Pub Date : 2018-08-06DOI: 10.1002/9781119483946.ch6
Sanford Gordon
{"title":"Probability and Random Variables","authors":"Sanford Gordon","doi":"10.1002/9781119483946.ch6","DOIUrl":"https://doi.org/10.1002/9781119483946.ch6","url":null,"abstract":"","PeriodicalId":100895,"journal":{"name":"Mathematical Modelling","volume":"115 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73083342","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 : 2017-01-01DOI: 10.18287/1613-0073-2017-1904-35-39
V. Lyubimov, V. Lashin
The aim of this study is to analyze the resonant attractor-repeller points during the atmospheric descent of a spacecraft with small asymmetry. The mathematical simulation of spacecraft rotational motion uses an approximate non-linear system of equations obtained by the method of integral manifolds. Application of the averaging method and the Lyapunov method makes it possible to obtain realization conditions of attractor-repeller points on non-resonance parts of the motion. By analyzing of the said conditions, we have identified specific cases when the principal resonance is either an attractor point or a repeller point.
{"title":"About the Attractor-Repeller points during the descent of an asymmetric spacecraft in the atmosphere","authors":"V. Lyubimov, V. Lashin","doi":"10.18287/1613-0073-2017-1904-35-39","DOIUrl":"https://doi.org/10.18287/1613-0073-2017-1904-35-39","url":null,"abstract":"The aim of this study is to analyze the resonant attractor-repeller points during the atmospheric descent of a spacecraft with small asymmetry. The mathematical simulation of spacecraft rotational motion uses an approximate non-linear system of equations obtained by the method of integral manifolds. Application of the averaging method and the Lyapunov method makes it possible to obtain realization conditions of attractor-repeller points on non-resonance parts of the motion. By analyzing of the said conditions, we have identified specific cases when the principal resonance is either an attractor point or a repeller point.","PeriodicalId":100895,"journal":{"name":"Mathematical Modelling","volume":"53 1","pages":"35-39"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87462369","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 : 2012-02-14DOI: 10.3182/20120215-3-AT-3016.00197
A. Kröner
Abstract In this paper a posteriori error estimates for space-time finite element discretizations for optimal control problems governed by the dynamical Lame system are considered using the dual weighted residual method (DWR). We apply techniques developed in Kroner (2011a), where optimal control problems for second order hyperbolic equations are considered. The provided error estimator separates the influences of different parts of the discretization (time, space, and control discretization). This allows us to set up an adaptive algorithm which improves the accuracy of the computed solutions by construction of locally refined meshes. We present a numerical example showing a speedup in cpu-time as well as a reduction in degrees of freedom in comparison to uniform mesh refinement.
{"title":"Adaptive finite element methods for optimal control ofelastic waves","authors":"A. Kröner","doi":"10.3182/20120215-3-AT-3016.00197","DOIUrl":"https://doi.org/10.3182/20120215-3-AT-3016.00197","url":null,"abstract":"Abstract In this paper a posteriori error estimates for space-time finite element discretizations for optimal control problems governed by the dynamical Lame system are considered using the dual weighted residual method (DWR). We apply techniques developed in Kroner (2011a), where optimal control problems for second order hyperbolic equations are considered. The provided error estimator separates the influences of different parts of the discretization (time, space, and control discretization). This allows us to set up an adaptive algorithm which improves the accuracy of the computed solutions by construction of locally refined meshes. We present a numerical example showing a speedup in cpu-time as well as a reduction in degrees of freedom in comparison to uniform mesh refinement.","PeriodicalId":100895,"journal":{"name":"Mathematical Modelling","volume":"33 1","pages":"1112-1117"},"PeriodicalIF":0.0,"publicationDate":"2012-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76491007","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 : 2012-02-14DOI: 10.3182/20120215-3-AT-3016.00180
F. Maceri, M. Marino, G. Vairo
Abstract A multiscale model for the elasto-damage response of soft collagenous tissues is proposed, accounting for geometrical and constitutive non-linearities as well as for tissue microscale inhomogeneities. Models at very different length scales are integrated describing molecular damage onset and propagation by an internal-constrained approach employing convex analysis. Stress-strain constitutive relationships are obtained, predicting failure response of soft collagenous tissues in agreement with experimental evidences.
{"title":"Integrated mechanical models for collagenous biostructuresat different length scales","authors":"F. Maceri, M. Marino, G. Vairo","doi":"10.3182/20120215-3-AT-3016.00180","DOIUrl":"https://doi.org/10.3182/20120215-3-AT-3016.00180","url":null,"abstract":"Abstract A multiscale model for the elasto-damage response of soft collagenous tissues is proposed, accounting for geometrical and constitutive non-linearities as well as for tissue microscale inhomogeneities. Models at very different length scales are integrated describing molecular damage onset and propagation by an internal-constrained approach employing convex analysis. Stress-strain constitutive relationships are obtained, predicting failure response of soft collagenous tissues in agreement with experimental evidences.","PeriodicalId":100895,"journal":{"name":"Mathematical Modelling","volume":"47 1","pages":"1018-1022"},"PeriodicalIF":0.0,"publicationDate":"2012-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81136339","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 : 2008-11-14DOI: 10.1007/978-1-4020-8839-1
M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich
{"title":"Optimization with PDE Constraints","authors":"M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich","doi":"10.1007/978-1-4020-8839-1","DOIUrl":"https://doi.org/10.1007/978-1-4020-8839-1","url":null,"abstract":"","PeriodicalId":100895,"journal":{"name":"Mathematical Modelling","volume":"1 1","pages":"I-XI, 1-270"},"PeriodicalIF":0.0,"publicationDate":"2008-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75339477","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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