Dinámica estocástica en física y biología

Tesis de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Estructura de la Materia, Física Térmica y Electrónica, leída el 26-10-2018Stochastic processes are present in virtually any field of science. Actually, in general deterministic processes are no more than an approximation of more complex stochastic processes in some regime of validity. In the present thesis, we will study some systems that appear in Physics and Biology where the presence of these stochastic processes plays a major role. First, we will study the Brownian ratchet systems, which are able to generate a directed motion simply by rectifying the thermal fluctuations to which Brownian particles are subjected. These Brownian ratchets began to be studied in the field of Statistical Physics as a Gedanken experiment that apparently broke the Second Law of Thermodynamics. Later they were applied to study the operation of some molecular motors. In this thesis we will study different types of Brownian ratchets, characterizing the average flux, the efficiency, and the quality of the transport of particles they produce..En prácticamente cualquier rama de la ciencia están presentes los procesos estocásticos. De hecho, en general los procesos deterministas no son más que una aproximación de procesos estocásticos más complejos en algún régimen de validez. En la presente tesis, estudiaremos algunos sistemas que aparecen en Física y Biología donde la presencia de dichos procesos es crucial.Primero, estudiaremos los conocidos como trinquetes brownianos, que son capaces de generar movimiento dirigido simplemente a través de la rectificación de las fluctuaciones térmicas a las que se ven sometidas las partículas Brownianas. Estos trinquetes Brownianos se empezaron a estudiar en el campo de la Física Estadística como un experimento mental que aparentemente rompía la Segunda Ley de la Termodinámica. Sin embargo, más adelante se ha visto que pueden ser aplicados para estudiar el funcionamiento de algunos motores moleculares. En esta tesis estudiaremos distintos tipos de trinquetes Brownianos, caracterizando el flujo medio, la eficiencia, y la calidad del transporte de partículas que producen...Depto. de Estructura de la Materia, Física Térmica y ElectrónicaFac. de Ciencias FísicasTRUEunpu

Agujeros negros de Reissner-Nordstrom en teorías de electrodinámica modificada

Máster de Física Fundamental. Facultad de Ciencias Físicas. Curso 2013-2014.In the context of modified and gauge invariant Electrodynamics theories minimally coupled with gravitation we look for the U(1) Lagrangian densities supporting electric and magnetic monopoles which provide sta Nordström black-hole solutions. We achieve a sufficient condition for general Lagrangian densities supporting this kind of solutions, and we propose a simple model which can be interpreted as a small correction to the usual Electrodynamics theory, which is proven to be correct in the asymptotic limit r → ∞ . For these models we obtain their correspondent metrics, and then by employing the Euclidean Action approach we perform a thermodynam- ics analysis and study the existing phases depending on the sign of the heat capacity and the Helmholtz free energy. Thus, we obtain that modified Electrodynamics theories lead to ve different thermodynamics properties and, in some particular cases, to a new phase which does not appear in the usual theory.En el marco de las teorías de electrodinámica modificada, invariantes gauge y minimamente acopladas a la gravedad, buscamos las densidades lagrangianes con simetría U(1) que admiten monopolos eléctricos y magnéticos en soluciones de agujero negro de Reissner-Nordström estáticas, esféricamente simétricas y de curvatura constante. En este trabajo obtenemos una condición suficiente para que las densidades Lagrangianas posean este tipo de soluciones, y proponemos un modelo simple que puede ser interpretado como una pequeña corrección a la teoría electrodinámica usual, la cual sabemos que es correcta en el límite asintótico r → ∞ . Para dichos modelos obtenemos las correspondientes métricas, y empleando el método de la acción euclídea realizamos un análisis termodinámico y estudiamos las fases de estabilidad presentes, en función del signo de la capacidad calorífica y de la energía libre de Helmholtz. Así, obtenemos que las teorías de electrodinámica modificada conllevan propiedades termodinámicas muy diferentes para las soluciones y, en algunos casos particulares, una nueva fase de estabilidad que no aparece en la teoría usual.Depto. de Física TeóricaFac. de Ciencias FísicasTRUEunpu

