Invariant Variation Problems

The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of Lie's group theory. For special groups and problems in variation, this combination of methods is not new; I may cite Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker), Weyl and Klein for special infinite groups. Especially Klein's second Note and the present developments have been mutually influenced by each other, in which regard I may refer to the concluding remarks of Klein's Note.Comment: M. A. Tavel's English translation of Noether's Theorems (1918), reproduced by Frank Y. Wang. Thanks to Lloyd Kannenberg for corrigend

Nonadiabatic Electronic Interactions In The Ion-Pair States Of NelCl

Nonadiabatic interactions in the NeIC1 van der Waals complex have been explored in the lowest energy triad of IC1 ion-pair states (approximately 39 000 cm-1). Dispersed fluorescence measurements reveal emission characteristic of multiple ion-pair electronic states, with the relative contributions from the E(O+ ), beta(1), and D\u27(2) states changing with the initial IC1 vibrational excitation (v(IC1)). Emission directly from NeIC1 (v(IC1) = O) complexes indicates that the initially prepared NeIC1 levels have mixed electronic character and that the IC1 electronic parentage changes with the initial van der Waals vibrational level selected. NeIC1 complexes prepared with 1-4 quanta of IC1 stretch undergo rapid vibrational predissociation with a strong propensity for DELTA-V(IC1) = - 1 relaxation. The electronic state(s) populated in the IC1 fragments differ from the mixed electronic character of the initially prepared level, demonstrating that vibrational predissociation is accompanied by nonadiabatic electronic state changing processes. The observed final state selectivity may be attributed to the relative strength of the nonadiabatic couplings between the initial NeIC1 bound state and the final IC1 states or a momentum gap rationale based on the overlap between the NeIC1 bound state wave function and the highly oscillatory continuum wave function of the separating fragments

Infrared reflection nebulae in Orion molecular cloud 2

New obervations of Orion Molecular Cloud-2 have been made from 1-100 microns using the NASA Infrared Telescope Facility and the Kuiper Airborne Observatory. An extensive program of polarimetry, photometry and spectrophotometry has shown that the extended emission regions associated with two of the previously known near infrared sources, IRS1 and IRS4, are infrared reflection nebulae, and that the compact sources IRS1 and IRS4 are the main luminosity sources in the cloud. The constraints from the far infrared observations and an analysis of the scattered light from the IRS1 nebula show that OMC-2/IRS1 can be characterized by L less than or equal to 500 Solar luminosities and T approx. 1000 K. The near infrared (1-5) micron albedo of the grains in the IRS1 nebula is greater than 0.08

Standard model and supersymmetric flavor puzzles at the CERN large hadron collider

Can the Large Hadron Collider explain the masses and mixings of the known fermions? A promising possibility is that these masses and mixings are determined by flavor symmetries that also govern new particles that will appear at the LHC. We consider well-motivated examples in supersymmetry with both gravity- and gauge-mediation. Contrary to spreading belief, new physics need not be minimally flavor violating. We build non-minimally flavor violating models that successfully explain all known lepton masses and mixings, but span a wide range in their predictions for slepton flavor violation. In natural and favorable cases, these models have metastable sleptons and are characterized by fully reconstructible events. We outline many flavor measurements that are then possible and describe their prospects for resolving both the standard model and new physics flavor puzzles at the Large Hadron Collider

rf linewidth reduction in a quantum dot passively mode-locked laser subject to external optical feedback

International audienceThe effect of external optical feedback on an InAs/GaAs quantum dot passively mode-locked laser is investigated. The rf linewidth narrows from 8 KHz in the free-running situation to a value as low as 350 Hz under relatively low feedback. The rf linewidth characterization under resonant feedback at a multiple of the laser cavity length validates the prediction of a previous numerical simulation. It is also confirmed that the integrated rms timing jitter varies as the square root of the rf linewidth. The results are promising for the development of compact, monolithic semiconductor mode-locked lasers as low noise optoelectronic oscillators

An evaluation of metal removal during wastewater treatment: The potential to achieve more stringent final effluent standards

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2011 Taylor & Francis.Metals are of particular importance in relation to water quality, and concern regarding the impact of these contaminants on biodiversity is being encapsulated within the latest water-related legislation such as the Water Framework Directive in Europe and criteria revisions to the Clean Water Act in the United States. This review undertakes an evaluation of the potential of 2-stage wastewater treatment consisting of primary sedimentation and biological treatment in the form of activated sludge processes, to meet more stringent discharge consents that are likely to be introduced as a consequence. The legislation, sources of metals, and mechanisms responsible for their removal are discussed, to elucidate possible pathways by which the performance of conventional processes may be optimized or enhanced. Improvements in effluent quality, achievable by reducing concentrations of suspended solids or biochemical oxygen demand, may also reduce metal concentrations although meeting possible requirements for the removal of copper my be challenging

Optical feedback instabilities in a monolithic InAs/GaAs quantum dot passively mode-locked laser

International audienceThe impact of optical feedback on the direct performance of a monolithic InAs/GaAs quantum dot passively mode-locked laser intended for applications such as multigigahertz interchip/intrachip clock distribution is experimentally investigated. Evaluation of the feedback resistance is an important feature, as the laser is to be monolithically integrated on chip with other devices, in which case optical isolation is difficult. This work shows that a feedback level on the order of −24 dB is detrimental for mode-locking operation, enhancing noise in the rf electrical signal, strongly narrowing the useful mode-locking region as well as causing central frequency shift, and severe instabilities