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The perils of automated fitting of datasets: The case of a wind turbine cost model 自动拟合数据集的危险:以风力涡轮机成本模型为例
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100059
Claude Klöckl, Katharina Gruber, Peter Regner, Sebastian Wehrle, Johannes Schmidt
{"title":"The perils of automated fitting of datasets: The case of a wind turbine cost model","authors":"Claude Klöckl,&nbsp;Katharina Gruber,&nbsp;Peter Regner,&nbsp;Sebastian Wehrle,&nbsp;Johannes Schmidt","doi":"10.1016/j.exco.2022.100059","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100059","url":null,"abstract":"<div><p>Rinne et al. (2018) conduct a detailed analysis of the impact of wind turbine technology and land-use on wind power potentials, which allows important insights into each factor’s contribution to overall potentials. The paper presents a detailed and very valuable model of site-specific wind turbine investment cost (i.e. road- and grid access costs), complemented by a model used to estimate site-independent costs.</p><p>However, the site-independent cost model is flawed in our opinion. This flaw most likely does not impact the results on cost supply-curves of wind power presented in the paper. However, we expect a considerable generalization error. Thus the application of the wind turbine cost model in other contexts may lead to unreasonable results. More generally, the derivation of the wind turbine cost model serves as an example of how applications of automated regression analysis can go wrong.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100059"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000064/pdfft?md5=fdac94d105872fd1eb33da6ecfceea1a&pid=1-s2.0-S2666657X22000064-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828286","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}
引用次数: 1
Numerical treatment of fractal boundary value problems for heat conduction in polar bear with spatial variation of thermal conductivity 考虑热导率空间变化的北极熊热传导分形边值问题的数值处理
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100088
Navnit Jha
{"title":"Numerical treatment of fractal boundary value problems for heat conduction in polar bear with spatial variation of thermal conductivity","authors":"Navnit Jha","doi":"10.1016/j.exco.2022.100088","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100088","url":null,"abstract":"<div><p>A high-resolution compact discretization scheme for the numerical approximation of two-point nonlinear fractal boundary value problems is presented to study the stationary anomalous diffusion process. Hausdorff derivative is applied to derive the models in fractal media. The proposed scheme solves the nonlinear fractal model and achieves an accuracy of order four by employing only three mesh points in a stencil and consumes short computing time. Numerical simulations with heat conduction in polar bear, convection–diffusion, boundary layer, Bessel’s and Burgers equation in a fractal medium are carried out to illustrate the utility of the scheme and their numerical rate of convergence.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100088"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000210/pdfft?md5=072080d010ecc5a7c70a88203588807f&pid=1-s2.0-S2666657X22000210-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828825","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}
引用次数: 0
On robust discretization methods for poroelastic problems: Numerical examples and counter-examples 多孔弹性问题的鲁棒离散化方法:数值实例和反例
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100087
Fleurianne Bertrand , Maximilian Brodbeck , Tim Ricken
{"title":"On robust discretization methods for poroelastic problems: Numerical examples and counter-examples","authors":"Fleurianne Bertrand ,&nbsp;Maximilian Brodbeck ,&nbsp;Tim Ricken","doi":"10.1016/j.exco.2022.100087","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100087","url":null,"abstract":"<div><p>Finite element approximations of poroelastic materials are nowadays used within multiple applications. Due to wide variation of possible material parameters, robustness of the considered discretization is important. Within this contribution robust of discretization schemes, initially developed for Biot’s theory, will be applied within the Theory of Porous Media. Selected numerical test-cases, special attention will be paid to incompressible and impermeable regimes, are conducted.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100087"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000209/pdfft?md5=34ba4d9728edf7f37992d4a62b749171&pid=1-s2.0-S2666657X22000209-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828819","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}
引用次数: 4
Some examples of Swift–Hohenberg equation Swift-Hohenberg方程的一些例子
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100090
Haresh P. Jani, Twinkle R. Singh
{"title":"Some examples of Swift–Hohenberg equation","authors":"Haresh P. Jani,&nbsp;Twinkle R. Singh","doi":"10.1016/j.exco.2022.100090","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100090","url":null,"abstract":"<div><p>In this work, we solve partial differential equations using the Aboodh transform and the homotopy perturbation method (HPM). The Swift–Hohenberg equation accurately describes pattern development and evolution. The Swift–Hohenberg (S–H) model is linked to fluid dynamics, temperature, and thermal convection, and it can be used to describe how liquid surfaces with a horizontally well-conducting boundary form.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100090"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000234/pdfft?md5=858850a7e53372b937f273f5a13392f6&pid=1-s2.0-S2666657X22000234-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828824","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}
引用次数: 0
Explanation of wind gusts induced by pressure changes. Turbulence in the air 气压变化引起阵风的解释。空气中的乱流
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100085
Alexander Yakovlevich Braginsky
