Digital Materiality of the Internet-of-Things

date-added: 2015-01-19 04:14:58 +0000 date-modified: 2015-04-01 06:51:10 +0000date-added: 2015-01-19 04:14:58 +0000 date-modified: 2015-04-01 06:51:10 +0000This work was supported by the Arts and Humanities Research Council, CreativeWorks London Hub, grant AH/J005142/1, and the European Regional Development Fund, London Creative and Digital Fusion

Energy thresholds for discrete breathers

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. An important issue, not only from a theoretical point of view but also for their experimental detection, are their energy properties. We considerably enlarge the scenario of possible energy properties presented by Flach, Kladko, and MacKay [Phys. Rev. Lett. 78, 1207 (1997)]. Breather energies have a positive lower bound if the lattice dimension is greater than or equal to a certain critical value d_c. We show that d_c can generically be greater than two for a large class of Hamiltonian systems. Furthermore, examples are provided for systems where discrete breathers exist but do not emerge from the bifurcation of a band edge plane wave. Some of these systems support breathers of arbitrarily low energy in any spatial dimension.Comment: 4 pages, 4 figure

The nature and evolution of the highly ionized near-zones in the absorption spectra of z~6 quasars

We use state-of-the-art hydrodynamical simulations combined with a 1D radiative transfer code to assess the extent to which the highly ionized regions observed close to z~6 quasars, which we refer to as near-zones, can constrain the ionization state of the surrounding IGM. We find the appearance in Lya absorption of a quasar HII ionization front expanding into a neutral IGM can be very similar to a classical proximity zone, produced by the enhancement in ionizing flux close to a quasar embedded in a highly ionized IGM. The observed sizes of these highly ionized near-zones and their redshift evolution can be reproduced for a wide range of IGM neutral hydrogen fractions for plausible values of the luminosity and lifetime of the quasars. The observed near-zone sizes at the highest observed redshifts are equally consistent with a significantly neutral and a highly ionized surrounding IGM. Stronger constraints on the IGM neutral hydrogen fraction can be obtained by considering the relative size of the near-zones in the Lya and Lyb regions of a quasar spectrum. A large sample of high quality quasar absorption spectra with accurate determinations of near-zone sizes and their redshift evolution in both the Lya and Lyb regions should confirm or exclude the possibility that the Universe is predominantly neutral at the highest observed redshifts. The width of the discrete absorption features in these near-zones will contain important additional information on the ionization state and the previous thermal history of the IGM at these redshifts.Comment: 25 pages, 11 figures, accepted for publication in MNRA

On the rapid demise of Lyman-alpha emitters at z>7 due to the increasing incidence of optically thick absorption systems

A variety of independent observational studies have now reported a significant decline in the fraction of Lyman-break galaxies which exhibit Ly-a emission over the redshift interval z=6-7. In combination with the strong damping wing extending redward of Ly-a in the spectrum of the bright z=7.085 quasar ULAS 1120+0641, this has strengthened suggestions that the hydrogen in the intergalactic medium (IGM) is still substantially neutral at z~7. Current theoretical models imply HI fractions as large as 40-90 per cent may be required to explain these data assuming there is no intrinsic evolution in the Ly-a emitter population. We propose that such large neutral fractions are not necessary. Based on a hydrodynamical simulation which reproduces the absorption spectra of high-redshift (z~6-7) quasars, we demonstrate that the opacity of the intervening IGM redward of rest-frame Ly-a can rise rapidly in average regions of the Universe simply because of the increasing incidence of absorption systems which are optically thick to Lyman continuum photons as the tail-end of reionisation is approached. Our simulations suggest these data do not require a large change in the IGM neutral fraction by several tens of per cent from z=6-7, but may instead be indicative of the rapid decrease in the typical mean free path for ionising photons expected during the final stages of reionisation.Comment: 11 pages, 6 figures, accepted to MNRA

