{"title":"Every Clutter Is a Tree of Blobs","authors":"G. Wiseman","doi":"10.3888/tmj.19-7","DOIUrl":"https://doi.org/10.3888/tmj.19-7","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962292","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}
{"title":"Calculating RRKM Rate Constants from Vibrational Frequencies and Their Dynamic Interpretation","authors":"A. Mansell, D. Kahle, D. Bellert","doi":"10.3888/TMJ.19-5","DOIUrl":"https://doi.org/10.3888/TMJ.19-5","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962746","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}
We propose and implement an algorithm to compute the exact cumulative density function (CDF) of the distance from an arbitrary reference point to a randomly located node within an arbitrarily shaped (convex or concave) simple polygon. Using this result, we also obtain the closed-form probability density function (PDF) of the Euclidean distance between an arbitrary reference point and its ith neighbor node when N nodes are uniformly and independently distributed inside the arbitrarily shaped polygon. The implementation is based on the recursive approach proposed by Ahmadi and Pan [1] in order to obtain the distance distributions associated with arbitrary triangles. The algorithm in [1] is extended for arbitrarily shaped polygons by using a modified form of the shoelace formula. This modification allows tractable computation of the overlap area between a disk of radius r centered at the arbitrary reference point and the arbitrarily shaped polygon, which is a key part of the implementation. The obtained distance distributions can be used in the modeling of wireless networks, especially in the context of emerging ultra-dense small cell deployment scenarios, where network regions can be arbitrarily shaped. They can also be applied in other branches of science, such as forestry, mathematics, operations research, and material sciences.
{"title":"Computing Exact Closed-Form Distance Distributions in Arbitrarily Shaped Polygons with Arbitrary Reference Point","authors":"Ross Pure, S. Durrani","doi":"10.3888/TMJ.17-6","DOIUrl":"https://doi.org/10.3888/TMJ.17-6","url":null,"abstract":"We propose and implement an algorithm to compute the exact cumulative density function (CDF) of the distance from an arbitrary reference point to a randomly located node within an arbitrarily shaped (convex or concave) simple polygon. Using this result, we also obtain the closed-form probability density function (PDF) of the Euclidean distance between an arbitrary reference point and its ith neighbor node when N nodes are uniformly and independently distributed inside the arbitrarily shaped polygon. The implementation is based on the recursive approach proposed by Ahmadi and Pan [1] in order to obtain the distance distributions associated with arbitrary triangles. The algorithm in [1] is extended for arbitrarily shaped polygons by using a modified form of the shoelace formula. This modification allows tractable computation of the overlap area between a disk of radius r centered at the arbitrary reference point and the arbitrarily shaped polygon, which is a key part of the implementation. The obtained distance distributions can be used in the modeling of wireless networks, especially in the context of emerging ultra-dense small cell deployment scenarios, where network regions can be arbitrarily shaped. They can also be applied in other branches of science, such as forestry, mathematics, operations research, and material sciences.","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69961887","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}
Pub Date : 2017-01-01Epub Date: 2017-03-28DOI: 10.3888/tmj.19-1
Zachary H Levine, J J Curry
The derivation of the scattering force and the gradient force on a spherical particle due to an electromagnetic wave often invokes the Clausius-Mossotti factor, based on an ad hoc physical model. In this article, we derive the expressions including the Clausius-Mossotti factor directly from the fundamental equations of classical electromagnetism. Starting from an analytic expression for the force on a spherical particle in a vacuum using the Maxwell stress tensor, as well as the Mie solution for the response of dielectric particles to an electromagnetic plane wave, we derive the scattering and gradient forces. In both cases, the Clausius-Mossotti factor arises rigorously from the derivation without any physical argumentation. The limits agree with expressions in the literature.
{"title":"Scattering and Gradient Forces from the Electromagnetic Stress Tensor Acting on a Dielectric Sphere.","authors":"Zachary H Levine, J J Curry","doi":"10.3888/tmj.19-1","DOIUrl":"10.3888/tmj.19-1","url":null,"abstract":"<p><p>The derivation of the scattering force and the gradient force on a spherical particle due to an electromagnetic wave often invokes the Clausius-Mossotti factor, based on an ad hoc physical model. In this article, we derive the expressions including the Clausius-Mossotti factor directly from the fundamental equations of classical electromagnetism. Starting from an analytic expression for the force on a spherical particle in a vacuum using the Maxwell stress tensor, as well as the Mie solution for the response of dielectric particles to an electromagnetic plane wave, we derive the scattering and gradient forces. In both cases, the Clausius-Mossotti factor arises rigorously from the derivation without any physical argumentation. The limits agree with expressions in the literature.</p>","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"19 ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5915281/pdf/nihms875068.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36055815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stochastic Simulation and Parameter Estimation of the FitzHugh–Nagumo Mode","authors":"B. Paláncz","doi":"10.3888/TMJ.18-6","DOIUrl":"https://doi.org/10.3888/TMJ.18-6","url":null,"abstract":"","PeriodicalId":91418,"journal":{"name":"The Mathematica journal","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69962674","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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