Seminars 2015

We present a new mechanism for the formation of bounded states in the continuum in lattices with chiral symmetry connected to leads. Bounded states in the continuum are square integrable solutions of the time-independent Schrödinger equation with eigenenergies above the potential threshold. We derive some algebraic rules for the number of states that remain bounded depending on the dimensionality and rank of the system Hamiltonian including the coupling to the leads. We study the transport properties of some relevant physical examples and propose different experiments for measuring consequences of the presence of these bounded state in the continuum.

[1] ‍ V. Fernández-Hurtado, J. Mur-Petit, J.J. García-Ripoll, R.A. Molina, New J. Phys. 16, 035005 (2014).
[2] ‍ J. Mur-Petit, R.A. Molina, Phys. Rev. B 90, 035404 (2014).

We show that the dynamics of particles suspended in an electrolyte confined between corrugated charged surfaces exhibits new and surprising phenomena such as particle separation, mixing for low-Reynolds micro- and nano-metric devices and negative mobility. Such phenomena originate from the interplay between the electrostatic double layer and the confinement; the new effects become more important when the width of the channel is comparable to the Debye length. We outline the relevance of the predicted effects in a wide variety of systems, from nano- and micro-fluidic devices to biological systems.

We present two classes of incomplete Riemann solvers, whose viscosity matrices are defined in terms of functional matrix approximations computed by means of an appropriate elementary real function $R(x)$, that approximates the continuous function $|x|$. The resulting approximate Riemann solvers are incomplete, in the sense that we do not use the complete spectral decomposition of the system, and only some information about the maximum in absolute value of the characteristic speeds are needed. We shall explore two approaches, Roe solver and Osher-Solomon approximations, respectively. Some numerical tests will be presented to show robustness, afficiency, and accuracy.

Course outline: and abstract:

La teoría de inestabilidad lineal modal y no modal aplicada en hidrodinámica ha demostrado ser una herramienta útil en el estudio del proceso de transición de flujos laminares a turbulentos, permitiendo con ello ir entendiendo los mecanismos que conducen a dicha transición, así como el desarrollo de estrategias de control activas y/o pasivas en dispositivos aerodinámicos sobre los que se producen estos procesos.
La teoría clásica de inestabilidad modal, centrada en el estudio de flujos paralelos (Lin, The Theory of Hydrodynamic Stability, Cambridge Univ. Press, 1955 y Drazin & Reid, Hydrodynamic Stability, Cambridge Univ. Press, 1981), se ha ido ampliado en las últimas décadas, entre otros, al estudio de flujos no paralelos, inestabilidades secundarias, inestabilidades en problemas con flujos base periódicos (Floquet) o al estudio de perturbaciones no modales basado en problemas de valor inicial (Schmid & Henningson, Stability and Transition in Shear Flows. Berlin: Springer, 2001).
La charla comenzará con una breve introducción de los problemas de estudio así como de las teorías de estabilidad modal y no modal utilizadas en éstos, entre otras: métodos modales con formación y sin formación de matriz, estudio no modal y algoritmo de los residuos (para más detalle véase Theofilis, Annu. Rev. Fluid Mech. 2011).
A continuación se presentarán los estudios de estabilidad sobre dichos problemas en el límite de flujo laminar incompresible, estos son: (a) estudio de estabilidad del flujo de capa límite oblicuo entorno a la línea de estancamiento, para lo que se utiliza como flujo base la solución de Dorrepall (Dorrepall Fluid Mech., 1986) a la que se añade la contribución del flujo en la dirección homogénea (envergadura), (b) aplicación de estrategias del tipo desplazamiento-inversión en códigos de estabilidad basados en integradores lineales de las Navier-Stokes (códigos sin formación de matriz) en flujo estenótico y flujo sobre un escalón (backward-facing step), (c) estudio de estabilidad modal y no modal en canales divergentes bidimensionales en función del número de Reynolds y el ángulo de divergencia del canal, (d) estudio de Floquet sobre el Naca 0012 y (e) estudio de inestabilidades modales en códigos de simulación numérica Lattice Boltzmann mediante la aplicación del método de los residuos en flujos confinados (ejemplo: lid-driven cavity).