{"title":"Explanation of wind gusts induced by pressure changes. Turbulence in the air","authors":"Alexander Yakovlevich Braginsky","doi":"10.1016/j.exco.2022.100085","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100085","url":null,"abstract":"<div><p>The paper researches wind gusts that are caused by changes in pressure on a flat surface. To describe this phenomenon the equations of the state of a continuous medium are used. In the stationary case, these equations in the air are the equation of the decreasing exponent for the pressure gradient. Consequently, the volume force in the air cannot act permanently. It decreases at a distance of about a kilometer. This exponential damping solution is due to wind gusts. The paper concludes that the periodic dumping of volumetric forces leads to turbulence in the air. These disruptions or turbulence are also observed when the air rotates in cyclones and anticyclones. In the water, pressure fluctuation leads to periodic waves.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100085"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000192/pdfft?md5=e690703acae3c1787b38de1124d98d7b&pid=1-s2.0-S2666657X22000192-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828827","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}
引用次数: 0
Painlevé analysis, Bäcklund transformation and Exact solutions for the (3+1)-dimensional nonlinear partial differential equation represented by Burgers’ equation 以Burgers方程为代表的(3+1)维非线性偏微分方程的painlev<s:1>分析、Bäcklund变换和精确解
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100081
M.H.M. Moussa, Zidan M. Abd Al-Halim
{"title":"Painlevé analysis, Bäcklund transformation and Exact solutions for the (3+1)-dimensional nonlinear partial differential equation represented by Burgers’ equation","authors":"M.H.M. Moussa,&nbsp;Zidan M. Abd Al-Halim","doi":"10.1016/j.exco.2022.100081","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100081","url":null,"abstract":"<div><p>Herein, the Painlevé analysis and Bäcklund transformation for the  (3+1) dimensional Burger equation are presented. Using this analysis, it is shown that the equation under consideration non-integrable. But, it is under a constraint equation may be integrable. We construct the Bäcklund transformation for that equation. Similarity solutions for the mentioned equation have been obtained. Some of these solutions are completely new.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100081"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000179/pdfft?md5=007e91f8e4bfa868782a7c5be15704e5&pid=1-s2.0-S2666657X22000179-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828828","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}
引用次数: 2
Painlevé analysis, Bäcklund transformation and Exact solutions for the (3+1)-dimensional nonlinear partial differential equation represented by Burgers’ equation 以Burgers方程为代表的(3+1)维非线性偏微分方程的painlev<s:1>分析、Bäcklund变换和精确解
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100081
M. Moussa, Zidan M. Abd Al-Halim
{"title":"Painlevé analysis, Bäcklund transformation and Exact solutions for the (3+1)-dimensional nonlinear partial differential equation represented by Burgers’ equation","authors":"M. Moussa, Zidan M. Abd Al-Halim","doi":"10.1016/j.exco.2022.100081","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100081","url":null,"abstract":"","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78343658","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}
引用次数: 2
Solutions of equations x2−(p2q2±3p)y2=±kt 方程x2−(p2q2±3p)y2=±kt的解
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2021.100043
Roji Bala, Vinod Mishra
{"title":"Solutions of equations x2−(p2q2±3p)y2=±kt","authors":"Roji Bala,&nbsp;Vinod Mishra","doi":"10.1016/j.exco.2021.100043","DOIUrl":"https://doi.org/10.1016/j.exco.2021.100043","url":null,"abstract":"<div><p>In the present paper, we have solved the equation <span><math><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mrow><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>±</mo><mn>3</mn><mi>p</mi><mo>)</mo></mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msup><mo>,</mo><mspace></mspace><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mrow><mo>(</mo><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>±</mo><mn>5</mn><mi>p</mi><mo>)</mo></mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><msup><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msup></mrow></math></span> and expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences. With the help of this equation, we have found units of <span><math><mrow><mi>Z</mi><mrow><mo>[</mo><msqrt><mrow><mn>885</mn></mrow></msqrt><mo>]</mo></mrow></mrow></math></span> and <span><math><mrow><mi>Z</mi><mrow><mo>[</mo><msqrt><mrow><mn>915</mn></mrow></msqrt><mo>]</mo></mrow></mrow></math></span> in terms of generalized Fibonacci, generalized Lucas, generalized Pell and generalized Pell–Lucas numbers.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100043"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X21000239/pdfft?md5=ca9fffbadacbdefbd419ff95b70172cd&pid=1-s2.0-S2666657X21000239-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828284","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}
引用次数: 0
Maximal monotone operators with non-maximal graphical limit 具有非极大图极限的极大单调算子
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100073
Gerd Wachsmuth
{"title":"Maximal monotone operators with non-maximal graphical limit","authors":"Gerd Wachsmuth","doi":"10.1016/j.exco.2022.100073","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100073","url":null,"abstract":"<div><p>We present a counterexample showing that the graphical limit of maximally monotone operators might not be maximally monotone. We also characterize the directional differentiability of the resolvent of an operator <span><math><mi>B</mi></math></span> in terms of existence and maximal monotonicity of the proto-derivative of <span><math><mi>B</mi></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100073"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000131/pdfft?md5=663e4b30d499d928ad6f94f949cd2209&pid=1-s2.0-S2666657X22000131-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828831","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}
引用次数: 0
On the spectrum of the finite element approximation of a three field formulation for linear elasticity 线性弹性三场公式的有限元近似谱
Examples and Counterexamples Pub Date : 2022-11-01 DOI: 10.1016/j.exco.2022.100076
Linda Alzaben , Fleurianne Bertrand , Daniele Boffi
{"title":"On the spectrum of the finite element approximation of a three field formulation for linear elasticity","authors":"Linda Alzaben ,&nbsp;Fleurianne Bertrand ,&nbsp;Daniele Boffi","doi":"10.1016/j.exco.2022.100076","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100076","url":null,"abstract":"<div><p>We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100076"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000155/pdfft?md5=fb9d2e5112e427f0af0000cd842cd071&pid=1-s2.0-S2666657X22000155-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71828818","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}
引用次数: 0
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