The emergence of environmental homeostasis in complex ecosystems

The Earth, with its core-driven magnetic field, convective mantle, mobile lid tectonics, oceans of liquid water, dynamic climate and abundant life is arguably the most complex system in the known universe. This system has exhibited stability in the sense of, bar a number of notable exceptions, surface temperature remaining within the bounds required for liquid water and so a significant biosphere. Explanations for this range from anthropic principles in which the Earth was essentially lucky, to homeostatic Gaia in which the abiotic and biotic components of the Earth system self-organise into homeostatic states that are robust to a wide range of external perturbations. Here we present results from a conceptual model that demonstrates the emergence of homeostasis as a consequence of the feedback loop operating between life and its environment. Formulating the model in terms of Gaussian processes allows the development of novel computational methods in order to provide solutions. We find that the stability of this system will typically increase then remain constant with an increase in biological diversity and that the number of attractors within the phase space exponentially increases with the number of environmental variables while the probability of the system being in an attractor that lies within prescribed boundaries decreases approximately linearly. We argue that the cybernetic concept of rein control provides insights into how this model system, and potentially any system that is comprised of biological to environmental feedback loops, self-organises into homeostatic states

In search of Robbins stability

We speculate on whether a certain p-adic stability phenomenon, observed by David Robbins empirically for Dodgson condensation, appears in other nonlinear recurrence relations that "unexpectedly" produce integer or nearly-integer sequences. We exhibit an example (number friezes) where this phenomenon provably occurs.Comment: 10 pages; to appear in the David Robbins memorial issue of Advances in Applied Mathematic

The observed ionization rate of the intergalactic medium and the ionizing emissivity at z >5: Evidence for a photon starved and extended epoch of reionization

We use a large set of hydrodynamical simulations, combined with measurements of the Lyman alpha opacity of the IGM taken from the literature, to obtain robust estimates for the photoionization rate per hydrogen atom at z=5 and 6. We find the photoionization rate drops by a factor of two and four, respectively, compared to our recent measurements at z = 2 - 4. The number of ionizing photons emitted by known sources at z=5 and 6, based on an extrapolation of source numbers below the detection limit and standard assumptions for the relationship between the ionizing emissivity and observed luminosity density at 1500 Angstroms, are in reasonable agreement with the photoionization rates inferred from the Lyman alpha forest if the escape fraction of ionizing photons from galaxies is large (>= 20 per cent). Claims to the contrary may be attributed to the adoption of an unduly high value for the clumping factor of ionized hydrogen. Using physically motivated assumptions for the mean free path of ionizing photons our measurements of the photoionization rate can be turned into an estimate of the ionizing emissivity. In comoving units the inferred ionizing emissivity is nearly constant over the redshift range 2-6 and corresponds to 1.5-3 photons emitted per hydrogen atom over a time interval corresponding to the age of the Universe at z=6. This strongly suggests that the epoch of reionization was photon-starved and extended. [Abridged]Comment: 20 pages, 9 figures, accepted for publication in MNRA

A closer look at using quasar near-zones as a probe of neutral hydrogen in the intergalactic medium

We examine a large set of synthetic quasar spectra to realistically assess the potential of using the relative sizes of highly ionized near-zones in the Lya and Lyb forest as a probe of the neutral hydrogen content of the intergalactic medium (IGM) at z>6. The scatter in the relative near-zone size distribution, induced by underlying fluctuations in the baryonic density field and the filtering of ionizing radiation, is considerable even for fixed assumptions about the IGM neutral fraction. As a consequence, the current observational data cannot distinguish between an IGM which is significantly neutral or highly ionized just above z=6. Under standard assumptions for quasar ages and ionizing luminosities, a future sample of several tens of high resolution Lya and Lyb near-zone spectra should be capable of distinguishing between a volume weighted neutral hydrogen fraction in the IGM which is greater or less than 10 per cent.Comment: 6 pages, 3 figures, accepted for publication in MNRAS letter

Tipping points in complex coupled life-environment systems

Simple models of complex phenomena provide powerful insights and suggest low-level mechanistic descriptions. The Earth system arises from the interaction of subsystems with multi-scale temporal and spatial variability; from the microbial to continental scales, operating over the course of days to geological time. System-level homeostasis has been demonstrated in a number of conceptual, artificial life, models which share the advantage of a thorough and transparent analysis. We reintroduce a general model for a coupled life-environment model, concentrating on a minimal set of assumptions, and explore the consequences of interaction between simple life elements and their shared, multidimensional environment. In particular stability, criticality and transitions are of great relevance to understanding the history, and future of the Earth system. The model is shown to share salient features with other abstract systems such as Ashby's Homeostat and Watson and Lovelock's Daisyworld. Our generic description is free to explore high-dimensional, complex environments, and in doing so we show that even a small increase in the environmental complexity gives rise to very complex attractor landscapes which require a much richer conception of critical transitions and hysteresi