Standard Bubble Research Articles

A posteriori error estimate for a WG method of H(curl)-elliptic problems

Abstract This paper presents a posteriori error estimate for the weak Galerkin (WG) finite element method used to solve H (curl)-elliptic problems. Firstly, we introduce a WG method for solving H (curl)-elliptic problems and a corresponding residual type error estimator without a stabilization term. Secondly, we establish the reliability of the error estimator by demonstrating that the stabilization term is controlled by the error estimator. We also evaluate the efficiency of the error estimator using standard bubble functions. Finally, we present some numerical results to show the performances of the error estimator in both uniform and adaptive meshes.

Explosive behavior in the Chinese stock market: A sectoral analysis

This paper examines the existence of explosiveness in the Chinese stock market from a sectoral perspective. To that end, the method recently developed by Phillips and Shi (2019), which is an extension of the standard bubble detection technique of Phillips et al. (2015a,b), is used. The empirical results reveal the presence of several explosivity periods in all equity sectors and the aggregate equity market, showing the high propensity of the Chinese stock market to the appearance of episodes of explosiveness. One possible explanation for this frequent explosive dynamics stems from the fact that the Chinese equity market has numerous unique features and is still in an early stage of development. The two main periods of explosiveness common to many Chinese equity sectors correspond to the well-known 2007 and 2015 Chinese stock market bubbles. However, there seems to be some heterogeneity across sectors in terms of the number and duration of explosivity episodes. Furthermore, the significant degree of co-movement of periods of explosiveness in different equity sectors suggests potential contagion effects of explosive dynamics to the whole Chinese equity market, with the consequent detrimental impact on the Chinese real economy.

Consistent and flexible thermodynamics in atmospheric models using internal energy as a thermodynamic potential. Part I: Equilibrium regime

Approximations in the moist thermodynamics of atmospheric models can often be inconsistent; different parts of numerical models may handle the thermodynamics in different ways, or the approximations may disagree with the laws of thermodynamics. To address these problems, all relevant thermodynamic quantities may be derived from a defined thermodynamic potential; approximations are instead made to the potential itself—this guarantees self‐consistency, as well as flexibility. Previous work showed that this concept is viable for vapour and liquid water mixtures in a moist atmospheric system using the Gibbs potential. However, on extension to include the ice phase, an ambiguity is encountered at the triple point. To resolve this ambiguity, here the internal energy is used instead. Constrained maximisation methods on the entropy can then be used to solve for the system equilibrium state. Nevertheless, a further extension is necessary for realistic atmospheric systems, where many importantnon‐equilibriumprocesses take place; for example, freezing of supercooled water and evaporation into subsaturated air. To capture processes such as these fully, the equilibrium method must be reformulated to involve finite rates of approach towards equilibrium. Here the principles of non‐equilibrium thermodynamics are used, beginning with a set of phenomenological equations, to show how non‐equilibrium moist processes may be coupled to a semi‐implicit semi‐Lagrangian dynamical core. Standard bubble test cases and simulations of idealised cloudy thermals are presented to demonstrate the viability of the approach for the equilibrium regime. Further details and results for non‐equilibrium regimes are presented in Part II.

Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary

We study the Yamabe equation in the Euclidean half-space. We prove that any sign-changing solution has at least twice the energy of a standard bubble. Moreover, a sharper energy lower bound of the sign-changing solution set is also established via the method of moving planes. This bound increases the energy range for which Palais–Smale sequences of related variational problem has a non-trivial weak limit.

Forecasting a bubbly-intermittent flow regime transition in helically coiled tubes

Simulations of gas–liquid turbulent flows in helically coiled tubes are conducted by a two-fluid hydrodynamic model coupled with the population balance equation. A model of bubble breakup in a turbulent flow, recently developed by the authors, is incorporated into the ANSYS Fluent CFD code employed as a computational tool. The population balance equation is solved by a discrete method. A realizable k-epsilon turbulence model is used for all computations. Numerous simulations of gas-liquid flows in vertically oriented coiled tubes are conducted. Three different coil diameters are employed for simulations. Computed bubble chord distributions are close to experimental data. Simulated dependencies of the superficial liquid velocity on the superficial gas velocity, corresponding the bubbly-intermittent flow regime transition, are in excelled agreement with measured ones. On the other hand, dependencies, obtained using standard bubble breakup models, significantly deviate from experimental results. Thus, it is demonstrated that employment of the novel bubble breakup model greatly enhances a computational accuracy of gas-liquid flows in helically coiled tubes.

