The warmer temperatures of global climate change strengthen the water cycle, evaporation and precipitation increase. But the extremes of heavy rain, floods, dry periods and droughts will also increase. How does this fit together? Simple physical considerations show which factors mainly regulate the strength of the water cycle in the Earth system, and how this determines water availability on land. This can be used to interpret the observed changes in the water balance in Germany and explain the increasing dryness in Germany.
{"title":"Droughts in Germany -- Why global climate change amplifies hydrological extremes","authors":"Axel Kleidon","doi":"arxiv-2403.16551","DOIUrl":"https://doi.org/arxiv-2403.16551","url":null,"abstract":"The warmer temperatures of global climate change strengthen the water cycle,\u0000evaporation and precipitation increase. But the extremes of heavy rain, floods,\u0000dry periods and droughts will also increase. How does this fit together? Simple\u0000physical considerations show which factors mainly regulate the strength of the\u0000water cycle in the Earth system, and how this determines water availability on\u0000land. This can be used to interpret the observed changes in the water balance\u0000in Germany and explain the increasing dryness in Germany.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Data are given, commentary is supplied and explanations are provided with regard to the technical, the organizational and, of course, the human history connected to the time of research, which resulted to the paper entitled "Soil sampling and Cs-137 analysis of the Chernobyl fallout in Greece", written by late Professor S.E. Simopoulos. This paper has been provided in Greek translation within an issued honorary volume (ISBN 978-960-254-714-4). Reasonably, the narration starts with the review of the political, the financial and the social situation of Greece around 1986. Subsequently, an analysis is given on the then available means, the persons involved, the methods used, the lessons learned and any other connection with the oral history of the NTUA's Nuclear Engineering Laboratory and other relevant Greek Laboratories. For this history, written proof is now scarce and the persons available to pass it on are growing less and less. N.P. Petropoulos, now Laboratory member and then student of Professor S.E. Simopoulos was in charge of preparation of this text.
{"title":"Technical, organizational and oral history regarding the soil samples measurements for Cs-137 because of the Chernobyl accident fallout","authors":"Nick P. Petropoulos","doi":"arxiv-2405.00692","DOIUrl":"https://doi.org/arxiv-2405.00692","url":null,"abstract":"Data are given, commentary is supplied and explanations are provided with\u0000regard to the technical, the organizational and, of course, the human history\u0000connected to the time of research, which resulted to the paper entitled \"Soil\u0000sampling and Cs-137 analysis of the Chernobyl fallout in Greece\", written by\u0000late Professor S.E. Simopoulos. This paper has been provided in Greek\u0000translation within an issued honorary volume (ISBN 978-960-254-714-4).\u0000Reasonably, the narration starts with the review of the political, the\u0000financial and the social situation of Greece around 1986. Subsequently, an\u0000analysis is given on the then available means, the persons involved, the\u0000methods used, the lessons learned and any other connection with the oral\u0000history of the NTUA's Nuclear Engineering Laboratory and other relevant Greek\u0000Laboratories. For this history, written proof is now scarce and the persons\u0000available to pass it on are growing less and less. N.P. Petropoulos, now\u0000Laboratory member and then student of Professor S.E. Simopoulos was in charge\u0000of preparation of this text.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140836877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Empirical studies have demonstrated that humans possess the remarkable capacity to distinguish whether a glass of water is hot or cold solely by the sound of pouring it. However, the underlying physical mechanisms governing the disparities in the acoustic signatures of hot versus cold water remain to be deciphered. In this paper, we conducted a series of experiments to extract the intrinsic features of pouring sounds at contrasting temperatures. The results of our spectral analysis revealed that the sound of pouring hot water exhibited more pronounced low-frequency components and diminished high-frequency components relative to cold water. High-speed photographic evidence elucidated that pouring hot water could generate larger air bubbles in greater abundance. We conjecture that the Minnaert resonance arising from these larger entrained bubbles in hot water produces a lower-frequency acoustic signature, thereby constituting the foundational mechanistic explanation for the auditory distinction between pouring hot and cold water.
