Journal articles: 'Square-tiled surfaces'

1

Johnson, Charles C. "Cutting sequences on square-tiled surfaces." Geometriae Dedicata 190, no. 1 (February 9, 2017): 53–80. http://dx.doi.org/10.1007/s10711-017-0227-z.

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Hillairet, Luc. "Spectral decomposition of square-tiled surfaces." Mathematische Zeitschrift 260, no. 2 (November 22, 2007): 393–408. http://dx.doi.org/10.1007/s00209-007-0280-7.

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Hubert, Pascal, Samuel Lelièvre, Luca Marchese, and Corinna Ulcigrai. "The Lagrange spectrum of some square-tiled surfaces." Israel Journal of Mathematics 225, no. 2 (April 2018): 553–607. http://dx.doi.org/10.1007/s11856-018-1667-3.

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Chen, Dawei. "Square-tiled surfaces and rigid curves on moduli spaces." Advances in Mathematics 228, no. 2 (October 2011): 1135–62. http://dx.doi.org/10.1016/j.aim.2011.06.002.

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Shrestha, Sunrose T. "Counting Formulae for Square-tiled Surfaces in Genus Two." Annales Mathématiques Blaise Pascal 27, no. 1 (August 26, 2020): 83–123. http://dx.doi.org/10.5802/ambp.392.

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Colognese, Paul, and Mark Pollicott. "Minimizing entropy for translation surfaces." Conformal Geometry and Dynamics of the American Mathematical Society 26, no. 6 (August 17, 2022): 97–110. http://dx.doi.org/10.1090/ecgd/374.

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In this note we consider the entropy by Dankwart [On the large-scale geometry of flat surfaces, 2014, PhD thesis. https://bib.math.uni-bonn.de/downloads/bms/BMS-401.pdf] of unit area translation surfaces in the S L ( 2 , R ) SL(2, \mathbb R) orbits of square tiled surfaces that are the union of squares, where the singularities occur at the vertices and the singularities have a common cone angle. We show that the entropy over such orbits is minimized at those surfaces tiled by equilateral triangles where the singularities occur precisely at the vertices. We also provide a method for approximating the entropy of surfaces in the orbits.

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Wright, Alex. "Schwarz triangle mappings and Teichmüller curves: Abelian square-tiled surfaces." Journal of Modern Dynamics 6, no. 3 (2012): 405–26. http://dx.doi.org/10.3934/jmd.2012.6.405.

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Lidjan, Edin, and Ðordje Baralic. "Homology of polyomino tilings on flat surfaces." Applicable Analysis and Discrete Mathematics, no. 00 (2021): 31. http://dx.doi.org/10.2298/aadm210307031l.

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The homology group of a tiling introduced by M. Reid is studied for certain topological tilings. As in the planar case, for finite square grids on topological surfaces, the method of homology groups, namely the non-triviality of some specific element in the group allows a ?coloring proof? of impossibility of a tiling. Several results about the non-existence of polyomino tilings on certain square-tiled surfaces are proved in the paper.

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Vincent DELECROIX, Elise GOUJARD, Peter ZOGRAF, Anton ZORICH, and Philip ENGEL. "Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes." Astérisque 415 (2020): 223–74. http://dx.doi.org/10.24033/ast.1107.

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Vincent DELECROIX, Elise GOUJARD, Peter ZOGRAF, Anton ZORICH, and Philip ENGEL. "Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes." Astérisque 415 (2020): 223–74. http://dx.doi.org/10.24033/ast.11107.

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Lekili, Yankı, and Alexander Polishchuk. "Associative Yang–Baxter equation and Fukaya categories of square-tiled surfaces." Advances in Mathematics 343 (February 2019): 273–315. http://dx.doi.org/10.1016/j.aim.2018.11.018.

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Jeffreys, Luke. "Single-cylinder square-tiled surfaces and the ubiquity of ratio-optimising pseudo-Anosovs." Transactions of the American Mathematical Society 374, no. 08 (May 20, 2021): 5739–81. http://dx.doi.org/10.1090/tran/8374.

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Matheus, Carlos, Martin Möller, and Jean-Christophe Yoccoz. "A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces." Inventiones mathematicae 202, no. 1 (November 26, 2014): 333–425. http://dx.doi.org/10.1007/s00222-014-0565-5.

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Arana-Herrera, Francisco. "Counting square-tiled surfaces with prescribed real and imaginary foliations and connections to Mirzakhani's asymptotics for simple closed hyperbolic geodesics." Journal of Modern Dynamics 16 (2020): 81–107. http://dx.doi.org/10.3934/jmd.2020004.

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15

Ali Shah, Faaiz, Mian Amjad Ali, Naeemullah Naeemullah, and Muhammad Bilal. "A Study of Paediatric Supracondylar Fractures of the Humerus Presented During the COVID-19 Pandemic." Athens Journal of Health and Medical Sciences 9, no. 1 (January 27, 2022): 23–38. http://dx.doi.org/10.30958/ajhms.9-1-2.

