Dynamics of Cellular Communities: Insights from Antibiotic-Induced Biofilms, Self-Replicating Oscillators, and Spatially-Extended Communities

Collective behavior is a fascinating phenomenon occurring at many scales in biology. From flocking of birds to synchronization in neural populations, examples abound where local interactions give rise to “macroscopic”, often counterintuitive behavior, at the level of the community. In this thesis, I investigate community behavior in three distinct systems using a combination of theoretical and experimental approaches. The work spans a broad range of topics inspired by dynamics in microbial communities. In Chapter II, we provide a comprehensive theoretical study of synchronization in coupled oscillators, a topic that is among the most widely studied in dynamical systems. However, while past work has focused almost exclusively on populations of a fixed size, I introduce a new model of self-dividing oscillator populations that exhibits a remarkable range of synchronization phenomena as growth rate is varied. Chapter III describes a largely experiment-driven effort to understand a specific and counterintuitive phenomenon: the promotion of microbial community (biofilm) growth by low doses of antibiotic drugs in a medically relevant bacterial species, E. faecalis. We show that for cell wall synthesis inhibitors–which have for decades been among the most widely prescribed classes of antibiotics–low doses stimulate cell lysis and are associated with an increase in extracellular DNA, long believed to be an important structural component of biofilms. We also develop a simple mathematical model that highlights the interplay between the toxicity of the drug and the “beneficial” effects of cell lysis and can be used to predict the impact of various chemical perturbations that impact optimal biofilm growth. Finally, Chapter IV is devoted to ongoing work on spatial pattern formation in two bacterial species, E. coli and E. faecalis, exhibiting cooperative antibiotic resistance via the production of a community good–an enzyme that targets and degrades antibiotics. The work draws on previous theoretical models to predict pattern formation in simple (non-cooperative) populations, which we quantify using customized experimental tools for quantitatively characterizing colony growth over time and space. In addition, we observe a range of new pattern-formation phenomena driven, in part, by the interplay between cell motility, cooperation, and density-dependent cell growth.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138719/1/ywenv_1.pd

Cold atoms in cavity-generated dynamical optical potentials

We review state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the back-action of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is non-conservative and in general enables cooling and confining the motion of polarizable particles. In addition, the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to sub-wavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides correlated motion of distant particles, one finds critical behavior and non-equilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum degenerate gases inside optical resonators can be used to emulate opto-mechanics as well as novel quantum phases like supersolids and spin glasses. Non-equilibrium quantum phase transitions, as predicted by e.g. the Dicke Hamiltonian, can be controlled and explored in real-time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for non-destructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.Comment: 55 page review pape

Spatio-temporal dynamics of lasers and photorefractive oscillators under rocking: phase-bistable patterns and localized structures