Efficiency at maximum power of a discrete feedback ratchet

Efficiency at maximum power is found to be of the same order for a feedback ratchet and for its open-loop counterpart. However, feedback increases the output power up to a factor of five. This increase in output power is due to the increase in energy input and the effective entropy reduction obtained as a consequence of feedback. Optimal efficiency at maximum power is reached for time intervals between feedback actions two orders of magnitude smaller than the characteristic time of diffusion over a ratchet period length. The efficiency is computed consistently taking into account the correlation between the control actions. We consider a feedback control protocol for a discrete feedback flashing ratchet, which works against an external load. We maximize the power output optimizing the parameters of the ratchet, the controller, and the external load. The maximum power output is found to be upper bounded, so the attainable extracted power is limited. After, we compute an upper bound for the efficiency of this isothermal feedback ratchet at maximum power output. We make this computation applying recent developments of the thermodynamics of feedback-controlled systems, which give an equation to compute the entropy reduction due to information. However, this equation requires the computation of the probability of each of the possible sequences of the controller's actions. This computation becomes involved when the sequence of the controller's actions is non-Markovian, as is the case in most feedback ratchets. We here introduce an alternative procedure to set strong bounds to the entropy reduction in order to compute its value. In this procedure the bounds are evaluated in a quasi-Markovian limit, which emerge when there are big differences between the stationary probabilities of the system states. These big differences are an effect of the potential strength, which minimizes the departures from the Markovianicity of the sequence of control actions, allowing also to minimize the departures from the optimal performance of the system. This procedure can be applied to other feedback ratchets and, more in general, to other control systems

Long wavelength local density of states oscillations near graphene step edges

Using scanning tunneling microscopy and spectroscopy, we have studied the local density of states (LDOS) of graphene over step edges in boron nitride. Long wavelength oscillations in the LDOS are observed with maxima parallel to the step edge. Their wavelength and amplitude are controlled by the energy of the quasiparticles allowing a direct probe of the graphene dispersion relation. We also observe a faster decay of the LDOS oscillations away from the step edge than in conventional metals. This is due to the chiral nature of the Dirac fermions in graphene.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Quantum Hall Effect, Screening and Layer-Polarized Insulating States in Twisted Bilayer Graphene

We investigate electronic transport in dual-gated twisted bilayer graphene. Despite the sub-nanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite inter-layer screening and extract the capacitance between the atomically-spaced layers. At zero filling factor, we observe magnetic and displacement field dependent insulating states, which indicate the presence of counter-propagating edge states with inter-layer coupling.Comment: 4 pages, 3 figure

Dispersal-induced resilience to stochastic environmental fluctuations in populations with Allee effect

Many species are unsustainable at small population densities (Allee Effect). This implies that for population densities below a threshold, named Allee threshold, the population decreases instead of growing. In a closed local population, this makes that environmental fluctuations always leads to extinction. Here, we show how, in spatially extended habitats, dispersal can lead to a sustainable population in a region, provided the amplitude of environmental fluctuations is below an extinction threshold. We have identified two types of sustainable populations: high-density and low-density populations (through a mean-field approximation, valid in the limit of large dispersal length). Our results show that close to global extinction patches where population density is high, low or extinct coexist (even for homogeneous habitats). The extinction threshold increases proportionally to the squared root of the dispersal rate, decreases with the Allee threshold, and it is maximum for characteristic dispersal distances much larger than the spatial scale of synchrony of environmental fluctuations. The low-density population solution can be particularly interesting for future applications, as to understand non-recovery events after harvesting. This theoretical framework allows novel approaches to address the impact of other factors, as habitat fragmentation, on the population resilience to environmental fluctuations.Comment: 24 pages, 3 figures, 1 tabl

Spatial and Ecological Scaling of Stability in Spatial Community Networks

There are many scales at which to quantify stability in spatial and ecological networks. Local-scale analyses focus on specific nodes of the spatial network, while regional-scale analyses consider the whole network. Similarly, species- and community-level analyses either account for single species or for the whole community. Furthermore, stability itself can be defined in multiple ways, including resistance (the inverse of the relative displacement caused by a perturbation), initial resilience (the rate of return after a perturbation), and invariability (the inverse of the relative amplitude of the population fluctuations). Here, we analyze the scale-dependence of these stability properties. More specifically, we ask how spatial scale (local vs regional) and ecological scale (species vs community) influence these stability properties. We find that regional initial resilience is the weighted arithmetic mean of the local initial resiliences. The regional resistance is the harmonic mean of local resistances, which makes regional resistance particularly vulnerable to nodes with low stability, unlike regional initial resilience. Analogous results hold for the relationship between community- and species-level initial resilience and resistance. Both resistance and initial resilience are ``scale-free'' properties: regional and community values are simply the biomass-weighted means of the local and species values, respectively. Thus, one can easily estimate both stability metrics of whole networks from partial sampling. In contrast, invariability generally is greater at the regional and community-level than at the local and species-level, respectively. Hence, estimating the invariability of spatial or ecological networks from measurements at the local or species level is more complicated, requiring an unbiased estimate of the network (i.e. region or community) size

