If Loud Aliens Explain Human Earliness, Quiet Aliens Are Also Rare

If life on Earth had to achieve n “hard steps“ to reach humanity's level, then the chance of this event rose as time to the nth power. Integrating this over habitable star formation and planet lifetime distributions predicts >99% of advanced life appears after today, unless n < 3 and max planet duration <50 Gyr. That is, we seem early. We offer this explanation: a deadline is set by loud aliens who are born according to a hard steps power law, expand at a common rate, change their volume appearances, and prevent advanced life like us from appearing in their volumes. Quiet aliens, in contrast, are much harder to see. We fit this three-parameter model of loud aliens to data: (1) birth power from the number of hard steps seen in Earth’s history, (2) birth constant by assuming a inform distribution over our rank among loud alien birth dates, and (3) expansion speed from our not seeing alien volumes in our sky. We estimate that loud alien civilizations now control 40%–50% of universe volume, each will later control ∼ 105–3 × 107 galaxies, and we could meet them in ∼200 Myr–2 Gyr. If loud aliens arise from quiet ones, a depressingly low transition chance (<∼10−4 ) is required to expect that even one other quiet alien civilization has ever been active in our galaxy. Which seems to be bad news for the Search for Extraterrestrial Intelligence. But perhaps alien volume appearances are subtle, and their expansion speed lower, in which case we predict many long circular arcs to find in our sky.

Ram Horn-Shaped Inspired Folded Compact Antenna for 4G LTE-A and WLAN Portable Mobile Applications

A compact dual-band ram horn-like folded antenna is presented in this work. The antenna is based on a ram horn-like folded strip, asymmetric microstrip feeding (AMF) technique, partial ground, and protruding stub at the ground plane. The dimension of the proposed antenna is 0.11 λ g × 0.17 λ g at 2.3 GHz (10 × 15 mm2). The proposed shape is achieved through the combination of two circular arcs with different radii. The antenna operates at 2.3 GHz and 5.8 GHz with a measured bandwidth of 100 MHz and 820 MHz, a gain of 0.62 dBi and 2.2 dBi, and radiation efficiency of 93.67% and 99.87%, respectively. The prototype of the proposed antenna is fabricated and measured. The measured result shows a good agreement with the simulated result. The parametric study of the proposed antenna is performed and results are presented. Besides, a comparative study between the antennas proposed in this work and the state of the art is performed and presented. The proposed antenna is comparatively small in size than all the recently reported works in the literature while ensuring good radiation characteristics. Therefore, the antenna proposed in this work is a better candidate for future portable sub-6GHz fifth-generation (5G), Advance Long-term Evolution (LTE-A), Worldwide Interoperability for Microwave Access (WiMAX), and Wireless Local Area Network (WLAN) applications.

Comparative analysis of soil discarding by spherical disks

The article presents data on the influence of various types of spherical disks on the discarding of soil in the horizontal and vertical planes during its processing. These studies were conducted in order to optimize the selection of working bodies of disk tillage machines in terms of resistance and processing quality. Three types of disks were used in the comparative analysis. Two types of discs with cutouts and one solid spherical disc. On one type of disk, the cutouts are made in the form of circular arcs, and on the other-in the form of arcs of a logarithmic spiral. The conducted studies have shown that within the working surface of the disk, the trajectories of movement of soil particles under the influence of the three types of disks under study differ little from each other. Although it can be noted that the steeper rise of the trajectory in the vertical plane provides a solid disk, and the smallest rise of the trajectory - at the disk with cutouts in the form of a logarithmic spiral. In the horizontal plane, the longitudinal movement of the soil mass is less in disks with cutouts, especially in a disk with cutouts along the arc of a logarithmic spiral. As a result of these studies, it was revealed that the disk working bodies with cutouts on the cutting edge in the form of arcs of a logarithmic spiral showed the best quality and energy indicators.

An Approximation of Bézier Curves by a Sequence of Circular Arcs

Some researches have investigated that a Bézier curve can be treated as circular arcs. This work is to proposea new scheme for approximating an arbitrary degree Bézier curve by a sequence of circular arcs. The sequenceof circular arcs represents the shape of the given Bézier curve which cannot be expressed using any other algebraicapproximation schemes. The technique used for segmentation is to simply investigate the inner anglesand the tangent vectors along the corresponding circles. It is obvious that a Bézier curve can be subdivided intothe form of subcurves. Hence, a given Bézier curve can be expressed by a sequence of calculated points on thecurve corresponding to a parametric variable t. Although the resulting points can be used in the circular arcconstruction, some duplicate and irrelevant vertices should be removed. Then, the sequence of inner angles arecalculated and clustered from a sequence of consecutive pixels. As a result, the output dots are now appropriateto determine the optimal circular path. Finally, a sequence of circular segments of a Bézier curve can be approximatedwith the pre-defined resolution satisfaction. Furthermore, the result of the circular arc representationis not exceeding a user-specified tolerance. Examples of approximated nth-degree Bézier curves by circular arcsare shown to illustrate efficiency of the new method.

