A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Collective Organization of Complex Networks: Emergent Scales, Vulnerability, and Targeting of Desired Dynamics

Cuando una colectividad de sistemas dinámicos acoplados mediante una estructura irregular de interacciones evoluciona, se observan dinámicas de gran complejidad y fenómenos emergentes imposibles de predecir a partir de las propiedades de los sistemas individuales. El objetivo principal de esta tesis es precisamente avanzar en nuestra comprensión de la relación existente entre la topología de interacciones y las dinámicas colectivas que una red compleja es capaz de mantener. Siendo este un tema amplio que se puede abordar desde distintos puntos de vista, en esta tesis se han estudiado tres problemas importantes dentro del mismo que están relacionados entre sí. Por un lado, en numerosos sistemas naturales y artificiales que se pueden describir mediante una red compleja la topología no es estática, sino que depende de la dinámica que se desarrolla en la red: un ejemplo son las redes de neuronas del cerebro. En estas redes adaptativas la propia topología emerge como consecuencia de una autoorganización del sistema. Para conocer mejor cómo pueden emerger espontáneamente las propiedades comúnmente observadas en redes reales, hemos estudiado el comportamiento de sistemas que evolucionan según reglas adaptativas locales con base empírica. Nuestros resultados numéricos y analíticos muestran que la autoorganización del sistema da lugar a dos de las propiedades más universales de las redes complejas: a escala mesoscópica, la aparición de una estructura de comunidades, y, a escala macroscópica, la existencia de una ley de potencias en la distribución de las interacciones en la red. El hecho de que estas propiedades aparecen en dos modelos con leyes de evolución cuantitativamente distintas que siguen unos mismos principios adaptativos sugiere que estamos ante un fenómeno que puede ser muy general, y estar en el origen de estas propiedades en sistemas reales. En segundo lugar, proponemos una medida que permite clasificar los elementos de una red compleja en función de su relevancia para el mantenimiento de dinámicas colectivas. En concreto, estudiamos la vulnerabilidad de los distintos elementos de una red frente a perturbaciones o grandes fluctuaciones, entendida como una medida del impacto que estos acontecimientos externos tienen en la interrupción de una dinámica colectiva. Los resultados que se obtienen indican que la vulnerabilidad dinámica es sobre todo dependiente de propiedades locales, por tanto nuestras conclusiones abarcan diferentes topologías, y muestran la existencia de una dependencia no trivial entre la vulnerabilidad y la conectividad de los elementos de una red. Finalmente, proponemos una estrategia de imposición de una dinámica objetivo genérica en una red dada e investigamos su validez en redes con diversas topologías que mantienen regímenes dinámicos turbulentos. Se obtiene como resultado que las redes heterogéneas (y la amplia mayora de las redes reales estudiadas lo son) son las más adecuadas para nuestra estrategia de targeting de dinámicas deseadas, siendo la estrategia muy efectiva incluso en caso de disponer de un conocimiento muy imperfecto de la topología de la red. Aparte de la relevancia teórica para la comprensión de fenómenos colectivos en sistemas complejos, los métodos y resultados propuestos podrán dar lugar a aplicaciones en sistemas experimentales y tecnológicos, como por ejemplo los sistemas neuronales in vitro, el sistema nervioso central (en el estudio de actividades síncronas de carácter patológico), las redes eléctricas o los sistemas de comunicaciones. ABSTRACT The time evolution of an ensemble of dynamical systems coupled through an irregular interaction scheme gives rise to dynamics of great of complexity and emergent phenomena that cannot be predicted from the properties of the individual systems. The main objective of this thesis is precisely to increase our understanding of the interplay between the interaction topology and the collective dynamics that a complex network can support. This is a very broad subject, so in this thesis we will limit ourselves to the study of three relevant problems that have strong connections among them. First, it is a well-known fact that in many natural and manmade systems that can be represented as complex networks the topology is not static; rather, it depends on the dynamics taking place on the network (as it happens, for instance, in the neuronal networks in the brain). In these adaptive networks the topology itself emerges from the self-organization in the system. To better understand how the properties that are commonly observed in real networks spontaneously emerge, we have studied the behavior of systems that evolve according to local adaptive rules that are empirically motivated. Our numerical and analytical results show that self-organization brings about two of the most universally found properties in complex networks: at the mesoscopic scale, the appearance of a community structure, and, at the macroscopic scale, the existence of a power law in the weight distribution of the network interactions. The fact that these properties show up in two models with quantitatively different mechanisms that follow the same general adaptive principles suggests that our results may be generalized to other systems as well, and they may be behind the origin of these properties in some real systems. We also propose a new measure that provides a ranking of the elements in a network in terms of their relevance for the maintenance of collective dynamics. Specifically, we study the vulnerability of the elements under perturbations or large fluctuations, interpreted as a measure of the impact these external events have on the disruption of collective motion. Our results suggest that the dynamic vulnerability measure depends largely on local properties (our conclusions thus being valid for different topologies) and they show a non-trivial dependence of the vulnerability on the connectivity of the network elements. Finally, we propose a strategy for the imposition of generic goal dynamics on a given network, and we explore its performance in networks with different topologies that support turbulent dynamical regimes. It turns out that heterogeneous networks (and most real networks that have been studied belong in this category) are the most suitable for our strategy for the targeting of desired dynamics, the strategy being very effective even when the knowledge on the network topology is far from accurate. Aside from their theoretical relevance for the understanding of collective phenomena in complex systems, the methods and results here discussed might lead to applications in experimental and technological systems, such as in vitro neuronal systems, the central nervous system (where pathological synchronous activity sometimes occurs), communication systems or power grids.

