Moduli for principal bundles over algebraic curves: I

We classify principal bundles on a compact Riemann surface. A moduli space for semistable principal bundles with a reductive structure group is constructed using Mumford's geometric invarian theory.     

The applicability of an approximate expression for radiative heating

An analysis considering small departures from radiative equilibrium within a gas, for which radiative heating is approximately formulated in terms of a radiative response time, is compared with an exact solution. It is shown that the approximate formulation does not properly describe local departures from radiative equilibrium, although it is useful in a spatially averaged context.     

Electrochemical impedance spectroscopic studies of copper dissolution in glycine–hydrogen peroxide solutions

Anodic dissolution of copper in glycine solution at various hydrogen peroxide concentrations was investigated. The dissolution rate increases, reaches a maximum, and then decreases with hydrogen peroxide concentration. Anodic polarization studies and electrochemical impedance spectroscopy (EIS) studies were carried out to determine the mechanistic pathway of anodic dissolution of copper in glycine system at three different hydrogen peroxide concentrations: one at low hydrogen peroxide concentration in the active dissolution region, another in the maximum dissolution region, and the third at the high hydrogen peroxide concentration in the post-peak-dissolution region. The EIS data in complex plane plots show presence of two capacitance loops and one negative capacitance loop. The impedance plot patterns strongly depend on the hydrogen peroxide concentration in solution. Reaction mechanism analysis technique was employed to model the EIS data. A three-step mechanism with two intermediate adsorbates and a parallel dissolution by catalytic mechanism simulates EIS patterns which match the experimental trends. The intermediates are likely to be cupric and cuprous oxides. The essential features of impedance spectra at various overpotentials at three different hydrogen peroxide concentrations are captured by the proposed mechanism. The results also show that the film present on the copper surface in glycine and hydrogen peroxide solutions does not passivate the surface.     

Effect of finite chemical potential on QGP-Hadron phase transition in a statistical model of fireball formation

We study the effect of finite chemical potential for the QGP constituents in the Ramanathan et al. statistical model [Phys. Rev. C70, 027903, (2004)]. While the earlier computations using this model with vanishing chemical potentials indicated a weakly first order phase transition for the system in the vicinity of 170 MeV [Pramana 68 757 (2007)], the introduction of finite values for the chemical potentials of the constituents makes the transition a smooth roll over of the phases, while allowing fireball formation with radius of a few ‘fermi’ to take place. This seems to be in conformity with the latest consensus on the nature of the QGP-Hadron phase transition.     

Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link

We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.     

Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood

We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility of the result. We have also shown that our argument can be extended to the m-tuple conjecture of Hardy and Littlewood.     

Measurement of Large Dipolar Couplings of a Liquid Crystal with Terminal Phenyl Rings and Estimation of the Order Parameters

NMR spectroscopy is a powerful means of studying liquid‐crystalline systems at atomic resolutions. Of the many parameters that can provide information on the dynamics and order of the systems, ¹H–¹³C dipolar couplings are an important means of obtaining such information. Depending on the details of the molecular structure and the magnitude of the order parameters, the dipolar couplings can vary over a wide range of values. Thus the method employed to estimate the dipolar couplings should be capable of estimating both large and small dipolar couplings at the same time. For this purpose, we consider here a two‐dimensional NMR experiment that works similar to the insensitive nuclei enhanced by polarization transfer (INEPT) experiment in solution. With the incorporation of a modification proposed earlier for experiments with low radio frequency power, the scheme is observed to enable a wide range of dipolar couplings to be estimated at the same time. We utilized this approach to obtain dipolar couplings in a liquid crystal with phenyl rings attached to either end of the molecule, and estimated its local order parameters.     

Alternating Current Electrohydrodynamics Induced Nanoshearing and Fluid Micromixing for Specific Capture of Cancer Cells

We report a new tuneable alternating current (ac) electrohydrodynamics (ac‐EHD) force referred to as “nanoshearing” which involves fluid flow generated within a few nanometers of an electrode surface. This force can be externally tuned via manipulating the applied ac‐EHD field strength. The ability to manipulate ac‐EHD induced forces and concomitant fluid micromixing can enhance fluid transport within the capture domain of the channel (e.g., transport of analytes and hence increase target–sensor interactions). This also provides a new capability to preferentially select strongly bound analytes over nonspecifically bound cells and molecules. To demonstrate the utility and versatility of nanoshearing phenomenon to specifically capture cancer cells, we present proof‐of‐concept data in lysed blood using two microfluidic devices containing a long array of asymmetric planar electrode pairs. Under the optimal experimental conditions, we achieved high capture efficiency (e.g., approximately 90 %; % RSD=2, n=3) with a 10‐fold reduction in nonspecific adsorption of non‐target cells for the detection of whole cells expressing Human Epidermal Growth Factor Receptor 2 (HER2). We believe that our ac‐EHD devices and the use of tuneable nanoshearing phenomenon may find relevance in a wide variety of biological and medical applications.     

Studies on oxygen chemical surface exchange and electrical conduction in thin film nanostructured titania at high temperatures and varying oxygen pressure

We report on oxygen surface exchange studies in ～450-nm-thick nanocrystalline titania films with an average grain size of ～13 nm by electrical conductivity relaxation along with the conductivity measurements at varying temperatures and oxygen partial pressures (pO(2)s). By electrochemical impedance spectroscopy technique, the high temperature conductivity was measured in the pO(2) range from ～10(-16) to ～10(-6) Pa at temperatures from 973 to 1223 K and activation energy, ΔE(a), for conduction was estimated as ～3.23 eV at pO(2) ～10(-11) Pa. Under reducing atmosphere (pO(2) < 10(-6) Pa), two distinct n-type conduction regimes were observed and corresponding predominant defects are discussed while, at high pO(2) regime (pO(2) >10(-6) Pa), ionic conduction appears dominant leading to a conductivity plateau. The surface relaxation was observed to have two independent time constants likely originating from microstructural effects. The surface exchange coefficients are measured as ～10(-8)-10(-7) m∕s and ～10(-9)-10(-8) m∕s for each contribution with ΔE(a)s of 2.79 and 1.82 eV, respectively, without much pO(2) dependence across several orders of pO(2) range of ～10(-16)-10(-6) Pa in the temperature range between 973 and 1223 K. The results are of potential relevance to understanding the near-surface chemical phenomena in nanocrystalline titania which is of great interest for energy and environmental studies.