Optimization of non-cylindrical domains for the exact null controllability of the 1D wave equation

This work is concerned with the null controllability of the one-dimensional wave equation over non-cylindrical distributed domains. The controllability in that case has been obtained by Castro, C\^indea and M\"unch in SIAM J. Control Optim., 52 (2014) for domains satisfying the usual geometric optic condition. We analyze the problem of optimizing the non-cylindrical support $q$ of the control of minimal $L^2(q)$-norm. In this respect, we prove a uniform observability inequality for a class of domains $q$ satisfying the geometric optic condition. The proof based on the d'Alembert formula relies on arguments from graph theory. Numerical experiments are discussed and highlight the influence of the initial condition on the optimal domains.

The characteristics of laser scattered by droplets

Droplets are the primary factors which influence laser transmitting in bad weather. This paper researches the analytic expression of droplets influencing the laser, which is based on the geometric optic theory and distribution of raindrop size and shape. In this paper, the relationship between the incidence and emergence angle of droplets is discussed. The effects of an individual raindrop on Ladar divergence angle, illuminance and optical path difference are investigated, and then the cumulated influence of a large quantity of raindrops is analyzed. The illuminance of scanning the targets and laser radar received by the detector is presented.

From Geometric-Optical Remote Sensing Modeling to Quantitative Remote Sensing Science—In Memory of Academician Xiaowen Li

The academician Xiaowen Li devoted much of his life to pursuing fundamental research in remote sensing. A pioneer in the geometric-optical modeling of vegetation canopies, his work is held in high regard by the international remote sensing community. He codeveloped the Li–Strahler geometric-optic model, and this paper was selected by a member of the International Society for Optical Engineering (SPIE) milestone series. As a chief scientist, Xiaowen Li led a scientific team that made outstanding advances in bidirectional reflectance distribution modeling, directional thermal emission modeling, comprehensive experiments, and the understanding of spatial and temporal scale effects in remote sensing information, and of quantitative inversions utilizing remote sensing data. In addition to his broad research activities, he was noted for his humility and his dedication in making science more accessible for the general public. Here, the life and academic contributions of Xiaowen Li to the field of quantitative remote sensing science are briefly reviewed.

PENGGUNAAN METODE INKUIRI UNTUK MENGATASI MISKONSEPSI SISWA PADA MATERI POKOK OPTIKA GEOMETRI SERTA SEBAGAI UPAYA MENINGKATKAN KREATIVITAS SISWA DI SMK NEGERI 1 LUMAJANG

This research to determine the decrease in student misconceptions and increase students' creativity through the inquiry method of learning the subject matter of geometric optic. This research conducted in two stages, namely preparation stage tha t aims to develop the following 4-D design models of Thiagarajan (1974) followed by the implementation phase of the design of learning in the classroom using One Group Pretest-Posttest Design. This research conducted one time without replication with a sample of 32 class XI Multimedia SMK 1 Lumajang. Research data indicate feasibility study gained an average of ≥ 3.5 with observer assessme nt criteria well. There is a decline in number of students who have misconceptions after learning inquiry methods, among others: the concept of the eye can see misconceptions decreased 31%, to the concept of the location of the incident angle and the reflect ion angle misconceptions declined 28%, reflecting the legal concept of misconceptions declined 17%, the legal concept of light refraction misconceptions decreased 16%, to the concept of determining the angle of refraction misconceptions declined 34% in t he course of the concept of special convex lens ray misconceptions decreased 34%, i`n the eyes of the concept of disability deter mines the type of misconceptions decreased 28%, to determine the nature of the concept of the shadow of a convex lens occurs misconceptions decreased 19%, and the concept of determining the location of a concave lens shadow of misconceptions declined 9%. In addition, from the results of creativity tests before and after the inquiry method of learning gained increasing creativity of students with moderate category (<g> = 0,35). Based on the analysis of data, it can be concluded that the inquiry method can overcome misconceptions and capable students in an effort to enhance students' creativity, but limited to one class research sampl e. Therefore, it is still necessary adjustments to the situation and conditions in the school.Penelitian ini bertujuan untuk mengetahui penurunan miskonsepsi siswa dan peningkatan kreativitas siswa melalui pembelajaran dengan metode inkuiri pada materi pokok optika geometri. Penelitian ini dilaksanakan dalam dua tahap, yaitu tahap persiapan yang bertujuan mengembangkan perangkat mengikuti rancangan 4-D model dari Thiagarajan (1974) dilanjutkan dengan tahap pelaksanaan pembelajaran di kelas menggunakan rancangan One Group Pretest-Posttest Design. Penelitian ini dilaksanakan satu kali tanpa replikasi dengan jumlah sampel 32 kelas XI Multimedia SMKN 1 Lumajang. Data hasil penelitian menunjukkan keterlaksanaan pembelajaran diperoleh rata-rata dari penilaian pengamat ≥3,5 dengan kriteria baik. Terdapat penurunan sejumlah siswa yang mengalami miskonsepsi setelah pembelajaran dengan metode inkuri, antara lain: pada konsep proses mata dapat melihat miskonsepsi menurun 31%, pada konsep letak sudut datang dan sudut pantul miskonsepsi menurun 28%, pada konsep hukum pemantulan miskonsepsi menurun 17%, pada konsep hukum pembiasan cahaya miskonsepsi menurun 16%, pada konsep menentukan sudut bias miskonsepsi menurun 34% pada konsep jalannya sinar istimewa lensa cembung miskonsepsi menurun 34%, pada konsep menentukan jenis cacat mata miskonsepsi menurun 28%, pada konsep menentukan sifat bayangan lensa cembung terjadi miskonsepsi menurun 19%, dan pada konsep menentukan letak bayangan lensa cekung miskonsepsi menurun 9%. Selain itu dari hasil tes kreativitas sebelum dan setelah pembelajaran dengan metode inkuiri diperoleh peningkatan kreativitas siswa dengan kategori sedang (< g > = 0,35). Berdasarkan hasil analisis data, dapat disimpulkan bahwa metode inkuiri dapat mengatasi miskonsepsi siswa serta mampu dalam upaya meningkatkan kreativitas siswa, namun terbatas pada satu kelas yang dijadikan sampel penelitian. Oleh karena itu, masih diperlukan penyesuaian dengan situasi dan kondisi di sekolah

