Existence of nonstationary bubbles in higher dimensions

We are interested in the existence of travelling-waves for the nonlinear Schrödinger equation in R^N with “ψ³−ψ⁵”-type nonlinearity. First, we prove an abstract result in critical point theory (a local variant of the classical saddle-point theorem). Using this result, we get the existence of travelling-waves moving with sufficiently small velocity in space dimension N4.     

Polyconvex energies and cavitation

We study the existence of singular minimizers in the class of radial deformations for polyconvex energies that grow linearly with respect to the Jacobian.     

Numerical investigations of bubbles rising in water

The hydrodynamics of rising air bubbles in water filled bubble columns are examined using a transient numerical model following the Euler-Euler method. In this particular case the bubble-size distribution is assumed to be mono-disperse and the influence of this assumption on the specific mass-transfer area is discussed. Additionally, the influence of the bubble size is discussed with regard to the mass-transfer area, the air volume-fraction, and the axial air velocity profile. To validate the numerical model, experimental results from tomographic measurements at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) are used. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Buffer phenomenon in neurodynamics

Doklady Mathematics -     

Asymptotic asset pricing and bubbles

We define the concept of asymptotic superreplication, and prove a duality principle of asset pricing for sequences of financial markets (e.g., weakly converging financial markets and large financial markets) based on contiguous sequences of equivalent local martingale measures. This provides a pricing mechanism to calculate the fundamental value of a financial asset in the asymptotic market. We introduce the notion of asymptotic bubbles by showing that this fundamental value can be strictly lower than the current price of the asset. In the case of weakly converging markets, we show that this fundamental value is equal to an expectation of the terminal value of the asset in the weak-limit market. From a practical perspective, we relate the asymptotic superreplication price to a limit of quantile-hedging prices. This shows that even when a price process is a true martingale, it can have properties similar to a bubble, up to a set of small probability. For practical applications, we give examples of weakly converging discrete-time models (e.g. some GARCH models) and large financial models that present bubbles.     

The movement of bubbles in a vibrating liquid

The problem of movement of bubbles in a liquid in a rigid vertical cylindrical container with a rigid base is considered. The container vibrates vertically with a displacement amplitude Δ and an angular frequency ω with the acceleration g due to gravity.     

On the dynamics of bubbles in boiling water

We investigate the dynamics of many interacting bubbles in boiling water by using a laser scattering experiment. Specifically, we analyze the temporal variations of a laser intensity signal which passed through a sample of boiling water. Our empirical results indicate that the return interval distribution of the laser signal does not follow an exponential distribution; contrariwise, a heavy-tailed distribution has been found. Additionally, we compare the experimental results with those obtained from a minimalist phenomenological model, finding a good agreement.     

Soret phenomenon in porous Magneto-Hydrodynamics

Ricerche di Matematica - The onset of double-diffusive convection in horizontal porous layers filled by an electrically conducting fluid embedded in a magnetic field, is investigated on taking into...     

The structure of area-minimizing double bubbles

We show that the least area required to enclose two volumes in ℝⁿ orS ⁿ forn ≥ 3 is a strictly concave function of the two volumes. We deduce that minimal double bubbles in ℝⁿ have no empty chambers, and we show that the enclosed regions are connected in some cases. We give consequences for the structure of minimal double bubbles in ℝⁿ. We also prove a general symmetry theorem for minimal enclosures ofm volumes in ℝⁿ, based on an idea due to Brian White. Supported in part by NSF DMS-9409166.     

Asset bubbles and efficiency in a generalized two-sector model

We consider a multi-sector infinite-horizon general equilibrium model. The issues of equilibrium existence, efficiency, and bubble emergence are addressed. We show how different assets give rise to different rational bubbles. We also point out that efficient bubbly equilibria may exist.     

Particle simulation of large carbon dioxide bubbles in water

A method that can be applied to simulate the motion of fluid drops within fluids is described through a detailed study of a prototype problem, the motion of carbon dioxide bubbles in water. The mathematical formulation uses classical molecular dynamics type formulas and results in an n-body problem that is solved numerically. The rise of the bubbles is described, as is the motion of the water near the bubbles. For variety, both H₂O water and D₂O heavy water are considered. Only workstation computer capabilities are required.     

The Gibbs' phenomenon

This paper analyses the answers of a group of first-year university Mathematics students to a questionnaire, with the aim of determining the difficulties they have when carrying out non-routine tasks related to improper integrals. The questionnaire consisted of nine questions including not only calculus tasks and determining the convergence of given improper integrals, but also intuitive questions and some paradoxical results too (for example, a figure with an infinite longitude which closes the same area as the unit circumference, or an infinite figure with a finite volume). In particular, the students were asked to interpret most of the results they had obtained. Answers given by the students to each of the questions were categorized, which allowed some initial conclusions to be reached regarding this research. From analyses carried out, one can conclude that there are students who have difficulties in articulating the different systems of representation, and have problems in connecting and relating this knowledge as a generalization of previous concepts, such as definite integrals, series and sequences.