Extreme black hole anabasis

We study the SL(2) transformation properties of spherically symmetric perturbations of the Bertotti-Robinson universe and identify an invariant μ that characterizes the backreaction of these linear solutions. The only backreaction allowed by Birkhoff’s theorem is one that destroys the AdS2× S2 boundary and builds the exterior of an asymptotically flat Reissner-Nordström black hole with $$ Q=M\sqrt{1-\mu /4} $$ Q = M 1 − μ / 4 . We call such backreaction with boundary condition change an anabasis. We show that the addition of linear anabasis perturbations to Bertotti-Robinson may be thought of as a boundary condition that defines a connected AdS2×S2. The connected AdS2 is a nearly-AdS2 with its SL(2) broken appropriately for it to maintain connection to the asymptotically flat region of Reissner-Nordström. We perform a backreaction calculation with matter in the connected AdS2× S2 and show that it correctly captures the dynamics of the asymptotically flat black hole.

Super-Penrose process for extremal charged white holes

We consider collision of two particles 1 and 2 near the horizon of the extremal Reissner–Nordström (RN) black hole that produces two other particles 3 and 4. There exists such a scenario that both new particles fall into a black hole. One of them emerges from the white hole horizon in the asymptotically flat region, and the other one oscillates between turning points. However, the unbounded energies [Formula: see text] at infinity (super-Penrose process (SPP)) turn out to be impossible for any finite angular momenta [Formula: see text]. In this sense, the situation for such a white hole scenarios is opposite to the black hole ones, where the SPP is found earlier to be possible for the RN metric even for all [Formula: see text]. However, if [Formula: see text] themselves are unbounded, the SPP does exist for white holes.

Investigation on True Stress-Strain Curves of Flat and Corner Regions of Cold-Formed Section Using 3D Digital Image Correlation Method

The true stress-strain curve is the critical method to describe the practical material mechanical performance and the essential precondition to develop the advanced numerical simulation. Experimental, analytical, and numerical procedures were performed in present research to investigate the true stress-strain curves of flat and corner regions of the cold-formed channel section. The coupon tests with the 3D digital image correlation system were conducted on flat and corner specimens to directly obtain the true stress-strain curves. The experimental results indicate that the tensile secondary-hardening phenomenon at the plastic strain stage was observed in the true stress-strain curves of flat coupons, and initial strain hardening behavior was produced in that of corner coupons. Flat region exhibits a significant improvement of true ultimate strength compared to the engineering value. The stress status of the corner region is developed to ultimate strength at the early strain phase and exhibits a slight increase compared with the nominal values at the plastic phase. Cold-rolling action limits the ductility performance of the corner region, which highly restrains the tensile strain hardening at the plastic condition. Thus, the true yielding strength of the corner region is obviously higher, but the true ultimate strength is significantly lower than that of the flat region. Together with the optical measuring results, a trilinear model with two-stage strain hardening and a simplified trilinear models were established for describing the true stress-strain curves of flat and corner regions, respectively. The load-displacement curves from numerical simulations fit very well with those of coupon tests, which validate the reliability of the optic measurement and the dependability of the simplified constitutive models.

Non-edge-triggered inversion from Ga polarity to N polarity of c-GaN domains on an SiO2 mask during epitaxial lateral overgrowth

It was previously reported that N-polar c-GaN domains nucleated in window openings on c-plane sapphire were inverted to Ga-polar domains at the edge of an SiO2 mask during epitaxial lateral overgrowth, but it was asserted that polarity inversion of N-polar GaN domains could not occur beyond the edge of the SiO2 mask. However, that assertion was demonstrated only in the case of a-facet-exposed GaN. It is reported here that polarity inversion from Ga polarity to N polarity of m-facet-exposed c-GaN domains occurred during epitaxial lateral overgrowth on the flat region beyond the edge of a circular-patterned SiO2 mask. An increased flow rate of NH3 during the epitaxial lateral overgrowth is thought to induce this type of non-edge-triggered polarity inversion. Further investigation reveals that non-edge-triggered polarity inversion is also possible when the a facet is exposed at the lateral growth front of Ga-polar GaN domains.

Polígono: uma linha ou uma região? Polygon: is it a line or a region?

