Coexistence of collapse and stable spatiotemporal solitons in multimode fibers

We analyze spatiotemporal solitons in multimode optical fibers and demonstrate the existence of stable solitons, in a sharp contrast to earlier predictions of collapse of multidimensional solitons in three-dimensional media. We discuss the coexistence of blow-up solutions and collapse stabilization by a low-dimensional external potential in graded-index media, and also predict the existence of stable higher-order nonlinear waves such as dipole-mode spatiotemporal solitons. To support the main conclusions of our numerical studies we employ a variational approach and derive analytically the stability criterion for input powers for the collapse stabilization

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

On the speed of fast and slow rupture fronts along frictional interfaces

The transition from stick to slip at a dry frictional interface occurs through the breaking of the junctions between the two contacting surfaces. Typically, interactions between the junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasi-static fronts with speeds proportional to external loading rates, via fronts much slower than the Rayleigh wave speed, and fronts that propagate near the Rayleigh wave speed, to fronts that travel faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic 2D spring--block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that a proportionality between material slip speed and rupture front speed, previously reported for slow fronts, actually holds across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even in homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Lastly, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically-based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.Comment: 29 pages, 21 figure

THE THING Hamburg:A Temporary Democratization of the Local Art Field

THE THING Hamburg was an experimental Internet platform whose vocation was to contribute to the democratization of the art field, to negotiate new forms of art in practice, and to be a site for political learning and engagement. We, the authors, were actively involved in the project on various levels. In this paper, we trace the (local) circumstances that led to the emergence of the project and take a look at its historical precursor, we reflect on the organizational form of this collectively-run and participatory platform, and we investigate the role locality can play in the development of political agency. As a non-profit Internet platform built with free software, the project also invites a reflection of the role technology can play for the creation of independent experimental spaces for social innovation and how they make a difference against the backdrop of corporate social media. Relating the project to both the conceptual innovations of the Russian avant-garde as well as media-utopian projections shows that THE THING Hamburg stands in the tradition of an art that expands its own field by invoking a self-issued social assignment. Challenging the norms and in stitutions of the art field does not remain an exercise in self-referentiality; it rather redefines the role of art as an agent for political learning and how the use of technology in society at large can be emancipatory. And just as small projects like the THE THING Hamburg draw on old utopias for their contemporary negotiations of art, they equally produce more questions than they provide answers

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discretebreathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensionalFermi-Pasta-Ulam lattice is shown to model the charge storedwithin an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extendthe analysis to higher order and find a generalised$(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we findthat the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

Evolution beyond determinism - on Dennett's compatibilism and the too timeless free will debate

Most of the free will debate operates under the assumption that classic determinism and indeterminism are the only metaphysical options available. Through an analysis of Dennett’s view of free will as gradually evolving this article attempts to point to emergentist, interactivist and temporal metaphysical options, which have been left largely unexplored by contemporary theorists. Whereas, Dennett himself holds that “the kind of free will worth wanting” is compatible with classic determinism, I propose that his models of determinism fit poorly with his evolutionary theory and naturalist commitments. In particular, his so-called “intuition pumps” seem to rely on the assumption that reality will have a compositional bottom layer where appearance and reality coincide. I argue that instead of positing this and other “unexplained explainers” we should allow for the heretical possibility that there might not be any absolute bottom, smallest substances or universal laws, but relational interactions all the way down. Through the details of Dennett’s own account of the importance of horizontal transmission in evolution and the causal efficacy of epistemically limited but complex layered “selves,” it is argued that our autonomy is linked to the ability to affect reality by controlling appearances

Re-imagining the growth process: (co)-evolving metaphorical representations of entrepreneurial growth

We investigate the role and influence of the biological metaphor ‘growth’ in studies of organizations, specifically in entrepreneurial settings. We argue that we need to reconsider metaphorical expressions of growth processes in entrepreneurship studies in order to better understand growth in the light of contemporary challenges, such as environmental concerns. Our argument is developed in two stages: first, we review the role of metaphor in organization and entrepreneurship studies. Second, we reflect critically on three conceptualizations of growth that have drawn on biological metaphors: the growing organism, natural selection and co-evolution. We find the metaphor of co-evolution heuristically valuable but under-used and in need of further refinement. We propose three characteristics of the co-evolutionary metaphor that might enrich our understanding of entrepreneurial growth: relational epistemology; collectivity; and multidimensionality. Through this we provide a conceptual means of reconciling an economic impetus for entrepreneurial growth with an environmental imperative for sustainability

