Reducing or enhancing chaos using periodic orbits

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method

The sound of violets: the ethnographic potency of poetry?

This paper takes the form of a dialogue between the two authors, and is in two halves, the first half discursive and propositional, and the second half exemplifying the rhetorical, epistemological and metaphysical affordances of poetry in critically scrutinising the rhetoric, epistemology and metaphysics of educational management discourse. Phipps and Saunders explore, through ideas and poems, how poetry can interrupt and/or illuminate dominant values in education and in educational research methods, such as: • alternatives to the military metaphors – targets, strategies and the like – that dominate the soundscape of education; • the kinds and qualities of the cognitive and feeling spaces that might be opened up by the shifting of methodological boundaries; • the considerable work done in ethnography on the use of the poetic: anthropologists have long used poetry as a medium for expressing their sense of empathic connection to their field and their subjects, particularly in considering the creativity and meaning-making that characterise all human societies in different ways; • the particular rhetorical affordances of poetry, as a discipline, as a practice, as an art, as patterned breath; its capacity to shift phonemic, and therewith methodological, authority; its offering of redress to linear and reductive attempts at scripting social life, as always already given and without alternative

Mode-locked Bloch oscillations in a ring cavity

We present a new technique for stabilizing and monitoring Bloch oscillations of ultracold atoms in an optical lattice under the action of a constant external force. In the proposed scheme, the atoms also interact with a unidirectionally pumped optical ring cavity whose one arm is collinear with the optical lattice. For weak collective coupling, Bloch oscillations dominate over the collective atomic recoil lasing instability and develop a synchronized regime in which the atoms periodically exchange momentum with the cavity field.Comment: 7 pages, 5 figure

The Function of Bachelardian Epistemology in the Post-colonial Project of Mohammed ‘Abed al-Jabri

This paper explores the function of historical epistemology in the thought of Gaston Bachelard (1884–1962) and Mohammed ‘Abed al-Jabri (1935–2010). Attributing thought with a particular function challenges our tendency to explain the development of thought in other socio-historical contexts in terms of mere conceptual influence. Available English-language literature on al-Jabri commonly references Bachelard’s concept of epistemological rupture as a source of inspiration. Though the reference is astute, this term remains poorly understood and has long been overshadowed by Thomas Kuhn’s notion of ‘paradigm shift’. The broader function of Bachelard’s thought as a renegotiation of time, place, subject, and reason in the natural sciences has been largely neglected in historiographies of the philosophy of science outside of France. This paper emphasizes the level of insight and ingenuity with which al-Jabri employs the function of Bachelard’s epistemology by re-interpreting it within the framework of his own socio-historical context. Far from reducing al-Jabri’s thought to a mere programmatic reproduction of French thought, I suggest that al-Jabri was among the most astute interpreters of this long-misunderstood theorist

Targeted mixing in an array of alternating vortices

Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as effective transport barriers, while triggering chaotic advection. In this setting, mixing within the two dynamical barriers is enhanced while long range transport is prevented. A numerical analysis of mixing properties depending on parameter values is performed; regions for which optimal mixing is achieved are proposed. Robustness of the targeted mixing properties regarding errors in the applied perturbation are considered, as well as slip/no-slip boundary conditions for the flow

Experimental perspectives for systems based on long-range interactions

The possibility of observing phenomena peculiar to long-range interactions, and more specifically in the so-called Quasi-Stationary State (QSS) regime is investigated within the framework of two devices, namely the Free-Electron Laser (FEL) and the Collective Atomic Recoil Laser (CARL). The QSS dynamics has been mostly studied using the Hamiltonian Mean-Field (HMF) toy model, demonstrating in particular the presence of first versus second order phase transitions from magnetized to unmagnetized regimes in the case of HMF. Here, we give evidence of the strong connections between the HMF model and the dynamics of the two mentioned devices, and we discuss the perspectives to observe some specific QSS features experimentally. In particular, a dynamical analog of the phase transition is present in the FEL and in the CARL in its conservative regime. Regarding the dissipative CARL, a formal link is established with the HMF model. For both FEL and CARL, calculations are performed with reference to existing experimental devices, namely the FERMI@Elettra FEL under construction at Sincrotrone Trieste (Italy) and the CARL system at LENS in Florence (Italy)

Chaos in free electron laser oscillators

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.Comment: Accepted in EPJ

Phase transitions of quasistationary states in the Hamiltonian Mean Field model

The out-of-equilibrium dynamics of the Hamiltonian Mean Field (HMF) model is studied in presence of an externally imposed magnetic field h. Lynden-Bell's theory of violent relaxation is revisited and shown to adequately capture the system dynamics, as revealed by direct Vlasov based numerical simulations in the limit of vanishing field. This includes the existence of an out-of-equilibrium phase transition separating magnetized and non magnetized phases. We also monitor the fluctuations in time of the magnetization, which allows us to elaborate on the choice of the correct order parameter when challenging the performance of Lynden-Bell's theory. The presence of the field h removes the phase transition, as it happens at equilibrium. Moreover, regions with negative susceptibility are numerically found to occur, in agreement with the predictions of the theory.Comment: 6 pages, 7 figure

Bodily relations and reciprocity in the art of Sonia Khurana

This article explores the significance of the ‘somatic’ and ‘ontological turn’ in locating the radical politics articulated in the contemporary performance, installation, video and digital art practices of New Delhi-based artist, Sonia Khurana (b. 1968). Since the late 1990s Khurana has fashioned a range of artworks that require new sorts of reciprocal and embodied relations with their viewers. While this line of art practice suggests the need for a primarily philosophical mode of inquiry into an art of the body, such affective relations need to be historicised also in relation to a discursive field of ‘difference’ and public expectations about the artist’s ethnic, gendered and national identity. Thus, this intimate, visceral and emotional field of inter- and intra-action is a novel contribution to recent transdisciplinary perspectives on the gendered, social and sentient body, that in turn prompts a wider debate on the ethics of cultural commentary and art historiography