The Euler characteristic as a basis for teaching topology concepts to crystallographers

The simple Euler polyhedral formula, expressed as an alternating count of the bounding faces, edges and vertices of any polyhedron, V − E + F = 2, is a fundamental concept in several branches of mathematics. Obviously, it is important in geometry, but it is also well known in topology, where a similar telescoping sum is known as the Euler characteristic χ of any finite space. The value of χ can also be computed for the unit polyhedra (such as the unit cell, the asymmetric unit or Dirichlet domain) which build, in a symmetric fashion, the infinite crystal lattices in all space groups. In this application χ has a modified form (χm) and value because the addends have to be weighted according to their symmetry. Although derived in geometry (in fact in crystallography), χm has an elegant topological interpretation through the concept of orbifolds. Alternatively, χm can be illustrated using the theorems of Harriot and Descartes, which predate the discovery made by Euler. Those historical theorems, which focus on angular defects of polyhedra, are beautifully expressed in the formula of de Gua de Malves. In a still more general interpretation, the theorem of Gauss–Bonnet links the Euler characteristic with the general curvature of any closed space. This article presents an overview of these interesting aspects of mathematics with Euler's formula as the leitmotif. Finally, a game is designed, allowing readers to absorb the concept of the Euler characteristic in an entertaining way.

Simulación mediante CDF de una chimenea solar inclinada sobre la cubierta

In recent years, energy consumption from electrical devices to foster air movement in regions with warm climates has risen, with the resulting negative impact on the environment. The purpose of this paper is to evaluate the performance of a solar chimney used to induce natural ventilation in a closed space, under the weather conditions of the hot humid Mexican climate. For this purpose, CFD simulations were run using the RNG k- ɛ turbulence model and the DO radiation model, considering only natural convection phenomena. The solar chimney performance was evaluated, comparing the results of the simulations with experimental measurements, analysis which showed a good match. Temperatures of up to 46.5%°C in the air within the chimney, and of 77.1°C on the absorption plate, were obtained, results that allow verifying the influence of the heat discharge phenomenon by the natural flotation of air in the chimney.

Analisis Penerimaan Pengguna Kereta Api terhadap Penerapan Protokol Covid-19

Pandemi COVID–19 menyebabkan perlunya penerapan protokol kesehatan pada pengoperasian kereta api. Protokol kesehatan tersebut berbasis pada minimalisasi kondisi 3C (Closed Space, Crowded Place, Closed Contact Setting). Penerapan protokol kesehatan dalam operasional KA memerlukan penerimaan pengguna agar dapat berjalan secara efisien. Untuk mengetahui kemauan pengguna kereta api terhadap penerapan protokol kesehatan, dilakukan survei online dengan metode stated preference. Parameter yang diuji meliputi tarif, kelengkapan dokumen kesehatan, protokol di stasiun, protokol di kereta, serta protokol pribadi. Hasil analisis memperlihatkan tingginya penerimaan penumpang terhadap penerapan protokol Covid pada perkeretaapian, yang diperlihatkan dengan kemauan menggunakan kereta yang lebih tinggi pada penerapan protokol kesehatan secara ketat dibandingkan penerapan secara longgar. Kondisi ini terjadi pada kereta api antar kota maupun kereta Jabodetabek. Kata kunci: pandemi, covid 19, stated preference, persepsi, kereta api

What is a Theme Park? A Synthesis and Research Framework

Theme parks have attracted extensive scholarly attention within and outside the tourism literature. These parks have been studied from various stances, yet a uniform definition and integrated framework remain lacking for theme park research and practice. Based on a comprehensive review and research synthesis, this article defines a theme park as a dedicated space featuring five main characteristics: thematic identity, closed space with controlled access, hybrid consumption, performative labor, and merchandising. This article further considers multidisciplinary lenses in theme park studies, particularly in terms of how these five characteristics can be assessed. A research framework covering four domains (industry, tourists/visitors, environment, and impacts) is accordingly proposed to inspire theoretical advances, identify research gaps, promote relevant research, and facilitate managerial practices. This article encourages scholars to move beyond current empirical confines and shape the interdisciplinary future of theme park tourism research.

ELIMINATION OF IMPACT WHEN CLOSING THE DISC VALVE ON THE DRAINAGE OF HORIZONTAL SEDIMENTS

The reasons for the occurrence of an impact when closing a butt erfl y valve installed on pipelines that discharge sludge water from horizontal sedimentation tanks of treatment facilities are considered. The assumption about the possibility of water hammer was experimentally refuted. It is hypothesized that the cause of the impact is the disruption of the fl uid fl ow when fl owing around a fl at plate at critical angles of att ack. A numerical experiment was carried out, which consists in modeling the movement of a water fl ow in a completely fi lled, closed space of a pipe. As a result of the experiment, it was revealed that the fl ow stall was caused by the formation of zones of high and low pressure, respectively, before and after the valve. This provides additional energy to increase the closing torque, comparable to the force of a pneumatic actuator, and results in an impact.

Assessment of threat arising by closed - volume explosions of fuel - air mixtures

The method of estimation of maximal parameters of combustion of gaseous mixtures in closed space is presented. Estimation of chemical composition of combustion products is based on simplified rules of decomposition of reactive medium. Exemplary calculations of temperature, pressure, heat of combustion of hydrocarbon/air mixtures are presented. The accuracy of presented method was validated by comparison with calculations performed by thermodynamic numerical code that include wide list of chemical substances present in combustion products. The obtained results confirm applicability of the proposed method to predict closed space combustion parameters of gaseous mixtures. Semi-empirical methods of estimation of flammability limits are briefly referred

Ocular Surface Erosion after Suspected Exposure to Evaporated COVID-19 Vaccine

The purpose is to report ocular surface erosion of health personnel who were exposed to evaporated CoronaVac during a vaccination campaign. A campaign for CoronaVac vaccination was conducted in a closed space of 11.04 × 5.96 m, partially divided into 6 rooms with interconnected area among the rooms. A total of 20 health personnel worked in the vaccination rooms. On the third day of campaign, a vial, containing a single dose of 0.5 mL, of the vaccine was dropped accidentally onto the floor and broken by an administering nurse. A total of 15 personnel had symptoms and signs of ocular surface erosion at the average time from the accident to the onset of 10.2 ± 7.1 h; 4 personnel also had skin rash. These personnel included all 13 persons who already worked in the rooms when the accident occurred and continued for additional 4–6 h and 2 personnel who presented in the rooms 1–2 h after the accident and stayed for 2–3 h. Proximity and timing suggest CoronaVac correlation with the ocular and skin reactions. Cautions should be taken to avoid broken vials, spills, and aerosolization of CoronaVac during the vaccination.