In the haze: on narrativization and air pollution in Shanghai

This article explores psychic experiences of air pollution and the ways these experiences have become narrated in various texts, especially but not exclusively those responding to one weekend in December 2013 when Shanghai purportedly experienced the highest levels of fine-particle, or PM2.5, pollution on record. This paper is also concerned, more generally, with processes associated with attempts to transform the messiness, or figurative haze, of fieldwork into an authoritative written account. These dual concerns—with air pollution and writing—are mutually informing since both seem to translate troubling, and often socially unacceptable, emotions into more presentable and tolerable forms. Through narrativization, namely acts of authorship and inscription, persons implicated in this article attempt to relieve, figuratively write over, or otherwise repress anxieties. While it is understandable, and perhaps even normal, to perpetuate such processes, this article argues we should engage rather than erase them since they not only animate persons and texts but also illuminate efforts to understand human responses to air pollution

Towards a classification of continuity and on the emergence of generality

This dissertation has for its primary task the investigation, articulation, and comparison of a variety of concepts of continuity, as developed throughout the history of philosophy and a part of mathematics. It also motivates and aims to better understand some of the conceptual and historical connections between characterizations of the continuous, on the one hand, and ideas and commitments about what makes for generality (and universality), on the other. Many thinkers of the past have acknowledged the need for advanced science and philosophy to pass through the “labyrinth of the continuum” and to develop a sufficiently rich and precise model or description of the continuous; but it has been far less widely appreciated how the resulting description informs our ideas and commitments regarding how (and whether) things become general (or how we think about universality). The introduction provides some motivation for the project and gives some overview of the chapters. The first two chapters are devoted to Aristotle, as Aristotle’s Physics is arguably the foundational book on continuity. The first two chapters show that Aristotle\u27s efforts to understand and formulate a rich and demanding concept of the continuous reached across many of his investigations; in particular, these two chapters aim to better situate certain structural similarities and conceptual overlaps between his Posterior Analytics and his Physics, further revealing connections between the structure of demonstration or proof (the subject of logic and the sciences) and the structure of bodies in motion (the subject of physics and study of nature). This chapter also contributes to the larger narrative about continuity, where Aristotle emerges as one of the more articulate and influential early proponents of an account that aligns continuity with closeness or relations of nearness. Chapter 3 is devoted to Duns Scotus and Nicolas Oresme, and more generally, to the Medieval debate surrounding the “latitude of forms” or the “intension and remission of forms,” in which concerted efforts were made to re-focus attention onto the type of continuous motions mostly ignored by the tradition that followed in the wake of Aristotelian physics. In this context, the traditional appropriation of Aristotle’s thoughts on unity, contrariety, genera, forms, quantity and quality, and continuity is challenged in a number of important ways, reclaiming some of the largely overlooked insights of Aristotle into the intimate connections between continua and genera. By realizing certain of Scotus’s ideas concerning the intension and remission of qualities, Oresme initiates a radical transformation in the concept of continuity, and this chapter argues that Oresme’s efforts are best understood as an early attempt at freeing the concept of continuity from its ancient connection to closeness. Chapters 4 and 5 are devoted to unpacking and re-interpreting Spinoza’s powerful theory of what makes for the ‘oneness’ of a body in general and how ‘ones’ can compose to form ever more composite ‘ones’ (all the way up to Nature as a whole). Much of Spinoza reads like an elaboration on Oresme’s new model of continuity; however, the legacy of the Cartesian emphasis on local motion makes it difficult for Spinoza to give up on closeness altogether. Chapter 4 is dedicated to a closer look at some subtleties and arguments surrounding Descartes’ definition of local motion and ‘one body’, and Chapter 5 builds on this to develop Spinoza’s ideas about how the concept of ‘one body’ scales, in which context a number of far-reaching connections between continuity and generality are also unpacked. Chapter 6 leaves the realm of philosophy and is dedicated to the contributions to the continuitygenerality connection from one field of contemporary mathematics: sheaf theory (and, more generally, category theory). The aim of this chapter is to present something like a “tour” of the main philosophical contributions made by the idea of a sheaf to the specification of the concept of continuity (with particular regard for its connections to universality). The concluding chapter steps back and discusses a number of distinct characterizations of continuity in more abstract and synthetic terms, while touching on some of the corresponding representations of generality to which each such model gives rise. This chapter ends with a brief discussion of some of the arguments that have been deployed in the past to claim that continuity (or discreteness) is “better.

Gaps: When Not Even Nothing Is There

A paradox, it is claimed, is a radical form of contradiction, one that produces gaps in meaning. In order to approach this idea, two senses of “separation” are distinguished: separation by something and separation by nothing. The latter does not refer to nothing in an ordinary sense, however, since in that sense what’s intended is actually less than nothing. Numerous ordinary nothings in philosophy as well as in other fields are surveyed so as to clarify the contrast. Then follows the suggestion that philosophies which one would expect to have room for paradoxes actually tend either to exclude them altogether or to dull them. There is a clear alternative, however, one that fully recognizes paradoxes and yet also strives to overcome them