Subpicosecond pulse generation in synchronously pumped and hybrid ring dye lasers

Subpicosecond pulse generation has been examined in synchronously pumped mode-locked ring dye laser systems. These include hybrid and composite absorber/gain media arrangements as well as a simple synchronous cavity. The shortest pulses recorded were 0.3 ps for the hybrid system, and this has been shown to be critically dependent on the positioning of the absorber jet in the centre of the cavity to better than 50 m. Stable operation for subpicosecond pulse generation has been achieved in the ring configuration with greater wavelength tunability and higher average power conversion efficiency than with conventional cavity arrangements.     

Hypernuclear fine structure in (9)(lambda)Be

With a germanium detector array (Hyperball), we observed two gamma-ray peaks corresponding to the two transitions (5/2(+)-->1/2(+) and 3/2(+)-->1/2(+)) in the (9)(Lambda)Be hypernucleus which was produced by the 9Be(K-,pi(-)) reaction. The energies of the gamma rays are 3029 +/- 2 +/- 1 keV and 3060 +/- 2 +/- 1 keV. The energy difference was measured to be 31.4(+2.5)(-3.6) keV, which indicates a very small Lambda-spin-dependent spin-orbit force between a Lambda and a nucleon. This is the smallest level splitting by far ever measured in a hypernucleus.     

A Functional Equation Whose Unknown is \mathcal{P}([0,1]) Valued

We study a functional equation whose unknown maps a Euclidean space into the space of probability distributions on [0,1]. We prove existence and uniqueness of its solution under suitable regularity and boundary conditions, we show that it depends continuously on the boundary datum, and we characterize solutions that are diffuse on [0,1]. A canonical solution is obtained by means of a Randomly Reinforced Urn with different reinforcement distributions having equal means. The general solution to the functional equation defines a new parametric collection of distributions on [0,1] generalizing the Beta family.     

A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

Numerical schemes using piecewise polynomial approximation are very popular for high order discretization of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Difference scheme has often been found attractive as well, because of its simplicity of formulation and implementation. However, recently it has been shown that the scheme is not linearly stable on triangles. In this paper we present an alternate formulation of the scheme, featuring a new flux interpolation technique using Raviart–Thomas spaces, which proves stable under a similar linear analysis in which the standard scheme failed. We demonstrate viability of the concept by showing linear stability both in the semi-discrete sense and for time stepping schemes of the SSP Runge–Kutta type. Furthermore, we present convergence studies, as well as case studies in compressible flow simulation using the Euler equations.     

Stable Algebraic Topology and Stable Topological Algebra

Algebraic topology is a young subject, and its foundations arenot yet firmly in place. I shall give some history, examplesand modern developments in that part of the subject called stablealgebraic topology, or stable homotopy theory. This is by farthe most calculationally accessible part of algebraic topology,although it is also the least intuitively grounded in visualizablegeometric objects. It has a great many applications to othersubjects such as algebraic geometry and geometric topology.Time will not allow me to say as much as I would like aboutthat. Rather, I shall emphasize some foundational issues thathave been central to this part of algebraic topology since theearly 1960s, but that have been satisfactorily resolved onlyin the last few years. 1991 Mathematics Subject Classification55P42, 55N20.     

Students’ conceptual understanding of a function and its derivative in an experimental calculus course

Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its derivative as viewed by students of a reformed Calculus 1 course offered in two experimental sections at the Lebanese American University in Beirut, Lebanon. Results have shown that the general approach adopted in the course proved to be unpopular for a great majority of the students, but rewarding for others. Interviews conducted with some students and a study of their performance on very specific exam questions reveal that for most students, the algebraic representation of a function still dominated their thinking; however, these students showed an almost complete understanding of the derivative, particularly the idea of the instantaneous rate of change and/or the slope of a curve at a given point. Furthermore, very few of these students referred to the mechanical methods for finding derivatives.     

Experimental characterization of bi-directional terahertz emission from gold-coated nanogratings

The THz radiation emission of Au-coated nanogratings (fused silica substrate, 30?nm Au layer thickness, 500?nm grating constant) upon fs laser irradiation (785?nm, 150?fs, 1?kHz,???1?mJ/pulse) is observed in both directions along the laser beam axis (forward and backward) and for both, illumination of the Au/air or the Au/silica interface. THz radiation along the laser beam propagation is emitted in a narrow solid angle of about 15°?fwhm independent on the laser pulse fluence, the angle of incidence and the nanograting profile. The bar width and groove depth of the nanograting as well as the angle of laser beam incidence strongly affect the THz radiation yield. The energy of single THz light pulses is measured absolutely (2?fJ in the 0.3?C0.38?THz range) using a highly sensitive and fast superconducting transition edge sensor. The bi-directional emission of THz radiation is in agreement with the model assumption of surface plasmon polaritons propagating simultaneously on both Au layer interfaces (Au/air and Au/silica).     

Fast‐Track,One‐Step E. coli Detection: A Miniaturized Hydrogel Array Permits Specific Direct PCR and DNA Hybridization while Amplification

A timesaving and convenient method for bacterial detection based on one‐step, one‐tube deoxyribonucleic acid (DNA) hybridization on hydrogel array while target gene amplification is described. The hydrogel array is generated by a fast one‐pot synthesis, where N,N′‐dimethylacrylamide/polyethyleneglycol(PEG₁₉₀₀)‐bisacrylamide mixture polymerizes via radical photoinitiation by visible light within 20 min concomitant with in situ capture probe immobilization. These DNA‐functionalized hydrogel droplets arrayed on a planar glass surface are placed in the polymerase chain reaction (PCR) mixture during the thermal amplification cycles. The bacterial cells can be implemented in a direct PCR reaction, omitting the need for prior template DNA extraction. The resulting fluorescence signal is immediately detectable after the end of the PCR (1 h) following one short washing step by microscopy. Therefore a valid signal can be reached within 1.5 h including 10 min for pipetting and placement of the tubes and chips. The performance of this novel hydrogel DNA array was successfully proven with varying cell numbers down to a limit of 10¹Escherichia coli cells.

     

Self-trapping of the N-H vibrational mode in alpha-helical polypeptides

Recent calculations on the formation of self-trapped amide group vibrational states in alpha-helical polypeptides [J. Chem. Phys. 124, 134907 (2006)] are extended to the amide N-H normal mode vibrations. First, the adiabatic N-H vibrational single- and two-exciton states are examined by treating the longitudinal chain coordinates as parameters. Then, in using the multiconfiguration time-dependent Hartree method coupled exciton-chain vibrational quantum dynamics are accounted for. Based on the respective exciton-chain vibrational wave function propagation the infrared transient absorption related to a sequential pump-probe experiment is calculated. The modulation of local amide vibrational energies by the longitudinal chain coordinates is found to have a pronounced effect on the broadening of absorption lines. Moreover, the ultrafast exciton transfer in the system is studied in order to characterize the dynamics of the self-trapped single-exciton states on a time scale below 10 ps.