Volume Charge Density in Geometric Product Lorentz Transformation

Lorentz Transformation is the relationship between two different coordinate frames time and space when one inertial reference frame is relative to another inertial reference frame with traveling at relative speed. In this paper, we have derived the transformation formula for the volume charge density in Geometric Product Lorentz Transformation. The changes of volume charge density of moving frame in terms of that rest frame in Geometric Product Lorentz Transformation at various velocities and angles were studied as well.

Three-dimensional scanning electron microscopy used as a profilometer for the surface characterization of polyethylene-coated paperboard

In food packaging, low-density polyethylene (PE) coating is applied to paperboards to act as a functional barrier and to provide the smoothness required to enhance printability. These characteristics are related to the material’s surface roughness, the parameter monitored during the manufacturing process. Measurement of surface roughness using optical profilometry has gained importance in the paper industry. The optical instruments used to measure surface roughness are limited spatially by the relationship with the light wavelength at which they operate. A scanning electron microscope (SEM) is an alternative for overcoming the spatial resolution limitation, and the use of stereo-photogrammetry on SEM images can be seen as an alternative profilometry technique to measure surface roughness. In this investigation, the surface topography of industrially manufactured high-quality PE-coated paperboard was studied, comparing the SEM stereo-photogrammetry technique with a reference profilometry method, i. e., chromatic confocal microscopy (CCM). We found close agreement between the calculated surface roughness and the results of the techniques used and compared them according to the new ISO 25178 Geometric Product Specifications. We concluded that SEM stereo-photogrammetry provides comparable accurate alternative profilometry method for characterizing the surface roughness of PE-coated paperboard in the micrometer scale.

A Concept for Process-Oriented Interdisciplinary Tolerance Management Considering Production-Specific Deviations

To meet rising customer requirements, increasingly complex products have to be virtually validated. To achieve this within the framework of virtual product development, a wide range of aspects has to be taken into account. In this context, tolerance analysis has established itself as a proven tool to evaluate the consequences of geometric part deviations on geometric product characteristics. Existing approaches, however, do not sufficiently take into account production-specific deviations, leading to time-consuming iterations during the product development process. Therefore, the focus of this contribution is on process-oriented interdisciplinary tolerance management that allows the integration of manufacturing simulations into the tolerance analysis. In contrast to the conventional approach, this novel methodology allows to avoid unnecessary iterations in the context of product development and validation. Following the presentation of the novel procedure, the application on a case study of an X- ray shutter is carried out, whereby surrogate models are integrated in order to reduce the computing time.

Horizon Areas and Logarithmic Correction to the Charged Accelerating Black Hole Entropy

It has been shown by explicit and exact calculation that the geometric product formula i.e., area (or entropy) product formula of outer horizon ( H + ) and inner horizon ( H - ) for charged accelerating black hole (BH) should neither be mass-independent nor quantized. This implies that the area (or entropy ) product is mass-independent conjecture has been broken down for charged accelerating BH. This also further implies that the mass-independent feature of the area product of H ± is not a generic feature at all. We also compute the Cosmic-Censorship-Inequality for this BH. Moreover, we compute the specific heat for this BH to determine the local thermodynamic stability. Under certain criterion, the BH shows the second order phase transition. Furthermore, we compute logarithmic corrections to the entropy for the said BH due to small statistical fluctuations around the thermal equilibrium.

Group technology in the flexible manufacturing system

Flexible manufacturing systems enable rapid changes in production. These changes may be due to changes in the product itself, such as different variations of the product or changes in conditions in the production itself. Currently, most products are designed on a computer using a variety of CAD software. Using sophisticated CAD tools, the resulting 3D product model can include not only the geometric product data but the process plan and technology data. Group technology is very often used to quickly create a technological process. Where, based on similarity, parts are assigned to individual groups and each group has the same basis for the technological process.

Evaluation and Optimization of Task-oriented Measurement Uncertainty for Coordinate Measuring Machines Based on Geometrical Product Specifications

Measuring instruments are intended to be intelligent, precise, multi-functional and developing multidirectionally, scientific, and reasonable; the reliable evaluation of measurement uncertainty of precision instruments is also becoming more and more difficult, and the evaluation of the Coordinate Measuring Machines (CMM) measurement uncertainty is among the typical problems. Based on Geometric Product Specification (GPS), this paper has systematically studied the CMM uncertainty for evaluating the size and geometrical errors oriented toward measurement tasks, and thus has realized the rapid and reliable evaluation of the CMM uncertainty for task-oriented measurement. For overestimation of the CMM uncertainty for task-oriented measurements in the initial evaluation, a systematic optimization solution has been proposed. Finally, the feasibility and validity of the evaluation model and the optimization method have been verified by three different types of measurement examples of diameter, flatness and perpendicularity. It is typical and representative to systematically solve the problem of the CMM uncertainty for evaluating the measurement tasks targeted at dimensions and geometric errors, and the research contents can be effectively applied to solve the uncertainty evaluation problems of other precision instruments, which are of great practical significance not only for promoting the combination of modern uncertainty theory and practical applications but also for improving the application values of precision measurement instruments.

ON THE TIME-DEPENDENT BEHAVIOR OF A MARKOVIAN REENTRANT-LINE MODEL

We use the random-product technique from [5] to study both the steady-state and time-dependent behavior of a Markovian reentrant-line model, which is a generalization of the preemptive reentrant-line model studied in the work of Adan and Weiss [2]. Our results/observations yield additional insight into why the stationary distribution of the reentrant-line model from [2] exhibits an almost-geometric product-form structure: indeed, our generalized reentrant-line model, when stable, admits a stationary distribution with a similar product-form representation as well. Not only that, the Laplace transforms of the transition functions of our reentrant-line model also have a product-form structure if it is further assumed that both Buffers 2 and 3 are empty at time zero.

GPS on the example of an auto-generating 3D model with free tolerance

GPS, i.e. geometric product specification, is a graphical system consisting of symbols, rules, and definitions that describe the requirements for dimensions, shapes, profiles, directions, and positioning and milling of a finished product in a three- -dimensional space. The paper focuses on the group of tolerances within the product shape, taking into account the so-called free tolerance. For the purposes of this work, a 3D model of the cylinder described using the functional dependencies, has been created, which is used to illustrate the concept of GPS in three-dimensional space. The CATIA engineering environment has been applied for this purpose and a suitable numerical parameters have been assigned to each of the dimensions and tolerances. The use of a self-generating 3D model makes it easier to illustrate the GPS concept by graphically displaying the resulting tolerance field. The autogenerating model has been used to verify the correctness of the piston gauge.