{"title":"Why do hot and cold water sound different when poured?","authors":"Xiaotian Bi, Dike Su, Qianyun Zhou","doi":"arxiv-2403.14740","DOIUrl":"https://doi.org/arxiv-2403.14740","url":null,"abstract":"Empirical studies have demonstrated that humans possess the remarkable\u0000capacity to distinguish whether a glass of water is hot or cold solely by the\u0000sound of pouring it. However, the underlying physical mechanisms governing the\u0000disparities in the acoustic signatures of hot versus cold water remain to be\u0000deciphered. In this paper, we conducted a series of experiments to extract the\u0000intrinsic features of pouring sounds at contrasting temperatures. The results\u0000of our spectral analysis revealed that the sound of pouring hot water exhibited\u0000more pronounced low-frequency components and diminished high-frequency\u0000components relative to cold water. High-speed photographic evidence elucidated\u0000that pouring hot water could generate larger air bubbles in greater abundance.\u0000We conjecture that the Minnaert resonance arising from these larger entrained\u0000bubbles in hot water produces a lower-frequency acoustic signature, thereby\u0000constituting the foundational mechanistic explanation for the auditory\u0000distinction between pouring hot and cold water.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Douglas J. BuettnerDepartment of Mechanical Engineering, University of Utah, Salt Lake City, UT, USAAcquisition Innovation Research Center, Stevens Institute of Technology, Hoboken, NJ, USASr. Member of the AIAA, Richard E. GriffithsDepartment of Physics & Astronomy, University of Hawaii at Hilo, Hilo, HI, USADepartment of Physics, Carnegie Mellon University, Pittsburgh, PA, USA, Nick SnellDepartment of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA, John StilleyDepartment of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA
Over the past several years, the misidentification of SpaceX Starlink satellites as Unidentified Aerial Phenomena (UAP) by pilots and laypersons has generated unnecessary aviation risk and confusion. The many deployment and orbital evolution strategies, coupled with changing sun specular reflection angles, contribute to this gap in space situational awareness. In this paper we present a case analysis of an incident that generated multiple, corroborating reports of a UAP from five pilots on two commercial airline flights over the Pacific Ocean on August 10th, 2022. This incident included two cell phone photos and a video of an unrecognizable and possibly anomalous phenomenon. We then use supplemental two-line elements (TLEs) for the Starlink train of satellites launched that same day and Automatic Dependent Surveillance Broadcast (ADS-B) data from the flight with the photographs to reconstruct a view of these satellites from the cockpit at the time and place of the sighting. The success of this work demonstrates an approach that could, in principle, warn aviators about satellites that could be visible in unusual or novel illumination configurations, thus increasing space situational awareness and supporting aviation safety. We conclude with recommendations for governments and satellite operators to provide better a-priori data that can be used to create advisories to aviators and the public. The automated simulation of known specular reflection off constellations of satellites could also support researchers investigating sightings of unfamiliar aerial or aerospace objects as likely being from normal versus novel space events.
{"title":"Enhancing Space Situational Awareness to Mitigate Risk: A Case Study in the Misidentification of Starlink Satellites as UAP in Commercial Aviation","authors":"Douglas J. BuettnerDepartment of Mechanical Engineering, University of Utah, Salt Lake City, UT, USAAcquisition Innovation Research Center, Stevens Institute of Technology, Hoboken, NJ, USASr. Member of the AIAA, Richard E. GriffithsDepartment of Physics & Astronomy, University of Hawaii at Hilo, Hilo, HI, USADepartment of Physics, Carnegie Mellon University, Pittsburgh, PA, USA, Nick SnellDepartment of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA, John StilleyDepartment of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA","doi":"arxiv-2403.08155","DOIUrl":"https://doi.org/arxiv-2403.08155","url":null,"abstract":"Over the past several years, the misidentification of SpaceX Starlink\u0000satellites as Unidentified Aerial Phenomena (UAP) by pilots and laypersons has\u0000generated unnecessary aviation risk and confusion. The many deployment and\u0000orbital evolution strategies, coupled with changing sun specular reflection\u0000angles, contribute to this gap in space situational awareness. In this paper we\u0000present a case analysis of an incident that generated multiple, corroborating\u0000reports of a UAP from five pilots on two commercial airline flights over the\u0000Pacific Ocean on August 10th, 2022. This incident included two cell phone\u0000photos and a video of an unrecognizable and possibly anomalous phenomenon. We\u0000then use supplemental two-line elements (TLEs) for the Starlink train of\u0000satellites launched that same day and Automatic Dependent Surveillance\u0000Broadcast (ADS-B) data from the flight with the photographs to reconstruct a\u0000view of these satellites from the cockpit at the time and place of the\u0000sighting. The success of this work demonstrates an approach that could, in\u0000principle, warn aviators about satellites that could be visible in unusual or\u0000novel illumination configurations, thus increasing space situational awareness\u0000and supporting aviation safety. We conclude with recommendations for\u0000governments and satellite operators to provide better a-priori data that can be\u0000used to create advisories to aviators and the public. The automated simulation\u0000of known specular reflection off constellations of satellites could also\u0000support researchers investigating sightings of unfamiliar aerial or aerospace\u0000objects as likely being from normal versus novel space events.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Right before Nolan's movie was released, I gave a talk on Oppenheimer, trying to anticipate what elements of Bird and Sherwin's biography on which the movie is based would make it into the movie. In this article, written for the October 2023 edition of the newsletter of the Forum on Science and Society of the APS, I elaborate on some of the elements I missed. I used this article as the basis for a post-movie version of my talk. I corrected some errors and made some additions to this article before submitting it right before Nolan's movie is expected to clean up at the Oscars (links to recordings of the pre- and post-movie versions of my talk are included).
就在诺兰的电影上映之前，我做了一次关于奥本海默的演讲，试图预测电影所依据的伯德和谢尔文的传记中的哪些内容会被写进电影中。本文是我为美国物理学会科学与社会论坛（Forum on Science and Society of the APS）2023 年 10 月版通讯撰写的，我在文中详细阐述了我所忽略的一些元素。我用这篇文章作为我演讲的电影后版本的基础。在诺兰的电影有望在奥斯卡颁奖礼上一鸣惊人之前，我纠正了一些错误，并对本文做了一些补充（文中附有我的演讲电影前和电影后版本的录音链接）。
{"title":"Oppie Op-ed: Reflections on Christopher Nolan's Oppenheimer","authors":"Michel Janssen","doi":"arxiv-2403.05212","DOIUrl":"https://doi.org/arxiv-2403.05212","url":null,"abstract":"Right before Nolan's movie was released, I gave a talk on Oppenheimer, trying\u0000to anticipate what elements of Bird and Sherwin's biography on which the movie\u0000is based would make it into the movie. In this article, written for the October\u00002023 edition of the newsletter of the Forum on Science and Society of the APS,\u0000I elaborate on some of the elements I missed. I used this article as the basis\u0000for a post-movie version of my talk. I corrected some errors and made some\u0000additions to this article before submitting it right before Nolan's movie is\u0000expected to clean up at the Oscars (links to recordings of the pre- and\u0000post-movie versions of my talk are included).","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"147 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140100090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Len Bos, Michael A. Slawinski, Raphaël A. Slawinski, Theodore Stanoev
We prove that, given an average power, the ascent time is minimized if a cyclist maintains a constant ground speed regardless of the slope. Herein, minimizing the time is equivalent to maximizing -- for a given uphill -- the corresponding mean ascent velocity (VAM: velocit`a ascensionale media), which is a common training metric. We illustrate the proof with numerical examples, and show that, in general, maintaining a constant instantaneous power results in longer ascent times; both strategies result in the same time if the slope is constant. Given standard available information -- including level of fitness, quantified by the power output, and ascent profile -- our results allow for reliable and convenient strategies of uphill timetrials.
