Suppressing the Rayleigh-Taylor instability with a rotating magnetic field

The Rayleigh-Taylor instability of a magnetic fluid superimposed on a non-magnetic liquid of lower density may be suppressed with the help of a spatially homogeneous magnetic field rotating in the plane of the undisturbed interface. Starting from the complete set of Navier-Stokes equations for both liquids a Floquet analysis is performed which consistently takes into account the viscosities of the fluids. Using experimentally relevant values of the parameters we suggest to use this stabilization mechanism to provide controlled initial conditions for an experimental investigation of the Rayleigh-Taylor instability

Double Rosensweig instability in a ferrofluid sandwich structure

We consider a horizontal ferrofluid layer sandwiched between two layers of immiscible non-magnetic fluids. In a sufficiently strong vertical magnetic field the flat interfaces between magnetic and non-magnetic fluids become unstable to the formation of peaks. We theoretically investigate the interplay between these two instabilities for different combinations of the parameters of the fluids and analyze the evolving interfacial patterns. We also estimate the critical magnetic field strength at which thin layers disintegrate into an ordered array of individual drops

Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods

This article is devoted to computing the lower and upper bounds of the Laplace eigenvalue problem. By using the special nonconforming finite elements, i.e., enriched Crouzeix-Raviart element and extension $Q_1^{\rm rot}$, we get the lower bound of the eigenvalue. Additionally, we also use conforming finite elements to do the postprocessing to get the upper bound of the eigenvalue. The postprocessing method need only to solve the corresponding source problems and a small eigenvalue problem if higher order postprocessing method is implemented. Thus, we can obtain the lower and upper bounds of the eigenvalues simultaneously by solving eigenvalue problem only once. Some numerical results are also presented to validate our theoretical analysis.Comment: 19 pages, 4 figure

Positive finite difference schemes for a partial integro-differential option pricing model

[EN] This paper provides a numerical analysis for European options under partial integro-differential Bates model. An explicit finite difference scheme has been used for the differential part, while the integral part has been approximated using the four-points open type formula. The stability and consistency have been studied. Moreover, conditions guaranteing positivity of the solutions are provided. Illustrative numerical examples are included.This work has been partially supported by the European Union in the FP7-PEOPLE-2012-ITN program under Grant Agreement Number 304617 (FP7 Marie Curie Action, Project Multi-ITN STRIKE-Novel Methods in Computational Finance) and the Ministerio de Economia y Competitividad Spanish grant MTM2013-41765-P.Fakharany, M.; Company Rossi, R.; Jódar Sánchez, LA. (2014). Positive finite difference schemes for a partial integro-differential option pricing model. Applied Mathematics and Computation. 249:320-332. https://doi.org/10.1016/j.amc.2014.10.064S32033224

Iron and bismuth bound human serum transferrin reveals a partially-opened conformation in the N-lobe

Human serum transferrin (hTF) binds Fe(III) tightly but reversibly, and delivers it to cells via a receptor-mediated endocytosis process. The metal-binding and release result in significant conformational changes of the protein. Here, we report the crystal structures of diferric-hTF (Fe N Fe C-hTF) and bismuth-bound hTF (Bi N Fe C-hTF) at 2.8 and 2.4 Å resolutions respectively. Notably, the N-lobes of both structures exhibit unique 'partially-opened' conformations between those of the apo-hTF and holo-hTF. Fe(III) and Bi(III) in the N-lobe coordinate to, besides anions, only two (Tyr95 and Tyr188) and one (Tyr188) tyrosine residues, respectively, in contrast to four residues in the holo-hTF. The C-lobe of both structures are fully closed with iron coordinating to four residues and a carbonate. The structures of hTF observed here represent key conformers captured in the dynamic nature of the transferrin family proteins and provide a structural basis for understanding the mechanism of metal uptake and release in transferrin families. © 2012 Macmillan Publishers Limited. All rights reserved.published_or_final_versio

Theory of rotating electrohydrodynamic flows in a liquid film

The mathematical model of rotating electrohydrodynamic flows in a thin suspended liquid film is proposed and studied. The flows are driven by the given difference of potentials in one direction and constant external electric field E-out in another direction in the plane of a film. To derive the model, we employ the spatial averaging over the normal coordinate to a film that leads to the average Reynolds stress that is proportional to vertical bar E-out vertical bar(3). This stress generates tangential velocity in the vicinity of the edges of a film that, in turn, causes the rotational motion of a liquid. The proposed model is used to explain the experimental observations of the liquid film motor

Adaptive Radial Basis Function Methods for Pricing Options Under Jump-Diffusion Models

The aim of this paper is to show that option prices in jump-diffusion models can be computed using meshless methods based on radial basis function (RBF) interpolation instead of traditional mesh-based methods like finite differences or finite elements. The RBF technique is demonstrated by solving the partial integro-differential equation for American and European options on non-dividend-paying stocks in the Merton jump-diffusion model, using the inverse multiquadric radial basis function. The method can in principle be extended to Lévy-models. Moreover, an adaptive method is proposed to tackle the accuracy problem caused by a singularity in the initial condition so that the accuracy in option pricing in particular for small time to maturity can be improved