On maximum norm contractivity of second order damped single step methods

In this paper we consider A(θ)-stable finite difference methods for numerical solutions of dissipative partial differential equations of parabolic type. Combining two rational approximation methods with different orders of accuracy, where the lower order method is applied n ₀ times (n ₀ fixed) at each time step, we prove the existence of a second order method which is contractive for all time steps. Moreover, we shed light on the conditions on the lower order method which are sufficient (and sometimes necessary) to obtain the optimal order of accuracy. For the one-dimensional heat equation we construct a family of numerical methods which are contractive in the maximum norm for all values of the discretization parameters. We also present numerical examples to illustrate our results. Received: May 2002 / Accepted: January 2003     

The thermal behavior of mechanically activated galena by thermogravimetry analysis

The thermal decompositions of mechanically activated and nonactivated galenas were studied by thermogravimetry analysis (TGA) at the heating rate of 10 K min⁻¹ in argon. Results indicate that the initial temperature of thermal decomposition (abbreviated as T _di) in the TGA curves for different galenas decreases gradually with increased grinding time. The specific granulometric surface area (S _G), the structural disorder, and the content of elemental sulfur of mechanically activated galenas were analyzed by an X-ray diffraction (XRD) laser particle-size analyzer, XRD analysis, and the gravimetric method, respectively, which shows that the specific granulometric surface area of mechanically activated galenas remains almost constant after a certain grinding time, but the lattice distortions (ε) rise, the crystallite sizes (D) decrease, and the elemental sulfur contents of mechanically activated galenas increase with increased grinding time. The results imply that the decrease of the initial temperature of thermal decomposition in the TGA curves for mechanically activated galenas is mainly caused by the increase of lattice distortions, and the formation of new dangling bonds resulted from the production of elemental sulfur of mechanically activated galenas with increased grinding time. Finally, the differences in the thermal-decomposition reactivity between nonactivated and mechanically activated galenas were also discussed.     

Minimum-Energy Translational Trajectory Generation for Differential-Driven Wheeled Mobile Robots

Mobile robots can be used in many applications, such as exploration, search and rescue, reconnaissance, security, and cleaning. Mobile robots usually carry batteries as their energy source and their operational time is restricted by the finite energy available from the batteries. Therefore, energy constraints are critical to the service time of mobile robots. This paper investigates the minimum-energy control problem for translational trajectory generation, which minimizes the energy drawn from the batteries. Optimal control theory is used to find the optimal velocity trajectory in analytic form. To demonstrate energy efficiency obtainable, we performed simulations of minimum-energy velocity control and compared the results with loss-minimization control and energy-optimal trapezoidal velocity profiles. Simulation results showed that significant energy savings can be achieved, of up to 9% compared with loss-minimization control and up to 10% compared with energy-optimal trapezoidal velocity profile. We also performed an actual robot experiment using Pioneer 3-AT platform to show the validity of the proposed minimum-energy velocity control. The experimental results revealed that the proposed minimum-energy velocity control can save the battery energy up to 10% compared with loss-minimization control. Categories (3): Robot control, (5): RobotMotion Planning     

Case Study of an Aerosol Explosion and a Method to Determine Explosion Temperatures

A failure analysis case study is presented for a two-piece aerosol containing tetrafluoroethane, commonly referred to as Refrigerant 134a. A gentleman was preparing to recharge the air conditioning system of an automobile when the bottom exploded off the aerosol container, propelling the body of the aerosol container like a rocket, which hit the man in the eye and blinded him in that eye. The aerosol was never connected to the air conditioner, therefore backpressure from the air conditioner (AC) compressor was ruled out as a cause for the explosion. The objective of the study was to determine why the aerosol exploded. Several recently developed test methods were used, including two types of heat-to-burst tests and a puncture chamber to measure the pressure-versus-temperature behavior of aerosols. More common test methods were also used, such as water bath pressure tests, hydro pressure burst tests, pneumatic pressure burst tests, hardness measurements, weight measurements, metallography, scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), and an accident scenario recreation. A semi-empirical correlation between the hardness and weights of the container bottoms was used to determine the explosion temperature and/or pressure. This semi-empirical correlation agrees in principle with an analysis of the explosion pressures using finite-element analysis (FEA). The root cause for the explosion was determined to be a lack of strength of the bottom of the two-piece aerosol coupled with heating the aerosol to temperatures significantly above room temperature.     