An adaptive edge element method and its convergence for an electromagnetic constrained optimal control problem

In this work, an adaptive edge element method is developed for anH(curl)-elliptic constrained optimal control problem. We use the lowest-order Nédélec’s edge elements of first family and the piecewise (element-wise) constant functions to approximate the state and the control, respectively, and propose a new adaptive algorithm with error estimators involving both residual-type error estimators and lower-order data oscillations. By using a local regular decomposition forH(curl)-functions and the standard bubble function techniques, we derive thea posteriorierror estimates for the proposed error estimators. Then we exploit the convergence properties of the orthogonalL2-projections and the mesh-size functions to demonstrate that the sequences of the discrete states and controls generated by the adaptive algorithm converge strongly to the exact solutions of the state and control in the energy-norm andL2-norm, respectively, by first achieving the strong convergence towards the solution to a limiting control problem. Three-dimensional numerical experiments are also presented to confirm our theoretical results and the quasi-optimality of the adaptive edge element method.

Eulerian simulations of liquid distribution generated by chimney and bubble cap distributors

• Measurements on flow through single units of industrial gas-liquid distributors. • Liquid flow morphology analyzed using dual-tip voidage probes. • Development of Eulerian CFD model with weighted drag formulation and validation. • Performance analysis of chimney and bubble cap distributor configurations. • Effect of addition of liquid dispersion plates on liquid distribution. Gas–liquid distributors form an integral part of an industrial packed bed reactor, esp. trickle bed reactors used for hydrodesulphurization of liquid fuels. Among several process parameters that influence performance of trickle bed reactors, gas–liquid distributors are of foremost importance. In the present work, we have developed a computational model based on Eulerian two-fluid approach to simulate the gas–liquid flow in widely–varying flow regimes encountered in a distributor unit. The predictions are validated using the liquid distribution measured using high-speed imaging, morphology of gas–liquid flow measured using in–house developed voidage probes, and pressure drop measurements. Owing to the difference in the inherent nature of flow through the standard chimney and standard bubble cap distributors, the liquid discharge pattern, uniformity and symmetry of flow streams, and pressure drop across the distributor were found to be significantly different from each other. Further, the addition of liquid dispersion plates to the outlet of the main distributor unit not only resulted in improved liquid discharge pattern and wider coverage span, but also in a highly dispersed stream. Lastly, the application of the above study and the presented methodology was demonstrated for predicting the gas–liquid distribution through industrial trays, using standard bubble cap and chimney trays.

Lower a posteriori error estimates on anisotropic meshes

Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such bounds are not sharp. Hence, for linear finite element approximations of the Laplace equation in polygonal domains, a new approach is employed to obtain essentially sharper lower a posteriori error bounds and thus to show that the upper error estimator in the recent paper (Kopteva in Numer Math 137:607–642, 2017) is efficient on partially structured anisotropic meshes.

BUBBLE PREDICTION AND COMPARATIVE ANALYSIS OF EMERGING AND MATURE MARKETS

By analyzing the financial bubbles, it can be observed that every bubble burst causes financial turmoil and severe economic recession. The paper utilize the technical analysis indicators for providing warning conditions for predicting the stock market bubbles. The significance of the technical analysis indicators are that they can provide early warning system for financial crisis and can help in avoiding such problems. We applied the early warning technical indicators to the stock market of US, South Korea, Brazil, China, Germany, and Japan for the period of 1995 to 2018. We also made comparison of the bubble warning conditions of emerging markets and the mature markets. The standard bubble warning conditions include K value 90, Bias 10%, and RSI value of 90. Empirical results shows that mature market shows less degree of volatility and lowering the warning baseline can improve the accuracy of bubble predictions. Furthermore, results shows that mature markets bursting time is about 6 months while in emerging market, the time is reduced to only 3 months. These results also indicate that mature market has good antirisk ability compare to the emerging markets.

Classification of solutions to a system of n^{\rm th} order equations on \mathbb R^n

<p style='text-indent:20px;'>This work concerns the distributional solutions of a conformally invariant system of <inline-formula><tex-math id="M3">\begin{document}$ n^{\rm th} $\end{document}</tex-math></inline-formula>-order elliptic equations on <inline-formula><tex-math id="M4">\begin{document}$ \mathbb R^n $\end{document}</tex-math></inline-formula> having exponential type nonlinearity. The system in question is a natural generalization of the constant <inline-formula><tex-math id="M5">\begin{document}$ Q $\end{document}</tex-math></inline-formula>-curvature equation on <inline-formula><tex-math id="M6">\begin{document}$ \mathbb R^n $\end{document}</tex-math></inline-formula>. Under an <inline-formula><tex-math id="M7">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula>-finiteness assumption and some assumptions on the coupling coefficients, an asymptotic estimate for solutions as <inline-formula><tex-math id="M8">\begin{document}$ \left|x\right|\to \infty $\end{document}</tex-math></inline-formula> is obtained. Under a growth constraint and further <inline-formula><tex-math id="M9">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula>-norm assumptions the method of moving spheres is used to show that, up to an additive polynomial of low degree, each of the unknown functions is a standard bubble with common center and scale parameters.

