On Nonlinear Dynamics and an Optimal Control Design to a Longitudinal Flight

In this work, we analyzed a bifurcational behavior of a longitudinal flight nonlinear dynamics, taking as an example the F-8 aircraft Crusader. We deal with an analysis of high angles of attack in order to stabilize the oscillations; those were close to the critical angle of the aircraft, in the flight conditions, established. We proposed a linear optimal control design applied to the considered nonlinear aircraft model below angle of stall, taking into account regions of Hopf and saddled noddle bifurcations.

Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

PHENOMENOLOGICAL APPLICATION OF THE PROJECTION-OPERATOR METHOD AND ITS CONNECTION WITH CRITICAL-DYNAMICS

We consider the dynamics of a system of interacting spins described by the Ginzburg-Landau Hamiltonian. The method used is Zwanzig's version of the projection-operator method, in contrast to previous derivations in which we used Mori's version of this method. It is proved that both methods produce the same answer for the Green's function. We also make contact between the projection-operator method and critical dynamics.

Food-web composition affects cross-ecosystem interactions and subsidies

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

BLACKBIRD AND STARLING ROOSTING DYNAMICS: MPLICATIONS FOR ANIMAL DAMAGE CONTROL

Each winter an estimated 350 million starlings, red-winged blackbirds (Agelaius phoeniceus), common grackles (Quiscalus quiscula), and brown-headed cowbirds (Molothrus ater) congregate in roosts in the southeastern United States (Meanley 1971, Meanley and Royall 1976). These birds have been of increasing concern because of agricultural damage claims (Stickley et al. 1976, Dolbeer et al. 1978), reputed health hazards (Monroe and Cronholm 1977), and other nuisance problems associated with them. Historical population trends (Dolbeer and Stehn 1979) and the source of winter-roosting blackbirds (Meanley 1971, Meanley and Dolbeer 1978, and Dolbeer 1978) have been summarized, but little information on the number of consecutive nights a bird returns to the same roost (roost fidelity) or the dynamics of a winter roost is available. The purpose of this paper is to present information on roost fidelity and population dynamics needed to better understand and manage winter blackbird and starling roosts.

Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics. (C) 2011 Elsevier B.V. All rights reserved.

Analysis of nonlinear dynamics of vocal folds using high-speed video observation and biomechanical modeling

Primary voice production occurs in the larynx through vibrational movements carried out by vocal folds. However, many problems can affect this complex system resulting in voice disorders. In this context, time-frequency-shape analysis based on embedding phase space plots and nonlinear dynamics methods have been used to evaluate the vocal fold dynamics during phonation. For this purpose, the present work used high-speed video to record the vocal fold movements of three subjects and extract the glottal area time series using an image segmentation algorithm. This signal is used for an optimization method which combines genetic algorithms and a quasi-Newton method to optimize the parameters of a biomechanical model of vocal folds based on lumped elements (masses, springs and dampers). After optimization, this model is capable of simulating the dynamics of recorded vocal folds and their glottal pulse. Bifurcation diagrams and phase space analysis were used to evaluate the behavior of this deterministic system in different circumstances. The results showed that this methodology can be used to extract some physiological parameters of vocal folds and reproduce some complex behaviors of these structures contributing to the scientific and clinical evaluation of voice production. (C) 2010 Elsevier Inc. All rights reserved.

Numerical simulations of magma chamber dynamics at Campi Flegrei, and associated seismicity, deformation and gravity changes