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Supracondylar fracture of the humerus is one of the most common fractures in children. The purpose of our study was to analyze the temporal variations and mechanisms of paediatric supracondylar fractures presented to our hospital during the COVID-19 pandemic lockdown period. As the schools and parks were closed and children were confined to their homes, they were thus more prone to injuries while playing inside. We claim that this would be the first study in Pakistan to provide unique information about these fractures. We conducted this descriptive study in the Accident and Emergency Department at Lady Reading Hospital in Peshawar, Pakistan from 18th March 2020 to 18th June 2020. In the enrolled children data regarding day and time of fracture occurrence, mechanism of fracture, height of furniture or play equipment from which the children fall and types of landing surfaces were all noted. Important variables were compared and a Chi-square test was applied to calculate P value (P<0.05 was considered significant). The total number of children in our study was 160 with a mean age of 5.3±1.3 years. The most common mechanism of fracture was fall from furniture (63.1%, n=101) and the landing surface was cemented or tiled floor in the majority (84.1%, n=101) of children. Maximum (40.6%, n=65) number of fractures were reported in the month of April and on a Monday (23.7%, n=38). Most (65.6%, n=105) children sustained fractures in PM time. The peak time of occurrence of fracture was 1700 h. We concluded that the majority of children sustained fractures due to a fall from furniture landing on hard cemented or tiled surfaces. Maximum number of fractures was reported in the month of April and on a Monday. Most of these injuries occurred in the evening and were operated on at night. The increased frequency of paediatric supracondylar fractures in the COVID-19 pandemic supports that preventative strategies should focus more on adult supervision, prevention of falls from furniture and provision of softer landing surfaces to lessen the impact of injury. Keywords: fracture, gartland, humerus, paediatric, supracondylar, surface resilience, temporal variations, weekday

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Davidson-Arnott, Robin G. D., Davina C. White, and Jeff Ollerhead. "The effects of artificial pebble concentrations on eolion sand transport on a beach." Canadian Journal of Earth Sciences 34, no. 11 (November 1, 1997): 1499–508. http://dx.doi.org/10.1139/e17-122.

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A field experiment to measure the effects of differing concentrations of pebbles on rate of eoliao sediment transport was carried out on a sand beach on the Northumberland Strait, New Brunswick. Square ceramic tiles (0.15 m × 0.15 m) were used to replicate pebbles. These were deployed in a stratified random array in a rectangular plot 5 m wide and 2 m deep at five different concentrations (surface covers of 19, 24, 29, 34, and 44%) and both singly (two dimensional) and stacked three high (three dimensional). An adjacent plot of similar size was left bare and served as a control. Sediment transport was measured with pairs of vertical traps deployed downwind from each plot and wind speed with three-cup anemometers. Nine data sets totalling 45 runs of 10 min duration each were collected over a total of 4 days. Sediment transport over the tiled plot was normalized against transport over the bare plot. The results show an increase in sediment transport compared with the bare surface for the lowest coverage, followed by a continuous decrease in transport with increasing coverage up to the maximum coverage employed. The rate of decrease was greatest for runs that utilized a three-dimensional form, reflecting an increase in the effective area protected. The results confirm laboratory experiments, which suggest that erosion and transport are initially enhanced by acceleration of flow around pebbles and more efficient transport over the hard surface, but that this is counteracted at higher coverage densities by the increasing area of protected surface.

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Mintorogo, Danny Santoso. "THE AQUATIC-POLYCARBONATE SKYLIGHT FOR SURABAYA INDONESIA." DIMENSI (Journal of Architecture and Built Environment) 35, no. 1 (July 9, 2007): 100–106. http://dx.doi.org/10.9744/dimensi.35.1.100-106.

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This paper will indicate of how appropriate use of aquatic skylight module installed on buildings in the tropical zone compared to the ones in the subtropical climate. In order for energy saving strategies, the aquatic-polycarbonate skylight system is used in the tropical climate. In the tropical hot humid climate, Indonesia has received huge amount of global direct and diffuse radiations on horizontal roofs throughout the year, approximately 525 watts per square meter of solar radiation will impact on flat roofs or skylights on a clear sunny day in Surabaya city. Ironically, most of the commercial and institution buildings are equipped with Western skylight styles in Surabaya without any modifications. The aquatic-polycarbonate skylight is the system that will control daylight, scatter direct solar heat radiation, cool the indoor polycarbonate surface temperature, and collect solar hot water at the same time. The concept of using the water as shading device has three goals: first of all, the flushing water in the polycarbonate holes tries to scatter horizontal or tiled skylight direct sun-ray radiation, and minimize the direct sun heat temperature on the polycarbonate with flushing water continuously. Secondly, the sparkle flushing water in series of square holes of polycarbonate will bounce and disperse the direct sunlight into the space below enhancing daylight patterns. Finally, while bouncing, sparkling and scattering direct sunlight, those series of flushing water holes would also collect the solar heat radiation as solar hot water. Each system could works nicely to absorb, to scatter, to minimize, and to obtain the solar heat radiation for solar hot water in buildings. This strategy aims to provide a clean environment living zones with applying passive heating and cooling systems.