Lee-Yang zeros of the antiferromagnetic Ising model

We investigate the location of zeros for the partition function of the anti-ferromagnetic Ising model, focusing on the zeros lying on the unit circle. We give a precise characterization for the class of rooted Cayley trees, showing that the zeros are nowhere dense on the most interesting circular arcs. In contrast, we prove that when considering all graphs with a given degree bound, the zeros are dense in a circular sub-arc, implying that Cayley trees are in this sense not extremal. The proofs rely on describing the rational dynamical systems arising when considering ratios of partition functions on recursively defined trees.

A Generalised Solution to the Point to Target Problem Using the Minimum Curvature Method

An explicit solution to the general 3D point to target problem based on the minimum curvature method has been sought for more than four decades. The general case involves the trajectory's start and target points connected by two circular arcs joined by a straight line with the position and direction defined at both ends. It is known that the solutions are multi-valued and efficient iterative schemes to find the principal root have been established. This construction is an essential component of all major trajectory construction packages. However, convergence issues have been reported in cases where the intermediate tangent section is either small or vanishes and rigorous mathematical conditions under which solutions are both possible and are guaranteed to converge have not been published. An implicit expression has now been determined that enables all the roots to be identified and permits either exact, or polynomial type solution methods to be employed. Most historical attempts at solving the problem have been purely algebraic, but a geometric interpretation of related problems has been attempted, showing that a single circular arc and a tangent section can be encapsulated in the surface of a horn torus. These ideas have now been extended, revealing that the solution to the general 3D point to target problem can be represented as a 10th order self-intersecting geometric surface, characterised by the trajectory's start and end points, the radii of the two arcs and the length of the tangent section. An outline of the solution's derivation is provided in the paper together with complete details of the general expression and its various degenerate forms so that readers can implement the algorithms for practical application. Most of the degenerate conditions reduce the order of the governing equation. Full details of the critical and degenerate conditions are also provided and together these indicate the most convenient solution method for each case. In the presence of a tangent section the principal root is still most easily obtained using an iterative scheme, but the mathematical constraints are now known. It is also shown that all other cases degenerate to quadratic forms that can be solved using conventional methods. It is shown how the general expression for the general point to target problem can be modified to give the known solutions to the 3D landing problem and how the example in the published works on this subject is much simplified by the geometric, rather than algebraic treatment.

A Generalized Solution to the Point-to-Target Problem Using the Minimum Curvature Method

Summary An explicit solution to the general 3D point-to-target problem based on the minimum curvature method has been sought for more than four decades. The general case involves the trajectory's start and target points connected by two circular arcs joined by a straight line with the position and direction defined at both ends. It is known that the solutions are multivalued, and efficient iterative schemes to find the principal root have been established. This construction is an essential component of all major trajectory construction packages. However, convergence issues have been reported in cases where the intermediate tangent section is either small or vanishes and rigorous mathematical conditions under which solutions are both possible and are guaranteed to converge have not been published. An implicit expression has now been determined that enables all the roots to be identified and permits either exact or polynomial-type solution methods to be used. Most historical attempts at solving the problem have been purely algebraic, but a geometric interpretation of related problems has been attempted, showing that a single circular arc and a tangent section can be encapsulated in the surface of a horn torus. These ideas have now been extended, revealing that the solution to the general 3D point-to-target problem can be represented as a 10th-orderself-intersecting geometric surface, characterized by the trajectory's start and end points, the radii of the two arcs, and the length of the tangent section. An outline of the solution's derivation is provided in the paper together with complete details of the general expression and its various degenerate forms so that readers can implement the algorithms for practical application. Most of the degenerate conditions reduce the order of the governing equation. Full details of the critical and degenerate conditions are also provided, and together these indicate the most convenient solution method for each case. In the presence of a tangent section, the principal root is still most easily obtained using an iterative scheme, but the mathematical constraints are now known. It is also shown that all other cases degenerate to quadratic forms that can be solved using conventional methods. It is shown how the general expression for the general point-to-target problem can be modified to give the known solutions to the 3D landing problem and how the example in the published works on this subject is much simplified by the geometric, rather than algebraic treatment.

Application of laser scanning technology for structure gauge measurement

One of the basic conditions guaranteeing safe and collision-free operation of rail vehicles is maintaining the structure gauge. Verification of the location of rail infrastructure components is carried out using various measurement techniques. This article describes the accuracy of the gauge measurement with the use of a scanning tachymeter. Tachymetric measurements and laser scanning technology were used in the experimental study of the tram loop area. The analysis covered the possibility of using a point cloud to determine geometrical relationships among the track, traction poles and the overhead line. The quality of the laser scanning data in terms of the measurement frequency, the laser beam angle of incidence per object and the average reflection intensity was examined. Performed verification was based on the data from tachymetric measurements. In the tested area, the track consists of straight sections and several circular arcs of small radii and variable curvature. The specific geometry of the track required calculation of the gauge extension parameters depending on the curve radius. In addition, a horizontal track alignment design was prepared. The designed location of the track and extended dimensions of the structure gauge were used to verify the correct spatial position of the current track in relation to the infrastructure elements.