Understanding the complex relationships between quantities measured by volcanic monitoring network and shallow magma processes is a crucial headway for the comprehension of volcanic processes and a more realistic evaluation of the associated hazard. This question is very relevant at Campi Flegrei, a volcanic quiescent caldera immediately north-west of Napoli (Italy). The system activity shows a high fumarole release and periodic ground slow movement (bradyseism) with high seismicity. This activity, with the high people density and the presence of military and industrial buildings, makes Campi Flegrei one of the areas with higher volcanic hazard in the world. In such a context my thesis has been focused on magma dynamics due to the refilling of shallow magma chambers, and on the geophysical signals detectable by seismic, deformative and gravimetric monitoring networks that are associated with this phenomenologies. Indeed, the refilling of magma chambers is a process frequently occurring just before a volcanic eruption; therefore, the faculty of identifying this dynamics by means of recorded signal analysis is important to evaluate the short term volcanic hazard. The space-time evolution of dynamics due to injection of new magma in the magma chamber has been studied performing numerical simulations with, and implementing additional features in, the code GALES (Longo et al., 2006), recently developed and still on the upgrade at the Istituto Nazionale di Geofisica e Vulcanologia in Pisa (Italy). GALES is a finite element code based on a physico-mathematical two dimensional, transient model able to treat fluids as multiphase homogeneous mixtures, compressible to incompressible. The fundamental equations of mass, momentum and energy balance are discretised both in time and space using the Galerkin Least-Squares and discontinuity-capturing stabilisation technique. The physical properties of the mixture are computed as a function of local conditions of magma composition, pressure and temperature.The model features enable to study a broad range of phenomenologies characterizing pre and sin-eruptive magma dynamics in a wide domain from the volcanic crater to deep magma feeding zones. The study of displacement field associated with the simulated fluid dynamics has been carried out with a numerical code developed by the Geophysical group at the University College Dublin (O’Brien and Bean, 2004b), with whom we started a very profitable collaboration. In this code, the seismic wave propagation in heterogeneous media with free surface (e.g. the Earth’s surface) is simulated using a discrete elastic lattice where particle interactions are controlled by the Hooke’s law. This method allows to consider medium heterogeneities and complex topography. The initial and boundary conditions for the simulations have been defined within a coordinate project (INGV-DPC 2004-06 V3_2 “Research on active volcanoes, precursors, scenarios, hazard and risk - Campi Flegrei”), to which this thesis contributes, and many researchers experienced on Campi Flegrei in volcanological, seismic, petrological, geochemical fields, etc. collaborate. Numerical simulations of magma and rock dynamis have been coupled as described in the thesis. The first part of the thesis consists of a parametric study aimed at understanding the eect of the presence in magma of carbon dioxide in magma in the convection dynamics. Indeed, the presence of this volatile was relevant in many Campi Flegrei eruptions, including some eruptions commonly considered as reference for a future activity of this volcano. A set of simulations considering an elliptical magma chamber, compositionally uniform, refilled from below by a magma with volatile content equal or dierent from that of the resident magma has been performed. To do this, a multicomponent non-ideal magma saturation model (Papale et al., 2006) that considers the simultaneous presence of CO2 and H2O, has been implemented in GALES. Results show that the presence of CO2 in the incoming magma increases its buoyancy force promoting convection ad mixing. The simulated dynamics produce pressure transients with frequency and amplitude in the sensitivity range of modern geophysical monitoring networks such as the one installed at Campi Flegrei . In the second part, simulations more related with the Campi Flegrei volcanic system have been performed. The simulated system has been defined on the basis of conditions consistent with the bulk of knowledge of Campi Flegrei and in particular of the Agnano-Monte Spina eruption (4100 B.P.), commonly considered as reference for a future high intensity eruption in this area. The magmatic system has been modelled as a long dyke refilling a small shallow magma chamber; magmas with trachytic and phonolitic composition and variable volatile content of H2O and CO2 have been considered. The simulations have been carried out changing the condition of magma injection, the system configuration (magma chamber geometry, dyke size) and the resident and refilling magma composition and volatile content, in order to study the influence of these factors on the simulated dynamics. Simulation results allow to follow each step of the gas-rich magma ascent in the denser magma, highlighting the details of magma convection and mixing. In particular, the presence of more CO2 in the deep magma results in more ecient and faster dynamics. Through this simulations the variation of the gravimetric field has been determined. Afterward, the space-time distribution of stress resulting from numerical simulations have been used as boundary conditions for the simulations of the displacement field imposed by the magmatic dynamics on rocks. The properties of the simulated domain (rock density, P and S wave velocities) have been based on data from literature on active and passive tomographic experiments, obtained through a collaboration with A. Zollo at the Dept. of Physics of the Federici II Univeristy in Napoli. The elasto-dynamics simulations allow to determine the variations of the space-time distribution of deformation and the seismic signal associated with the studied magmatic dynamics. In particular, results show that these dynamics induce deformations similar to those measured at Campi Flegrei and seismic signals with energies concentrated on the typical frequency bands observed in volcanic areas. The present work shows that an approach based on the solution of equations describing the physics of processes within a magmatic fluid and the surrounding rock system is able to recognise and describe the relationships between geophysical signals detectable on the surface and deep magma dynamics. Therefore, the results suggest that the combined study of geophysical data and informations from numerical simulations can allow in a near future a more ecient evaluation of the short term volcanic hazard.