The late media emergency of smallpox vaccine, news coverage of Spanish press (1999-2004)

Introducción. Las discusiones sobre la necesidad de conservación del virus de la viruela en 1999 pusieron de actualidad una enfermedad erradicada veinte años atrás. El escenario de alarma internacional creado tras los incidentes del 11-S en EE.UU vino a resituar a la viruela como potencial candidata para ser utilizada como arma bioterrorista. La consecuencia directa fue la reactivación de una vacuna que permanecía en el olvido y cuyos destinatarios iniciales eran los cuerpos de seguridad estadounidenses. España también se interesó por adquirir la vacuna antivariólica. El objetivo de este estudio es valorar la cobertura mediática que la viruela obtuvo en nuestro país. Métodos. Revisión sistemática en la base documental Dow Jones Factiva de las noticias publicadas durante el periodo 1999-2004 en los cuatro diarios de mayor tirada nacional (ABC, El Mundo, El País y La Vanguardia), utilizando como palabra clave “viruela”. Se efectuó un análisis cuantitativo y cualitativo de los datos obtenidos. Resultados. Se analizaron 416 noticias. El Mundo, con un total de 158 (37.98%), fue el diario con más publicaciones. El mayor número de noticias (152, 36,5%) se editaron en 2003, coincidiendo con la adquisición de vacunas por España. El tipo de mensajes emitidos fue variable a lo largo del sexenio, predominando los relacionados con “diplomacia y política”, “riesgo epidemiológico”, “bioterrorismo” y “vacuna”, concentrados en años diferentes. Conclusiones. La alarma creada en torno a la vacunación antivariólica fue un fenómeno mediático que obedeció a cuestiones de estrategia política más que a un problema real de salud pública.Introduction. Discussions on the need for smallpox virus preservation in 1999 focused attention on an eradicated disease 20 years ago. Smallpox was replaced as a potential candidate to be used as a bioterrorist weapon because of the international alarm scenario produced after the 11/9 events in USA. The reactivation of a vaccine which remained forgotten was the direct consequence. The initial target groups were the security forces of America. Spain was also among the countries that were interested in acquiring the smallpox vaccine. The aim of this study is to analyze the considerable media coverage of smallpox obtained in our country. Methods. Systematic review of published news in the four largest national daily newspapers (ABC, El Mundo, El País and La Vanguardia) for the period 1999-2004 of the Dow Jones Factiva document database. “Smallpox” were used as a key word. From the obtained data, a qualitative and quantitative analysis was done. Results. 416 reviews were analyzed; the newspaper El Mundo was the most interested in these news (158 citations, 37.98%). Most of the news were published in 2003 (152, 36.5%) The year with more news about smallpox (2003) coincides with the purchase of vaccines in Spain. The type of messages in the news was highly changeable over this six-year period. Those related to “politics and diplomacy”, “epidemiological risk”, “bioterrorism” and “vaccine” were predominant. Conclusions. The alarm raised around the smallpox vaccination was a media phenomenon due to political strategy issues rather than a real public health problem

Tunneling in graphene-topological insulator hybrid devices

Hybrid graphene-topological insulator (TI) devices were fabricated using a mechanical transfer method and studied via electronic transport. Devices consisting of bilayer graphene (BLG) under the TI Bi$_2$Se$_3$ exhibit differential conductance characteristics which appear to be dominated by tunneling, roughly reproducing the Bi$_2$Se$_3$ density of states. Similar results were obtained for BLG on top of Bi$_2$Se$_3$, with 10-fold greater conductance consistent with a larger contact area due to better surface conformity. The devices further show evidence of inelastic phonon-assisted tunneling processes involving both Bi$_2$Se$_3$ and graphene phonons. These processes favor phonons which compensate for momentum mismatch between the TI $\Gamma$ and graphene $K, K'$ points. Finally, the utility of these tunnel junctions is demonstrated on a density-tunable BLG device, where the charge-neutrality point is traced along the energy-density trajectory. This trajectory is used as a measure of the ground-state density of states