A model for individual and collective cell movement in Dictyostelium discoideum

The cellular slime mold Dictyostelium discoideum is a widely used model system for studying a variety of basic processes in development, including cell–cell signaling, signal transduction, pattern formation, cell motility, and the movement of tissue-like aggregates of cells. Many aspects of cell motion are poorly understood, including how individual cell behavior produces the collective motion of cells observed within the mound and slug. Herein, we describe a biologically realistic model for motile D. discoideum cells that can generate active forces, that interact via surface molecules, and that can detect and respond to chemotactic signals. We model the cells as deformable viscoelastic ellipsoids and incorporate signal transduction and cell–cell signaling by using a previously developed model. The shape constraint restricts the admissible deformations but makes the simulation of a large number of interacting cells feasible. Because the model is based on known processes, the parameters can be estimated or measured experimentally. We show that this model can reproduce the observations on the chemotactic behavior of single cells, streaming during aggregation, and the collective motion of an aggregate of cells driven by a small group of pacemakers. The model predicts that the motion of two-dimensional slugs [Bonner, J. T. (1998) Proc. Natl. Acad. Sci. USA 95, 9355–9359] results from the same behaviors that are exhibited by individual cells; it is not necessary to invoke different mechanisms or behaviors. Our computational experiments also suggest previously uncharacterized phenomena that may be experimentally observable.

Guided Migration and Collective Behavior: Cell Dynamics during Cancer Progression