Supramolecular order and dynamics of functional materials studied by solid state NMR

The goal of this thesis was the investigation of the structure, conformation, supramolecular order and molecular dynamics of different classes of functional materials (phthalocyanine, perylene and hexa-peri-hexabenzocoronene derivatives and mixtures of those), all having planar aromatic cores modified with various types of alkyl chains. The planar aromatic systems are known to stack in the solid and the liquid-crystalline state due to p-p interactions forming columnar superstructures with high one-dimensional charge carrier mobility and potential application in photovoltaic devices. The different functionalities attached to the aromatic cores significantly influence the behavior of these systems allowing the experimentalists to modify the structures to fine-tune the desired thermotropic properties or charge carrier mobility. The aim of the presented studies was to understand the interplay between the driving forces causing self-assembly by relating the structural and dynamic information about the investigated systems. The supramolecular organization is investigated by applying 1H solid state NMR recoupling techniques. The results are related with DSC and X-ray scattering data. Detailed information about the site-specific molecular dynamics is gained by recording spinning sideband patterns using 1H-1H and 13C-1H solid state NMR recoupling techniques. The determined dipole-dipole coupling constants are then related with the coupling constants of the respective rigid pairs, thus providing local dynamic order parameters for the respective moieties. The investigations presented reveal that in the crystalline state the preferred arrangement in the columnar stack of discotic molecules modified with alkyl chains is tilted. This leads to characteristic differences in the 1H chemical shifts of otherwise chemically equivalent protons. Introducing branches and increasing the length of the alkyl chains results in lower mesophase transitions and disordered columnar stacks. In the liquid-crystalline state some of the discs lose the tilted orientation, others do not, but all start a rapid rotation about the columnar axis.

Structure, organization and dynamics of functional supramolecular materials studied by solid-state NMR

Functional materials have great importance due to their many important applications. The characterization of supramolecular architectures which are held together by non-covalent interactions is of most importance to understand their properties. Solid-state NMR methods have recently been proven to be able to unravel such structure-property relations with the help of fast magic-angle spinning and advanced pulse sequences. The aim of the current work is to understand the structure and dynamics of functional supramolecular materials which are potentially important for fuel-cell (proton conducting membrane materials) and solar-cell or plastic-electronic applications (photo-reactive aromatic materials). In particular, hydrogen-bonding networks, local proton mobility, molecular packing arrangements, and local dynamics will be studied by the use of advanced solid-state NMR methods. The first class of materials studied in this work is proton conducting polymers which also form hydrogen-bonding network. Different materials, which are prepared for high 1H conduction by different approaches are studied: PAA-P4VP, PVPA-ABPBI, Tz5Si, and Triazole-functional systems. The materials are examples of the following major groups; - Homopolymers with specific functional groups (Triazole functional polysiloxanes). - Acid-base polymer blends approach (PAA-P4VP, PVPA-ABPBI). - Acid-base copolymer approach (Triazole-PVPA). - Acid doped polymers (Triazole functional polymer doped with H3PO4). Perylenebisimide (PBI) derivatives, a second type of important functional supramolecular materials with potent applications in plastic electronics, were also investigated by means of solid-state NMR. The preparation of conducting nanoscopic fibers based on the self-assembling functional units is an appealing aim as they may be incorporated in molecular electronic devices. In this category, perylene derivatives have attracted great attention due to their high charge carrier mobility. A detailed knowledge about their supramolecular structure and molecular dynamics is crucial for the understanding of their electronic properties. The aim is to understand the structure, dynamics and packing arrangements which lead to high electron conductivity in PBI derivatives.

