Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, u(tt) + Delta(2)u -M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u + f(u) + g(u(t)) = h in Omega x R(+), where Omega is a bounded domain of R(N), M is a nonnegative real function and h is an element of L(2)(Omega). The nonlinearities f(u) and g(u(t)) are essentially vertical bar u vertical bar(rho) u - vertical bar u vertical bar(sigma) u and vertical bar u(t)vertical bar(r) u(t) respectively, with rho, sigma, r > 0 and sigma < rho. This kind of problem models vibrations of extensible beams and plates. (C) 2010 Elsevier Ltd. All rights reserved.

Nanoindentation mechanical properties characterization of glassy polymeric carbon treated with ion beam

Phenolic resins when heat treated in inert atmosphere up to 1000 degreesC become glassy polymeric carbon (GPC), a chemically inert and biocompatible material useful for medical applications, such as in the manufacture of heart valves and prosthetic devices. In earlier work we have shown that ion bombardment can modify the surface of GPC, increasing its roughness. The enhanced roughness, which depends on the species, energy and fluence of the ion beam, can improve the biocompatibility of GPC prosthetic artifacts. In this work, ion bombardment was used to make a layer of implanted ions under the surface to avoid the propagation of microcracks in regions where cardiac valves should have pins for fixation of the leaflets. GPC samples prepared at 700 and 1500 degreesC were bombarded with ions of silicon. carbon, oxygen and gold at energies of 5, 6, 8 and 10 MeV, respectively, and fluences between 1.0 x 10(13) and 1.0 x 10(16) ions/cm(2). Nanoindentation hardness characterization was used to compare bombarded with non-bombarded samples prepared at temperatures up to 2500 degreesC. The results with samples not bombarded showed that the hardness of GPC increases strongly with the heat treatment temperature. Comparison with ion bombarded samples shows that the hardness changes according to the ion used, the energy and fluence. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Stability results for impulsive functional differential equations with infinite delay

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

Modal Analysis of a Beam with a Tip Rotor by Using a Fundamental Response

The shape modes of a damped-free beam model with a tip rotor are determined by using a dynamical basis that is generated by a fundamental spatial free response. This is a non-classical distributed model for the displacements in the transverse directions of the beam which turns out to be coupled through boundary conditions due to rotation. Numerical calculations are performed by using the Ritz-Rayleigh method with several approximating basis.

Latent track radius of PTFE irradiated with high energy ion beam

PTFE foils were irradiated with different ion beams (Xe, Au and U) with energies up to 1.5 GeV and fluences between 1 x 10(8) and 1 x 10(13) ions/cm(2) at room temperature. The induced modifications in the polymer were analyzed by FTIR, UV-Vis spectroscopy, and XRD. In the FTIR spectra, the CF2 degradation accompanied by the formation of CF3 terminal and side groups were observed. In the UV-Vis spectra, the observed increase in the absorption at UV wavelengths is an indication of polymer carbonization. From XRD, the amorphization of the material was evidenced by the decrease in the intensity of the main diffraction peak. An exponential fit of the intensity of the IR absorption peaks resulted in the following values: 2.9 +/- 0.8; 4.5 +/- 0.9 and 5.6 +/- 0.8 nm for the latent track radius after irradiation with Xe, Au and U beams, respectively. (C) 2011 Elsevier B.V. All rights reserved.

Measurement of Muon Antineutrino Oscillations with an Accelerator-Produced Off-Axis Beam

T2K reports its first measurements of the parameters governing the disappearance of νµ in an off-axis beam due to flavor change induced by neutrino oscillations. The quasimonochromatic νµ beam, produced with a peak energy of 0.6 GeV at J-PARC, is observed at the far detector SuperKamiokande, 295 km away, where the νµ survival probability is expected to be minimal. Using a dataset corresponding to 4.01×10²⁰ protons on target, 34 fully contained µ-like events were observed. The best-fit oscillation parameters are sin²(θ₂₃) = 0.45 and |∆m^2_32| = 2.51 × 10⁻³ eV² with 68% confidence intervals of 0.38 - 0.64 and 2.26 - 2.80 ×10⁻³ eV² respectively. These results are in agreement with existing antineutrino parameter measurements and also with the νµ disappearance parameters measured by T2K.