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Sun, Cheng, Meng Zhen, and Yu Shao. "Research on the Thermal Environment of Northeast China's Rural Residences." Open House International 42, no. 1 (March 1, 2017): 52–57. http://dx.doi.org/10.1108/ohi-01-2017-b0008.

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Rural residential energy consumption accounts for 46.6% of total building-related energy consumption of China. In Northeast China, energy consumption for space heating represents a significant proportion of total rural residential energy consumption and has reached 100 million tce (tons of standard coal equivalent), or more than 60% of total household energy consumption. In terms of energy consumption per square meter of gross floor area, rural residential energy consumption for heating is more than that of cities (20kgce/m2). However, the average indoor temperature of most rural residence is below 10°C, much less than that in cities (18°C). Hence, it is an important task for Chinese energy saving and emission reduction to reduce rural residential energy consumption, while enhancing indoor thermal comfort at the same time. Restricted by local technology and low economic level, rural residences currently have poor thermal insulation resulting in severe heat loss. This paper reports on research aimed at developing design strategies for improving thermal insulation properties of rural residences with appropriate technology. A field survey was conducted in six counties in severe cold areas of Northeast China, addressing the aspects of indoor and outdoor temperature, humidity, internal and external surface temperature of building envelop enclosure, and so on. The survey data show the following: 1. Modern (after 2000) brick-cement rural residences perform much better than the traditional adobe clay houses and Tatou houses (a regional type of rural residence in Northeast China – see figure A) in overall thermal performance and indoor thermal comfort; 2. Among the traditional residential house types, adobe clay houses have better heat stability and thermal storage capacity than Tatou houses; 3. Applying an internal or external thermal insulation layer can greatly improve rural residential thermal insulation properties, and is an economical and efficient solution in rural areas; 4. In terms of roofing materials, tiled roofs show much better thermal insulation properties than thatch roofs; 5. Adopting passive solar techniques can form a transition space (greenhouse) against frigid temperatures, resulting in interior temperatures 5.91°C higher than the outside surroundings. It is evident that local passive solar room design offers significant heat preservation effects and lower cost ($12/m2), embodies the ecological wisdom of rural residents, and is therefore important to popularize. The above experimental results can provide guidance in energy conservation design for both self-built residences and rural residences designed by architects. In addition, the results can also provide experimental data for energy-saving studies for rural residences in China.

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19

Shrestha, Sunrose. "The topology and geometry of random square-tiled surfaces." Geometriae Dedicata 216, no. 4 (May 26, 2022). http://dx.doi.org/10.1007/s10711-022-00700-y.

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20

Shrestha, Sunrose T., and Jane Wang. "Statistics of Square-Tiled Surfaces: Symmetry and Short Loops." Experimental Mathematics, August 17, 2020, 1–27. http://dx.doi.org/10.1080/10586458.2020.1786864.

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21

Kany, Manuel, and Carlos Matheus. "Arithmeticity of the Kontsevich–Zorich monodromies of certain families of square‐tiled surfaces II." Mathematische Nachrichten, January 23, 2024. http://dx.doi.org/10.1002/mana.202300085.

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AbstractIn this note, we extend the scope of our previous work joint with Bonnafoux, Kattler, Niño, Sedano‐Mendoza, Valdez, and Weitze‐Schmithüsen by showing the arithmeticity of the Kontsevich–Zorich monodromies of infinite families of square‐tiled surfaces of genera four, five, and six.

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22

Delecroix, Vincent, Élise Goujard, Peter Zograf, and Anton Zorich. "Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves." Inventiones mathematicae, June 20, 2022. http://dx.doi.org/10.1007/s00222-022-01123-y.

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23

Yakovlev, Ivan. "Contribution of n-cylinder square-tiled surfaces to Masur–Veech volume of $\mathcal{H}(2g-2)$." Geometric and Functional Analysis, October 12, 2023. http://dx.doi.org/10.1007/s00039-023-00652-9.

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24

Beck, József, William W. L. Chen, and Yuxuan Yang. "New Kronecker–Weyl type equidistribution results and Diophantine approximation." European Journal of Mathematics 9, no. 2 (May 16, 2023). http://dx.doi.org/10.1007/s40879-023-00623-2.