This dissertation focuses on gaining understanding of cell migration and collective behavior through a combination of experiment, analysis, and modeling techniques. Cell migration is a ubiquitous process that plays an important role during embryonic development and wound healing as well as in diseases like cancer, which is a particular focus of this work. As cancer cells become increasingly malignant, they acquire the ability to migrate away from the primary tumor and spread throughout the body to form metastatic tumors. During this process, changes in gene expression and the surrounding tumor environment can lead to changes in cell migration characteristics. In this thesis, I analyze how cells are guided by the texture of their environment and how cells cooperate with their neighbors to move collectively. The emergent properties of collectively moving groups are a particular focus of this work as collective cell dynamics are known to change in diseases such as cancer. The internal machinery for cell migration involves polymerization of the actin cytoskeleton to create protrusions that---in coordination with retraction of the rear of the cell---lead to cell motion. This actin machinery has been previously shown to respond to the topography of the surrounding surface, leading to guided migration of amoeboid cells. Here we show that epithelial cells on nanoscale ridge structures also show changes in the morphology of their cytoskeletons; actin is found to align with the ridge structures. The migration of the cells is also guided preferentially along the ridge length. These ridge structures are on length scales similar to those found in tumor microenvironments and as such provide a system for studying the response of the cells' internal migration machinery to physiologically relevant topographical cues. In addition to sensing surface topography, individual cells can also be influenced by the pushing and pulling of neighboring cells. The emergent properties of collectively migrating cells show interesting dynamics and are relevant for cancer progression, but have been less studied than the motion of individual cells. We use Particle Image Velocimetry (PIV) to extract the motion of a collectively migrating cell sheet from time lapse images. The resulting flow fields allow us to analyze collective behavior over multiple length and time scales. To analyze the connection between individual cell properties and collective migration behavior, we compare experimental flow fields with the migration of simulated cell groups. Our collective migration metrics allow for a quantitative comparison between experimental and simulated results. This comparison shows that tissue-scale decreases in collective behavior can result from changes in individual cell activity without the need to postulate the existence of subpopulations of leader cells or global gradients. In addition to tissue-scale trends in collective behavior, the migration of cell groups includes localized dynamic features such as cell rearrangements. An individual cell may smoothly follow the motion of its neighbors (affine motion) or move in a more individualistic manner (non-affine motion). By decomposing individual motion into both affine and non-affine components, we measure cell rearrangements within a collective sheet. Finally, finite-time Lyapunov exponent (FTLE) values capture the stretching of the flow field and reflect its chaotic character. Applying collective migration analysis techniques to experimental data on both malignant and non-malignant human breast epithelial cells reveals differences in collective behavior that are not found from analyzing migration speeds alone. Non-malignant cells show increased cooperative motion on long time scales whereas malignant cells remain uncooperative as time progresses. Combining multiple analysis techniques also shows that these two cell types differ in their response to a perturbation of cell-cell adhesion through the molecule E-cadherin. Non-malignant MCF10A cells use E-cadherin for short time coordination of collective motion, yet even with decreased E-cadherin expression, the cells remain coordinated over long time scales. In contrast, the migration behavior of malignant and invasive MCF10CA1a cells, which already shows decreased collective dynamics on both time scales, is insensitive to the change in E-cadherin expression.

Guided Migration and Collective Behavior: Cell Dynamics during Cancer Progression

This dissertation focuses on gaining understanding of cell migration and collective behavior through a combination of experiment, analysis, and modeling techniques. Cell migration is a ubiquitous process that plays an important role during embryonic development and wound healing as well as in diseases like cancer, which is a particular focus of this work. As cancer cells become increasingly malignant, they acquire the ability to migrate away from the primary tumor and spread throughout the body to form metastatic tumors. During this process, changes in gene expression and the surrounding tumor environment can lead to changes in cell migration characteristics. In this thesis, I analyze how cells are guided by the texture of their environment and how cells cooperate with their neighbors to move collectively. The emergent properties of collectively moving groups are a particular focus of this work as collective cell dynamics are known to change in diseases such as cancer. The internal machinery for cell migration involves polymerization of the actin cytoskeleton to create protrusions that---in coordination with retraction of the rear of the cell---lead to cell motion. This actin machinery has been previously shown to respond to the topography of the surrounding surface, leading to guided migration of amoeboid cells. Here we show that epithelial cells on nanoscale ridge structures also show changes in the morphology of their cytoskeletons; actin is found to align with the ridge structures. The migration of the cells is also guided preferentially along the ridge length. These ridge structures are on length scales similar to those found in tumor microenvironments and as such provide a system for studying the response of the cells' internal migration machinery to physiologically relevant topographical cues. In addition to sensing surface topography, individual cells can also be influenced by the pushing and pulling of neighboring cells. The emergent properties of collectively migrating cells show interesting dynamics and are relevant for cancer progression, but have been less studied than the motion of individual cells. We use Particle Image Velocimetry (PIV) to extract the motion of a collectively migrating cell sheet from time lapse images. The resulting flow fields allow us to analyze collective behavior over multiple length and time scales. To analyze the connection between individual cell properties and collective migration behavior, we compare experimental flow fields with the migration of simulated cell groups. Our collective migration metrics allow for a quantitative comparison between experimental and simulated results. This comparison shows that tissue-scale decreases in collective behavior can result from changes in individual cell activity without the need to postulate the existence of subpopulations of leader cells or global gradients. In addition to tissue-scale trends in collective behavior, the migration of cell groups includes localized dynamic features such as cell rearrangements. An individual cell may smoothly follow the motion of its neighbors (affine motion) or move in a more individualistic manner (non-affine motion). By decomposing individual motion into both affine and non-affine components, we measure cell rearrangements within a collective sheet. Finally, finite-time Lyapunov exponent (FTLE) values capture the stretching of the flow field and reflect its chaotic character. Applying collective migration analysis techniques to experimental data on both malignant and non-malignant human breast epithelial cells reveals differences in collective behavior that are not found from analyzing migration speeds alone. Non-malignant cells show increased cooperative motion on long time scales whereas malignant cells remain uncooperative as time progresses. Combining multiple analysis techniques also shows that these two cell types differ in their response to a perturbation of cell-cell adhesion through the molecule E-cadherin. Non-malignant MCF10A cells use E-cadherin for short time coordination of collective motion, yet even with decreased E-cadherin expression, the cells remain coordinated over long time scales. In contrast, the migration behavior of malignant and invasive MCF10CA1a cells, which already shows decreased collective dynamics on both time scales, is insensitive to the change in E-cadherin expression.

