Exploring a rheonomic system

A simple and illustrative rheonomic system is explored in the Lagrangian formalism. The difference between Jacobi's integral and energy is highlighted. A sharp contrast with remarks found in the literature is pointed out. The non-conservative system possess a Lagrangian not explicitly dependent on time and consequently there is a Jacobi's integral. The Lagrange undetermined multiplier method is used as a complement to obtain a few interesting conclusion

Ricci Solitons and Einstein-Scalar Field Theory

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to associate to each static Ricci flat spacetime a local Ricci soliton in one higher dimension. As well, solutions of Euclidean-signature Einstein gravity coupled to a free massless scalar field with nonzero cosmological constant are associated to shrinking or expanding Ricci solitons. We exhibit examples, including an explicit family of complete expanding solitons which can be thought of as a Ricci flow for a complete Lorentzian metric. The possible generalization to Ricci-flat stationary metrics leads us to consider an alternative to Ricci flow.Comment: 17 pages, 1 figure; Revised version (organizational changes, other minor revisions and corrections, citations corrected and added), to appear in CQ

Context Mining of Sedentary Behavior for Promoting Self-Awareness Using Smartphone

Sedentary behaviour is increasing due to societal changes and is related to prolonged periods of sitting. There is sufficient evidence proving that sedentary behaviour has a negative impact on people’s health and wellness. This paper presents our research findings on how to mine the temporal contexts of sedentary behaviour by utilizing the on-board sensors of a smartphone. We use the accelerometer sensor of the smartphone to recognize user situations (i.e., still or active). If our model confirms that the user context is still, then there is a high probability of being sedentary. Then, we process the environmental sound to recognize the micro-context, such as working on a computer or watching television during leisure time. Our goal is to reduce sedentary behaviour by suggesting preventive interventions to take short breaks during prolonged sitting to be more active. We achieve this goal by providing the visualization to the user, who wants to monitor his/her sedentary behaviour to reduce unhealthy routines for self-management purposes. The main contribution of this paper is two-fold: (i) an initial implementation of the proposed framework supporting real-time context identification; (ii) testing and evaluation of the framework, which suggest that our application is capable of substantially reducing sedentary behaviour and assisting users to be active

Componential coding in the condition monitoring of electrical machines Part 2: application to a conventional machine and a novel machine

This paper (Part 2) presents the practical application of componential coding, the principles of which were described in the accompanying Part 1 paper. Four major issues are addressed, including optimization of the neural network, assessment of the anomaly detection results, development of diagnostic approaches (based on the reconstruction error) and also benchmarking of componential coding with other techniques (including waveform measures, Fourier-based signal reconstruction and principal component analysis). This is achieved by applying componential coding to the data monitored from both a conventional induction motor and from a novel transverse flux motor. The results reveal that machine condition monitoring using componential coding is not only capable of detecting and then diagnosing anomalies but it also outperforms other conventional techniques in that it is able to separate very small and localized anomalies

Velocity autocorrelation function of a Brownian particle

In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [6] and an approximate result combining the predictions from hydrodynamics at short and long times. The physical quantities which determine the decay were determined from separate bulk simulations of the Lennard-Jones fluid at the same thermodynamic state point.We observe that the long-time regime of the VACF compares well the predictions from the macroscopic hydrodynamics, but the intermediate decay is sensitive to the viscoelastic nature of the solvent.Comment: 7 pages, 6 figure

Actions of the braid group, and new algebraic proofs of results of Dehornoy and Larue

This article surveys many standard results about the braid group with emphasis on simplifying the usual algebraic proofs. We use van der Waerden's trick to illuminate the Artin-Magnus proof of the classic presentation of the algebraic mapping-class group of a punctured disc. We give a simple, new proof of the Dehornoy-Larue braid-group trichotomy, and, hence, recover the Dehornoy right-ordering of the braid group. We then turn to the Birman-Hilden theorem concerning braid-group actions on free products of cyclic groups, and the consequences derived by Perron-Vannier, and the connections with the Wada representations. We recall the very simple Crisp-Paris proof of the Birman-Hilden theorem that uses the Larue-Shpilrain technique. Studying ends of free groups permits a deeper understanding of the braid group; this gives us a generalization of the Birman-Hilden theorem. Studying Jordan curves in the punctured disc permits a still deeper understanding of the braid group; this gave Larue, in his PhD thesis, correspondingly deeper results, and, in an appendix, we recall the essence of Larue's thesis, giving simpler combinatorial proofs.Comment: 51`pages, 13 figure

Manifolds with 1/4-pinched flag curvature

We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao

Threshold effects in excited charmed baryon decays

Motivated by recent results on charmed baryons from CLEO and FOCUS, we reexamine the couplings of the orbitally excited charmed baryons. Due to its proximity to the [Sigma_c pi] threshold, the strong decays of the Lambda_c(2593) are sensitive to finite width effects. This distorts the shape of the invariant mass spectrum in Lambda_{c1}-> Lambda_c pi^+pi^- from a simple Breit-Wigner resonance, which has implications for the experimental extraction of the Lambda_c(2593) mass and couplings. We perform a fit to unpublished CLEO data which gives M(Lambda_c(2593)) - M(Lambda_c) = 305.6 +- 0.3 MeV and h2^2 = 0.24^{+0.23}_{-0.11}, with h2 the Lambda_{c1}-> Sigma_c pi strong coupling in the chiral Lagrangian. We also comment on the new orbitally excited states recently observed by CLEO.Comment: 9 pages, 3 figure

T helper cell polarisation as a measure of the maturation of the immune response.

BACKGROUND: T helper cell polarisation is important under chronic immune stimulatory conditions and drives the type of the evolving immune response. Mice treated with superantigens in vivo display strong effects on Th subset differentiation. The aim of the study was to detect the intrinsic capacity of T cells to polarise under various ex vivo conditions. METHODS: Purified CD4+ T cells obtained from super-antigen-treated mice were cultured under Th polarising conditions in vitro. By combining intracellular cytokine staining and subsequent flow cytometric analysis with quantitative cytokine measurements in culture supernatants by enzyme-linked immunosorbent assay (ELISA), the differential Th polarising capacity of the treatment can be detected in a qualitative and quantitative manner. RESULTS AND CONCLUSIONS: BALB/c mice were shown to be biased to develop strong Th2 polarised immune responses using Th0 stimulation of purified CD4+ T cells from phosphate-buffered saline-treated mice. Nevertheless, our analysis methodology convincingly showed that even in these mice, Toxic Shock Syndrome Toxin-1 treatment in vivo resulted in a significantly stronger Th1 polarising effect than control treatment. Our results indicate that populations of Th cells can be assessed individually for their differential Th1 or Th2 maturation capacity in vivo by analysing robust in vitro polarisation cultures combined with intracellular cytokine staining and ELISA