Nonequilibrium vibration-dissociation phenomena behind a propagating shock wave: Vibrational population calculation

An analysis of nonequilibrium phenomena behind a plane shock is presented concerning the vibrational relaxation and the dissociation of a pure diatomic gas. In the first part, the temperature range is 600 K–2500 K and the dissociation processes are neglected. The population of each vibrational level is computed by solving relaxation and conservation equations. The relaxation process is described by the master equations of each vibrational level. The vibrational transition probabilities appearing in the relaxation equations are calculated analytically and take into account the anharmonicity of molecular vibration and the potential angular dependence. The populations obtained are compared to those calculated using a Treanor model and to those calculated with a nonequilibrium Boltzmann distribution. For moderately high levels significant differences may be observed. The importance of the V-V process is found to be weak for the transitions involving the lowest levels. In the second part, the temperature range is 2500 K–5500K and the dissociation process is taken into account as well as the gas dynamic behavior which did not appear in several recent works. The kinetic equations are transformed to obtain a first order differential system and the resolution of such a system coupled with the conservation equations leads to the population of each vibrational level. The vibrational transition probabilities associated with the atom-molecule interaction are deduced from the cross section calculation used in the first part. The bound-free transition probabilities are obtained, following Marrone and Treanor, assuming that dissociation must occur preferentially from the higher vibrational states: the Marrone and Treanor probability model is extended and employed with an anharmonic oscillator. In the present investigation, behind the shock wave, the evolution of the population distribution expressed as a function of the distance is not monotonous: a lag time appears as shown experimentally in previous works for the macroscopic parameters. For moderately high levels the influence of the anharmonicity and those of the V-V processes appear significant and strongly related. In a general way, in both temperature ranges investigated, the V-V processes reduce the effects of the T-V transfer. Finally the influence of thecharacteristic probability temperature U of Marrone and Treanor is analyzed and a method of determination of local varying U is proposed.     

A numerical study on the deformation and fracture modes of steel projectiles during Taylor bar impact tests

A heterogeneous material model based on macro-mechanical observations is proposed for simulation of fracture in steel projectiles during impact. A previous experimental study on the deformation and fracture of steel projectiles during Taylor bar impact tests resulted in a variety of failure modes. The accompanying material investigation showed that the materials used in the impact tests were heterogeneous on scales ranging from microstructure as investigated with SEM to variation in fracture strains from tensile tests. A normal distribution is employed to achieve a heterogeneous numerical model with respect to the fracture properties. The proposed material model is calibrated based on the tensile tests, and then used to independently simulate the Taylor bar impact tests. A preliminary investigation showed that the simulations are sensitive to assumptions regarding the anvil behaviour and friction properties. A flexible anvil and a yield-limited friction law are shown to be necessary to correctly reproduce the experimental behaviour. The proposed model is then shown to be capable of correctly reproducing all fracture modes but one, and also predict critical impact velocities for projectile fracture with reasonable accuracy. Fragmentation at velocities above the critical velocity is not well reproduced due to excessive element erosion. Measures to make the element erosion process more physical are proposed and discussed with their respective drawbacks. The use of a simple fracture criterion in combination with an element erosion technique accentuates the effect of distributing the fracture parameter.     

Constructing transient response probability density of non-linear system through complex fractional moments

The probability density function for transient response of non-linear stochastic system is investigated through the stochastic averaging and Mellin transform. The stochastic averaging based on the generalized harmonic functions is adopted to reduce the system dimension and derive the one-dimensional Itô stochastic differential equation with respect to amplitude response. To solve the Fokker–Plank–Kolmogorov equation governing the amplitude response probability density, the Mellin transform is first implemented to obtain the differential relation of complex fractional moments. Combining the expansion form of transient probability density with respect to complex fractional moments and the differential relations at different transform parameters yields a set of closed-form first-order ordinary differential equations. The complex fractional moments which are determined by the solution of the above equations can be used to directly construct the probability density function of system response. Numerical results for a van der Pol oscillator subject to stochastically external and parametric excitations are given to illustrate the application, the convergence and the precision of the proposed procedure.     

Reliability evaluation and control for wideband noise-excited viscoelastic systems

Reliability of first-passage type for wideband noise-excited viscoelastic systems and the quasi-optimal bounded control strategy for maximizing system reliability are investigated. The viscoelastic term is approximately replaced by equivalent damping and stiffness separately. By using the stochastic averaging method based on the generalized harmonic functions, the averaged Itô stochastic differential equation is obtained for the system amplitude. The associated backward Kolmogorov equation is derived and solved to obtain the system reliability. By applying the dynamic programming principle to the averaged system, the quasi-optimal bounded control is devised by maximizing system reliability. The application of the proposed analytical procedures and the effectiveness of the control strategy are illustrated through one example.     