A definição de um conceito é algo essencial na atividade matemática. No tocante à definição de polígono, alguns pesquisadores criticam autores de livros didáticos que definem polígono como uma região do plano, em vez de defini-lo como uma linha. Neste contexto, esta pesquisa objetivou analisar elementos históricos, epistemológicos e didáticos sobre a definição de polígono. Assim, foi realizada uma Análise Institucional, baseada nos conceitos da Teoria Antropológica do Didático, sobre Os Elementos, livros específicos de Geometria, Parâmetros Curriculares Nacionais, Base Nacional Comum Curricular e um livro didático de matemática do 6º ano. Desse modo, foi possível concluir que Os Elementos e o livro didático adotam a definição de polígono como região, as referências atuais como uma linha e os documentos oficiais são indiferentes. <br>The definition of a concept is something essential in mathematical activity.Concerning the polygon definition, some researchers criticize textbook authors who define polygon as a flat region, instead of defining it as a line.In this context, this research aimed to analyze historical, epistemological and didactic elements on the definition of polygon.Thus, it made an Institutional Analysis, based on the concepts of the Anthropological Theory of Didactic, on The Elements, specific books of Geometry, ParâmetrosCurriculares Nacionais, Base Nacional Comum Curricular and a textbook of mathematics for the 6th year. Thus, it concluded that The Elements and the textbook adopt the polygon conception as a flat region, the current references as a line and official documents are indifferent.

Effect of Various Parameters on Flat Region of Occupancy Function of non-Crystalline Silicon with Statistical Analysis

Non-crystalline silicon has a leading position in many fields of electronic industrial applications. With this type of silicon material, localized states in the middle of the energy gap, play an important role in determining the wafer characteristic. Therefore, the region around the middle of the energy gap is regarded as the center of charge carrier activities, whereas the occupancy function is employed to define the condition of the localized states, whether they are empty or filled with charge carriers. The occupancy function is divided into three parts within the energy gap. The most important part is the gap center which is always a flat region of a certain width and level. This paper investigates the effect of various parameters on width and level of the flat region of the silicon wafer occupancy function. The work was achieved with the aid of statistical approaches for curve fitting through regression equations. The main contribution is verified through creating a novel MATLAB-SIMULINK model for this case study. The proposed model may represent a significant addition to the Simulink library that does not have such a modelling block.

Design and Analysis of a High-Gain and Robust Multi-DOF Electro-thermally Actuated MEMS Gyroscope

This paper presents the design and analysis of a multi degree of freedom (DOF) electro-thermally actuated non-resonant MEMS gyroscope with a 3-DOF drive mode and 1-DOF sense mode system. The 3-DOF drive mode system consists of three masses coupled together using suspension beams. The 1-DOF system consists of a single mass whose motion is decoupled from the drive mode using a decoupling frame. The gyroscope is designed to be operated in the flat region between the first two resonant peaks in drive mode, thus minimizing the effect of environmental and fabrication process variations on device performance. The high gain in the flat operational region is achieved by tuning the suspension beams stiffness. A detailed analytical model, considering the dynamics of both the electro-thermal actuator and multi-mass system, is developed. A parametric optimization is carried out, considering the microfabrication process constraints of the Metal Multi-User MEMS Processes (MetalMUMPs), to achieve high gain. The stiffness of suspension beams is optimized such that the sense mode resonant frequency lies in the flat region between the first two resonant peaks in the drive mode. The results acquired through the developed analytical model are verified with the help of 3D finite element method (FEM)-based simulations. The first three resonant frequencies in the drive mode are designed to be 2.51 kHz, 3.68 kHz, and 5.77 kHz, respectively. The sense mode resonant frequency is designed to be 3.13 kHz. At an actuation voltage of 0.2 V, the dynamically amplified drive mode gain in the sense mass is obtained to be 18.6 µm. With this gain, a capacitive change of 28.11 f F and 862.13 f F is achieved corresponding to the sense mode amplitude of 0.15 μ m and 4.5 μ m at atmospheric air pressure and in a vacuum, respectively.

Final words

The Principle of Least Action has near-universal applicability, and the actual path taken by the system is the one that occurs in the flat region of the “space-of-paths.” While the Principle needs a whole book, maybe a whole library, to explain it, yet any candidate for a “TOE” (Theory of Everything) would share this feature. Teleological questions are dismissed, however the Principle can only be understood if concepts and philosophical implications are examined. It is probable that this must be done from within physics, that is, by a physicist. A comparison with economics is made. Finally, it is asked whether the Principle of Least Action is a necessary theory, that is, does it answer Einstein’s question: “[could] God … have made the world in a different way”?

Mathematics and physics preliminaries: of hills and plains and other things

The link between mathematics and physics is explained, and how the concepts “coordinates,” “generalized coordinates,” “time,” and “space” have evolved, starting with Galileo. It is also shown that “degrees of freedom” is a slippery but crucial idea. The important developments in “space research”, from Pythagoras to Riemann, are sketched. This is followed by the motivations for finding a flat region of “space”, and for Riemann’s invariant interval. A careful explanation of the three ways of taking an infinitesimal step (actual, virtual, and imperfect) is given. The programme of the Calculus of Variations is described and how this requires a virtual variation of a whole path, a path taken between fixed end-states. This then culminates in the Euler-Lagrange Equations or the Lagrange Equations of Motion. Along the way, the ideas virtual displacement and extremum are explained.