On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

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

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

Influence of nearest-neighbor Coulomb interactions on the phase diagram of the ferromagnetic Kondo model

The influence of a nearest-neighbor Coulomb repulsion of strength V on the properties of the ferromagnetic Kondo model is analyzed using computational techniques. The Hamiltonian studied here is defined on a chain using localized S = 1/2 spins, and one orbital per site. Special emphasis is given to the influence of the Coulomb repulsion on the regions of phase separation recently discovered in this family of models, as well as on the double-exchange-induced ferromagnetic ground state. When phase separation dominates at V= 0, the Coulomb interaction breaks the large domains of the two competing phases into small islands of one phase embedded into the other. This is in agreement with several experimental results, as discussed in the text. Vestiges of the original phase separation regime are found in the spin structure factor as incommensurate peaks, even at large values of V. In the ferromagnetic regime close to density n = 0.5, the Coulomb interaction induces tendencies to charge ordering without altering the fully polarized character of the state. This regime of charge-ordered ferromagnetism may be related with experimental observations of a similar phase by Chen and Cheong [Phys. Rev. Lett. 76, 4042 (1996)]. Our results reinforce the recently introduced notion [see, e.g., S. Yunoki et al., Phys. Rev. Lett. 80, 845 (1998)] that in realistic models for manganites analyzed with unbiased many-body techniques, the ground state properties arise from a competition between ferromagnetism and phase-separation - charge-ordering tendencies. ©1999 The American Physical Society.

Short-chain di-ureasil ormolytes doped with potassium triflate: Phase diagram and conductivity behavior

Di-urea cross-linked poly(oxyethylene)/siloxane hybrids, synthesized by the sol-gel process and containing a wide concentration range of potassium triflate, KCF3SO3, have been analyzed by x-ray diffraction and differential scanning calorimetry. The pseudo-phase diagram proposed has been taken into account in the interpretation of the complex impedance measurements. The xerogels prepared are obtained as transparent, thin monoliths. At room temperature the highest conductivity found was 2 × 10-6 Ω-1 cm-1.

Study of a hybrid solid oxide fuel cell: Energetic analysis and sankey diagram

In this paper a hybrid solid oxide fuel cell (SOFC) system is analyzed. This system applies a combined cycle utilizing gas turbine associated to a SOFC for rational decentralized energy production. Initially the relative concepts about the fuel cell are presented, followed by some chemical and technical informations such as the change of Gibbs free energy in isothermal fuel oxidation (or combustion) directly into electricity. This represents a very high fraction of the lower heating value (LHV) of a hydrocarbon fuel. In the next step a methodology for the study of SOFC associated with a gas turbine system is developed, considering the electricity and steam production for a hospital, as regard to the Brazilian conditions. This methodology is applied to energetic analysis. Natural gas is considered as a fuel. In conclusion, it is shown by a Sankey Diagram that the hybrid SOFC system may be an excellent opportunity to strengthen the decentralized energy production in Brazil. It is necessary to consider that the cogeneration in this version also is a sensible alternative from the technical point of view, demanding special methods of design, equipment selection and mainly of the contractual deals associated to electricity and fuel supply.

A note on non-degenerate umbilics and the path formulation for bifurcation problems

Path formulation can be used to classify and structure efficiently multiparameter bifurcation problems around fundamental singularities: the cores. The non-degenerate umbilic singularities are the generic cores for four situations in corank 2: the general or gradient problems and the ℤ 2-equivariant (general or gradient) problems. Those categories determine an interesting 'Russian doll' type of structure in the universal unfoldings of the umbilic singularities. One advantage of our approach is that we can handle one, two or more parameters using the same framework (even considering some special parameter structure, for instance, some internal hierarchy). We classify the generic bifurcations that occur in those cases with one or two parameters.

Sorption isotherm, glass transitions and state diagram for freeze-dried plum skin and pulp

Differential scanning calorimetry (DSC) was used to determine phase transitions of freeze-dried plums. Samples at low and intermediate moisture contents, were conditioned by adsorption at various water activities (0.11≤a w≤0.90) at 25°C, whereas in the high moisture content region (a w>0.90) samples were obtained by direct water addition, with the resulting sorption isotherm being well described by the Guggenheim-Anderson-deBoer (GAB) model. Freeze-dried samples of separated plum skin and pulp were also analysed. At a w≤0.75, two glass transitions were visible, with the glass transition temperature (T g) decreasing with increasing a w due to the water plasticising effect. The first T g was attributed to the matrix formed by sugars and water. The second one, less visible and less plasticised by water, was probably due to macromolecules of the fruit pulp. The Gordon-Taylor model represented satisfactorily the matrix glass transition curve for a w≤0.90. In the higher moisture content range T g remained practically constant around T g′ (-57.5°C). Analysis of the glass transition curve and the sorption isotherm indicated that stability at a temperature of 25°C, would be attained by freeze dried plum at a water activity of 0.04, corresponding to a moisture content of 12.9% (dry basis). © 2006 SAGE Publications.

3-Dimensional hopf bifurcation via averaging theory

We consider the Lorenz system ẋ = σ(y - x), ẏ = rx - y - xz and ż = -bz + xy; and the Rössler system ẋ = -(y + z), ẏ = x + ay and ż = b - cz + xz. Here, we study the Hopf bifurcation which takes place at q± = (±√br - b,±√br - b, r - 1), in the Lorenz case, and at s± = (c+√c2-4ab/2, -c+√c2-4ab/2a, c±√c2-4ab/2a) in the Rössler case. As usual this Hopf bifurcation is in the sense that an one-parameter family in ε of limit cycles bifurcates from the singular point when ε = 0. Moreover, we can determine the kind of stability of these limit cycles. In fact, for both systems we can prove that all the bifurcated limit cycles in a neighborhood of the singular point are either a local attractor, or a local repeller, or they have two invariant manifolds, one stable and the other unstable, which locally are formed by two 2-dimensional cylinders. These results are proved using averaging theory. The method of studying the Hopf bifurcation using the averaging theory is relatively general and can be applied to other 3- or n-dimensional differential systems.

Path formulation for multiparameter D3-equivariant bifurcation problems

We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.

Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)

In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system exhibits both regular and chaotic motions. The Poincaré sections for different sets of coupling parameters are verified. © 2011 World Scientific Publishing Company.

The dual currency bifurcation of Cuba's economy in the 1990s: causes, consequences and cures

Includes bibliography

Development of a thermoeconomic methodology for the optimization of biodiesel production - Part I: Biodiesel plant and thermoeconomic functional diagram

This work developed a methodology that uses the thermoeconomic functional diagram applied for allocating the cost of products produced by a biodiesel plant. The first part of this work discusses some definitions of exergy and thermoeconomy, with a detailed description of the biodiesel plant studied, identification of the system functions through Physical Diagram, calculation of the irreversibilities of the plant, construction of the Thermoeconomic Functional Diagram and determination of the expressions for the plant's exergetic functions. In order to calculate the exergetic increments and the physical exergy of certain flows in each step, the Chemical Engineering Simulation Software HYSYS 3.2 was used. The equipments that have the highest irreversibilities in the plant were identified after the exergy calculation. It was also found that the lowest irreversibility in the system refers to the process with a molar ratio of 6:1 and a reaction temperature of 60 °C in the transesterification process. In the second part of this work (Part II), it was calculated the thermoeconomic cost of producing biodiesel and related products, including the costs of carbon credits for the CO2 that is not released into the atmosphere, when a percentage of biodiesel is added to the petroleum diesel used by Brazil's internal diesel fleet (case study). © 2013 Elsevier Ltd. All rights reserved.