Elongated shape isomers in the (36)Ar nucleus

A recent analysis of the (12)C + (24)Mg scattering [W. Sciani et al., Phys. Rev. C 80, 034319 (2009)] suggests the existence of a hyperdeformed band in the (36)Ar nucleus, completely in line with the predictions of alpha [W. D. M. Rae and A. C. Merchant, Phys. Lett. B279, 207 (1992)] and binary cluster calculations [J. Cseh et al., Phys. Rev. C 70, 034311 (2004)]. Here we review the structural understanding of the superdeformed and the hyperdeformed states of (36)Ar and present new results on the shape isomers as well. Special attention is paid to the clusterization of these states, which indicates the appropriate reaction channels for their formation.

Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

Microscopic description of the twist mode in normal and superfluid trapped Fermi gases

We investigate the "twist" mode (rotation of the upper against the lower hemisphere) of a dilute atomic Fermi gas in a spherical trap. The normal and superfluid phases are considered. The linear response to this external perturbation is calculated within the microscopic Hartree-Fock-Bogoliubov approach. In the normal phase the excitation spectrum is concentrated in a rather narrow peak very close to the trapping frequency. In the superfluid phase the strength starts to be damped and fragmented and the collectivity of the mode is progressively lost when the temperature decreases. In the weak-pairing regime some reminiscence of the collective motion still exists, whereas in the strong-pairing regime the twist mode is completely washed out. The disappearance of the twist mode in the strong-pairing regime with decreasing temperature is interpreted in the framework of the two-fluid model.

Spontaneous aggregation and global polar ordering in squirmer suspensions

We have developed numerical simulations of three dimensional suspensions of active particles to characterize the capabilities of the hydrodynamic stresses induced by active swimmers to promote global order and emergent structures in active suspensions. We have considered squirmer suspensions embedded in a fluid modeled under a Lattice Boltzmann scheme. We have found that active stresses play a central role to decorrelate the collective motion of squirmers and that contractile squirmers develop significant aggregates.

Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at root s(NN)=2.76 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics of epithelial monolayers assessed by acoustic and impedimetric whole cell biosensors