El objectiu de aquesta tesi es l’estudi teòric, analític i numèric, de la dinàmica espaciotemporal d’oscil·ladors òptics no lineals sotmesos a un forçament bicromàtic (rocking). Aquest tipus d’injecció té la característica principal de trencar la invariància de fase (qualsevol fase del camp complex) del sistema lliure (sense forçament) i genera un sistema que és biestable en fase, ja que únicament dues fases (separades per ¼) són permeses per a les solucions estacionàries homogènies. Aquest canvi en la naturalesa del sistema provoca l’aparició d’una nova dinàmica caracteritzada per la presència d’un nou tipus d’estructures espacials en el pla transversal bidimensional: patrons biestables de fase en els quals dominis d’ambdues fases conviuen separades per parets de domini (Ising si la intensitat s’anul·la en elles o Bloch, en cas contrari). Aquests dominis poden evolucionar a patrons homogenis (d’una de les dues fases) o uns altres, més complexos, que els efectes de curvatura condueixen a la creació de patrons laberíntics segons els valors dels paràmetres del sistema. A més, poden existir estructures localitzades (dominis de grandària mínima estables) en la forma de solitons de cavitat d’anell fosc. Altres mètodes de trencament de la simetria de fase han sigut usats per a controlar la dinàmica de molts sistemes. Un dels més populars és la ressonància paramètrica, i.e. injectar un camp la freqüència del qual és aproximadament el doble de la freqüència natural de oscil·lació del sistema. No obstant això, aquests mètodes són menys versàtils que el rocking, el qual pot aplicar-se a una àmplia gamma de sistemes com el làser, que són insensibles a la ressonància paramètrica. De fet, s’han fet múltiples propostes teòriques i experimentals d’aplicació del rocking a diferents sistemes (òptics i no òptics). En el domini d’aquesta tesi, ens centrarem en la influència del rocking en dos sistemes que han sigut estudiats profusament en la literatura, donat el seu gran interès tant des del punt de vista fonamental compràctic:làsers i oscil·ladors fotorrefractius. Al llarg d’aquesta tesi, estudiarem detalladament la influència del rocking en aquests sistemes. Com és usual en el camp de la ciència no lineal, és convenient deduir equacions que descriguen el comportament d’aquests sistemes prop dels punts (punts crítics) on emergeixen les solucions estacionàries del sistema. Aquestes equacions (anomenades de paràmetre d’ordre) tenen una forma aparentment simple i són capaces de descriure multitud de sistemes no lineals, físics, químics, biològics.. (l’única diferència és el significat dels diferents paràmetres, però l’estructura matemàtica és la mateixa), per la qual cosa posseeixen un caràcter universal. Així mateix, analitzarem l’estabilitat de les solucions trobades i realitzarem simulacions numèriques dels diferents models teòrics. Es presentaran els següents resultats: A partir de les equacions de MB amb injecció rocking, es deduirà una equació de paràmetre d’ordre per a làsers de classe C amb desintonia positiva de la cavitat i s’estudiaran numèricament els patrons del sistema. Per a làsers de classe B, s’obtindrà un model reduït de dues equacions i s’analitzarà la seua dinàmica temporal i la influència de la desintonia de la injecció rocking. També esmostraran patrons espacials obtinguts a partir de la simulació de les equacions de MB.Es desenvoluparà un model unificat (vàlid per a desintonies de la cavitat positives i negatives) per a làsers de dos nivells (classe C i A) i oscil·ladors fotrorefractius, proporcionant els dominis d’estabilitat dels estats biestables en fase i estudiant numèricament els patrons espacials que apareixen. S’analitzarà la dinàmica temporal d’un làser bidireccional amb injecció rocking i es presentaran alguns resultats preliminars de patrons espacialsThe objective of this thesis is the theoretical, analytical and numerical, study of the spatio-temporal dynamics of optical oscillators under bichromatic forcing (rocking). This kind of injection possesses the feature of breaking the phase invariance (any phase of the complex field is possible) of the free-running system and generates a phase-bistable system in which two only phases are allowed for the homogeneous stationary solutions. This change in the nature of the system enables a new dynamics characterized by the presence of a new kind of spatial structures in the bidimensional transverse plane: bistable phase patterns in which both phases coexist separated by domain walls (Ising if they have null intensity or Bloch if it is different from zero). These domains can evolve either to homogeneous patterns (in which only one phase is present) or to more complex ones, in which curvature effects lead to the emergence of labyrinthic patterns depending on the value of the parameters of the system. Moreover, localized structures (stable minimum-size domains) as dark-ring cavity solitons can exist. In the scope of this thesis, we have focused on the influence of rocking in two systems which have been studied profusely in the literature, as they are very interesting both from a fundamental and a practical point of views: lasers and photorefractive oscillators. Along this thesis, we will study the influence of rocking in those systems in detail. As it is usual in nonlinear science, is convenient to derive equations describing the behaviour of those systems close to (critical) points where the stationary solutions emerge. These equations (called order parameter equations) are relatively simple and are able to describe a large number of nonlinear systems: physical, chemical, biological.. (the meaning ot the parameters being the only difference , but the mathematical structure is the same). Moreover, we will analyze the stability of the solutions and we will perform numerical simulations of the theoretical models. The following results will be presented: Starting from the MB equations under rocking injection, an order parameter equation will be derived for class C lasers with positive cavity detuning and the patterns of the system will be studied numerically. A reduced model of two equations will be obtained for class B lasers and its temporal dynamics and the influence of the detuning of rocking injection will be studied. We will also show spatial patterns obtained from simulations of the MB equations. A unified model (valid for positive and negative cavity detunings) for two level lasers (class C and A) and photorefractive oscillators will be developed, providing the stability domains of the phase bistable states and studying numerically the spatial patterns that arise from the system. The temporal dynamics of a bidirectional laser under rocking injection will be analyzed and some preliminary results regarding spatial patterns will be given

Рискен-Нумедал-Грахам-Хакен нестабилности и само-пулсирање у квантним каскадним ласерима.

A theoretical study on low-threshold multimode instabilities in quantum cascade lasers (QCLs) with Fabry-Pérot cavity is presented. Previously, low threshold Risken-Nummedal-Graham-Haken (RNGH) instabilities were reported in several experimental investigations of QCLs...Приказано је теоријско истраживање мултимодних нестабилности са ниским прагом у квантним каскадним ласерима (ККЛ). Претходно су у више експерименталних студија о ККЛ-у уочене нестабилности Рискен- Нумедал-Грахам-Хакен (РНГХ) типа мало изнад ласерског прага..

