Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

The generator coordinate method for a reaction coordinate coupled to a harmonic oscillator bath

This paper investigates the usefulness of the generator coordinate method (GCM) for treating the dynamics of a reaction coordinate coupled to a bath of harmonic degrees of freedom. Models for the unimolecular dissociation and isomerization process (proton transfer) are analyzed. The GCM results, presented in analytical form, provide a very good description and are compared to other methods Like the basis set method and multiconfiguration time dependent self-consistent field. (C) 1998 American Institute of Physics. [S0021-9606(98)50934-8].

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

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

On energy transfer phenomena, in a nonlinear ideal and nonideal essential vibrating systems, coupled to a (MR) magneto-rheological damper

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

Affine Toda systems coupled to matter fields

We investigate higher grading integrable generalizations of the affine Toda systems, where the flat connections defining the models take values in eigensubspaces of an integral gradation of an affine Kac-Moody algebra, with grades varying from l to -l (l > 1). The corresponding target space possesses nontrivial vacua and soliton configurations, which can be interpreted as particles of the theory, on the same footing as those associated to fundamental fields. The models can also be formulated by a hamiltonian reduction procedure from the so-called two-loop WZNW models. We construct the general solution and show the classes corresponding to the solitons. Some of the particles and solitons become massive when the conformal symmetry is spontaneously broken by a mechanism with an intriguing topological character and leading to a very simple mass formula. The massive fields associated to nonzero grade generators obey field equations of the Dirac type and may be regarded as matter fields. A special class of models is remarkable. These theories possess a U(1 ) Noether current, which, after a special gauge fixing of the conformal symmetry, is proportional to a topological current. This leads to the confinement of the matter field inside the solitons, which can be regarded as a one-dimensional bag model for QCD. These models are also relevant to the study of electron self-localization in (quasi-)one-dimensional electron-phonon systems.

A virtual experiment for the detection of specific features in the frequency response of a coupled nonlinear and linear oscillator

This paper presents an investigation into some practical issues that may be present in a real experiment, when trying to validate the theoretical frequency response curve of a two degree-of-freedom nonlinear system consisting of coupled linear and nonlinear oscillators. Some specific features, such as detached resonance curves, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation, and the system parameters have been shown to be fundamental in achieving such features. When based on a simplified model, approximate analytical expression for the frequency response curves may be derived, which may be validated by the numerical solutions. In a real experiment, however, the practical achievability of such features was previously shown to be greatly affected by small disturbances induced by gravity and inertia, which led to some solutions becoming unstable which had been predicted to be stable. In this work a practical system configuration is proposed where such effects are reduced so that the previous limitations are overcome. A virtual experiment is carried out where a detailed multi-body model of the oscillator is assembled and the effects on the system response are investigated.

Nonlinear dynamics of a periodically driven Duffing resonator coupled to a Van der Pol oscillator

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1?:?1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequency-amplitude modulation. The internal resonance leads to an antiresonance response of the Duffing resonator and a stagnant response (a small shoulder in the curve) of the van der Pol oscillator. The stability of the dynamic motions is also analyzed. The coupled system shows a hysteretic response pattern and symmetry-breaking facets. Chaotic behaviour of the coupled system is also observed and the dependence of the system dynamics on the parameters are also studied using bifurcation analysis.

Statistics of noise-driven coupled nonlinear oscillators:applications to systems with Kerr nonlinearity

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength. © 2005 Elsevier B.V. All rights reserved.

Ancient clam gardens, traditional management portfolios, and the resilience of coupled human-ocean systems

Indigenous communities have actively managed their environments for millennia using a diversity of resource use and conservation strategies. Clam gardens, ancient rock-walled intertidal beach terraces, represent one example of an early mariculture technology that may have been used to improve food security and confer resilience to coupled human-ocean systems. We surveyed a coastal landscape for evidence of past resource use and management to gain insight into ancient resource stewardship practices on the central coast of British Columbia, Canada. We found that clam gardens are embedded within a diverse portfolio of resource use and management strategies and were likely one component of a larger, complex resource management system. We compared clam diversity, density, recruitment, and biomass in three clam gardens and three unmodified nonwalled beaches. Evidence suggests that butter clams (Saxidomus gigantea) had 1.96 times the biomass and 2.44 times the density in clam gardens relative to unmodified beaches. This was due to a reduction in beach slope and thus an increase in the optimal tidal range where clams grow and survive best. The most pronounced differences in butter clam density between nonwalled beaches and clam gardens were found at high tidal elevations at the top of the beach. Finally, clam recruits (0.5-2 mm in length) tended to be greater in clam gardens compared to nonwalled beaches and may be attributed to the addition of shell hash by ancient people, which remains on the landscape today. As part of a broader social-ecological system, clam garden sites were among several modifications made by humans that collectively may have conferred resilience to past communities by providing reliable and diverse access to food resources.