Prediction of the effective elastic moduli of materials with irregularly-shaped pores based on the pore projected areas

Statistical modeling is used to correlate geometric parameters of pores with their contributions to the overall Young’s moduli of linearly elastic solids. The statistical model is based on individual pore contribution parameters evaluated by finite element simulations for a small pore subset selected using the design of experiments approach, so there is no need to solve the elasticity problem for all pores in the material. A polynomial relating pore geometric parameters to the contribution parameters is then fitted to the results of the simulations. We found a good correlation between normalized projected areas of the pores on three coordinate planes and their contributions to the corresponding effective Young’s moduli. The model is applied and validated for two large sets of pore geometries obtained by X-ray microcomputed tomography of a carbon/carbon and a 3D woven carbon/epoxy composite specimens.     

An empirical MM2 augmented force field for the cycloimmonium ylides

An original procedure approach taking into account the implementation of parameters determined, using calculations based on density functional theory, for the amidocyano-pyridinium methylide in the MM2 augmented harmonic potential function has been proposed. A good agreement between theoretical force field calculation and X-ray diffraction data has been observed. Thus an empirical force field for cycloimmonium ylides has been established. It provides good quality geometries for cycloimmonium ylide molecules by energy minimization. In this study we proposed a new MM2 augmented atom-type for the ylidic carbon atom. To our knowledge no attempt has been done in this way for such organic systems. Thus, we have shown that parameterization established by the DFT method is able to reproduce or to predict with good accuracy the structures of the cycloimmonium ylide compounds. This study also includes a full conformational analysis.     

An integrated operation module for individual risk management

In this study, we used the cumulative prospect theory to propose the individual risk management process (IRM) which includes risk analysis and risk response stages. According to an individual’s preferential structure, the process has been developed into an operational module which includes two sub-modules. From this, the individual’s risk level for the confronted risk can be identified from the risk analysis, while the response strategies can be assessed at the risk response stage. Therefore, optimal response strategies can be recommended based on individual risk tolerance levels.     

The ‘Temperature Integral’ — Its use and abuse

This paper first reviews the history of the temperature dependence of reaction rate in reaction kinetics. The various equations which are in use today for expressing this dependence were delineated by van't Hoff almost one hundred years ago. Since an exponential form best describes this dependence for most thermal analysis reactions and, due to the fact that the simple Arrhenius equation (with a temperature-independent preexponential factor) has traditionally been used for this purpose, the mathematically intractable temperature integral often has become a necessary evil in the analysis of thermal analysis kinetics. Methods which avoid the temperature integral in kinetics analysis are discussed. The merits of various evaluations and approximations for the temperature integral are described and assessed in this paper.     

Biologically-inspired stochastic vector matching for noise-robust information processing

“End of Moore’s Law” has recently become a topic. Keeping the signal-to-noise ratio (SNR) at the same level in the future will surely increase the energy density of smaller-sized transistors. Lowering the operating voltage will prevent this, but the SNR would inevitably degrade. Meanwhile, biological systems such as cells and brains possess robustness against noise in their information processing in spite of the strong influence of stochastic thermal noise. Inspired by the information processing of organisms, we propose a stochastic computing model to acquire information from noisy signals. Our model is based on vector matching, in which the similarities between the input vector carrying external noisy signals and the reference vectors prepared in advance as memorized templates are evaluated in a stochastic manner. This model exhibited robustness against the noise strength and its performance was improved by addition of noise with an appropriate strength, which is similar to a phenomenon observed in stochastic resonance. Because the stochastic vector matching we propose here has robustness against noise, it is a candidate for noisy information processing that is driven by stochastically-operating devices with low energy consumption in future. Moreover, the stochastic vector matching may be applied to memory-based information processing like that of the brain.     

Expected Residual Minimization Method for Stochastic Variational Inequality Problems

This paper considers a stochastic variational inequality problem (SVIP). We first formulate SVIP as an optimization problem (ERM problem) that minimizes the expected residual of the so-called regularized gap function. Then, we focus on a SVIP subclass in which the function involved is assumed to be affine. We study the properties of the ERM problem and propose a quasi-Monte Carlo method for solving the problem. Comprehensive convergence analysis is included as well. This work was supported in part by SRF for ROCS, SEM and Project 10771025 supported by NSFC.