Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models

Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global phase space properties, which are the underlying cause of observed structures. The potentials needed to describe self-consistent models are time-dependent. Here, we aim to investigate dynamical properties (regular/chaotic motion) of a non-autonomous galactic system, whose time-dependent potential adequately mimics certain realistic trends arising from N-body barred galaxy simulations. We construct a fully time-dependent analytical potential, modeling the gravitational potentials of disc, bar and dark matter halo, whose time-dependent parameters are derived from a simulation. We study the dynamical stability of its reduced time-independent 2-degrees of freedom model, charting the different islands of stability associated with certain orbital morphologies and detecting the chaotic and regular regions. In the full 3-degrees of freedom time-dependent case, we show representative trajectories experiencing typical dynamical behaviours, i.e., interplay between regular and chaotic motion for different epochs. Finally, we study its underlying global dynamical transitions, estimating fractions of (un)stable motion of an ensemble of initial conditions taken from the simulation. For such an ensemble, the fraction of regular motion increases with time.Comment: 17 pages, 11 figures (revised version, accepted for publication in Mon. Not. R. Astron. Soc.

Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method

As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its realm of applicability by using it to investigate the local dynamics of periodic orbits. We show theoretically and verify numerically that for stable periodic orbits the GALIs tend to zero following particular power laws for Hamiltonian flows, while they fluctuate around non-zero values for symplectic maps. By comparison, the GALIs of unstable periodic orbits tend exponentially to zero, both for flows and maps. We also apply the GALIs for investigating the dynamics in the neighborhood of periodic orbits, and show that for chaotic solutions influenced by the homoclinic tangle of unstable periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during which their amplitudes change by many orders of magnitude. Finally, we use the GALI method to elucidate further the connection between the dynamics of Hamiltonian flows and symplectic maps. In particular, we show that, using for the computation of GALIs the components of deviation vectors orthogonal to the direction of motion, the indices of stable periodic orbits behave for flows as they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of Bifurcation and Chaos

Numerical integration of variational equations

We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom, and investigate their efficiency in accurately reproducing well-known properties of chaos indicators like the Lyapunov Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs). We find that the best numerical performance is exhibited by the \textit{`tangent map (TM) method'}, a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton's equations of motion by the repeated action of a symplectic map $S$, while the corresponding tangent map $TS$, is used for the integration of the variational equations. A simple and systematic technique to construct $TS$ is also presented.Comment: 27 pages, 11 figures, to appear in Phys. Rev.

Computational Fluid Dynamic (CFD) and Reaction Modelling Study 6 of Bio-oil Catalytic Hydrodeoxygenation in Microreactors

A Computational Fluid Dynamic (CFD) model was derived and validated, in order to, investigate the hydrodeoxygenation 9 reaction of 4-propylguaiacol, which is a lignin-derived compound present in bio-oil. A 2-D packed bed microreactor was 10 simulated using pre-sulphided NiMo/Al2O3 solid catalyst in isothermal operation. A pseudo-homogeneous model was first 11 created to validate the experimental results from literature. Various operational parameters were investigated and validated 12 with the experimental data, such as temperature, pressure and liquid flow rate; and it was found that the CFD findings were 13 in very good agreement with the results from literature. The model was then upgraded to that of a detailed multiphase 14 configuration; and phenomena such as internal and external mass transfer limitations were investigated, as well as, reactant 15 concentrations on the rate of 4-propylguaiacol. Both models agreed with the experimental data, and therefore confirm their 16 ability for applications related to the prediction of the behaviour of bio-oil compounds hydrodeoxygenation

Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred Galaxy Model

We study the distinction and quantification of chaotic and regular motion in a time-dependent Hamiltonian barred galaxy model. Recently, a strong correlation was found between the strength of the bar and the presence of chaotic motion in this system, as models with relatively strong bars were shown to exhibit stronger chaotic behavior compared to those having a weaker bar component. Here, we attempt to further explore this connection by studying the interplay between chaotic and regular behavior of star orbits when the parameters of the model evolve in time. This happens for example when one introduces linear time dependence in the mass parameters of the model to mimic, in some general sense, the effect of self-consistent interactions of the actual N-body problem. We thus observe, in this simple time-dependent model also, that the increase of the bar's mass leads to an increase of the system's chaoticity. We propose a new way of using the Generalized Alignment Index (GALI) method as a reliable criterion to estimate the relative fraction of chaotic vs. regular orbits in such time-dependent potentials, which proves to be much more efficient than the computation of Lyapunov exponents. In particular, GALI is able to capture subtle changes in the nature of an orbit (or ensemble of orbits) even for relatively small time intervals, which makes it ideal for detecting dynamical transitions in time-dependent systems.Comment: 21 pages, 9 figures (minor typos fixed) to appear in J. Phys. A: Math. Theo

Process Simulation Modelling of the Catalytic Hydrodeoxygenation of 4-Propylguaiacol in Microreactors

