Geometric approach to Fletcher's ideal penalty function

Original article can be found at: www.springerlink.com Copyright Springer. [Originally produced as UH Technical Report 280, 1993]In this note, we derive a geometric formulation of an ideal penalty function for equality constrained problems. This differentiable penalty function requires no parameter estimation or adjustment, has numerical conditioning similar to that of the target function from which it is constructed, and also has the desirable property that the strict second-order constrained minima of the target function are precisely those strict second-order unconstrained minima of the penalty function which satisfy the constraints. Such a penalty function can be used to establish termination properties for algorithms which avoid ill-conditioned steps. Numerical values for the penalty function and its derivatives can be calculated efficiently using automatic differentiation techniques.Peer reviewe

Interpretation of the angular dependence of the de Haas-van Alphen effect in MgB_2

We present detailed results for the amplitude and field dependence of the de Haas-van Alphen (dHvA) signal arising from the electron-like $\pi$ sheet of Fermi surface in MgB_2. Our data and analysis show that the dip in dHvA amplitude when the field is close to the basal plane is caused by a beat between two very similar dHvA frequencies and not a spin-zero effect as previously assumed. Our results imply that the Stoner enhancement factors in MgB_2 are small on both the Sigma and Pi sheets.Comment: 4 pages with figures. Submitted to PR

Classical noise and flux: the limits of multi-state atom lasers

By direct comparison between experiment and theory, we show how the classical noise on a multi-state atom laser beam increases with increasing flux. The trade off between classical noise and flux is an important consideration in precision interferometric measurement. We use periodic 10 microsecond radio-frequency pulses to couple atoms out of an F=2 87Rb Bose-Einstein condensate. The resulting atom laser beam has suprising structure which is explained using three dimensional simulations of the five state Gross-Pitaevskii equations.Comment: 4 pages, 3 figure

Polyimide processing additives

A process for preparing polyimides having enhanced melt flow properties is described. The process consists of heating a mixture of a high molecular weight poly-(amic acid) or polyimide with a low molecular weight amic acid or imide additive in the range of 0.05 to 15 percent by weight of additive. The polyimide powders so obtained show improved processability, as evidenced by lower melt viscosity by capillary rheometry. Likewise, films prepared from mixtures of polymers with additives show improved processability with earlier onset of stretching by TMA

Dynamics of ripple formation on silicon surfaces by ultrashort laser pulses in sub-ablation conditions

An investigation of ultrashort pulsed laser induced surface modification due to conditions that result in a superheated melted liquid layer and material evaporation are considered. To describe the surface modification occurring after cooling and resolidification of the melted layer and understand the underlying physical fundamental mechanisms, a unified model is presented to account for crater and subwavelength ripple formation based on a synergy of electron excitation and capillary waves solidification. The proposed theoretical framework aims to address the laser-material interaction in sub-ablation conditions and thus minimal mass removal in combination with a hydrodynamics-based scenario of the crater creation and ripple formation following surface irradiation with single and multiple pulses, respectively. The development of the periodic structures is attributed to the interference of the incident wave with a surface plasmon wave. Details of the surface morphology attained are elaborated as a function of the imposed conditions and results are tested against experimental data

A simplified protocol for detecting two systemic bait markers (Rhodamine B and iophenoxic acid) in small mammals

We developed a method of quantifying levels of fluorescence in the whiskers of wild stoats (Mustela erminea) using fluorescence microscopy and Axiovision 3.0.6.1 software. The method allows for discrimination between natural fluorescence present in or on a whisker, and the fluorescence resulting from the ingestion of the systemic marker Rhodamine B (RB), although some visual judgement is still required. We also developed a new high performance liquid chromatography (HPLC) protocol for detecting the systemic marker iophenoxic acid (IPA) in the blood of laboratory rats (Rattus norvegicus) and wild stoats. With this method, the blood of an animal that has consumed IPA can be tested for the presence of the foreign IPA compound itself. This is a more reliable test than the previous method, which measured the raised level of natural blood protein-bound iodine correlated with IPA absorption. The quantity of blood required from animal subjects is very small (10 μl), so the testing is less intrusive and the method can be extended to smaller species. The extraction technique uses methanol, rather than acids and heavy metal salts, thereby simplifying the procedure. Recovery of IPA is quantitative, giving a highly reliable reading. In experiments on captive rats the IPA method proved successful. Of 12 positively marked carcasses, two that had not been frozen for the 24 h before blood samples were taken showed relatively lower IPA levels. The same IPA detection method, as well as the whisker analysis for RB, was applied successfully to a population of wild stoats to which both Rhodamine B and IPA were made available at bait stations. The presence of both bait markers was detectable in rats for at least 21 days and in stoats for at least 27 days

Damping of the de Haas-van Alphen oscillations in the superconducting state of MgB_2

The de Haas-van Alphen (dHvA) signal arising from orbits on the $\pi$ Fermi surface sheet of the two-gap superconductor MgB$_2$ has been observed in the vortex state below $H_{c2}$. An extra attenuation of the dHvA signal, beyond those effects described in the conventional Lifshitz-Kosevich expression, is seen due to the opening of the superconducting gap. Our data show that the $\pi$ band gap is still present up to $H_{c2}$. The data are compared to current theories of dHvA oscillations in the superconducting state which allow us to extract estimates for the evolution of the $\pi$ band gap with magnetic field. Contrary to results for other materials, we find that the most recent theories dramatically underestimate the damping in MgB$_2$.Comment: 10 pages with figures. Submitted to Phys. Rev. B. PDF version with higher quality figures can be found at http://www.phy.bris.ac.uk/research/cond_matt/PdfPubs/mgb2RSdhva.pd

The Physicist's Guide to the Orchestra

An experimental study of strings, woodwinds (organ pipe, flute, clarinet, saxophone and recorder), and the voice was undertaken to illustrate the basic principles of sound production in music instruments. The setup used is simple and consists of common laboratory equipment. Although the canonical examples (standing wave on a string, in an open and closed pipe) are easily reproduced, they fail to explain the majority of the measurements. The reasons for these deviations are outlined and discussed.Comment: 11 pages, 10 figures (jpg files). Submitted to European Journal of Physic