Dynamics of Granular Crystals with Elastic-Plastic Contacts

We study the behavior of granular crystals subjected to impact loading that creates plastic deformation at the contacts between constituent particles. Granular crystals are highly periodic arrangements of spherical particles, arranged into densely packed structures resembling crystals. This special class of granular materials has been shown to have unique dynamics with suggested applications in impact protection. However, previous work has focused on very low amplitude impacts where every contact point can be described using the Hertzian contact law, valid only for purely elastic deformation. In this thesis, we extend previous investigation of the dynamics of granular crystals to significantly higher impact energies more suitable for the majority of applications. Additionally, we demonstrate new properties specific to elastic-plastic granular crystals and discuss their potential applications as well. We first develop a new contact law to describe the interaction between particles for large amplitude compression of elastic-plastic spherical particles including a formulation for strain-rate dependent plasticity. We numerically and experimentally demonstrate the applicability of this contact law to a variety of materials typically used in granular crystals. We then extend our investigation to one-dimensional chains of elastic-plastic particles, including chains of alternating dissimilar materials. We show that, using the new elastic-plastic contact law, we can predict the speed at which impact waves with plastic dissipation propagate based on the material properties of the constituent particles. Finally, we experimentally and numerically investigate the dynamics of two-dimensional and three-dimensional granular crystals with elastic-plastic contacts. We first show that the predicted wave speeds for 1D granular crystals can be extended to 2D and 3D materials. We then investigate the behavior of waves propagating across oblique interfaces of dissimilar particles. We show that the character of the refracted wave can be predicted using an analog to Snell's law for elastic-plastic granular crystals and ultimately show how it can be used to design impact guiding "lenses" for mitigation applications.

Shaping transverse beam distributions by means of adiabatic crossing of resonances

Non-linear effects are responsible for peculiar phenomena in charged particles dynamics in circular accelerators. Recently, they have been used to propose novel beam manipulations where one can modify the transverse beam distribution in a controlled way, to fulfil the constraints posed by new applications. One example is the resonant beam splitting used at CERN for the Multi-Turn Extraction (MTE), to transfer proton beams from PS to SPS. The theoretical description of these effects relies on the formulation of the particle's dynamics in terms of Hamiltonian systems and symplectic maps, and on the theory of adiabatic invariance and resonant separatrix crossing. Close to resonance, new stable regions and new separatrices appear in the phase space. As non-linear effects do not preserve the Courant-Snyder invariant, it is possible for a particle to cross a separatrix, changing the value of its adiabatic invariant. This process opens the path to new beam manipulations. This thesis deals with various possible effects that can be used to shape the transverse beam dynamics, using 2D and 4D models of particles' motion. We show the possibility of splitting a beam using a resonant external exciter, or combining its action with MTE-like tune modulation close to resonance. Non-linear effects can also be used to cool a beam acting on its transverse beam distribution. We discuss the case of an annular beam distribution, showing that emittance can be reduced modulating amplitude and frequency of a resonant oscillating dipole. We then consider 4D models where, close to resonance, motion in the two transverse planes is coupled. This is exploited to operate on the transverse emittances with a 2D resonance crossing. Depending on the resonance, the result is an emittance exchange between the two planes, or an emittance sharing. These phenomena are described and understood in terms of adiabatic invariance theory.

