Measurement and chemical kinetic model predictions of detonation cell size in methanol–oxygen mixtures

In this study, detonation cell sizes of methanol–oxygen mixtures are experimentally measured at different initial pressures and compositions. Good agreement is found between the experiment data and predictions based on the chemical length scales obtained from a detailed chemical kinetic model. To assess the detonation sensitivity in methanol–oxygen mixtures, the results are compared with those of hydrogen–oxygen and methane–oxygen mixtures. Based on the cell size comparison, it is shown that methanol–oxygen is more detonation sensitive than methane–oxygen but less sensitive than hydrogen–oxygen.     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Comparison of four different versions of the variable metric method for solving inverse heat conduction problems

In this study, four different versions of the variable metric method (VMM) are investigated in solving standard one-dimensional inverse heat conduction problems in order to evaluate their efficiency and accuracy. These versions include Davidon–Fletcher–Powell (DFP), Broydon–Fletcher–Goldfarb–Shanno (BFGS), Symmetric Rank-one (SR1), and Biggs formula of the VMM. These investigations are carried out using temperature data obtained from numerical simulations.     

Characteristics of liquid sheets formed by splash plate nozzles

An experimental study was conducted to identify the effect of viscosity on the characteristics of liquid sheets formed by a splash plate nozzle. Various mixtures of corn syrup and water are used to obtain viscosities in the range 1–170 mPa.s. Four different splash plates with nozzle diameters of 0.5, 0.75, 1, and 2 mm, with a constant plate angle of 55° were tested. Liquid sheets formed under various operating conditions were directly visualized. The sheet atomization process for the range of parameters studied here is governed by two different mechanisms: Rayleigh–Plateau (R–P) and Rayleigh–Taylor (R–T) instabilities. R–P occurs at the rim and R–T occurs on the thin sheet. The rim instability can be laminar or turbulent, depending on the jet Reynolds number. The R–T instability of the sheet is observed at the outer edges of the radially spreading sheet, where the sheet is the thinnest. It can also occur inside the sheet, due to formation of holes and ruptures.     

Temperature dependence of the interfacial tension of PS/PMMA, PS/PE, and PMMA/PE blends

The effect of temperature on the interfacial tension for PS/PMMA, PS/PE, and PMMA/PE was measured using the imbedded fiber retraction method. Interfacial tensions for PS/PMMA, PS/PE, and PMMA/PE were measured over temperature ranges of 160–250 °C, 140–220 °C, and 140–220 °C, respectively. The interfacial tension was found to follow a dependence of 3.6–0.013 T dyn/cm, 7.6–0.051 T dyn/cm and 11.8–0.017 T dyn/cm for PS/PMMA, PS/PE, and PMMA/PE, respectively. Comparison of the data with the mean field theory of Helfand and Sapse were made; however, a simple linear fit to the data described the temperature dependence in the experimental window as well as the predictions of the mean field theory. Received: 6 July 1999 Accepted: 23 March 2000     

Estimation of Chaotic and Regular (Stick–Slip and Slip–Slip) Oscillations Exhibited by Coupled Oscillators with Dry Friction

In this paper, we present a novel approach to quantify regular or chaotic dynamics of either smooth or non-smooth dynamical systems. The introduced method is applied to trace regular and chaotic stick–slip and slip–slip dynamics. Stick–slip and slip–slip periodic and chaotic trajectories are analyzed (for the investigated parameters, a stick–slip dynamics dominates). Advantages of the proposed numerical technique are given.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Formulation of Multidimensional Scalar Conservation Laws

We show that Kruzhkov’s theory of entropy solutions to multidimensional scalar conservation laws (Kruzhkov in Mat Sb (N.S.), 81(123), 228–255, 1970) can be entirely recast in L ² and fits into the general theory of maximal monotone operators in Hilbert spaces. Our approach is based on a combination of level-set, kinetic and transport-collapse approximations, in the spirit of previous works by Brenier (in C R Acad Sci Paris Ser I Math, 292, 563–566, 1981; in J Diff Equ, 50, 375–390, 1983; in SIAM J Numer Anal, 21, 1013–1037; in Methods Appl Anal, 11, 515–532, 2004), Giga and Miyakawa (in Duke Math J, 50, 505–515, 1983), and Tsai et al. (in Math Comp, 72, 159–181, 2003).     

