Manipulating line waves in flat graphene for agile terahertz applications

Reducing open waveguides enabled by surface waves, such as surface plasmon polaritons, to a one-dimensional line is attractive due to the potentially enhanced control over light confinement and transport. This was recently shown to be possible by simply interfacing two co-planar surfaces with complementary surface impedances, which support transverse-magnetic and transverse-electric modes, respectively. Attractively, the resultant “line wave” at the interface line features singular field enhancement and robust direction-dependent polarizations. Current implementations, however, are limited to microwave frequencies and have fixed functionality due to the lack of dynamic control. In this article, we examine the potential of using gate-tunable graphene sheets for supporting line waves in the terahertz regime and propose an adequate graphene-metasurface configuration for operation at room temperature and low voltage conditions. In addition, we show the occurrence of quasi-line wave under certain conditions of non-complementary boundaries and qualify the degradation in line wave confinement due to dissipation losses. Furthermore, we show the possibility to alter the orientation of the line wave’s spin angular momentum on demand unlike conventional surface waves. Our results on active manipulation of electromagnetic line waves in graphene could be useful for various applications including reconfigurable integrated circuits, modulation, sensing and signal processes.

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT) berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research,HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT) played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews, observations, and field notes. The findings of the study showed that this instructional design could stimulate students to provide reflection characteristics and other transformation geometry informally, to classify them in the transformation isometry in the second level, and to find the reflection supporting line in the more formal level. In addition, the reflection supporting line was used by the students to draw the reflection image and the mirroring pattern and to understand the rotation and translation shapes as a combination of reflection at the highest level. Keyword: geometric transformation, rotation, translation, and HLT

A Method for Determination of Elastohydrodynamic Behavior of Line Shafting Bearings in Their Environment

Safe operation of a rotating line shafting needs to use proper tools and methodology for an accurate determination of its static and steady state behavior in running conditions. Taking into account properly the characteristics of shaft environment is of primary importance. These characteristics are mainly bearing material behavior, oil film dynamic coefficients (stiffness and damping), flexibility and deformations of structure supporting line shafting bearings. Global non linear behavior of the entire system needs to be analyzed to get an accurate solution, as oil film dynamic coefficients depend on steady state location of shaft inside the considered bearing, which depends itself on oil film stiffness, and also on flexibility and deformations of supporting structure. Calculations of structure flexibility and deformations, as well as line shafting stiffness characteristics are performed straightforwardly using finite element method. Solving global matrix equilibrium equation needs to solve elastohydrodynamic (EHD) problem on each bearing. A specific finite element method is developed for this purpose. This method is attractive for taking into account thick and flexible bearing materials such as multi layer synthetic materials. It can also support further developments (effects of geometry defects on bearings, solving thermoelastohydrodynamic problem). The application of the method to the propulsion line shafting of a large LNGC ship (Liquid Natural Gas Carrier) is presented, the final target being the determination of the most optimum bearing offsets for operating safely the vessel in all relevant conditions.

An Efficient Method for Detecting Packaging Supporting Space

This paper presents an efficient method to generate packaging space that can be used to create molded foam. This method first reduces the number of facets presenting the product and then detects heights of supporting lines from an evenly spaced mesh grid on the bottom space of a pre-defined bounding box. The height of each supporting line is further relaxed and smoothed to form the final supporting surface. Based on the supporting surface, an STL format is created so it can be fabricated using RP machines. Three examples are presented to demonstrate this method.

Geometric Inequalities for Plane Convex Bodies

In what follows we shall mean by a plane convex body K a compact convex subset of the Euclidean plane having nonempty interior. We shall denote by h (K, θ) the supporting function of K restricted to the unit circle. This measures the signed distances from the origin to the supporting line of K with outward normal (cos θ, sin θ). The right hand and left hand derivatives of h (K, θ) exist everywhere and are equal except on a countable set.