Evaluation of Femtosecond Laser-Induced Breakdown Spectroscopy for Analysis of Animal Tissues

The aim of this work was to evaluate the performance of femtosecond laser-induced breakdown spectroscopy (fs-LIBS) for the determination of elements in animal tissues. Sample pellets were prepared from certified reference materials, such as liver, kidney, muscle, hepatopancreas, and oyster, after cryogenic grinding assisted homogenization. Individual samples were placed in a two-axis computer-controlled translation stage that moved in the plane orthogonal to a beam originating from a Ti:Sapphire chirped-pulse amplification (CPA) laser system operating at 800 mu and producing a train of 840 mu J and 40 fs pulses at 90 Hz. The plasma emission was coupled into the optical fiber of a high-resolution intensified charge-coupled device (ICCD)-echelle spectrometer. Time-resolved characteristics of the laser-produced plasmas showed that the best results were obtained with delay times between 80 and 120 ns. Data obtained indicate both that it is a matrix-independent sampling process and that fs-LIBS can be used for the determination of Ca, Cu, Fe, K, Mg, Na, and P, but efforts must be made to obtain more appropriate detection limits for Al, Sr, and Zn.

Electron beam irradiation of Matricaria chamomilla L. for microbial decontamination

Wild chamomile (Matricaria chamomilla L.) is one of the most popular herbal materials with both internal and external use to cure different health disturbances. As a consequence of its origin, chamomile could carry various microbial contaminants which offer different hazards to the final consumer. Reduction of the microbial load to the in force regulation limits represents an important phase in the technological process of vegetal materials, and the electron beam treatment might be an efficient alternative to the classical methods of hygienic quality assurance. The purpose of the study was to analyze the potential application of the electron beam treatment in order to assure the microbial safety of the wild chamomile. Samples of chamomile dry inflorescences were treated in electron beam (e-beam) of 6 MeV mean energy, at room temperature and ambient pressure. Some loss of the chemical compounds with bioactive role could be noticed, but the number of microorganisms decreased as a function on the absorbed dose. Consequently, the microbial quality of studied vegetal material inflorescences was improved by e-beam. irradiation. (C) 2008 Elsevier B.V. All rights reserved.

Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

Surface foam film waves studied with high-speed linescan camera

Dynamic foam films have been investigated using an improved experimental set-up with a CCD high-speed linescan camera in conjunction with the Scheludko micro-interferometric cell for studying the drainage and rupture of liquid foam films. The improved experimental set-up increased the sensibility of detection of the local thickness heterogeneities and domains during the film evolution. The evolution of the foam films up to the formation of black spots was recorded in the time intervals of 50ms. The wavelengths of the propagating surface waves and their frequencies were determined experimentally. The experimental results show that the current quasi-static hydrodynamic theory does not properly describe the wave dynamics with inter-domain channels. However, the thermodynamic condition for formation of black spots in the foam films was met by the experimental results. (c) 2005 Elsevier B.V. All rights reserved.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Patch dynamics and metapopulation theory: the case of successional species

We present a mathematical framework that combines extinction-colonization dynamics with the dynamics of patch succession. We draw an analogy between the epidemiological categorization of individuals (infected, susceptible, latent and resistant) and the patch structure of a spatially heterogeneous landscape (occupied-suitable, empty-suitable, occupied-unsuitable and empty-unsuitable). This approach allows one to consider life-history attributes that influence persistence in patchy environments (e.g., longevity, colonization ability) in concert with extrinsic processes (e.g., disturbances, succession) that lead to spatial heterogeneity in patch suitability. It also allows the incorporation of seed banks and other dormant life forms, thus broadening patch occupancy dynamics to include sink habitats. We use the model to investigate how equilibrium patch occupancy is influenced by four critical parameters: colonization rate? extinction rate, disturbance frequency and the rate of habitat succession. This analysis leads to general predictions about how the temporal scaling of patch succession and extinction-colonization dynamics influences long-term persistence. We apply the model to herbaceous, early-successional species that inhabit open patches created by periodic disturbances. We predict the minimum disturbance frequency required far viable management of such species in the Florida scrub ecosystem. (C) 2001 Academic Press.