Mit der Zielsetzung der vorliegenden Arbeit wurde die detailierten Analyse von Migrationsdynamiken epithelilaler Monolayer anhand zweier neuartiger in vitro Biosensoren verfolgt, der elektrischen Zell-Substrat Impedanz Spektroskopie (electrical cell-substrate impedance sensing, ECIS) sowie der Quarz Kristall Mikrowaage (quartz crystal microbalance, QCM). Beide Methoden erwiesen sich als sensitiv gegenüber der Zellmotilität und der Nanozytotoxizität.rnInnerhalb des ersten Projektes wurde ein Fingerprinting von Krebszellen anhand ihrer Motilitätsdynamiken und der daraus generierten elektrischen oder akkustischen Fluktuationen auf ECIS oder QCM Basis vorgenommen; diese Echtzeitsensoren wurdene mit Hilfe klassicher in vitro Boyden-Kammer Migrations- und Invasions-assays validiert. Fluktuationssignaturen, also Langzeitkorrelationen oder fraktale Selbstähnlichkeit aufgrund der kollektiven Zellbewegung, wurden über Varianz-, Fourier- sowie trendbereinigende Fluktuationsanalyse quantifiziert. Stochastische Langzeitgedächtnisphänomene erwiesen sich als maßgebliche Beiträge zur Antwort adhärenter Zellen auf den QCM und ECIS-Sensoren. Des weiteren wurde der Einfluss niedermolekularer Toxine auf die Zytoslelettdynamiken verfolgt: die Auswirkungen von Cytochalasin D, Phalloidin und Blebbistatin sowie Taxol, Nocodazol und Colchicin wurden dabei über die QCM und ECIS Fluktuationsanalyse erfasst.rnIn einem zweiten Projektschwerpunkt wurden Adhäsionsprozesse sowie Zell-Zell und Zell-Substrat Degradationsprozesse bei Nanopartikelgabe charackterisiert, um ein Maß für Nanozytotoxizität in Abhangigkeit der Form, Funktionalisierung Stabilität oder Ladung der Partikel zu erhalten.rnAls Schlussfolgerung ist zu nennen, dass die neuartigen Echtzeit-Biosensoren QCM und ECIS eine hohe Zellspezifität besitzen, auf Zytoskelettdynamiken reagieren sowie als sensitive Detektoren für die Zellvitalität fungieren können.

Quantifying the complexity of chaos in multibasin multidimensional dynamics of molecular systems

The simulated classical dynamics of a small molecule exhibiting self-organizing behavior via a fast transition between two states is analyzed by calculation of the statistical complexity of the system. It is shown that the complexity of molecular descriptors such as atom coordinates and dihedral angles have different values before and after the transition. This provides a new tool to identify metastable states during molecular self-organization. The highly concerted collective motion of the molecule is revealed. Low-dimensional subspaces dynamics is found sensitive to the processes in the whole, high-dimensional phase space of the system. © 2004 Wiley Periodicals, Inc.

Towards optical polarization control of laser-driven proton acceleration in foils undergoing relativistic transparency

Control of the collective response of plasma particles to intense laser light is intrinsic to relativistic optics, the development of compact laser-driven particle and radiation sources, as well as investigations of some laboratory astrophysics phenomena. We recently demonstrated that a relativistic plasma aperture produced in an ultra-thin foil at the focus of intense laser radiation can induce diffraction, enabling polarization-based control of the collective motion of plasma electrons. Here we show that under these conditions the electron dynamics are mapped into the beam of protons accelerated via strong charge-separation-induced electrostatic fields. It is demonstrated experimentally and numerically via 3D particle-in-cell simulations that the degree of ellipticity of the laser polarization strongly influences the spatial-intensity distribution of the beam of multi-MeV protons. The influence on both sheath-accelerated and radiation pressure-accelerated protons is investigated. This approach opens up a potential new route to control laser-driven ion sources.

Collective agreements on time and motion study;

Mode of access: Internet.

Cooperative motion of intrinsic and actuated semiflexible swimmers

We examine the phenomenon of hydrodynamic-induced cooperativity for pairs of flagellated micro-organism swimmers, of which spermatozoa cells are an example. We consider semiflexible swimmers, where inextensible filaments are driven by an internal intrinsic force and torque-free mechanism (intrinsic swimmers). The velocity gain for swimming cooperatively, which depends on both the geometry and the driving, develops as a result of the near-field coupling of bending and hydrodynamic stresses. We identify the regimes where hydrodynamic cooperativity is advantageous and quantify the change in efficiency. When the filaments' axes are parallel, hydrodynamic interaction induces a directional instability that causes semiflexible swimmers that profit from swimming together to move apart from each other. Biologically, this implies that flagella need to select different synchronized collective states and to compensate for directional instabilities (e.g., by binding) in order to profit from swimming together. By analyzing the cooperative motion of pairs of externally actuated filaments, we assess the impact that stress distribution along the filaments has on their collective displacements.