Kinetics of chlorination of tantalum pentoxide in mixture with sucrose carbon by chlorine gas

The mechanism and kinetics of β-Ta₂O₅ chlorination, mixed with sucrose carbon, have been studied by a thermogravimetric technique. The investigated temperature range was 500 °C to 850 °C. The reactants and reaction residues were analyzed by scanning electronic microscopy (SEM), X-ray diffraction (XRD), and Brunauer-Emmett-Teller method for surface area (BET). The effect of various experimental parameters was studied, such as carbon percentage, temperature, chlorine partial pressure, and flow, use of the multiple sample method, and carbon previous oxidation. The carbon percentage and previous treatment have an effect on the system reactivity. The temperature has a marked effect on the reaction rate. In the 500 °C to 600 °C temperature interval, the apparent activation energy is 144 kJ/mol of oxide, while at higher temperatures, the activation energy decreases. With high chorine partial pressures, the order of reaction is near zero. The kinetic contractile plate model, X=kt, considering carbon oxidation as the controlling stage, is the one with the best fit to the experimental data. A probable mechanism for the carbochlorination of β-Ta₂O₅ is proposed: (1) activation of chlorine on the carbon surface, (2) chlorination of Ta₂O₅, (3) oxidation of carbon, and (4) recrystallization of β-Ta₂O₅.     

Transition to turbulence in rotating-disk boundary layers—convective and absolute instabilities

This work is an experimental study of mechanisms for transition to turbulence in the boundary layer on a rotating disk. In one case, the focus was on a triad resonance between pairs of traveling cross-flow modes and a stationary cross-flow mode. The other was on the temporal growth of traveling modes through a linear absolute instability mechanism first discovered by Lingwood (1995, J Fluid Mech 314:373–405). Both research directions made use of methods for introducing controlled initial disturbances. One used a distributed array of ink dots placed on the disk surface to enhance a narrow band of azimuthal and radial wave numbers of both stationary and traveling modes. The size of the dots was small so that the disturbances they produce were linear. Another approach introduced temporal disturbances by a short-duration air pulse from a hypodermic tube located above the disk and outside the boundary layer. Hot-wire sensors primarily sensitive to the azimuthal velocity component, were positioned at different spatial (r,θ) locations on the disk to document the growth of disturbances. Spatial correlation measurements were used with two simultaneous sensors to obtain wavenumber vectors. Cross-bicoherence was used to identify three-frequency phase locking. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. The space–time evolution of the leading and trailing edges of the wave packets were followed past the critical radius for the absolute instability, r _{c A} . With documented linear amplitudes, the spreading of the disturbance wave packets did not continue to grow in time as r _{c A} was approached. Rather, the spreading of the trailing edge of the wave packet decelerated and asymptotically approached a constant. This result supports the linear DNS simulations of Davies and Carpenter (2003, J Fluid Mech 486:287–329) who concluded that the absolute instability mechanism does not result in a global mode, and that linear-disturbance wave packets are dominated by the convective instability. In contrast, wave-number matching between traveling cross-flow modes confirmed a triad resonance that lead to the growth of a low azimuthal number (n = 4) stationary mode. At transition, this mode had the largest amplitude. Signs of this mechanism can be found in past flow visualization of transition to turbulence in rotating disk flows.     

Formal techniques for performance analysis: blending SAN and PEPA

In this paper we consider two performance modelling techniques from the perspectives of model construction, generation of an underlying continuous time Markov process, and the potential for reduction in the Markov process. Such careful comparison of modelling techniques allows us to appreciate the strengths and weaknesses of different approaches, and facilitates cross-fertilization between them. In the present case we take a characteristic of one formalism, functional rates in Stochastic Automata Networks, and introduce it to the other formalism, Performance Evaluation Process Algebra. We investigate the benefits of this cross-fertilization, particularly from the perspectives of Markov process generation and reduction.