Problems of regularity of linear extensions of dynamical systems on a torus

We investigate the problem of the existence of a Green–Samoilenko function for some linear extensions of dynamical systems. Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 99–109, January–March, 2009.     

Aspect-ratio dependence of transient Taylor vortices close to threshold

We perform a detailed numerical study of transient Taylor vortices arising from the instability of cylindrical Couette flow with the exterior cylinder at rest for radius ratio η = 0.5 and variable aspect ratio Γ. The result of Abshagen et al. (J Fluid Mech 476:335–343, 2003) that onset transients apparently evolve on a much smaller time–scale than decay transients is recovered. It is shown to be an artefact of time scale estimations based on the Stuart–Landau amplitude equation which assumes frozen space dependence while full space–time dependence embedded in the Ginzburg–Landau formalism needs to be taken into account to understand transients already at moderate aspect ratio. Sub-critical pattern induction is shown to explain the apparently anomalous behaviour of the system at onset while decay follows the Stuart–Landau prediction more closely. The dependence of time scales on boundary effects is studied for a wide range of aspect ratios, including non-integer ones, showing general agreement with the Ginzburg–Landau picture able to account for solutions modulated by Ekman pumping at the disks bounding the cylinders.      

Solving initial–boundary-value creep problems

The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form of operators in the mathematical problem formulation     

Effect of yaw on the starting point of curvature for reflected diffracted shock wave (subsonic and sonic cases)

Lighthill (Proc. R. Soc. A 198, 454–470, 1949) considered the diffraction of a normal shock wave passing over a small bend. The bend being small Lighthill was able to linearize the flow equations and solved the problem through several mathematical techniques. Following Lighthill (Proc. R. Soc. A 198, 454–470, 1949), Srivastava and Chopra (J. Fluid Mech. 40, 821–831, 1970) extended the work to the diffraction of oblique shock waves. Srivastava (AIAAJ 33, 2230–2231, 1995) considered the problem of starting point of curvature and extended the work to yawed wedges (Srivastava in Proceedings of the 14th International Mach reflection symposium Sun Marina Hotel, Yonezawa, Japan, 1–5 October 2000, pp. 225–249, 2002). Srivastava (Shock waves 13, 323–326, 2003) considered the problem for starting point of curvature when the relative outflow behind reflected shock before diffraction has been subsonic and sonic. The present work is an extension of the work published in Srivastava (Shock waves 13, 323–326, 2003) when the wedge has been yawed through an angle. The results have been obtained for two angles χ = 60° and χ = 40° (χ is the angle of yaw).      

A comparison of three adsorption equations and sensitivity study of parameter uncertainty effects on adsorption refrigeration thermal performance estimation

This paper presents isosteric-based adsorption equilibrium tests of three activated carbon samples with methanol as an adsorbate. Experimental data was fitted into Langmuir equation, Freundlich equation and Dubinin-Astakov (D–A) equation, respectively. The fitted adsorption equations were compared in terms of agreement with experimental data. Moreover, equation format’s impacts on calculation of the coefficient of performance (COP) and refrigeration capacity of an adsorption refrigeration system was analyzed. In addition, the sensitivity of each parameter in each adsorption equation format to the estimation of cycle’s COP and refrigeration capacity was investigated. It was found that the D–A equation is the best form for presenting the adsorptive property of a carbon-methanol working pair. The D–A equation is recommended for estimating thermal performance of an adsorption refrigeration system because simulation results obtained using the D–A equation are less sensitive to errors of experimentally determined D–A equation’s parameters.     