Coupled Ge/Si and Ge isotope ratios as geochemical tracers of seafloor hydrothermal systems: Case studies at Loihi Seamount and East Pacific Rise 9°50’N

Germanium (Ge) and Silicon (Si) exhibit similar geochemical behaviour in marine environments but are variably enriched in seafloor hydrothermal fluids relative to seawater. In this study, Ge isotope and Ge/Si ratio systematics were investigated in low temperature hydrothermal vents from Loihi Seamount (Pacific Ocean, 18°54’N, 155°15’W) and results were compared to high-temperature vents from the East Pacific Rise (EPR) at 9°50’N. Loihi offers the opportunity to understand contrasting Ge and Si behaviour in low temperature seafloor hydrothermal systems characterized by abundant Fe oxyhydroxide deposition at the seafloor. The results show that both Ge/Si and δ74/70Ge in hydrothermal fluids are fractionated relative to the basaltic host rocks. The enrichment in Ge vs. Si relative to fresh basalts, together with Ge isotope fractionation (Δ74/70Ge fluid-basalt up to 1.15 ‰ at EPR 9°50’N and 1.64 ‰ at Loihi) are best explained by the precipitation of minerals (e.g. quartz and Fe-sulfides) during higher temperature seawater-rock reactions in the subsurface. The study of Fe-rich hydrothermal deposits at Loihi, largely composed of Fe-oxyhydroxides, shows that Ge isotopes are also fractionated upon mineral precipitation at the seafloor. We obtained an average Ge isotope fractionation factor between Fe-oxyhydroxide (ferrihydrite) and dissolved Ge in the fluid of -2.0 ± 0.6 ‰ (2sd), and a maximum value of -3.6 ± 0.6 ‰ (2sd), which is consistent with recent theoretical and experimental studies. The study of a hydrothermal chimney at Bio 9 vent at EPR 9°50’N also demonstrates that Ge isotopes are fractionated by approximately -5.6 ± 0.6 ‰ (2sd) during precipitation of metal sulfides under hydrothermal conditions. Using combined Ge/Si and estimated Ge isotope signatures of Ge sinks and sources in seawater, we propose a preliminary oceanic budget of Ge which reveals that an important sink, referred as the “missing Ge sink”, may correspond to Ge sequestration into authigenic Fe-oxyhydroxides in marine sediments. This study shows that combining Ge/Si and δ74/70Ge systematics provides a useful tool to trace hydrothermal Ge and Si sources in marine environments and to understand formation processes of seafloor hydrothermal deposits.

Long distance coupling of a quantum mechanical oscillator to the internal states of an atomic ensemble

We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which allows the coupling of the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benefit from the rich toolbox of quantum control over internal atomic states. Previous schemes involving atomic motional states are rather limited in both of these aspects. We derive a full quantum model for the effective coupling including the main sources of decoherence. As an application we show that sympathetic ground-state cooling and strong coupling between the two systems is possible.

IMPROVED SAMPLE INTRODUCTION SYSTEMS FOR INDUCTIVELY COUPLED PLASMA OPTICAL EMISSION SPECTROMETRY AND THEIR APPLICATION TO THE ANALYSIS OF SIMPLE AND COMPLEX MATRICES

The objective of this thesis is to explore new and improved methods for greater sample introduction efficiency and enhanced analytical performance with inductively coupled plasma optical emission spectrometry (ICP-OES). Three projects are discussed in which the capabilities and applications of ICP-OES are expanded: 1. In the first project, a conventional ultrasonic nebuliser was modified to replace the heater/condenser with an infrared heated pre-evaporation tube. In continuation from previous works with pre-evaporation, the current work investigated the effects of heating with infrared block and rope heaters on two different ICP-OES instruments. Comparisons were made between several methods and setups in which temperatures were varied. By monitoring changes to sensitivity, detection limit, precision, and robustness, and analyzing two certified reference materials, a method with improved sample introduction efficiency and comparable analytical performance to a previous method was established. 2. The second project involved improvements to a previous work in which a multimode sample introduction system (MSIS) was modified by inserting a pre-evaporation tube between the MSIS and torch. The new work focused on applying an infrared heated ceramic rope for pre-evaporation. This research was conducted in all three MSIS modes (nebulisation mode, hydride generation mode, and dual mode) and on two different ICP-OES instruments, and comparisons were made between conventional setups in terms of sensitivity, detection limit, precision, and robustness. By tracking both hydride-forming and non-hydride forming elements, the effects of heating in combination with hydride generation were probed. Finally, optimal methods were validated by analysis of two certified reference materials. 3. A final project was completed in collaboration with ZincNyx Energy Solutions. This project sought to develop a method for the overall analysis of a 12 M KOH zincate fuel, which is used in green energy backup systems. By employing various techniques including flow injection analysis and standard additions, a final procedure was formulated for the verification of K concentration, as well as the measurement of additives (Al, Fe, Mg, In, Si), corrosion products (such C from CO₃²¯), and Zn particles both in and filtered from solution. Furthermore, the effects of exposing the potassium zincate electrolyte fuel to air were assessed.

Systems of coupled clamped beams equations with full nonlinear terms: Existence and location results

This work gives sufficient conditions for the solvability of the fourth order coupled system┊ u⁽⁴⁾(t)=f(t,u(t),u′(t),u′′(t),u′′′(t),v(t),v′(t),v′′(t),v′′′(t)) v⁽⁴⁾(t)=h(t,u(t),u′(t),u′′(t),u′′′(t),v(t),v′(t),v′′(t),v′′′(t)) with f,h: [0,1]×ℝ⁸→ℝ some L¹- Carathéodory functions, and the boundary conditions {┊ u(0)=u′(0)=u′′(0)=u′′(1)=0 v(0)=v′(0)=v′′(0)=v′′(1)=0. To the best of our knowledge, it is the first time in the literature where two beam equations are considered with full nonlinearities, that is, with dependence on all derivatives of u and v. An application to the study of the bending of two elastic coupled campled beams is considered.