Invariant metrics and Hamiltonian Systems

Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of them and finally find commuting functions under the corresponding Lie-Poisson bracketComment: 16 pages corrected typos, changed contents (Prop. 3.4 and Theorem in Section 3

BEAMS Lab at MIT: Status report

The Biological Engineering Accelerator Mass Spectrometry (BEAMS) Lab at the Massachusetts Institute of Technology is a facility dedicated to incorporating AMS into life sciences research. As such, it is focused exclusively on radiocarbon and tritium AMS and makes use of a particularly compact instrument of a size compatible with most laboratory space. Recent developments at the BEAMS Lab were aimed to improve different stages of the measurement process, such as the carbon sample injection interface, the simultaneous detection of tritium and hydrogen and finally, the overall operation of the system. Upgrades and results of those efforts are presented here.United States. National Institutes of Health (grant P30-ES02109)United States. National Institutes of Health (grant R42-CA084688)National Institutes of Health. National Center for Research Resources (grant UL1 RR 025005)GlaxoSmithKlin

Linear stability of planar premixed flames: reactive Navier-Stokes equations with finite activation energy and arbitrary Lewis number

A numerical shooting method for performing linear stability analyses of travelling waves is described and applied to the problem of freely propagating planar premixed flames. Previous linear stability analyses of premixed flames either employ high activation temperature asymptotics or have been performed numerically with finite activation temperature, but either for unit Lewis numbers (which ignores thermal-diffusive effects) or in the limit of small heat release (which ignores hydrodynamic effects). In this paper the full reactive Navier-Stokes equations are used with arbitrary values of the parameters (activation temperature, Lewis number, heat of reaction, Prandtl number), for which both thermal-diffusive and hydrodynamic effects on the instability, and their interactions, are taken into account. Comparisons are made with previous asymptotic and numerical results. For Lewis numbers very close to or above unity, for which hydrodynamic effects caused by thermal expansion are the dominant destablizing mechanism, it is shown that slowly varying flame analyses give qualitatively good but quantitatively poor predictions, and also that the stability is insensitive to the activation temperature. However, for Lewis numbers sufficiently below unity for which thermal-diffusive effects play a major role, the stability of the flame becomes very sensitive to the activation temperature. Indeed, unphysically high activation temperatures are required for the high activation temperature analysis to give quantitatively good predictions at such low Lewis numbers. It is also shown that state-insensitive viscosity has a small destabilizing effect on the cellular instability at low Lewis numbers

Nonlinear equation for curved stationary flames

A nonlinear equation describing curved stationary flames with arbitrary gas expansion $\theta = \rho_{{\rm fuel}}/\rho_{{\rm burnt}}$, subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for $\theta \to 1,$ the new equation gives the true solution to the problem of stationary flame propagation with the accuracy of the sixth order in $\theta - 1.$ In particular, it reproduces the stationary version of the well-known Sivashinsky equation at the second order corresponding to the approximation of zero vorticity production. At higher orders, the new equation describes influence of the vorticity drift behind the flame front on the front structure. Its asymptotic expansion is carried out explicitly, and the resulting equation is solved analytically at the third order. For arbitrary values of $\theta,$ the highly nonlinear regime of fast flow burning is investigated, for which case a large flame velocity expansion of the nonlinear equation is proposed.Comment: 29 pages 4 figures LaTe

Stable Mode Sorting by Two-Dimensional Parity of Photonic Transverse Spatial States

We describe a mode sorter for two-dimensional parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. Both Hermite-Gauss (HG) and Laguerre-Gauss (LG) modes can be guided into one of two output ports according to the two-dimensional parity of the mode in question. Our interferometer sorts HG_nm input modes depending upon whether they have even or odd order n+m; it equivalently sorts LG modes depending upon whether they have an even or odd value of their orbital angular momentum. It functions efficiently at the single-photon level, and therefore can be used to sort single-photon states. Due to the inherent phase stability of this type of interferometer as compared to those of the Mach-Zehnder type, it provides a promising tool for the manipulation and filtering of higher order transverse spatial modes for the purposes of quantum information processing. For example, several similar Sagnacs cascaded together may allow, for the first time, a stable measurement of the orbital angular momentum of a true single-photon state. Furthermore, as an alternative to well-known holographic techniques, one can use the Sagnac in conjunction with a multi-mode fiber as a spatial mode filter, which can be used to produce spatial-mode entangled Bell states and heralded single photons in arbitrary first-order (n+m=1) spatial states, covering the entire Poincare sphere of first-order transverse modes.Comment: 11 pages, 12 figures, 2 appendice

Cochlear neuropathy and the coding of supra-threshold sound

Many listeners with hearing thresholds within the clinically normal range nonetheless complain of difficulty hearing in everyday settings and understanding speech in noise. Converging evidence from human and animal studies points to one potential source of such difficulties: differences in the fidelity with which supra-threshold sound is encoded in the early portions of the auditory pathway. Measures of auditory subcortical steady-state responses (SSSRs) in humans and animals support the idea that the temporal precision of the early auditory representation can be poor even when hearing thresholds are normal. In humans with normal hearing thresholds (NHTs), paradigms that require listeners to make use of the detailed spectro-temporal structure of supra-threshold sound, such as selective attention and discrimination of frequency modulation (FM), reveal individual differences that correlate with subcortical temporal coding precision. Animal studies show that noise exposure and aging can cause a loss of a large percentage of auditory nerve fibers (ANFs) without any significant change in measured audiograms. Here, we argue that cochlear neuropathy may reduce encoding precision of supra-threshold sound, and that this manifests both behaviorally and in SSSRs in humans. Furthermore, recent studies suggest that noise-induced neuropathy may be selective for higher-threshold, lower-spontaneous-rate nerve fibers. Based on our hypothesis, we suggest some approaches that may yield particularly sensitive, objective measures of supra-threshold coding deficits that arise due to neuropathy. Finally, we comment on the potential clinical significance of these ideas and identify areas for future investigation

Ultrasound-guided core-needle biopsy of breast lesions

Ultrasound-guided CNB has proven to be a reliable technique for performing a biopsy for breast lesions that can be clearly seen on ultrasoun

Understanding Anthropological Understanding: for a merological anthropology

In this paper I argue for a merological anthropology in which ideas of ‘partiality’ and ‘practical adequacy’ provide a way out of the impasse of relativism which is implied by post-modernism and the related abandonment of a concern with ‘truth’. Ideas such as ‘aptness’ and ‘faithfulness’ enable us to re-establish empirical foundations without having to espouse a simple realism which has been rightly criticised. Ideas taken from ethnomethodology, particularly the way we bootstrap from ‘practical adequacy’ to ‘warrants for confidence’ point to a merological anthropology in which we recognize that we do not and cannot know everything, but that we can have reasons for being confident in the little we know