A process simulation model was created using Aspen Plus to investigate the hydrodeoxygenation of 4-propylguaiacol, a model component in lignin-derived pyrolysis oil, over a presulphided NiMo/Al2O3 solid catalyst. Process simulation modelling methods were used to develop the pseudo-homogeneous packed bed microreactor. The reaction was conducted at 400 °C and an operating pressure of 300 psig with a 4-propylguaiacol liquid flow rate of 0.03 mL·min−1 and a hydrogen gas flow rate of 0.09 mL·min−1. Various operational parameters were investigated and compared to the experimental results in order to establish their effect on the conversion of 4-propylguaiacol. The parameters studied included reaction temperature, pressure, and residence time. Further changes to the simulation were made to study additional effects. In doing so, the operation of the same reactor was studied adiabatically, rather than isothermally. Moreover, different equations of state were used. It was observed that the conversion was enhanced with increasing temperature, pressure, and residence time. The results obtained demonstrated a good model validation when compared to the experimental results, thereby confirming that the model is suitable to predict the hydrodeoxygenation of pyrolysis oil

CO2 capture using membrane contactors: a systematic literature review

With fossil fuel being the major source of energy, CO2 emission levels need to be reduced to a minimal amount namely from anthropogenic sources. Energy consumption is expected to rise by 48% in the next 30 years, and global warming is becoming an alarming issue which needs to be addressed on a thorough technical basis. Nonetheless, exploring CO2 capture using membrane contactor technology has shown great potential to be applied and utilised by industry to deal with post- and pre-combustion of CO2. A systematic review has been conducted to analyse and assess CO2 removal using membrane contactors for capturing techniques in industrial processes. The review began with a total of 2650 papers, which were obtained from three major databases, and then were excluded down to a final number of 525 papers following a defined set of criteria. The results showed that hollow fibre membranes have demonstrated popularity, as well as the use of amine solvents for CO2 removal. This current systematic review in CO2 removal and capture is an important milestone in the acknowledgment of up to date research with the potential to serve as a benchmark databank for further research in similar areas of work. This study provides the first systematic enquiry in the evidence to research further sustainable methods to capture and separate CO2

Process Simulation Modelling of the Catalytic Hydrodeoxygenation of 4-Propylguaiacol in Microreactors

A process simulation model was created using Aspen Plus to investigate the hydrodeoxygenation of 4-propylguaiacol, a model component in lignin-derived pyrolysis oil, over a presulphided NiMo/Al2O3 solid catalyst. Process simulation modelling methods were used to develop the pseudo-homogeneous packed bed microreactor. The reaction was conducted at 400 °C and an operating pressure of 300 psig with a 4-propylguaiacol liquid flow rate of 0.03 mL·min−1 and a hydrogen gas flow rate of 0.09 mL·min−1. Various operational parameters were investigated and compared to the experimental results in order to establish their effect on the conversion of 4-propylguaiacol. The parameters studied included reaction temperature, pressure, and residence time. Further changes to the simulation were made to study additional effects. In doing so, the operation of the same reactor was studied adiabatically, rather than isothermally. Moreover, different equations of state were used. It was observed that the conversion was enhanced with increasing temperature, pressure, and residence time. The results obtained demonstrated a good model validation when compared to the experimental results, thereby confirming that the model is suitable to predict the hydrodeoxygenation of pyrolysis oil

Modelagem social computacional como instrumento de análise de sistemas sociais territoriais complexos: o caso do Território Sul sergipano, Brasil.

O governo brasileiro e os governos locais recorreram à abordagem territorial para a elaboração de suas estratégias de desenvolvimento regional sustentável. Espaço geográfico delimitado, dotado de uma governança própria e animado por processos específicos, o território é visto como o lugar de integração das dimensões social, econômica e ambiental das diversas políticas públicas. Todavia, apesar do discurso sobre a integração das diferentes dimensões do desenvolvimento sustentável, a maioria das ações está polarizada entre a economia e a conservação ambiental. A pesquisa apresentada neste artigo visa à adoção de um quadro conceitual para avaliação da dimensão social dos processos territoriais segundo a teoria dos sistemas. Seguindo uma abordagem iterativa e interdisciplinar, foi estudado o Território Rural Sul Sergipano, Brasil, considerando o território como um sistema complexo de atores e utilizando um método de modelagem social computacional baseada na Sociologia da Ação Organizada. Os resultados mostraram que essa abordagem permitiu a identificação dos atores pertinentes, assim como os jogos de atores nos quais eles se engajam, fundamentados, principalmente, nas relações de poder e dependência, contribuindo assim para a compreensão da estrutura social do território

Computational Studies on Microreactors for the Decomposition of Formic Acid for Hydrogen Production Using Heterogeneous Catalysts

Sustainable alternatives to conventional fuels have emerged recently, focusing on a hydrogen-based economy. The idea of using hydrogen (H2) as an energy carrier is very promising due to its zero-emission properties. The present study investigates the formic acid (FA) decomposition for H2 generation using a commercial 5 wt.% Pd/C catalyst. Three different 2D microreactor configurations (packed bed, single membrane, and double membrane) were studied using computational fluid dynamics (CFD). Parameters such as temperature, porosity, concentration, and flow rate of reactant were investigated. The packed bed configuration resulted in high conversions, but due to catalyst poisoning by carbon monoxide (CO), the catalytic activity decreased with time. For the single and double membrane microreactors, the same trends were observed, but the double membrane microreactor showed superior performance compared with the other configurations. Conversions higher than 80% were achieved, and even though deactivation decreased the conversion after 1 h of reaction, the selective removal of CO from the system with the use of membranes lead to an increase in the conversion afterwards. These results prove that the incorporation of membranes in the system for the separation of CO is improving the efficiency of the microreactor