Charge density waves and their transitions in anisotropic quantum Hall systems

In recent experiments, external anisotropy has been a useful tool to tune different phases and study their competitions. In this paper, we look at the quantum Hall charge density wave states in the N = 2 Landau level. Without anisotropy, there are two first-order phase transitions between the Wigner crystal, the 2-electron bubble phase, and the stripe phase. By adding mass anisotropy, our analytical and numerical studies show that the 2-electron bubble phase disappears and the stripe phase significantly enlarges its domain in the phase diagram. Meanwhile, a regime of stripe crystals that may be observed experimentally is unveiled after the bubble phase gets out. Upon increase of the anisotropy, the energy of the phases at the transitions becomes progressively smooth as a function of the filling. We conclude that all first-order phase transitions are replaced by continuous phase transitions, providing a possible realisation of continuous quantum crystalline phase transitions.

Diagnosis and Prediction of IIGPS’ Countries Bubble Crashes during BREXIT

We herein employ an alternative approach to model the financial bubbles prior to crashes and fit a log-periodic power law (LPPL) to IIGPS countries (Italy, Ireland, Greece, Portugal, and Spain) during Brexit. These countries represent the five financially troubled economies of the Eurozone that have suffered the most during the Brexit referendum. It was found that all 77 crashes across the five IIGPS nations from 19 January 2015 until 17 February 2020 strictly followed a log-periodic power law or other LPPL signature. They all had a speculative bubble phase (following the power law growth) that was then followed by a sudden crash immediately after reaching a critical point. Furthermore, their pattern coefficients were similar as well. This study would surely assist policymakers around the Eurozone to predict future crashes with the help of these parameters.

Comparison between bubbling and turbulent regime for the simulation of batch pharmaceutical powders fluidized bed drying

The two-phase theory has been frequently used to model fluidised bed drying. At high air velocities, a transition from the bubbling regime to the turbulent regime may occur. In this work, we compare a bubbling model and a turbulent model for the simulation of a two pharmaceutical powders drying in a pilot plant and an industrial plant fluidised bed. The bubbling model was based on a discrete variable bubble size. Heat and mass transfer coefficients were based on the Kunii and Levenspiel correlation [1]. Flow regime was supposed to be completely mixed for the emulsion phase. For the turbulent model, the bubble size is not anymore discrete but continuous and bubble phase is less distinguishable than in the bubbling regime. Heat and mass transfer were those proposed by Foka[2]. In addition, the freeboard section was considered since high entrainment is specific of this regime. Gas backmixing was taken into account by considering a plug flow with axial dispersion for the interstitial gas flow. The bubble phase being dilute, was modeled by a plug flow. A plug flow was also considered for the freeboard gas. The solid phase was supposed to be completely mixed. The bubbling regime simulation gave good agreement with experiment in the case of the pilot plant experiment, while the turbulent model better simulated the industrial scale experiment. Key words: batch fluidized bed, pharmaceutical powder, drying, modeling, bubbling, turbulent

Bubble entrainment and liquid–bubble interaction under unsteady breaking waves

Liquid–bubble interaction, especially in complex two-phase bubbly flow under breaking waves, is still poorly understood. In the present study, we perform a large-eddy simulation using a Navier–Stokes solver extended to incorporate entrained bubble populations, using an Eulerian–Eulerian formulation for a polydisperse bubble phase. The volume-of-fluid method is used for free-surface tracking. We consider an isolated unsteady deep water breaking event generated by a focused wavepacket. Bubble contributions to dissipation and momentum transfer between the water and air phases are considered. The model is shown to predict free-surface evolution, mean and turbulent velocities, and integral properties of the entrained dispersed bubbles fairly well. We investigate turbulence modulation by dispersed bubbles as well as shear- and bubble-induced dissipation, in both spilling and plunging breakers. We find that the total bubble-induced dissipation accounts for more than 50 % of the total dissipation in the breaking region. The average dissipation rate per unit length of breaking crest is usually written as $b{\it\rho}g^{-1}c_{b}^{5}$, where ${\it\rho}$ is the water density, $g$ is the gravitational acceleration and $c_{b}$ is the phase speed of the breaking wave. The breaking parameter, $b$, has been poorly constrained by experiments and field measurements. We examine the time-dependent evolution of $b$ for both constant-steepness and constant-amplitude wavepackets. A scaling law for the averaged breaking parameter is obtained. The exact two-phase transport equation for turbulent kinetic energy (TKE) is compared with the conventional single-phase transport equation, and it is found that the former overpredicts the total subgrid-scale dissipation and turbulence production by mean shear during active breaking. All of the simulations are also repeated without the inclusion of a dispersed bubble phase, and it is shown that the integrated TKE in the breaking region is damped by the dispersed bubbles by approximately 20 % for a large plunging breaker to 50 % for spilling breakers. In the plunging breakers, the TKE is damped slightly or even enhanced during the initial stage of active breaking.

Two Phase Dynamic Model for Gas Phase Propylene Copolymerization in Fluidized Bed Reactor

A two-phase model is proposed for describing the dynamics of a fluidized bed reactor used for polypropylene production. In the proposed model, the fluidized bed is divided into an emulsion phase and bubble phase where the bubble phase flow pattern is assumed to be plug flow and the emulsion phase is considered to be perfectly mixed. Similar previous models consider the reaction in the emulsion phase only. In this work the contribution of reaction in the bubble phase is considered and its effect on the overall polypropylene production is investigated. The kinetic model combined with hydrodynamic model in order to develop a comprehensive model for gas-phase propylene copolymerization reactor. Simulation profiles of the proposed model were compared with those of well mixed model for the emulsion phase temperature. The simulated temperature profile showed a lower rate of change compared to the previously reported models due to lower polymerization rate. Model simulation showed that about 13% of the produced polymer comes from the bubble phase and this considerable amount of polymerization in the bubbles should not be neglected in any modeling attempt.

Multiphase Digital Particle Image Velocimetry in a Dispersed, Bubbly, Axisymmetric Jet

A particle image velocimetry (PIV) technique developed for application to two-phase flows is presented and validated. The technique is capable of simultaneously measuring carrier and bubble phase velocities on a plane. The validation experiments have been conducted in a vertical upwards, two-phase (water-air) bubbly jet flow at a Reynolds numbers of 5,673 and 11,345 and low bubble concentration matching the experiments of Stanley and Nikitopoulos (1998). Comparisons with measurements obtained by Stanley and Nikitopoulos (1998) using Phase Doppler Analysis (PDA) experiments indicate that the agreement between the two techniques is very satisfactory (deviations of the order of 5%) for both single-phase and two-phase jet carrier-flow velocities. In addition, bubble phase velocity measurements obtained from backlit visualizations of the bubbly jet flow using the bubble-tracking method of Fiedler et al. (2001) are successfully compared to those obtained from PIV. The PIV study confirms that bubbles experience a substantial deceleration in the unmixed core of the jet near field and illustrates carrier-phase mean-flow modification consistent with past point-wise measurements.