Solvability of Uniformly Elliptic Fully Nonlinear PDE

We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of the Hamilton–Jacobi–Bellman–Isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.     

On the Camassa–Holm and K–dV Hierarchies

It is known that a transform of Liouville type allows one to pass from an equation of the Korteweg–de Vries (K–dV) hierarchy to a corresponding equation of the Camassa–Holm (CH) hierarchy (Beals et al., Adv Math 154:229–257, 2000; McKean, Commun Pure Appl Math 56(7):998–1015, 2003). We give a systematic development of the correspondence between these hierarchies by using the coefficients of asymptotic expansions of certain Green’s functions. We illustrate our procedure with some examples.     

Non-Ergodicity of the Nosé–Hoover Thermostatted Harmonic Oscillator

The Nosé–Hoover thermostat is a deterministic dynamical system designed for computing phase space integrals for the canonical Gibbs distribution. Newton’s equations are modified by coupling an additional reservoir variable to the physical variables. The correct sampling of the phase space according to the Gibbs measure is dependent on the Nosé–Hoover dynamics being ergodic. Hoover presented numerical experiments to show that the Nosé–Hoover dynamics are non-ergodic when applied to the harmonic oscillator. In this article, we prove that the Nosé–Hoover thermostat does not give an ergodynamical system for the one- dimensional harmonic oscillator when the “mass” of the reservoir is large. Our proof of non-ergodicity uses KAM theory to demonstrate the existence of invariant tori for the Nosé–Hoover dynamical system that separate phase space into invariant regions. We present numerical experiments motivated by our analysis that seem to show that the dynamical system is not ergodic even for a moderate thermostat mass.     

On the Range of Applicability of the Reissner–Mindlin and Kirchhoff–Love Plate Bending Models

We show that the Reissner–Mindlin plate bending model has a wider range of applicability than the Kirchhoff–Love model for the approximation of clamped linearly elastic plates. Under the assumption that the body force density is constant in the transverse direction, the Reissner–Mindlin model solution converges to the three-dimensional linear elasticity solution in the relative energy norm for the full range of surface loads. However, for loads with a significant transverse shear effect, the Kirchhoff–Love model fails. This revised version was published online in June 2006 with corrections to the Cover Date.     

In situ force-balance tensiometry

 Although a fundamental physical parameter, surface tension is difficult to measure. Common tensiometry inaccuracy comes from failure to control air–liquid–solid contact conditions, or account for liquid meniscus geometry and buoyancy corrections. This paper describes an in situ tensiometry technique, based on withdrawal of a thin-walled tube from the liquid interface, that enforces a known air–liquid–solid contact condition. This technique can be pursued at any level of experimental hygiene. Experimental results for filtered tap water, an alcohol–water solution, and a surfactant–water solution show that results repeatable to three significant digits are obtained with modest effort for a variety of geometrical parameters. Received: 7 October 1997/Accepted: 23 April 1998     

Vlasov–Maxwell–Boltzmann Diffusive Limit

Inspired by the work (Bastea et al. in J Stat Phys 1011087–1136, 2000) for binary fluids, we study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov–Maxwell–Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of dissipative new macroscopic PDEs, the incompressible Vlasov–Navier–Stokes–Fourier system and its higher order corrections for describing a charged fluid, where the self-consistent electromagnetic field is present. The uniform estimate on the remainders is established via a unified nonlinear energy method and it guarantees the global in time validity of such an expansion up to any order.     

Deformation and short-term damage of physically nonlinear stochastic composites

The studies on the deformation and short-term damage of physically nonlinear homogeneous and composite materials are systemized. A single microdamage is modeled by an empty quasispherical pore in place of a microvolume damaged in accordance with the Huber–von Mises failure criterion. The ultimate microstrength is assumed to be a random function of coordinates. The porosity balance equation is derived. Together with the macrostress–macrostrain relationship, it constitutes a closed-form system of equations. The damage–macrostrain relationship and macrostress–macrostrain curves for homogeneous and composite materials are analyzed