Collective dynamics of driven-dissipative atomic systems in optical cavities

This thesis reports the theoretical description of spatio-temporal pattern forming in atomic ensembles interacting with photons. The atoms are confined in a cavity, are driven by one or several external lasers, and scatter or emit light into the resonator. Ordered structures emerge in parameter ranges where the emitted photons constructively interfere. The formation of spatial patterns can be understood as a consequence of long-range interactions between the atoms mediated by the multiple-scattered cavity photons. In this thesis we develop mean-field models to characterize the out-of-equilibrium dynamics of the atoms including the onset, the transient, and the stationary state of the ordered structures. Here, we identify the conditions for which the emerging dynamical phases exhibit features of spatial self-organization and synchronization. We point out that these features can be measured by observing the light at the cavity output. Finally, we argue that the statistical mechanics of this driven-dissipative systems provides key insights into the dynamics of long-range interacting systems, which is to date largely unexplored.Diese Arbeit behandelt die theoretische Beschreibung von raumzeitlichen Strukturen in mit Licht wechselwirkenden atomaren Ensembles. Die Atome befinden sich in einem Resonator, werden von einem oder mehreren externen Lasern getrieben und emittieren Photonen in den Resonator. Geordnete Strukturen entstehen für Parameterbereiche, in denen die emittierten Photonen konstruktiv interferieren. Das Ausbilden von räumlichen Strukturen kann als Folge einer langreichweitigen Wechselwirkung zwischen den Atomen verstanden werden, welche durch die mehrfach gestreuten Photonen vermittelt wird. In dieser Doktorarbeit entwickeln wir Molekularfeldmodelle um die Nichtgleichgewichtsdynamik der Atome, unter Einbezug des Einsetzen, der vorübergehenden Dynamik und dem stationären Zustand der geordneten Strukturen, zu charakterisieren. Dabei identifizieren wir die Bedingungen für welche die ausbildenden dynamischen Phasen Eigenschaften von räumlicher Selbstorganisation und Synchronisation zeigen. Wir weisen darauf hin, dass diese Eigenschaften durch das von dem Resonator abgegebene Licht gemessen werden können. Schließlich argumentieren wir, dass die statistische Mechanik dieser getriebenen dissipativen Systeme Schlüsselerkenntnisse über die Dynamik von langreichweitig wechselwirkenden Systemen bereitstellt, welche bis heute weitgehend unerforscht sind

Nonlinear vibration energy harvesters for powering the internet of things

The ever decreasing power consumption in electronic devices and sensors have facilitated the development of autonomous wireless sensor nodes (WSNs), which ushered in the era of the Internet of Things (IoT). However, the problem of long-term power supply to the numerous WSNs pervasively dispersed to enable the IoT is yet to be resolved. This work focuses on the development of novel vibration energy harvesting (VEH) devices and technologies for effective transduction of mostly wide-band and noisy ambient mechanical vibrations to power WSNs. In this thesis meso-scale and MEMS-scale nonlinear and frequency tunable VEH devices have been designed, fabricated and characterized. The first meso-scale VEH prototype developed in this thesis combines a nonlinear bistable oscillator with mechanical impact induced nonlinearity, which exhibits upto 118% broadening in the frequency response over a standalone bistable system. The second meso-scale prototype combines magnetic repulsion induced bistable nonlinearity with stretching induced monostable cubic nonlinearity in a single device structure. The device effectively merged the beneficial features of the individual nonlinear bistable and monostable systems, and demonstrates upto 85% enhanced spectral performance compared to the bistable device. The third prototype is a MEMS-scale device fabricated using spiral silicon spring structure and double-layer planar micro-coils. A magnetic repulsion induced frequency tuning mechanism was incorporated in the prototype, and it was demonstrated that both linear and nonlinear hysteretic frequency responses could be tuned (by upto 18.6%) to match various ambient vibration frequencies. In order to enhance the power generating capability of MEMS-scale electromagnetic devices, an ultra-dense multi-layer micro-coil architecture has been developed. The proposed ultra-dense micro-coil is designed to incorporate double number of turns within the same volume as a conventional micro-coil, and significantly enhance the magnetic flux linkage gradient resulting in higher power output (~4 times). However, attempts to fabricate the ultra-dense coil have not been successful due to lack of proper insulation between the successive coil layers. Finally, a power management system combining diode equivalent low voltage drop (DELVD) circuit and a boost regulator module was developed. It was demonstrated that energy harvested from harmonic and bandlimited random vibrations using linear, nonlinear bistable, and combined nonlinear VEH devices could be conditioned into usable electricity by the power management system with 60% - 75% efficiency. In addition to developing new prototypes and techniques, this thesis recommends directions towards future research for further improvement in vibration energy harvesting devices and technologies