Development of Near-Diffraction Limited, Low-Cost and High-Resolution CCD Camera System for Imaging Coulter Orifices

A low-cost CCD camera system for imaging Coulter orifices ranging in diameter between 20 µm and 2 mm has been developed and tested. The imaging system incorporates a 6X magnifying lens for viewing the required range of Coulter orifices and LEDs (Light emitting diodes) lamp for back illuminating the orifices. Geometric optic calculations using Zemax® for the micro-lens interfaced with the camera suggest that the spot diameter and the MTF spatial frequency at field of view equal to 0 ° and at the image plane are 5.13 µm and 271.6 lines/mm (at contrast= 37.6%), respectively. Images captured with the camera system for 20 µm, 100 µm and 2 mm diameter orifices are provided. Furthermore, a discussion for the camera micro-lens modulation transfer function, spot diagram, root-mean-square wavefront error versus field and optical path difference plots is given.

Microlocal defect measures for a degenerate thermoelasticity system

In this paper, we study a system of thermoelasticity with a degenerate second-order operator in the heat equation. We analyze the evolution of the energy density of a family of solutions. We consider two cases: when the set of points where the ellipticity of the heat operator fails is included in a hypersurface and when it is an open set. In the first case, and under special assumptions, we prove that the evolution of the energy density is that of a damped wave equation: propagation along the rays of the geometric optic and damping according to a microlocal process. In the second case, we show that the energy density propagates along rays which are distortions of the rays of the geometric optic.

Radiative Transfer in Dispersed Media: Comparison Between Homogeneous Phase and Multiphase Approaches

The radiative transfer in dispersed media in the geometric optic regime is investigated through two continuum-based approaches. The first one is the traditional treatment of dispersed media as continuous and homogeneous systems, referred here as the homogeneous phase approach (HPA). The second approach is based on a separate treatment of the radiative transfer in the continuous and dispersed phases, referred here as the multiphase approach (MPA). The effective radiative properties involved in the framework of the HPA are determined using the recent ray-tracing (RT) method, enabled to overcome the modeling difficulties such as the dependent scattering effects and the misunderstanding of the effective absorption coefficient. The two modeling approaches are compared with the direct Monte Carlo simulation. It is shown that (i) the HPA combined with effective radiative properties, such as those from the RT method, is satisfactory in analyzing the radiative transfer in dispersed media constituting of transparent, semitransparent, or opaque particles. Therefore, the use of more complex continuum models such as the dependence included discrete ordinate method (Singh, B. P., and Kaviany, M., 1992, “Modelling Radiative Heat Transfer in Packed Beds,” Int. J. Heat Mass Transfer, 35, pp. 1397–1405) is not imperative anymore. (ii) The MPA, though a possible candidate to handle nonequilibrium problems, is suitable if the particle (geometric) backscattering is weak or absent. It is the case, for example, for dispersed media constituted of opaque particles or air bubbles. However, caution should be taken with the MPA when dealing with the radiative transfer in dispersed media constituted of nonopaque particles having refractive indexes greater than that of the continuous host medium.

Independent and Dependent Scattering for Semitransparent Media Containing Bubbles

The objective of this present work is to provide a new approach for the radiative characteristics computation of semitransparent media containing spherical bubbles. The bubble size is considred much larger than the wavelength. First, previous models from the literature based on the independent theory are reviewed and established in the Geometric optic limit. Second, a predictive model using the Monte Carlo method is developed. The results obtained from the independent theory models and the Monte Carlo approach are compared. In addition, by varying the bubbles volume fraction, we investigate the limit of validity of the independent theory in such medium.