El efecto de la vibración en fluidos es de gran interés en muchos campos y puede dar resultados muy complejos. La configuración más simple y más estudiada es la de un recipiente de fluido agitado verticalmente, esto es así porque la solución básica (no excitada) está en reposo en el marco de referencia del recipiente en movimiento. Otras configuraciones son en general menos fáciles de tratar y han recibido menos atención, sobre todo en el límite en el que la frecuencia es grande en comparación con la del primer modo capilar-gravitatorio. En el caso de un contenedor sometido a vibración horizontal primero aparecen trenes de ondas paralelas a la paredes y, más allá de una aceleración crítica, también se pueden excitar un par de ondas casi perpendiculares que serán estudiadas semi-analíticamente. La vibración de las paredes produce un flujo que es el responsable de la inestabilidad paramétrica, es un mecanismo similar al de las ondas de Faraday con la salvedad de que se obtiene un forzamiento antisimétrico que no es uniforme espacialmente. La teoría se generalizará para estudiar el efecto que la vibración de un obstáculo completamente sumergido (que presenta unos mecanismos equivalentes) tiene en la superficie libre, al ser una forma sencilla de originar un forzamiento simétrico. La teoría se aplicará para calcular la aceleración crítica así como la orientación de los patrones.

Energy harvesting is the process by which energy is taken from the environment and transformed to provide power for electronics. Specifically, the conversion of thermal energy into electrical power, or thermoelectrics, can play a crucial role in future developments of alternative sources of energy. Unfortunately, present thermoelectrics have low efficiency. Therefore, an important task in condensed matter physics is to find new ways to harvest ambient thermal energy, particularly at the smallest length scales where electronics operate. To achieve this goal, there is on one hand the miniaturizing of electrical devices, and on the other, the maximization of either efficiency or power the devices produce.
Three terminal conductors permit separate directions of the heat and current flux [1]. We present a model of Coulomb coupled conductors one of which is connected via only one lead to a hot reservoir. The other conductor is connected to two leads. Such a geometry can be used for detection of non linear heat fluctuations [2]. We investigate the minimal conditions needed to generate directed current flow for a system of two quantum dot conductors in which both energy and charge states are quantized. In quantum dots energy to current conversion can be optimal with one electron transferred for every heat quantum given up by the hot reservoir. We show that this configuration achieves high efficiencies. However, the generated power is small.
To attain the two requirements of high efficiency and power, we propose a resonant tunneling quantum dot engine that can be operated either in the Carnot efficient mode, or maximal power mode. The ability to scale the power by putting many such engines in a "Swiss cheese sandwich" geometry gives a paradigmatic system for harvesting thermal energy at the nanoscale [3].
We also discuss alternative configurations based on resonant tunneling through quantum wells provide a comparable thermoelectric performance with the advantage of being easier to construct [4].

[1] ‍R. Sánchez, M. Büttiker, "Optimal energy quanta to current conversion" Phys. Rev. B 87, 075312 (2013).
[2] ‍R. Sánchez, M. Büttiker, "Detection of single-electron heat transfer statistics" Europhys. Lett. 100, 47008 (2012).
[3] ‍A.N. Jordan, B. Sothmann, R. Sánchez, M. Büttiker, "Powerful and efficient energy harvester with resonant-tunneling quantum dots", Phys. Rev. B 87, 075312 (2013).
[4] ‍B. Sothmann, R. Sánchez, A. N. Jordan, M. Büttiker, "Powerful energy harvester based on resonant-tunneling quantum wells", New J. Phys. 15, 095021 (2013).

The study of energy and charge transfer among organic molecules is of key importance in the description of optoelectronic processes taking within a variety of systems ranging from organic electronic devices (OD) to biological light-harvesting complexes (LHC). Therefore the understanding of the properties and conditions of such mechanisms is manifold, allowing for the design of new organic devices yielding better outputs, efficiencies and lower energy consumption, as the thin and flexible displays currently commercialized, while helping in the detailed understand of the first steps of the photosynthesis. This presentation will focus on the molecular dynamics and QM/MM results obtained on charge and energy transfer studies in both worlds (OD and LHC), used to validate the experimental data and to assess the information currently not available experimentally.

We consider the magnetohydrodynamics systems of equations closed with a general equation of state. We analyze materials response by characterizing the behavior of the wave structure of the system in terms of the thermodynamic properties of the material and the presence of magnetic field. We characterize the nonlinearity of the model and prove that magnetic field can neutralize the formation of non-classical wave structure induced by phase transitions in the material. We provide an analytical expression that allows us to determine the specific amount of magnetic field to revert non-classical behavior into classical. We present numerical experiments validating the performed analysis.