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Fontelos M.A.,Institute Ciencias Matematicas ICMAT | De La Hoz F.,University of the Basque Country
Journal of Fluid Mechanics | Year: 2010

We describe, by means of asymptotic methods and direct numerical simulation, the structure of singularities developing at the interface between two perfect, inviscid and irrotational fluids of different densities 1 and 2 and under the action of gravity. When the lighter fluid is on top of the heavier fluid, one encounters the water-wave problem for fluids of different densities. In the limit when the density of the lighter fluid is zero, one encounters the classical water-wave problem. Analogously, when the heavier fluid is on top of the lighter fluid, one encounters the Rayleigh-Taylor problem for fluids of different densities, with this being the case when one of the densities is zero for the classical Rayleigh-Taylor problem. We will show that both water-wave and Rayleigh-Taylor problems develop singularities of the Moore-type (singularities in the curvature) when both fluid densities are non-zero. For the classical water-wave problem, we propose and provide evidence of the development of a singularity in the form of a logarithmic spiral, and for the classical Rayleigh-Taylor problem no singularities were found. The regularizing effects of surface tension are also discussed, and estimates of the size and wavelength of the capillary waves, bubbles or blobs that are produced are provided. © 2010 Cambridge University Press.


PubMed | Complutense University of Madrid, Loughborough University, Technical University of Madrid, Institute Ciencias Matematicas ICMAT and Georgia Institute of Technology
Type: Journal Article | Journal: Physical review. E | Year: 2016

The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing-free dividing surface. We show here that it is possible to define such optimal dividing surface in systems with non-Markovian friction. However, a more direct approach to rate calculation is based on invariant manifolds and avoids the use of a dividing surface altogether, Using that method we obtain an explicit expression for the rate of crossing an anharmonic potential barrier. The excellent performance of our method is illustrated with an application to a realistic model for LiNCLiCN isomerization.


Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Hong S.H.,Pohang University of Science and Technology | Hwang H.J.,Pohang University of Science and Technology
Archive for Rational Mechanics and Analysis | Year: 2015

We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape. © 2014, Springer-Verlag Berlin Heidelberg.


PubMed | Institute Ciencias Matematicas ICMAT, Technical University of Madrid and Comision Nacional de la Energia Atomica
Type: Journal Article | Journal: The Journal of chemical physics | Year: 2017

In this paper, we extend a method recently reported [F. Revuelta et al., Phys. Rev. E 87, 042921 (2013)] for the calculation of the eigenstates of classically highly chaotic systems to cases of mixed dynamics, i.e., those presenting regular and irregular motions at the same energy. The efficiency of the method, which is based on the use of a semiclassical basis set of localized wave functions, is demonstrated by applying it to the determination of the vibrational states of a realistic molecular system, namely, the LiCN molecule.


PubMed | Institute Ciencias Matematicas ICMAT, Technical University of Madrid and Comision Nacional de la Energia Atomica
Type: Journal Article | Journal: The journal of physical chemistry. A | Year: 2016

The performance of a recently proposed method to efficiently calculate scar functions is analyzed in problems of chemical interest. An application to the computation of wave functions associated with barriers relevant for the LiNC LiCN isomerization reaction is presented as an illustration. These scar functions also constitute excellent elements for basis sets suitable for quantum calculation of vibrational energy levels. To illustrate their efficiency, a calculation of the LiNC/LiCN eigenfunctions is also presented.


Palazuelos C.,Institute Ciencias Matematicas ICMAT
Physical Review Letters | Year: 2012

In this Letter we show that quantum nonlocality can be superactivated. That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself. In the second part of this work we study how large these violations can be. In particular, we show the existence of quantum states with very low Bell violation but such that five copies of them give very large violations. In fact, this gap can be made arbitrarily large by increasing the dimension of the states. © 2012 American Physical Society.


Eggers J.,University of Bristol | Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Josserand C.,CNRS Jean Le Rond d'Alembert Institute | Zaleski S.,CNRS Jean Le Rond d'Alembert Institute
Physics of Fluids | Year: 2010

We study the impact of a fluid drop onto a planar solid surface at high speed so that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects. As the drop spreads, it deforms into a thin film, whose thickness is limited by the growth of a viscous boundary layer near the solid wall. Owing to surface tension, the edge of the film retracts relative to the flow in the film and fluid collects into a toroidal rim bounding the film. Using mass and momentum conservation, we construct a model for the radius of the deposit as a function of time. At each stage, we perform detailed comparisons between theory and numerical simulations of the Navier-Stokes equation. © 2010 American Institute of Physics.


Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Grun G.,Friedrich - Alexander - University, Erlangen - Nuremberg
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2013

We prove regularity results and, as a consequence, uniqueness for a system of partial differential equations arising in the study of dynamic electrowetting phenomena and more general electrokinetic processes in three space dimensions. The system consists of Stokes equations coupled with equations for the motion of electric charges, Poisson equation for computing the electric field generated by such charges and a Cahn-Hilliard equation for a phase field describing two fluids with different material parameters. The deduction and existence of weak solutions for this system was established in an earlier paper (Christof Eck et al., On a phase-field model for electrowetting, Interfaces Free Bound. 11 (2), 259-290, (2009)). © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.


Breschi G.,Institute Ciencias Matematicas ICMAT | Fontelos M.A.,Institute Ciencias Matematicas ICMAT
Nonlinearity | Year: 2014

We study the self-similar solutions of Smoluchowski's equation with kernel K(x, y) = x1-εy1-ε for ε > 0 and ε ≪ 1. We prove that by choosing the similarity exponents as suitable functions of ε, the self-similar solutions present correct behaviours at the origin and at infinity, which amounts to solving a nonlinear eigenvalue problem. This characterizes the self-similar solution found as being of the second kind in the notation introduced by Barenblatt. © 2014 IOP Publishing Ltd & London Mathematical Society.


Fontelos M.A.,Institute Ciencias Matematicas ICMAT | Kindelan U.,Technical University of Madrid
IOP Conference Series: Materials Science and Engineering | Year: 2014

In this work we study the static shape of charged drops of a conducting fluid placed over a solid substrate, surrounded by a gas, and in absence of gravitational forces. The problem can be posed, since Gauss, in a variational setting consisting of obtaining the configurations of a given mass of fluid that minimize (or in general make extremal) a certain energy involving the areas of the solid-liquid interface and of the liquid-gas interface, as well as the electric capacity of the drop. In [6] we have found, as a function of two parameters, Young's angle θYand the potential at the drop's surface V0, the axisymmetric minimizers of the energy. In the same article we have also described their shape and showed the existence of symmetry-breaking bifurcations such that, for given values of θYand V0, configurations for which the axial symmetry is lost are energetically more favorable than axially symmetric configurations. We have proved the existence of such bifurcations in the limits of very flat and almost spherical equilibrium shapes. In this work we study all other cases numerically. When dealing with radially perturbed equilibrium shapes we lose the axially symmetric properties and need to do a full three-dimensional approximation in order to compute area and capacity and hence the energy. We use a boundary element method that we have already implemented in [3] to compute the surface charge density. From the surface charge density we can obtain the capacity of the body. One conclusion of this study is that axisymmetric drops cannot spread indefinitely by introducing sufficient amount of electric charges, but can reach only a limiting (saturation) size, after which the axial symmetry would be lost and finger-like shapes energetically preferred. © 2010 IOP Publishing Ltd.

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