Complex Systems: Nonlinearity and Structural Complexity in spatially extended and discrete systems

Resumen Esta Tesis doctoral aborda el estudio de sistemas de muchos elementos (sistemas discretos) interactuantes. La fenomenología presente en estos sistemas esta dada por la presencia de dos ingredientes fundamentales: (i) Complejidad dinámica: Las ecuaciones del movimiento que rigen la evolución de los constituyentes son no lineales de manera que raramente podremos encontrar soluciones analíticas. En el espacio de fases de estos sistemas pueden coexistir diferentes tipos de trayectorias dinámicas (multiestabilidad) y su topología puede variar enormemente dependiendo de dos parámetros usados en las ecuaciones. La conjunción de dinámica no lineal y sistemas de muchos grados de libertad (como los que aquí se estudian) da lugar a propiedades emergentes como la existencia de soluciones localizadas en el espacio, sincronización, caos espacio-temporal, formación de patrones, etc... (ii) Complejidad estructural: Se refiere a la existencia de un alto grado de aleatoriedad en el patrón de las interacciones entre los componentes. En la mayoría de los sistemas estudiados esta aleatoriedad se presenta de forma que la descripción de la influencia del entorno sobre un único elemento del sistema no puede describirse mediante una aproximación de campo medio. El estudio de estos dos ingredientes en sistemas extendidos se realizará de forma separada (Partes I y II de esta Tesis) y conjunta (Parte III). Si bien en los dos primeros casos la fenomenología introducida por cada fuente de complejidad viene siendo objeto de amplios estudios independientes a lo largo de los últimos años, la conjunción de ambas da lugar a un campo abierto y enormemente prometedor, donde la interdisciplinariedad concerniente a los campos de aplicación implica un amplio esfuerzo de diversas comunidades científicas. En particular, este es el caso del estudio de la dinámica en sistemas biológicos cuyo análisis es difícil de abordar con técnicas exclusivas de la Bioquímica, la Física Estadística o la Física Matemática. En definitiva, el objetivo marcado en esta Tesis es estudiar por separado dos fuentes de complejidad inherentes a muchos sistemas de interés para, finalmente, estar en disposición de atacar con nuevas perspectivas problemas relevantes para la Física de procesos celulares, la Neurociencia, Dinámica Evolutiva, etc..

Fermeture de bulles de dénaturation de l'ADN couplées à l'élasticité de l'ADN

La compréhension physique des processus biologiques tels que la transcription nécessite de bien connaître la physique de l'ADN double brin. Une de ses propriétés thermodynamiques remarquable est sa dénaturation à une température particulière, lors de laquelle il se déroule et se sépare en deux brins après avoir formé des bulles (segments de paires de bases ouvertes consécutives). La dynamique de dénaturation jusqu'ici été étudiée l'échelle de la paire de base, ignorant ainsi les degrés de la chaîne. Ces études n'expliquent pas les temps de fermeture trés longs, de 20 $100\mu$s, mesurés par Alain-Bonnet et al.température ambiante pour des bulles de 18 paires de base. Dans cette thèse nous nous interessons la fermeture de grandes bulles de dénaturation thermalisées, l'aide de simulations de dynamique Brownienne d'un modèle simple "gros grains"de l'ADN. Nous montrons que la fermeture se fait en deux temps : d'abord, la bulle initiale se ferme rapidement jusqu'à ce qu'elle atteigne un état métastable, causé par les grandes énergies de courbure et de torsion emmagasinées dans la bulle. Ensuite, la fermeture de la bulle metastable se fait en fonction de la longueur de l'ADN et des parametres elastiques, soit apres la diffusion rotationnelle des "bras" rigides jusqu'à l'alignement de ceux-ci, soit lorsque la bulle a diffusée jusqu'un bout de la chaîne, ou soit localement lors d'une activation thermique. Nous montrons ainsi que le mécanisme physique associé des longs temps de fermeture est le couplage entre les degrés de liberté d'appariement et de conformations de l'ADN.The physical understainding of biological processes such as transcription requires the knowledge of double-stranded DNA (dsDNA) is its denaturation, at the melting temperature, in which it unwinds into two single-stranded DNAs via the formation of denaturation bubbles (segment of consecutive unpaired base-pairs). the dynamics of denaturation has beenstudies so far at the base-pair (bp) scale, ignoring conformational chaindegrees of freedom. These studies do not explain the very long closure times of 20 to 100µs, measured by atlan-Bonnet et al., of 18 bps long bubbles at room temperature. In this thesis, we study the closure of pre-equilibrated large bubbles, by using Brownian dynamics simulations of two simple DNA coarse-grained models. We show that the closure occurs via two steps : first, a fast zipping of the initial bubble occurs until a meta-stable state is reached, due to the large bending and twisting energies stored in the bubble. Then, the mete-stable bubble closes either via rotational diffusion of the stiff side arms until their alignment, or bubble diffusion until it reaches the chain end, or locally by thermal activation, depending on the DNA length and elastic moduli. We show that the physical mechanism behind these long timescales is therefore the dynamical coupling between base-pair and chain degrees of freedom