The impact of different glacial boundary conditions on atmospheric dynamics and precipitation in the North Atlantic region

Using a highly resolved atmospheric general circulation model, the impact of different glacial boundary conditions on precipitation and atmospheric dynamics in the North Atlantic region is investigated. Six 30-yr time slice experiments of the Last Glacial Maximum at 21 thousand years before the present (ka BP) and of a less pronounced glacial state – the Middle Weichselian (65 ka BP) – are compared to analyse the sensitivity to changes in the ice sheet distribution, in the radiative forcing and in the prescribed time-varying sea surface temperature and sea ice, which are taken from a lower-resolved, but fully coupled atmosphere-ocean general circulation model. The strongest differences are found for simulations with different heights of the Laurentide ice sheet. A high surface elevation of the Laurentide ice sheet leads to a southward displacement of the jet stream and the storm track in the North Atlantic region. These changes in the atmospheric dynamics generate a band of increased precipitation in the mid-latitudes across the Atlantic to southern Europe in winter, while the precipitation pattern in summer is only marginally affected. The impact of the radiative forcing differences between the two glacial periods and of the prescribed time-varying sea surface temperatures and sea ice are of second order importance compared to the one of the Laurentide ice sheet. They affect the atmospheric dynamics and precipitation in a similar but less pronounced manner compared with the topographic changes.

Dynamics and kinematics of eruptive activity at Fuego volcano, Guatemala 2005-2009

Volcanoes are the surficial expressions of complex pathways that vent magma and gasses generated deep in the Earth. Geophysical data record at least the partial history of magma and gas movement in the conduit and venting to the atmosphere. This work focuses on developing a more comprehensive understanding of explosive degassing at Fuego volcano, Guatemala through observations and analysis of geophysical data collected in 2005 – 2009. A pattern of eruptive activity was observed during 2005 – 2007 and quantified with seismic and infrasound, satellite thermal and gas measurements, and lava flow lengths. Eruptive styles are related to variable magma flux and accumulation of gas. Explosive degassing was recorded on broadband seismic and infrasound sensors in 2008 and 2009. Explosion energy partitioning between the ground and the atmosphere shows an increase in acoustic energy from 2008 to 2009, indicating a shift toward increased gas pressure in the conduit. Very-long-period (VLP) seismic signals are associated with the strongest explosions recorded in 2009 and waveform modeling in the 10 – 30 s band produces a best-fit source location 300 m west and 300 m below the summit crater. The calculated moment tensor indicates a volumetric source, which is modeled as a dike feeding a SW-dipping (35°) sill. The sill is the dominant component and its projection to the surface nearly intersects the summit crater. The deformation history of the sill is interpreted as: 1) an initial inflation due to pressurization, followed by 2) a rapid deflation as overpressure is explosively release, and finally 3) a reinflation as fresh magma flows into the sill and degasses. Tilt signals are derived from the horizontal components of the seismometer and show repetitive inflation deflation cycles with a 20 minute period coincident with strong explosions. These cycles represent the pressurization of the shallow conduit and explosive venting of overpressure that develops beneath a partially crystallized plug of magma. The energy released during the strong explosions has allowed for imaging of Fuego’s shallow conduit, which appears to have migrated west of the summit crater. In summary, Fuego is becoming more gas charged and its summit centered vent is shifting to the west - serious hazard consequences are likely.

Identity, Philosophy, and the Problem of Armenian History in the Sixth Century

History and Identity in the Late Antique Near East gathers together the work of distinguished historians and early career scholars with a broad range of expertise to investigate the significance of newly emerged, or recently resurrected, ethnic identities on the borders of the eastern Mediterranean world. It focuses on the "long late antiquity" from the eve of the Arab conquest of the Roman East to the formation of the Abbasid caliphate. The first half of the book offers papers on the Christian Orient on the cusp of the Islamic invasions. These papers discuss how Christians negotiated the end of Roman power, whether in the selective use of the patristic past to create confessional divisions or the emphasis of the shared philosophical legacy of the Greco-Roman world. The second half of the book considers Muslim attempts to negotiate the pasts of the conquered lands of the Near East, where the Christian histories of Hira or Egypt were used to create distinctive regional identities for Arab settlers. Like the first half, this section investigates the redeployment of a shared history, this time the historical imagination of the Qu'ran and the era of the first caliphs. All the papers in the volume bring together studies of the invention of the past across traditional divides between disciplines, placing the re-assessment of the past as a central feature of the long late antiquity. As a whole, History and Identity in the Late Antique Near East represents a distinctive contribution to recent writing on late antiquity, due to its cultural breadth, its interdisciplinary focus, and its novel definition of late antiquity itself.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.