Periodic Orbits and Escapes in Dynamical Systems

We study the periodic orbits and the escapes in two different dynamical systems, namely (1) a classical system of two coupled oscillators, and (2) the Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a general relativistic system). We find their simple periodic orbits, their characteristics and their stability. Then we find their ordered and chaotic domains. As the energy goes beyond the escape energy, most chaotic orbits escape. In the first case we consider escapes to infinity, while in the second case we emphasize escapes to the central "bumpy" black hole. When the energy reaches its escape value a particular family of periodic orbits reaches an infinite period and then the family disappears (the orbit escapes). As this family approaches termination it undergoes an infinity of equal period and double period bifurcations at transitions from stability to instability and vice versa. The bifurcating families continue to exist beyond the escape energy. We study the forms of the phase space for various energies, and the statistics of the chaotic and escaping orbits. The proportion of these orbits increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical Astronomy

A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems

By combining a standard symmetric, symplectic integrator with a new step size controller, we provide an integration scheme that is symmetric, reversible and conserves the values of the constants of motion. This new scheme is appropriate for long term numerical integrations of geodesic orbits in spacetime backgrounds, whose corresponding Hamiltonian system is non-integrable, and, in general, for any non-integrable Hamiltonian system whose kinetic part depends on the position variables. We show by numerical examples that the new integrator is faster and more accurate i) than the standard symplectic integration schemes with or without standard adaptive step size controllers and ii) than an adaptive step Runge-Kutta scheme.Comment: 12 pages, 8 figures, 3 table

The concept of solidarity: emerging from the theoretical shadows?

The concept of solidarity has been relatively neglected by social scientists since Durkheim's pioneering work in the late 19th century. The discipline of politics has been guilty of overlooking this 'subjective' element of community life, but recent works by Stjernø and Brunkhorst reflect a growing awareness of the theoretical significance of the concept. Whereas early liberal attempts to theorise solidarity took the nation state to be the appropriate community for its realisation, the emergence of globalisation raises the possibility of human solidarity developing in the global community. Traditional forms of solidarity have been dissipated by the social changes accompanying globalisation, but they were often locked into the defence of particular interests. New forms may be emerging to rekindle the broader vision of human solidarity. Recent work by writers such as Habermas, Honneth, Rorty and Touraine focuses on widening and deepening democratic participation and/or the articulation of our ethical obligations in various ways. It is argued here that these perspectives need to be supplemented by a radical humanist approach grounded in a normative theory of human self-realisation

Making Sense of Family Deaths in Urban Senegal: Diversities, Contexts, and Comparisons

Despite calls for cross-cultural research, Minority world perspectives still dominate death and bereavement studies, emphasizing individualized emotions and neglecting contextual diversities. In research concerned with contemporary African societies, on the other hand, death and loss are generally subsumed within concerns about AIDS or poverty, with little attention paid to the emotional and personal significance of a death. Here, we draw on interactionist sociology to present major themes from a qualitative study of family deaths in urban Senegal, theoretically framed through the duality of meanings-in-context. Such themes included family and community as support and motivation; religious beliefs and practices as frameworks for solace and (regulatory) meaning; and material circumstances as these are intrinsically bound up with emotions. Although we identify the experience of (embodied, emotional) pain as a common response across Minority and Majority worlds, we also explore significant divergencies, varying according to localized contexts and broader power dynamics

The Pseudosquares Prime Sieve

We present the pseudosquares prime sieve, which finds all primes up to n

Stability analysis and quasinormal modes of Reissner Nordstr{\o}m Space-time via Lyapunov exponent

We explicitly derive the proper time $(\tau)$ principal Lyapunov exponent ($\lambda_{p}$) and coordinate time ($t$) principal Lyapunov exponent ($\lambda_{c}$) for Reissner Nordstr{\o}m (RN) black hole (BH) . We also compute their ratio. For RN space-time, it is shown that the ratio is $\frac{\lambda_{p}}{\lambda_{c}}=\frac{r_{0}}{\sqrt{r_{0}^2-3Mr_{0}+2Q^2}}$ for time-like circular geodesics and for Schwarzschild BH it is $\frac{\lambda_{p}}{\lambda_{c}}=\frac{\sqrt{r_{0}}}{\sqrt{r_{0}-3M}}$. We further show that their ratio $\frac{\lambda_{p}}{\lambda_{c}}$ may vary from orbit to orbit. For instance, Schwarzschild BH at innermost stable circular orbit(ISCO), the ratio is $\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{ISCO}=6M}=\sqrt{2}$ and at marginally bound circular orbit (MBCO) the ratio is calculated to be $\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{mb}=4M}=2$. Similarly, for extremal RN BH the ratio at ISCO is $\frac{\lambda_{p}}{\lambda_{c}}\mid_{r_{ISCO}=4M}=\frac{2\sqrt{2}}{\sqrt{3}}$. We also further analyse the geodesic stability via this exponent. By evaluating the Lyapunov exponent, it is shown that in the eikonal limit , the real and imaginary parts of the quasi-normal modes of RN BH is given by the frequency and instability time scale of the unstable null circular geodesics.Comment: Accepted in Pramana, 07/09/201

The Paradox of Power in CSR: A Case Study on Implementation

Purpose Although current literature assumes positive outcomes for stakeholders resulting from an increase in power associated with CSR, this research suggests that this increase can lead to conflict within organizations, resulting in almost complete inactivity on CSR. Methods A single in-depth case study, focusing on power as an embedded concept. Results Empirical evidence is used to demonstrate how some actors use CSR to improve their own positions within an organization. Resource dependence theory is used to highlight why this may be a more significant concern for CSR. Conclusions Increasing power for CSR has the potential to offer actors associated with it increased personal power, and thus can attract opportunistic actors with little interest in realizing the benefits of CSR for the company and its stakeholders. Thus power can be an impediment to furthering CSR strategy and activities at the individual and organizational level

Application of Newtonian physics to predict the speed of a gravity racer

Gravity racing can be studied using numerical solutions to the equations of motion derived from Newton’s second law. This allows students to explore the physics of gravity racing and to understand how design and course selection influences vehicle speed. Using Euler’s method, we have developed a spreadsheet application that can be used to predict the speed of a gravity powered vehicle. The application includes the effects of air and rolling resistance. Examples of the use of the application for designing a gravity racer are presented and discussed. Predicted speeds are compared to the results of an official world record attempt

Legal origin and social solidarity: the continued relevance of Durkheim to comparative institutional analysis

By using the classic works of Durkheim as a theoretical platform, this research explores the relationship between legal systems and social solidarity. We found that certain types of civil law system, most notably those of Scandinavia, are associated with higher levels of social capital and better welfare state provision. However, we found the relationship between legal system and societal outcomes is considerably more complex than suggested by currently fashionable economistic legal origin approaches, and more in line with the later writings of Durkheim, and, indeed, the literature on comparative capitalisms. Relative communitarianism was strongly affected by relative development, reflecting the complex relationship between institutions, state capabilities and informal social ties and networks

Knowledge politics and new converging technologies: a social epistemological perspective

The “new converging technologies” refers to the prospect of advancing the human condition by the integrated study and application of nanotechnology, biotechnology, information technology and the cognitive sciences - or “NBIC”. In recent years, it has loomed large, albeit with somewhat different emphases, in national science policy agendas throughout the world. This article considers the political and intellectual sources - both historical and contemporary - of the converging technologies agenda. Underlying it is a fluid conception of humanity that is captured by the ethically challenging notion of “enhancing evolution”