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.     

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.     

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.     

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.     

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     

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     

Possibilities and Limitations of Computer Simulations of Industrial Turbulent Dispersed Multiphase Flows

We give an overview on the usage of computer simulations in industrial turbulent dispersed multiphase flows. We present a few examples of industrial flows: bubble columns and bubbly pipe flows, stirred tanks, cyclones, and a fluid catalytic cracking unit. The fluid catalytic cracking unit is used to illustrate the complexity of the physical phenomena involved, and the possibilities and limitations of the different approaches used: Eulerian–Lagrangian (particle-tracking) and Eulerian–Eulerian (two-fluid). In the first approach, the continuous phase is solved using either RANS simulations (Reynolds-Averaged Navier–Stokes simulations) or DNS/LES (Direct Numerical Simulations/Large-Eddy Simulations), and the individual particles are tracked. In the second approach, the dispersed phase is averaged, leading to two sets equations, which are quite similar to the RANS equations of single-phase flows. The Eulerian–Eulerian approach is the most commonly used in industrial applications, however, it requires a significant amount of modelling. Eulerian–Lagrangian RANS can be simpler to use; in particular in situations involving complex boundary conditions, polydisperse flows and agglomeration/breakup. The key issue for the success of the simulations is to have good models for the complex physics involved. A major weakness is the lack of good models for: the turbulence modification promoted by the particles, the inter-particle interactions, and the near-wall effects. Eulerian–Lagrangian DNS/LES can play an important role as a research tool, in order to get a better physical understanding, and to improve the models used in the RANS simulations (either Eulerian–Eulerian or Eulerian–Lagrangian).     

Solution of initial–boundary-value problems of electroelasticity revisited

The Hamilton–Ostrogradsky principle is used to substantiate the statement of initial–boundary-value problems of electroelasticity. The free vibrations of a piezoceramic layer are used as an example to illustrate some features of solving nonstationary problems of electroelasticity Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 62–69, December 2008.     

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.     

Fully Coupled THMC Modeling of Wellbore Stability with Thermal and Solute Convection Considered

Wellbore stability analysis is an important topic in petroleum geomechanics. Analytical and numerical analysis of wellbore stability involves the study of interactions among pressure, temperature and chemical changes, and the mechanical response of the rock, a coupled thermal–hydraulic–mechanical–chemical (THMC) process. Thermal and solute convection have usually been overlooked in numerical models. This is appropriate for shales with extremely low permeability, but for shales with intermediate and high permeability (e.g., shale with a disseminated microfissure network), thermal and solute convection should be considered. The challenge of considering advection lies in the numerical oscillation encountered when implementing the traditional Galerkin finite element approach for transient advection–diffusion problems. In this article, we present a fully coupled THMC model to analyze the stress, pressure, temperature, and solute concentration changes around a wellbore. In order to overcome spurious spatial temperature oscillations in the convection-dominated thermal advection–diffusion problem, we place the transient problem into an advection– diffusion-reaction problem framework, which is then efficiently addressed by a stabilized finite element approach, the subgrid scale/gradient subgrid scale method (SGS/GSGS).     

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.      

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).      

Seismic efficiency of a contact explosion and a high-velocity impact

The seismic energy transferred to an elastic half-space as a result of a contact explosion and a meteorite impact on a planet’s surface is estimated. The seismic efficiency of the explosion and impact are evaluated as the ratio of the energy of the generated seismic waves to the energy of explosion or the kinetic energy of the meteorite. In the case of contact explosions, this ratio is in the range of 10⁻⁴–10⁻³. In the case of wide-scale impact effects, where the crater in the planet’s crust is produced in the gravitational regime, a formula is derived that relates the seismic efficiency of an impact to its determining parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 3–12, March–April, 2007.     

On Lyapunov stability of impulsive Takagi–Sugeno fuzzy systems

We analyze the Lyapunov stability of impulsive Takagi–Sugeno fuzzy systems. Using the direct Lyapunov method, we establish sufficient conditions for the stability of these systems. We show that these conditions can be expressed in terms of a system of linear matrix inequalities. As an example, we consider an impulsive fuzzy control in a two-species “predator–prey” model. Translated from Neliniini Kolyvannya, Vol. 11, No. 4, pp. 481–494, October–December, 2008.     

Charging and coagulation of water aerosols with a small admixture of highly radioactive droplets

The mechanism of electrocoagulation of water aerosols with a small admixture of highly radioactive droplets is examined. A corresponding mathematical model describing the processes of ionization, electrization and coagulation of radioactive water aerosols is developed. The time dependence of the ion concentration and the charge and concentration of the nonradioactive droplets and of the charge and radius of the radioactive droplets is numerically investigated for a number of typical aerosols. It is shown that the electrocoagulation process may lead to an increase in the radius of the droplets from 5–10 to 30–40μm in ≃10⁴ sec ≃3 h and, consequently, may play a significant part in the development of aerosols with a droplet radius of up to 20μm, when gravitational coagulation is unimportant. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 90–96, March–April, 1994.     

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.     

Analysis of the temperature regime of operation of a filtering unit

The temperature regime of a filtering unit being cooled after an accident at a nuclear power plant is considered. A mathematical model is developed; the model is based on three-dimensional equations of thermohydrodynamics and takes into account heat-transfer mechanisms (convection, heat conduction, and radiation). For the unit variants considered, the maximum value of temperature in the sorbing module is less than 300°C, and the temperature reserve is 20–50°C. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 92–102, November–December, 2007.     

The Low Mach Number Limit for the Full Navier–Stokes–Fourier System

We study the low Mach number asymptotic limit for solutions to the full Navier–Stokes–Fourier system, supplemented with ill-prepared data and considered on an arbitrary time interval. Convergencetowards the incompressible Navier–Stokes equations is shown.