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AbstractAn interesting result of Veech more than 50 years ago is a parity, or mod 2, version of the Kronecker–Weyl equidistribution theorem concerning the irrational rotation sequence $$\{q\alpha \}$$ { q α } , $$q=0,1,2,3,\ldots $$ q = 0 , 1 , 2 , 3 , … If $$\alpha $$ α is badly approximable and $$b\in (0,1)$$ b ∈ ( 0 , 1 ) satisfies $$b\ne \{m\alpha \}$$ b ≠ { m α } for any $$m\in {\mathbb {Z}}$$ m ∈ Z , then the parity of cardinalities of the sets $$\{1\leqslant q\leqslant N\,{:}\,\{q\alpha \}\in [0,b)\}$$ { 1 ⩽ q ⩽ N : { q α } ∈ [ 0 , b ) } as $$N\rightarrow \infty $$ N → ∞ is evenly distributed. We first answer a question of Veech and establish a stronger form of the mod n analog of his result. Furthermore, for irrational $$\alpha $$ α and $$b=\{m\alpha \}$$ b = { m α } for some $$m\in {\mathbb {N}}$$ m ∈ N , we give a simple yet precise characterization of those cases that give rise to even distribution. We also obtain time-quantitative description of some very striking violations of uniformity—this part is particularly number theoretic in nature, and involves Ostrowski representations of positive integers and $$\alpha $$ α -expansions of real numbers. The Veech discrete 2-circle problem can also be visualized as a problem that concerns 1-direction geodesic flow on a surface obtained by modifying the surface comprising two side-by-side squares by the inclusion of symmetric barriers and gates on the vertical edges, with appropriate modification of the vertical edge identifications. We establish a far-reaching generalization of this case to ones that concern 1-direction geodesic flow on surfaces obtained by modifying a finite square tiled translation surface in analogous but not necessarily symmetric ways.

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DELECROIX, VINCENT, ÉLISE GOUJARD, PETER ZOGRAF, and ANTON ZORICH. "ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES." Forum of Mathematics, Pi 8 (2020). http://dx.doi.org/10.1017/fmp.2020.2.

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A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincaré and naturally appear in various areas of mathematics, theoretical physics and computational biology (in particular, they provide a model of polymer folding). Enumeration of meanders is an important open problem. The number of meanders with $2N$ crossings grows exponentially when $N$ grows, but the long-standing problem on the precise asymptotics is still out of reach. We show that the situation becomes more tractable if one additionally fixes the topological type (or the total number of minimal arcs) of a meander. Then we are able to derive simple asymptotic formulas for the numbers of meanders as $N$ tends to infinity. We also compute the asymptotic probability of getting a simple closed curve on a sphere by identifying the endpoints of two arc systems (one on each of the two hemispheres) along the common equator. The new tools we bring to bear are based on interpretation of meanders as square-tiled surfaces with one horizontal and one vertical cylinder. The proofs combine recent results on Masur–Veech volumes of moduli spaces of meromorphic quadratic differentials in genus zero with our new observation that horizontal and vertical separatrix diagrams of integer quadratic differentials are asymptotically uncorrelated. The additional combinatorial constraints we impose in this article yield explicit polynomial asymptotics.

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Zhang, Nan, Lichao Zhang, Senlin Wang, Shifeng Wen, and Yusheng Shi. "Region-based layered infill area generation of STL models for additive manufacturing." Rapid Prototyping Journal ahead-of-print, ahead-of-print (November 9, 2020). http://dx.doi.org/10.1108/rpj-12-2019-0308.

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Purpose In the implementation of large-size additive manufacturing (AM), the large printing area can be established by using the tiled and fixed multiple printing heads or the single dynamic printing head moving in the x–y plane, which requires a layer decomposition after the mesh slicing to generate segmented infill areas. The data processing flow of these schemes is redundant and inefficient to some extent, especially for the processing of complex stereolithograph (STL) models. It is of great importance in improving the overall efficiency of large-size AM technics software by simplifying the redundant steps. This paper aims to address these issues. Design/methodology/approach In this paper, a method of directly generating segmented layered infill areas is proposed for AM. Initially, a vertices–mesh hybrid representation of STL models is constructed based on a divide-and-conquer strategy. Then, a trimming–mapping procedure is performed on sliced contours acquired from partial surfaces. Finally, to link trimmed open contours and inside-signal square corners as segmented infill areas, a region-based open contour closing algorithm is carried out in virtue of the developed data structures. Findings In virtue of the proposed approach, the segmented layered infill areas can be directly generated from STL models. Experimental results indicate that the approach brings us the good property of efficiency, especially for complex STL models. Practical implications The proposed approach can generate segmented layered infill areas efficiently in some cases. Originality/value The region-based layered infill area generation approach discussed here will be a supplement to current data process technologies in large-size AM, which is very suitable for parallel processing and enables us to improve the efficiency of large-size AM technics software.

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Journal articles on the topic 'Square-tiled surfaces'

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