Generation of high-charge electron beam in a subcritical-density plasma through laser pulse self-trapping

To maximize the charge of a high-energy electron beam accelerated by an ultra-intense laser pulse propagating in a subcritical plasma, the pulse length should be longer than both the plasma wavelength and the laser pulse width, which is quite different from the standard bubble regime. In addition, the laser-plasma parameters should be chosen to produce the self-trapping regime of relativistic channeling, where the diffraction divergence is balanced by the relativistic nonlinearity such that the laser beam radius is unchanged during pulse propagation in a plasma over many Rayleigh lengths. The condition for such a self-trapping regime is the same as what was empirically found in several previous simulation studies in the form of the pulse width matching condition. Here, we prove these findings for a subcritical plasma, where the total charge of high-energy electrons reaches the multi-nC level, by optimization in a 3D PIC simulation study and compare the results with an analytic theory of relativistic self-focusing. A very efficient explicitly demonstrated generation of high-charge electron beams opens a way to a high-yield production of gammas, positrons, and photonuclear particles.

Vacuum Selection from Cosmology on Networks of String Geometries.

We introduce network science as a framework for studying the string landscape. Two large networks of string geometries are constructed, where nodes are extra-dimensional six-manifolds and edges represent topological transitions between them. We show that a standard bubble cosmology model on the networks has late-time behavior determined by the largest eigenvector of -(L+D), where L and D are the Laplacian and degree matrices of the networks, which provides a dynamical mechanism for vacuum selection in the string landscape.

Correction: Infant CPAP for low-income countries: An experimental comparison of standard bubble CPAP and the Pumani system.

[This corrects the article DOI: 10.1371/journal.pone.0196683.].

Frequency of Complications During Preparation of Corneal Lamellae Used in Posterior Lamellar Keratoplasty Using the Pneumodissection Technique (Big Bubble).

To determine the frequency of formation of various types of bubbles and the potential impact of donor and lamella parameters on this frequency, and to identify possible risk factors of unsuccessful "big-bubble" creation in preparation of pre-Descemet endothelial keratoplasty and Descemet membrane endothelial keratoplasty with peripheral stromal support. Donor age and sex, death to preservation time (DPT), storage time, presence of corneal scars (mainly a condition after cataract surgery), and endothelial cell density of 256 donor corneas were assessed before Descemet membrane endothelial keratoplasty with peripheral stromal support or pre-Descemet endothelial keratoplasty lamella preparation using the big-bubble technique. Mean donor age was 62.3 ± 8.5 years (28.3% women and 71.7% men). Mean endothelial cell density of the donor graft was 2866 ± 255 cells/mm. Mean DPT was 10.12 ± 4.88 hours, and mean storage time of the transplant before surgery was 6.5 ± 4.8 days. Corneal scars were present in 17 donor grafts (6.6%) after cataract surgery. Eleven corneas were devalued because of Descemet membrane rupture during preparation (4.3%). In 182 corneas, standard bubble type I was created (71.7%); in 27 corneas, bubble type II was created; eventually, both types of bubbles formed simultaneously (10.5%); in 47 corneas, no bubble was created (18.4%). We identified higher endothelial cell density, shorter DPT, and the presence of corneal scars after cataract surgery as risk factors threatening successful bubble formation. The only risk factor for creating type II bubbles was higher donor age in our study.

Assessment of the impact of bubble size modelling in CFD simulations of alternative bubble column configurations operating in the heterogeneous regime

Modelling bubble columns operating in the churn turbulent flow regime is a considerable challenge due to their complex and transient behaviour. A key modelling decision is how best to model the bubble size distribution, with a range of approaches existing from the relatively simple option of using a single, representative bubble size to more complex population balance approaches. In this comparative study, we have examined various approaches (i.e. constant and variable single bubble size models, dual bubble size models, and both homogeneous and inhomogeneous MUSIG models). Model predictions were compared with experimental data from three different configurations of a pilot-scale column (0.39 m in diameter and 2 m in height) operated at industrially relevant superficial gas velocities of 0.16 and 0.25 m s−1. The single bubble size models gave reasonable agreement with experimental data for the ‘symmetrical’ configuration, with the variable bubble size model having the major advantage of providing acceptable predictions of the mean bubble size (without this having to be provided as a model input). Implementation of multiple bubble size models did not lead to any substantial improvement in the modelling fit with the experimental data, leading to the inescapable conclusion that the standard bubble breakup and coalescence kernels proposed in the literature do not adequately describe bubble transformations taking place under heterogeneous operating conditions.

Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (iii) the heights of these bubbles are comparable by a universal factor. As an application of this result, we establish a quantitative Liouville theorem.

Abstract WP238: Utility of the Bubble Test With Cervical Triplex Ultrasound in Diagnosis of Patent Foramen Ovale in Patients With Inadequate Transtemporal Sonic Window

Introduction: Transcranial Doppler (TCD) detection of microbubble signals in the middle cerebral artery (MCA) after agitated saline injection, known as the bubble test, is a dependable method to detect right-to-left shunts (RLS) such as patent foramen ovale (PFO). In patients with inadequate temporal bone windows, cervical internal carotid or vertebral arteries (ICA and VA) are suggested to be alternatives of MCA. However, utility of the bubble test with cervical arteries has never been documented in this population. Methods: Using contrast transesophageal echocardiography (cTEE) as gold standard, the sensitivity (Se) and specificity (Sp) of unilateral hand-held cervical triplex ultrasound bubble test technique was computed and compared with other available TCD methods. RLS volume was graded per the International Consensus Criteria (ICC). Results: Of 796 patients who underwent the bubble test in 3 years, 41 (5.3%) patients had no adequate temporal bone windows for MCA insonation. cTEE was available for 184 patients. Se and Sp of cervical bubble test was excellent in patients without adequate bone windows (n=36, Se: 88% (57-98) and Sp: 91% (71-99) for ICA; n=33, Se: 85% (55-98) and Sp: 90% (68-98) for VA), and was to comparable to those with adequate bone windows (n=78, Se: 93% (95%CI: 82-99) and Sp: 79% (61-91) for ICA; n=48, Se: 92% (74-99) and Sp: 91% (72-99) for VA). Diagnostic yield is comparable to standard bubble test with bilateral MCA Doppler monitoring (n=56, Se: 74% (55-88) and Sp: 56% (35-76) for spectral Doppler and M-mode). Of note, unilateral hand-held transcranial Doppler (n=26, Se: 93% (66-99) and Sp: 58% (28-85) for spectral Doppler: Se: 93% (66-99) and Sp: 50% (21-79) for M-mode) and color-coded (n=125, Se: 88% (78-94) and Sp: 64% (48-78) for color-coded MCA) techniques are also acceptable and apparently more practical methods for RLS detection. Conclusions: Hand-held cervical artery bubble test has high Se/Sp enough for routine use for PFO screening. Yield is good in the setting of impermeable transtemporal bone windows.

Residual-baseda posteriorierror estimation for the Maxwell’s eigenvalue problem

We present an a posteriori estimator of the error in the L 2 -norm for the numerical approximation of the Maxwell's eigenvalue problem by means of N ed elec nite elements (see, for instance, (4)). As in (2), our analysis is based on a Helmholtz decomposition of the error, where, in particular, the L 2 -orthogonality property is used to derive a superconvergence result for the eigenfunction approximation. The analysis also makes use of a priori error estimates and the additional regularity of the eigenfunctions (see (3)). Inspired by (1), we prove a key result about superconvergence between the L 2 -orthogonal projection of the exact eigenfunction onto the curl of the N ed elec space and the eigenfunction approximation. Reliability of the a posteriori error estimator is proved up to higher order terms. Finally, the eciency of the error indicators is shown by using a standard bubble functions technique.

Experiments on Electronic Double Auctions and Abnormal Trades

The flash crash experienced by U.S. markets in May 2010 provided stark evidence that a large trade can have a powerful influence. We explore the impact of an unusual trade on behavior in experimental bubbles markets. We chose the experimental design proposed by Smith, Suchanek, and Williams (1988) because replication shows it produces markets prone to mispricing. After several rounds of trading, our markets receive a large quantity order at an extreme price. In a standard double auction bubble market, pricing is unaffected by an abnormal order. However, with increased uncertainty about the underlying economic value of the asset, over-pricing weakens on arrival of a negative price shock.

Sign-changing solutions to elliptic second order equations: glueing a peak to a degenerate critical manifold

We construct blowing-up sign-changing solutions to some nonlinear critical equations by glueing a standard bubble to a degenerate function. We develop a new method based on analyticity to perform the glueing when the critical manifold of solutions is degenerate and no Bianchi–Egnell type condition holds.