型进行了研究，指出了其中存在的问题，研究结果表明：基于实验静压数据的一维模型，若不借助必要的流场测量数据或分析结果，或借助于经验性的处理方法，单靠一维假设，无法获得较为完整的一维流场分析结果。改进后的一维模型降低了数据处理过程中的不确定性，提高了对一般情况的适应能力。用编制的计算程序SSC-2对两组典型的超燃燃烧室壁面静压实验数据进行了演算，取得了燃烧室出口总压恢复系数的计算值与测量值基本一致的好结果。

Roll Waves in Overland Flow

Roll waves are frequently observed in overland flow, especially in rill flow, which has an important effect on the development of soil erosion. Using one-dimensional St. Venant equations, this paper investigates the dynamics of periodic roll waves based on Dressler’s and Brock’s work. Under the assumption that the average flow depth equals the uniform flow depth, expressions of the roll-wave speed and roll-wave profile were obtained. Testing with the results observed by Brock (1970) for wave properties shows that these expressions can approximately describe the characteristics of periodic permanent roll waves. Numerical solutions of roll waves under specific conditions are found, which show that when a roll wave appears, the shear stress of flow increases, and the soil erosion accelerates.

A detailed chemistry multi-cycle simulation of a gasoline fueled HCCI engine operated with NVO

A previously developed Stochastic Reactor Model (SRM) is used to simulate combustion in a four cylinder in-line four-stroke naturally aspirated direct injection Spark Ignition (SI) engine modified to run in Homogeneous Charge Compression Ignition (HCCI) mode with a Negative Valve Overlap (NVO). A portion of the fuel is injected during NVO to increase the cylinder temperature and enable HCCI combustion at a compression ratio of 12:1. The model is coupled with GT-Power, a one-dimensional engine simulation tool used for the open valve portion of the engine cycle. The SRM is used to model in-cylinder mixing, heat transfer and chemistry during the NVO and main combustion. Direct injection is simulated during NVO in order to predict heat release and internal Exhaust Gas Recycle (EGR) composition and mass. The NOx emissions and simulated pressure profiles match experimental data well, including the cyclic fluctuations. The model predicts combustion characteristics at different fuel split ratios and injection timings. The effect of fuel reforming on ignition timing is investigated along with the causes of cycle to cycle variations and unstable operation. A detailed flux analysis during NVO unearths interesting results regarding the effect of NOx on ignition timing compared with its effect during the main combustion. © 2009 SAE International.

Pull-In Instability Of Micro-Switch Actuators: Model Review

The existing three widely used pull-in theoretical models (i.e., one-dimensional lumped model, linear supposition model and planar model) are compared with the nonlinear beam mode in this paper by considering both cantilever and fixed-fixed type micro and nano-switches. It is found that the error of the pull-in parameters between one-dimensional lumped model and the nonlinear beam model is large because the denominator of the electrostatic force is minimal when the electrostatic force is computed at the maximum deflection along the beam. Since both the linear superposition model and the slender planar model consider the variation of electrostatic force with the beam's deflection, these two models not only are of the same type but also own little error of the pull-in parameters with the nonlinear beam model, the error brought by these two models attributes to that the boundary conditions are not completely satisfied when computing the numerical integration of the deflection.

Reconsideration On The Role Of The Specific Heat Ratio In Arrhenius Law Applications

Arrhenius law implicates that only those molecules which possess the internal energy greater than the activation energy E-a can react. However, the internal energy will not be proportional to the gas temperature if the specific heat ratio gamma and the gas constant R vary during chemical reaction processes. The varying gamma may affect significantly the chemical reaction rate calculated with the Arrhenius law under the constant gamma assumption, which has been widely accepted in detonation and combustion simulations for many years. In this paper, the roles of variable gamma and R in Arrhenius law applications are reconsidered, and their effects on the chemical reaction rate are demonstrated by simulating one-dimensional C-J and two-dimensional cellular detonations. A new overall one-step detonation model with variable gamma and R is proposed to improve the Arrhenius law. Numerical experiments demonstrate that this improved Arrhenius law works well in predicting detonation phenomena with the numerical results being in good agreement with experimental data.