Cycle flows and multistabilty in oscillatory networks: an overview

The functions of many networked systems in physics, biology or engineering rely on a coordinated or synchronized dynamics of its constituents. In power grids for example, all generators must synchronize and run at the same frequency and their phases need to appoximately lock to guarantee a steady power flow. Here, we analyze the existence and multitude of such phase-locked states. Focusing on edge and cycle flows instead of the nodal phases we derive rigorous results on the existence and number of such states. Generally, multiple phase-locked states coexist in networks with strong edges, long elementary cycles and a homogeneous distribution of natural frequencies or power injections, respectively. We offer an algorithm to systematically compute multiple phase- locked states and demonstrate some surprising dynamical consequences of multistability

Formal Systems Architectures for Biology

When the word "systems" is used in systems biology, it invokes a variety of assumptions about what defines the subject under investigation, which in turn can lead to divergent research outcomes. We will take the position that systems are defined by their potential organizing and "control" mechanisms, 
which distinguishes complex, living systems from a primordial soup. This will be accomplished by defining and investigating three interesting control motifs in biological systems: dominoes and clocks, futile cycles, and complex feedforward regulation. Additional mechanisms that combine feedback and feedforward mechanisms will also be briefly elaborated upon. Throughout these examples, our focus will be on the connection between top-down control mechanisms and bottom-up self-organizing mechanisms

Collective effects enhancing power and efficiency

Energy conversion is most efficient for micro or nano machines with tight coupling between input and output power. To reach meaningful amounts of power, ensembles of $N$ such machines must be considered. We use a model system to demonstrate that interactions between $N$ tightly coupled nanomachines can enhance the power output per machine. Furthermore, while interactions break tight coupling and thus lower efficiency in finite ensembles, the macroscopic limit ($N \rightarrow \infty$) restores it and enhances both the efficiency and the output power per nanomachine.Comment: 5 pages, 3 figure

Simultaneous use of shape memory alloys and permanent magnets in multistable smart structures for morphing aircraft applications

This Thesis considers the simultaneous use of shape memory alloys and permanent magnets for achieving multistable smart structures aiming towards morphing applications. Motivation for this approach lies in the poor energetic efficiency of shape memory alloys, which can void system-level benefits provided by morphing technologies. Multistability can therefore be adopted to prevent continuous operation of shape memory alloy actuators. Objectives of the study involve the combination of shape memory alloys and permanent magnets in new geometrical arrangements to achieve multistable behavior; the development of a numerical modeling procedure that is able to simulate the multi-physics nature of the studied systems; and the proposal of a geometric arrangement for morphing applications that is based on a repeating pattern of unit cells which incorporate the combined use of shape memory alloy wires and permanent magnets for multistability. The proposed modeling strategy considers a geometrically nonlinear beam finite element; a thermo-mechanical constitutive behavior for shapememoryalloys;theinteractionofcuboidalpermanentmagnetswitharbitraryorienta- tions; and node-to-element contact. Experiments are performed with three distinct systems, including a proof-of-concept beam, a three cell morphing beam metastructure, and a morphing airfoil prototype with six unit cells. Results show that the combination of shape memory alloys and permanent magnets indeed allows for multistable behavior. Furthermore, the dis- tributedactuationcapabilitiesofthe morphingmetastructureallowforsmoothandlocalized geometrical shape changes.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorCNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoTese (Doutorado)Esta Tese considera o uso simultâneo de ligas com memória de forma e ímãs permanentes para a obtenção de estruturas inteligentes multiestáveis, com vistas a sua aplicação em aeronaves de geometria variável. A motivação para tal abordagem reside na baixa eficiência energética associada às ligas com memória de forma, a qual pode eliminar benefícios oriundos de tecnologias relacionadas a geometria variável. Multiestabilidade pode, desta forma, ser adotada para prevenir operação contínua de atuadores baseados em ligas com memória de forma. Objetivos do estudo envolvem a combinação de ligas com memória de forma e ímãs permanentes em novos arranjos geométricos para a obtenção de comportamento multiestável; o desenvolvimento de um procedimento de modelagem numérica que pode simular a natureza multifísica dos sistemas estudados; e a proposição de um arranjo geométrico para aplicações que envolvem geometria variável, o qual é baseado num padrão repetitivo de células unitárias que incorporam o uso combinado de ligas com memória de forma e ímãs permanentes para mul- tiestabilidade. A estratégia de modelagem proposta considera um elemento finito de viga com não-linearidades geométricas; um modelo constitutivo termomecânico para ligas com memória de forma; a interação entre ímãs permanentes cúbicos com orientação arbitrária; e contato entre elemento-e-nó no contexto de elementos finitos. Experimentos são realizados com três sistemas distintos, incluindo uma viga para prova de conceito, uma metaestrutura do tipo viga com geometria variável composta por três células unitárias, e um protótipo de aerofólio com geometria variável composto por seis células unitárias. Resultados mostram que a combinação de ligas com memória de forma e ímãs permanentes permite a obtenção de comportamento multiestável. Além disso, a característica de atuação distribuída das metaestruturas com geometria variável permite alterações de forma suaves e localizadas

Neural Cartography: Computer Assisted Poincare Return Mappings for Biological Oscillations

This dissertation creates practical methods for Poincaré return mappings of individual and networked neuron models. Elliptic bursting models are found in numerous biological systems, including the external Globus Pallidus (GPe) section of the brain; the focus for studies of epileptic seizures and Parkinson\u27s disease. However, the bifurcation structure for changes in dynamics remains incomplete. This dissertation develops computer-assisted Poincaré ́maps for mathematical and biologically relevant elliptic bursting neuron models and central pattern generators (CPGs). The first method, used for individual neurons, offers the advantage of an entire family of computationally smooth and complete mappings, which can explain all of the systems dynamical transitions. A complete bifurcation analysis was performed detailing the mechanisms for the transitions from tonic spiking to quiescence in elliptic bursters. A previously unknown, unstable torus bifurcation was found to give rise to small amplitude oscillations. The focus of the dissertation shifts from individual neuron models to small networks of neuron models, particularly 3-cell CPGs. A CPG is a small network which is able to produce specific phasic relationships between the cells. The output rhythms represent a number of biologically observable actions, i.e. walking or running gates. A 2-dimensional map is derived from the CPGs phase-lags. The cells are endogenously bursting neuron models mutually coupled with reciprocal inhibitory connections using the fast threshold synaptic paradigm. The mappings generate clear explanations for rhythmic outcomes, as well as basins of attraction for specific rhythms and possible mechanisms for switching between rhythms