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.

The construction, utilization, and evaluation of a series of exercises designed to improve the oral language of second grade children

Thesis (Ed.M.)--Boston Universit

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

Analysis of polyhedral domed sandwich structures

The finite element method was employed for the analysis of the polyhedral domed sandwich structures. Two different variational approaches were used for comparison reasons. These are the "displacement formulation" and the "mixed formulation" as they are commonly known. Initially seven sandwich plate bending models were developed. These models were used to solve a number of problems where a numerical or experimental solution existed and comparisons were made. The agreement varied from fair to excellent depending on the nature of the model and the type of the solved problem. As a result of this comparative study four of these models were consequently selected to be extended for the development of the sandwich dome models. The accuracy of these four sandwich dome models was tested by modelling five polyhedral dome structures. The results derived from each individual model were compared with experimental results obtained by other researchers and by the author himself. The author's contribution to the experimental work was the design, construction and subsequent testing of two full scale prototypes, namely, the 24 faced and the 36-faced domes. From the whole analysis it was established that the developed numerical models, when selectively applied in the most appropriate way with regard to their special characteristics and the nature of the problem, produce reliable results. Special problems were investigated arising from the boundary conditions as well as structural details! of the joint-lines. of the plates forming the polyhedron, and thus a solution was suggested. Finally, a data generation routine is also described in order to facilitate further application of the various developed models by future users or researchers

Predicting the Features of Methane Adsorption in Large Pore Metal-Organic Frameworks for Energy Storage

Abstract：Currently metal-organic frameworks (MOFs) are receiving significant attention as part of an international push to use their special properties in an extensive variety of energy applications. In particular, MOFs have exceptional potential for gas storage especially for methane and hydrogen for automobiles. However, using theoretical approaches to investigate this important problem presents various difficulties. Here we present the outcomes of a basic theoretical investigation of methane adsorption in large pore MOFs with the aim of capturing the unique features of this phenomenon. We have developed a pseudo one-dimensional statistical mechanical theory of adsorption of gas in a MOF with both narrow and large pores which is solved exactly using a transfer matrix technique in the Osmotic Ensemble (OE). The theory effectively describes the distinctive features of adsorption of gas isotherms in MOFs. The characteristic forms of adsorption isotherms in MOFs reflect changes in structure caused by adsorption of gas and compressive stress. Of extraordinary importance for gas storage for energy applications we find two regimes of Negative gas adsorption (NGA) where gas pressure causes the MOF to transform from the large pore to the narrow pore structure. These transformations can be induced by mechanical compression and conceivably used in an engine to discharge adsorbed gas from the MOF. The elements which govern NGA in MOFs with large pores are identified. Our study may help guide the difficult program of work of computer simulation studies of gas storage in MOFs with large pores

Fuel Production Using Membrane Reactors

The constant increase in population has led to greater fossil fuel consumption, and subsequently a significant increase in greenhouse gases emission to the atmosphere. This presents a serious threat to the environment and impacts climate change to a great extent. Fossil fuel supplies are depleting fast, and the price of these fuels is also increasing due to their heightened demand. The environmental concerns regarding this are the increased emissions of harmful pollutants such as carbon dioxide, sulphur dioxide and hydrocarbons. Here we review the alternative fuel technologies which are currently employed to aid the eradication of the current environmental problems. Most notably, this review will demonstrate how membrane reactors are implemented to improve and intensify the existing renewable fuel production processes. Furthermore, the advantages of membrane reactors when compared to the conventional ones, will be discussed; and the environmental benefits these particular reactors pose will also be highlighted. We will showcase how these membrane reactors have been applied successfully to improve biodiesel, hydrogen and Fischer-Tropsch synthesis processes. The application of membranes aids the increase in the conversion of desired products, whilst shifting the equilibrium of the reaction and reducing undesired by-products. Membrane reactors also overcome immiscibility issues that hinder conventional reactor processes. Moreover, they have also demonstrated a significant reduction in the separation and purification of impurities, as they couple them both in one step. This shows drastic economic and energy requirement reductions in the amount of wastewater treatment associated with conventional fuel production reactor

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.

A Mechanistic Model on Catalyst Deactivation by Coke Formation in a CSTR Reactor

A mechanistic model on catalyst deactivation by coke formation in a continuous stirred tank reactor (CSTR) has been developed in the paper. Catalyst deactivation by coke formation was treated as a surface reaction. Four reaction mechanisms representing coke formation through different routes were proposed. The evolved system of ordinary differential equations (ODEs) was solved numerically using MATLAB. This approach was validated by applying it to the skeletal isomerization of 1-pentene over ferrierite. Simulation results were compared qualitatively to those obtained from the literature. Simulation results indicated that coke formation is an extremely rapid process with fast formation of coke components on the strongest acid sites leading to final coke. The coke deposition is slower at higher residence times resulting in more stable product formation and weaker deactivation. The results obtained from this work revealed that the developed model is indeed able to successfully demonstrate the most essential features of catalyst deactivation by coke formation and are in agreement with the findings in the literature. Future work is aimed to extend the study to different reactors such as a plug flow reactor, in addition to analysis of the reaction system’s sensitivity to variables such as temperature and pressure

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