Optical design of a freeform TIR lens for LED streetlight

Secondary optics is a critical component determining the output efficiency and light distribution of the LED streetlight. A good roadway illumination requires the LED streetlight have a rectangular light pattern just cover the roadway and without excess spill light creeping into yards and shining into windows of neighbor residents. The adoption of the unsymmetrical freeform optics with different light distributions along X and Y directions is necessary. The whole LED streetlight can be constructed if only mounts these LED modules on the planar PCB plate. The mechanism, thermal management, and the power control electronics of the LED streetlight become very simple. In this paper, an optical design approach of a freeform TIR (total internal reflection) lens for the LED streetlight is investigated. With these freeform lenses, high output efficiency, even light distribution, and batwing far field beam angle distribution can be achieved.     

CW laser-induced fluorescence of toluene for time-resolved imaging of gaseous flows

A laser-induced fluorescence diagnostic is presented for high-speed measurements in gaseous flows. The technique employs a toluene tracer excited at 266 nm by a cavity-doubled 532 nm diode-pumped 5.5 W CW laser. The high power (600 mW) of UV light produced by cavity doubling, together with the high fluorescence yield of toluene, yields strong signal levels needed for high-speed recording. Fluctuation detection limits for tracer mole fraction were investigated by applying the diagnostic to an atmospheric temperature and pressure nitrogen jet. For single-point measurements with a photomultiplier tube, the detection limit for fluctuations in the toluene mole fraction was 0.028%, achieved with 430 mW of laser power and 8.5 kHz bandwidth for a 1×0.4×0.4 mm collection volume. Line (1-D) imaging with a kinetic-readout camera (512 pixels/row) achieved a detection limit of 0.23% with 440 mW of laser power, 9.7 kHz frame rate, and 0.3×0.2×0.4 mm collection volume per pixel, while planar (2-D) imaging with a 512×512 pixel intensified camera achieved a detection limit of 0.88% with 205 mW of laser power, 100 μs exposure time, and 0.4×0.4×0.4 mm volume per pixel. Line and planar imaging were applied to a turbulent jet with Re of about 10000.     

Recursive methods for a multi-dimensional risk process with common shocks

In this paper, a multi-dimensional risk model with common shocks is studied. Using a simple probabilistic approach via observing the risk processes at claim instants, recursive integral formulas are developed for the survival probabilities as well as for a class of Gerber-Shiu expected discounted penalty functions that include the surplus levels at ruin. Under the assumption of exponential or mixed Erlang claims, the recursive integrals can be simplified to give recursive sums which are computationally more tractable. Numerical examples including an optimal capital allocation problem are also given towards the end.     

Determination of fluorescence and non-radiative de-excitation rates of excited 3-pentanone at low pressures

3-Pentanone photophysics measurements and subsequent fluorescence quantum yield (FQY) model development are presented. A heated, flowing optical cell and laser excitation at 248, 266, 277, and 308 nm were utilized, allowing investigation of FQY and absorption cross-section values for 3-pentanone vapor from 298 to 690 K and 10 to 30 mbar. Measurements of FQY were also made for 20 mbar of 3-pentanone at 1.3 bar total pressure in nitrogen from 298 to 530 K and in air from 298 to 487 K. Absolute FQY was determined by calibration to Rayleigh scattering of nitrogen gas. Based on these FQY measurements and fluorescence lifetime data from previous work, the fluorescence rate k _f was determined to be 3.70×10⁵ s⁻¹. The current work extends knowledge of the non-radiative rate k _nr to vibrational energies of 15000 cm⁻¹, and the expression for k _nr was optimized to include a fit to these new data points. Finally, variation of FQY with 3-pentanone vapor pressure was used to optimize the vibrational relaxation cascade parameter α _3p . The updated FQY model for 3-pentanone vapor shows agreement within 8% to the current FQY data across the investigated range of temperatures and pressures.     

Full-field technique for measuring the spectral evolution of reconfigurable photonic filters

This Letter demonstrates a measurement technique based on frequency-to-time mapping and coherent detection, which enables the complete (i.e., amplitude and phase) characterization of dynamically reconfigurable photonic filters. We apply this technique to a unit cell from a silicon CMOS-compatible photonic lattice filter that has a rapidly changing transfer function with an 8.33 ns update time, 120 MHz spectral resolution, and 12 GHz bandwidth. These dynamic measurements allow characterization of transients, thermal effects, filter fidelity, and other time-dependent phenomena during switching.     

Two-parameter homotopy method for nonlinear equations

We introduce a second auxiliary parameter into the zero-order deformation equation and propose a generalization of the homotopy analysis method. This includes the derivation of a general solution in terms of the Bell polynomials for nonlinear equations. Numerical examples show that the proposed zero-order deformation equation improves the convergence region and rate of the series solution and allows greater freedom in the selection of auxiliary operators. This facilitates the development of a homotopy iteration scheme for nonlinear equations with discontinuous or zero derivatives that are not amenable to Newton-type iteration schemes. The homotopy iteration scheme represents a generalization of conventional iteration schemes and additional examples demonstrate its applicability for a wider range of nonlinear problems.     

Service constrained inventory models with random lifetimes and lead times

We consider continuous review inventory models with Poisson demands, exponentially distributed lifetimes and replenishment order processing times. The model is unique in that complete backorders, complete lost sales and partial backorders are all addressed. We derive exact expressions of the key operating characteristics. Based on these performance measures, we optimise the system parameters subject to fill rate and waiting time constraints. Numerical examples are also provided to validate our models and to generate useful managerial insights.     

Franck-Condon factors and r-centroids for the B2Σ-X2Σ systems of HgCl,HgBr, and HgI

Available spectroscopic data have been analyzed and used for calculations of Franck-Condon Factors and r-centroids for B²Σ-X²Σ bands of HgCl³⁵, HgCl³⁷, HgBr⁷⁹, HgBr⁸¹, and HgI.     

A novel electronic-hyperfine perturbation in the C4Σ− state of VO

The hyperfine structure of the level N = 37, $\text{J = 38}\text{1}\text{2}$ in the C⁴Σ^?, v = 0 state of VO is anomalous as a result of an electronic perturbation. Because of the high nuclear spin of ⁵¹V ($\text{I =}\text{7}\text{2}$), the hyperfine pattern has a sufficient number of lines that it can be analyzed in detail just as if it were a rotational branch fragment containing an avoided crossing. It is shown how the coefficient of F(F + 1) in the hyperfine energy expression for the perturbing state and the perturbation matrix element can be obtained very accurately, though because the nature of the perturbing state is unknown it has not been possible to interpret the coefficient in terms of conventional hyperfine parameters in this case. The conditions for the appearance of perturbations of this type and the results to be obtained from them are discussed.