A second-sound based, hyperbolic SIR model for high-diffusivity spread

We present an analytical study of one-dimensional (1D) kinematic wave phenomena under a hyperbolic SIR model based not on Fick's diffusion law, but rather on the inertial-type II flux law of second-sound theory. Unlike in the Ficken context, we are able to derive exact traveling wave solutions (TWS)s, as well as explicit asymptotic/approximate expressions, for both the susceptibles and infectives. We also determine, using singular surface theory, how shock-fronts resulting from initial jump discontinuities propagate and evolve under this model. In particular, critical values and special cases are examined and possible mitigation methods, which take the form of parameter-value manipulation(s), are noted.     

Global approximations to the principal real-valued branch of the Lambert W-function

W(z) is defined implicitly as the root of W exp(W) = z. It is shown that a simple analytic approximation has a relative error of less than 5% over the whole domain z ε [−exp(−1), ∞] of the principle branch—sufficiently accurate so that four Newton iterations refine this approximation to a relative error smaller than 1.E-12. As a second form of global approximation, the W-function is expanded as a series of rational Chebyshev functions TB_j in a shifted, logarithmic coordinate with an error that decreases exponentially fast with the series truncation.     

Combining linear polarization spectroscopy and the Representative Layer Theory to measure the Beer–Lambert law absorbance of highly scattering materials

Visible and Near Infrared (Vis–NIR) Spectroscopy is a powerful non destructive analytical method used to analyze major compounds in bulk materials and products and requiring no sample preparation. It is widely used in routine analysis and also in-line in industries, in-vivo with biomedical applications or in-field for agricultural and environmental applications. However, highly scattering samples subvert Beer–Lambert law's linear relationship between spectral absorbance and the concentrations. Instead of spectral pre-processing, which is commonly used by Vis–NIR spectroscopists to mitigate the scattering effect, we put forward an optical method, based on Polarized Light Spectroscopy to improve the absorbance signal measurement on highly scattering samples. This method selects part of the signal which is less impacted by scattering. The resulted signal is combined in the Absorption/Remission function defined in Dahm's Representative Layer Theory to compute an absorbance signal fulfilling Beer–Lambert's law, i.e. being linearly related to concentration of the chemicals composing the sample. The underpinning theories have been experimentally evaluated on scattering samples in liquid form and in powdered form. The method produced more accurate spectra and the Pearson's coefficient assessing the linearity between the absorbance spectra and the concentration of the added dye improved from 0.94 to 0.99 for liquid samples and 0.84–0.97 for powdered samples.     

J.-H. Lambert’s theory of probable syllogisms

In his Neues Organon of 1764, the mathematician and astronomer Jean-Henri Lambert [12] developed a theory of probable syllogisms, with the aim of formally describing the probabilist reasoning and then applying it to the probability of testimony, thus imparting an epistemic sense to the concept of probability. In the present text, we propose to study the principles of this theory and the difficulties it raises.     

Regression-based model of skin diffuse reflectance for skin color analysis

A simple regression-based model of skin diffuse reflectance is developed based on reflectance samples calculated by Monte Carlo simulation of light transport in a two-layered skin model. This reflectance model includes the values of spectral reflectance in the visible spectra for Japanese women. The modified Lambert Beer law holds in the proposed model with a modified mean free path length in non-linear density space. The averaged RMS and maximum errors of the proposed model were 1.1 and 3.1%, respectively, in the above range.     

Development of the parametric tolerance modeling and optimization schemes and cost-effective solutions

Most of previous research on tolerance optimization seeks the optimal tolerance allocation with process parameters such as fixed process mean and variance. This research, however, differs from the previous studies in two ways. First, an integrated optimization scheme is proposed to determine both the optimal settings of those process parameters and the optimal tolerance simultaneously which is called a parametric tolerance optimization problem in this paper. Second, most tolerance optimization models require rigorous optimization processes using numerical methods, since closed-form solutions are rarely found. This paper shows how the Lambert W function, which is often used in physics, can be applied efficiently to this parametric tolerance optimization problem. By using the Lambert W function, one can express the optimal solutions to the parametric tolerance optimization problem in a closed-form without resorting to numerical methods. For verification purposes, numerical examples for three cases are conducted and sensitivity analyses are performed.     

Illumination technique based on integrating sphere with an unequal radius, hyper-uniform luminance and large-field angle

In order to meet the measurement requirements of image sensors’ uniformity of the CCD system with a large-field angle, the design for the form and structure of the integrating sphere, with 600–800 mm and hyper-uniform luminance double hemisphere is presented. LightTools software is used for simulation. The simulation result indicates that the compact structure of the integrating sphere with asymmetric double hemisphere renders both the design values and systematic performance parameters superior to those of the common integrating sphere. The integrating sphere system designed is manufactured and its optical parameters are tested. The test result indicates that at the outlet of the integrating sphere, the variation of illuminance is less than 2.3%, and the variation of luminance on the inner surface is less than 4.4%. Hence, it is concluded that this system can be widely utilized in measuring image sensors’ uniformity of the photoelectric imaging system with a large-field angle.     

Prompt isothermal decay of thermoluminescence in MgB4O7:Dy,Na and LiB4O7:Cu,In dosimeters

According to standard delocalized kinetic models of thermoluminescence (TL), when an irradiated sample is held at a high temperature T, the isothermal TL signal will decay with a characteristic thermal decay constant λ which depends strongly on the temperature T. This prediction of standard delocalized kinetic theory is investigated in this paper by studying two TL dosimeters, MgB₄O₇:Dy, Na and LiB₄O₇:Cu, In (hereafter MBO and LBO correspondingly). In the case of LBO it was found that the thermal decay constant λ of the main dosimetric TL peak follows exactly the predictions of standard delocalized kinetic theory. Furthermore, the thermal activation energy of the main peak evaluated by the isothermal decay method is in full agreement with values obtained from initial rise and glow curve fitting methods. However, in the case of MBO it was found that the thermal decay constant λ varies little with the isothermal decay temperature T. In order to explain these unusual results for MBO, the TL glow curves and isothermal decay curves were analyzed using analytical expressions derived recently from a radiative tunneling recombination model. Based on the different behavior of the two TL dosimeters, it is suggested that the isothermal decay of TL at high temperatures can be used to discriminate between radiative delocalized recombination and radiative localized recombination processes.     

大视场CCD成像系统像面均匀性测试技术研究

以光度学为理论基础,研究了大视场CCD成像系统像面均匀性测试技术。论述了600~800mm非对称、双半球不等半径积分球的设计方案。对像面均匀性测试系统的积分球出口进行了测试,出口处的照度不均匀性不高于2.3%,照度不稳定性不高于2.7%,积分球后半球内表面的亮度不均匀性不高于4.4%。在对测试结果进行误差分析的基础上,对大视场CCD摄像机进行了实际测试。结果表明,该装置可广泛应用于光电成像系统的像面均匀性测量。     

Shock and traveling wave phenomena on an externally damped, non-linear string

We examine the propagation of shocks and traveling wave phenomena on a one-dimensional string that is executing finite-amplitude, transverse vibrations in a resisting medium. As part of our study, we develop an approach that allows us to describe, albeit approximately, the evolution and propagation of a shock front using analytical methods. In addition, exact traveling wave solutions, one of which involves the Lambert W-function, of the string's equation of motion are determined and analyzed. Lastly, a possible new form of the solution to the linearized problem is presented and extensions and other applications of the present work are briefly discussed.