{"title":"On minimizing cyclist's ascent times","authors":"Len Bos, Michael A. Slawinski, Raphaël A. Slawinski, Theodore Stanoev","doi":"arxiv-2403.03363","DOIUrl":"https://doi.org/arxiv-2403.03363","url":null,"abstract":"We prove that, given an average power, the ascent time is minimized if a\u0000cyclist maintains a constant ground speed regardless of the slope. Herein,\u0000minimizing the time is equivalent to maximizing -- for a given uphill -- the\u0000corresponding mean ascent velocity (VAM: velocit`a ascensionale media), which\u0000is a common training metric. We illustrate the proof with numerical examples,\u0000and show that, in general, maintaining a constant instantaneous power results\u0000in longer ascent times; both strategies result in the same time if the slope is\u0000constant. Given standard available information -- including level of fitness,\u0000quantified by the power output, and ascent profile -- our results allow for\u0000reliable and convenient strategies of uphill timetrials.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Flavour experiments promise insights into energy scales as high as 200 TeV and distances as small as Zeptometer and offer the chance to identify New Physics
味道实验有望深入洞察高达 200 TeV 的能量尺度和小至 Zeptometer 的距离，并为识别新物理学提供了机会。
{"title":"Expedition to the Zeptouniverse","authors":"Andrzej J. Buras","doi":"arxiv-2403.02387","DOIUrl":"https://doi.org/arxiv-2403.02387","url":null,"abstract":"Flavour experiments promise insights into energy scales as high as 200 TeV\u0000and distances as small as Zeptometer and offer the chance to identify New\u0000Physics","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140047493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Emma Johanna Puranen, Emily Finer, Christiane Helling, V Anne Smith
Interest in science fiction's (SF's) potential science communication use is hindered by concerns about SF misrepresenting science. This study addresses these concerns by asking how SF media reflects scientific findings in exoplanet science. A database of SF exoplanets was analysed using a Bayesian network to find interconnected interactions between planetary characterisation features and literary data. Results reveal SF exoplanets designed after the discovery of real exoplanets are less Earth-like, providing statistical evidence that SF incorporates rapidly-evolving science. Understanding SF's portrayal of science is crucial for its potential use in science communication.
人们对科幻小说（SF）潜在的科学传播用途的兴趣受到了科幻小说歪曲科学的担忧的阻碍。本研究通过探究 SF 媒体如何反映系外行星科学中的科学发现来解决这些问题。研究使用贝叶斯网络分析了 SF 太阳系外行星数据库，以发现行星特征与文学数据之间的相互联系。结果显示，在发现真正的系外行星之后设计的SF系外行星不太像地球，这为SF纳入快速发展的科学提供了统计证据。了解 SF 对科学的描绘对其在科学传播中的潜在用途至关重要。
{"title":"Science Fiction Media Representations of Exoplanets: Portrayals of Changing Astronomical Discoveries","authors":"Emma Johanna Puranen, Emily Finer, Christiane Helling, V Anne Smith","doi":"arxiv-2405.00684","DOIUrl":"https://doi.org/arxiv-2405.00684","url":null,"abstract":"Interest in science fiction's (SF's) potential science communication use is\u0000hindered by concerns about SF misrepresenting science. This study addresses\u0000these concerns by asking how SF media reflects scientific findings in exoplanet\u0000science. A database of SF exoplanets was analysed using a Bayesian network to\u0000find interconnected interactions between planetary characterisation features\u0000and literary data. Results reveal SF exoplanets designed after the discovery of\u0000real exoplanets are less Earth-like, providing statistical evidence that SF\u0000incorporates rapidly-evolving science. Understanding SF's portrayal of science\u0000is crucial for its potential use in science communication.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140836328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper addresses the problem of determining the optimum shape for a beer glass that minimizes the heat transfer while the liquid is consumed, thereby keeping it cold for as long as possible. The proposed solution avoids the use of insulating materials. The glass is modelled as a body of revolution generated by a smooth curve S, constructed from a material with negligible thermal resistance at the revolution surface but insulated at the bottom. The ordinary differential equation describing the problem is derived from the first law of Thermodynamics applied to a control volume encompassing the liquid. This is an inverse optimization problem, aiming to find the shape of the glass (represented by curve S) that minimizes the heat transfer rate. In contrast, the direct problem aims to determine the heat transfer rate for a given geometry. The solution obtained is analytic, and the resulting expression for S is in closed form, providing a family of optimal glass shapes that can be manufactured using conventional methods.