Dynamics of ion Coulomb crystals

The field of quantum simulations has achieved a remarkable success through the development of highly controllable and accessible quantum platforms, which pro- vide insights into the microscopic properties of complex large-scale systems that are otherwise difficult to analyze. Many of the platforms utilized in this pursuit are derived from the field of atomic, molecular, and optical physics. One particularly popular candidate is provided by trapped ions, whose vibrational and electronic degrees of freedom can be effectively combined through laser pulses to engineer desired model Hamiltonians or quantum circuits. Trapped ions constitute as well the basis for modern atomic clocks, the most precise frequency standards currently available. They find further applications in metrology, geodesy, and fundamental physics experiments. In this Thesis, we investigate the dynamics of vibrational modes in trapped ion crystals, utilizing them as a versatile platform to explore various many-body phenomena. We first focus on the expansion dynamics of local excitations and on heat transport within ion crystals hosting structural defects that undergo a sliding- to-pinned transition. We observe a significant reduction in conductivity when the crystal symmetry is spontaneously broken during the transition, and show that resonances between crystal eigenmodes lead to distinct softening signatures associated with energy localization. We then delve into the effects of thermal and quantum fluctuations on the vibrational modes of ion crystals near two distinct structural transitions. We observe the emergence of a prolonged symmetric phase stabilized by thermal and quantum fluctuations, and develop effective theories that reduce the degrees of freedom to the modes that drive the transitions. Finally, we discuss how to engineer spin-orbit coupling and on-site interaction energies for vibrational quantum excitations using two different external driving schemes. While the simulation of spin models with ions typically involves the use of two electronic states, we propose interpreting the two local oscillation modes in an ion crystal as a pseudospin. We show how using Floquet engineering ideas allows for spin flips in Coulomb-induced vibron hopping, resulting in a non-trivial coupling between spatial motion and spin evolution, that results in a markedly non-Abelian dynamics. Subsequently, we explore the simulation of Hubbard models in trapped ions by coupling the vibrational Fock states to an internal level system. Our findings include the observation of bound states in the strong interaction limit of the resulting Jaynes-Cummings-Hubbard model. By investigating these topics, we aim to contribute to the understanding of vibrational dynamics in trapped ion crystals, and shed light on their potential for simulating condensed matter systems, offering insights into phenomena that are otherwise challenging to explore.DFG/Sonderforschungsbereich 1227 DQ-mat/274200144/E

Marine Oil Spills

Major oil spills attract the attention of the public and the media. This was especially the case after the Deepwater Horizon spill. In recent years, this attention has created a global awareness of the risks of oil spills and the damage they do to the environment. Oil is a necessity in our industrial society, however, and a major component of our lifestyle. This means that the risk of major spills continues as does the interest in spills. The Deepwater Horizon spill began a new series of scientific studies that have greatly increased our understanding of oil spills. This book contains 10 such studies. These studies vary from toxicity studies to social studies of human reaction to spills and risk. Importantly, the book is a sampling of important new topics that have become important after the Deepwater Horizon spill. These new topics include new chemical and tracing techniques, new risk perception techniques, perspectives on human health and spills, and discussion on new fuels. This book makes a significant contribution to the understanding of facets of spills and explores 10 very different facets of oil spills