Dynamics of a linear beam with an attached local nonlinear energy sink

We provide numerical evidence of passive and broadband targeted energy transfer from a linear flexible beam under shock excitation to a local essentially nonlinear lightweight attachment that acts, in essence, as nonlinear energy sink—NES. It is shown that the NES absorbs shock energy in a one-way, irreversible fashion and dissipates this energy locally, without 'spreading' it back to the linear beam. Moreover, we show numerically that an appropriately designed and placed NES can passively absorb and locally dissipate a major portion of the shock energy of the beam, up to an optimal value of 87%. The implementation of the NES concept to the shock isolation of practical engineering structures and to other applications is discussed

Loop algebras, gauge invariants and a new completely integrable system

One fruitful motivating principle of much research on the family of integrable systems known as ``Toda lattices'' has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the nonperiodic Toda lattice in a finite-dimensional Lie algebra. This paper shows that the analogy is not perfect. A discrepancy arises because the natural generalization of the structure theory of finite-dimensional simple Lie algebras is not the structure theory of loop algebras but the structure theory of affine Kac-Moody algebras. In this paper we use this natural generalization to construct the natural analog of the nonperiodic Toda lattice. Surprisingly, the result is not the periodic Toda lattice but a new completely integrable system on the periodic Toda lattice phase space. This integrable system is prescribed purely in terms of Lie-theoretic data. The commuting functions are precisely the gauge-invariant functions one obtains by viewing elements of the loop algebra as connections on a bundle over $S^1$

Tracking Human Behavioural Consistency by Analysing Periodicity of Household Water Consumption

People are living longer than ever due to advances in healthcare, and this has prompted many healthcare providers to look towards remote patient care as a means to meet the needs of the future. It is now a priority to enable people to reside in their own homes rather than in overburdened facilities whenever possible. The increasing maturity of IoT technologies and the falling costs of connected sensors has made the deployment of remote healthcare at scale an increasingly attractive prospect. In this work we demonstrate that we can measure the consistency and regularity of the behaviour of a household using sensor readings generated from interaction with the home environment. We show that we can track changes in this behaviour regularity longitudinally and detect changes that may be related to significant life events or trends that may be medically significant. We achieve this using periodicity analysis on water usage readings sampled from the main household water meter every 15 minutes for over 8 months. We utilise an IoT Application Enablement Platform in conjunction with low cost LoRa-enabled sensors and a Low Power Wide Area Network in order to validate a data collection methodology that could be deployed at large scale in future. We envision the statistical methods described here being applied to data streams from the homes of elderly and at-risk groups, both as a means of early illness detection and for monitoring the well-being of those with known illnesses.Comment: 2019 2nd International Conference on Sensors, Signal and Image Processin

Self-force via a Green's function decomposition

The gravitational field of a particle of small mass \mu moving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(\mu). One part is an inhomogeneous field which, near the particle, looks like the \mu/r field distorted by the local Riemann tensor; it does not depend on the behavior of the source in either the infinite past or future. The other part is a homogeneous field and includes the ``tail term''; it completely determines the self force effects of the particle interacting with its own gravitational field, including radiation reaction. Self force effects for scalar, electromagnetic and gravitational fields are all described in this manner.Comment: PRD, in press. Enhanced emphasis on the equivalence principl

Uncovering CDM halo substructure with tidal streams

Models for the formation and growth of structure in a cold dark matter dominated universe predict that galaxy halos should contain significant substructure. Studies of the Milky Way, however, have yet to identify the expected few hundred sub-halos with masses greater than about 10^6 Msun. Here we propose a test for the presence of sub-halos in the halos of galaxies. We show that the structure of the tidal tails of ancient globular clusters is very sensitive to heating by repeated close encounters with the massive dark sub-halos. We discuss the detection of such an effect in the context of the next generation of astrometric missions, and conclude that it should be easily detectable with the GAIA dataset. The finding of a single extended cold stellar stream from a globular cluster would support alternative theories, such as self-interacting dark matter, that give rise to smoother halos.Comment: 7 pages, 7 figures, submitted to MNRA