本文探讨的问题是如何确定啤酒杯的最佳形状，以便在液体消耗时最大限度地减少热量传递，从而尽可能长时间地保持其低温状态。所提出的解决方案避免了使用隔热材料。玻璃杯被模拟为由光滑曲线 S 生成的旋转体，由旋转表面热阻可忽略不计但底部隔热的材料制成。描述该问题的超常微分方程是由热力学第一定律导出的，该定律适用于包含液体的控制体积。这是一个逆向优化问题，旨在找到使传热率最小的玻璃形状（用曲线 S 表示）。相比之下，直接问题旨在确定给定几何形状的传热率。得到的解是解析的，S 的表达式是闭合的，从而提供了一系列最佳玻璃形状，可以用传统方法制造。
{"title":"Optimizing Beer Glass Shapes to Minimize Heat Transfer During Consumption","authors":"Claudio de Castro Pellegrini","doi":"arxiv-2402.18544","DOIUrl":"https://doi.org/arxiv-2402.18544","url":null,"abstract":"This paper addresses the problem of determining the optimum shape for a beer\u0000glass that minimizes the heat transfer while the liquid is consumed, thereby\u0000keeping it cold for as long as possible. The proposed solution avoids the use\u0000of insulating materials. The glass is modelled as a body of revolution\u0000generated by a smooth curve S, constructed from a material with negligible\u0000thermal resistance at the revolution surface but insulated at the bottom. The\u0000ordinary differential equation describing the problem is derived from the first\u0000law of Thermodynamics applied to a control volume encompassing the liquid. This\u0000is an inverse optimization problem, aiming to find the shape of the glass\u0000(represented by curve S) that minimizes the heat transfer rate. In contrast,\u0000the direct problem aims to determine the heat transfer rate for a given\u0000geometry. The solution obtained is analytic, and the resulting expression for S\u0000is in closed form, providing a family of optimal glass shapes that can be\u0000manufactured using conventional methods.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"252 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Trees in works of art have stirred emotions in viewers for millennia. Leonardo da Vinci described geometric proportions in trees to provide both guidelines for painting and insights into tree form and function. Da Vinci's Rule of trees further implies fractal branching with a particular scaling exponent $alpha = 2$ governing both proportions between the diameters of adjoining boughs and the number of boughs of a given diameter. Contemporary biology increasingly supports an analogous rule with $alpha = 3$ known as Murray's Law. Here we relate trees in art to a theory of proportion inspired by both da Vinci and modern tree physiology. We measure $alpha$ in 16th century Islamic architecture, Edo period Japanese painting and 20th century European art, finding $alpha$ in the range 1.5 to 2.5. We find that both conformity and deviations from ideal branching create stylistic effect and accommodate constraints on design and implementation. Finally, we analyze an abstract tree by Piet Mondrian which forgoes explicit branching but accurately captures the modern scaling exponent $alpha = 3$, anticipating Murray's Law by 15 years. This perspective extends classical mathematical, biological and artistic ways to understand, recreate and appreciate the beauty of trees.
{"title":"Fractal scaling and the aesthetics of trees","authors":"Jingyi Gao, Mitchell Newberry","doi":"arxiv-2402.13520","DOIUrl":"https://doi.org/arxiv-2402.13520","url":null,"abstract":"Trees in works of art have stirred emotions in viewers for millennia.\u0000Leonardo da Vinci described geometric proportions in trees to provide both\u0000guidelines for painting and insights into tree form and function. Da Vinci's\u0000Rule of trees further implies fractal branching with a particular scaling\u0000exponent $alpha = 2$ governing both proportions between the diameters of\u0000adjoining boughs and the number of boughs of a given diameter. Contemporary\u0000biology increasingly supports an analogous rule with $alpha = 3$ known as\u0000Murray's Law. Here we relate trees in art to a theory of proportion inspired by\u0000both da Vinci and modern tree physiology. We measure $alpha$ in 16th century\u0000Islamic architecture, Edo period Japanese painting and 20th century European\u0000art, finding $alpha$ in the range 1.5 to 2.5. We find that both conformity and\u0000deviations from ideal branching create stylistic effect and accommodate\u0000constraints on design and implementation. Finally, we analyze an abstract tree\u0000by Piet Mondrian which forgoes explicit branching but accurately captures the\u0000modern scaling exponent $alpha = 3$, anticipating Murray's Law by 15 years.\u0000This perspective extends classical mathematical, biological and artistic ways\u0000to understand, recreate and appreciate the beauty of trees.","PeriodicalId":501348,"journal":{"name":"arXiv - PHYS - Popular Physics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139927171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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