Journal Of Applied Mathematics Research Articles

Propagation of Harmonic Plane Waves in a Rotating Elastic Medium under Two-Temperature Thermoelasticity with Relaxation Parameter

The present work investigates the propagation of harmonic plane waves in an isotropic and homogeneous elastic medium that is rotating with uniform angular velocity by employing the two-temperature generalized thermoelasticity, recently introduced by Youssef (IMA Journal of Applied Mathematics, 71, 383-390, 2006). Dispersion relation solutions for longitudinal as well as transverse plane waves are obtained analytically. Asymptotic expressions of several important characterizations of the wave fields, such as phase velocity, specific loss, penetration depth, amplitude coefficient factor and phase shift of thermodynamic temperature are obtained for high frequency as well as low frequency values. A critical value of the two-temperature parameter for the low frequency case is obtained. Using Mathematica, numerical values of the wave fields at intermediate values of frequency and for various values of the two- temperature parameter are computed. A detailed analysis of the effects of rotation on the plane wave is presented on the basis of analytical and numerical results. An in-depth comparative analysis of our results with the corresponding results of the special cases of absence of rotation of the body and with the case of generalized thermoelasticity is also presented. The most significant points are highlighted.

Singular controls in optimal collision avoidance for participants with unequal linear speeds

This article studies optimal collision avoidance strategies for participants with unequal linear speeds in a planar close proximity encounter. It is known that bang-bang collision avoidance strategies are optimal for encounters of participants with equal linear speeds. However, as shown recently, bang-bang collision avoidance strategies are not necessarily optimal when the linear speeds of the participants are not equal. We study the structure of optimal singular controls for collision avoidance of participants with unequal linear speeds, but equal turn capabilities. We prove that both controls cannot be singular simultaneously, and that the only possible singular control is a zero control. We use several optimization techniques compute optimal state, control and adjoint variables. Numerical simulations suggest that a zero control strategy only exists for a slower participant and that, at most, one switching from a bang-bang to a singular control occurs. Different types of structural changes of the controls with change in the initial conditions are identified via the numerical simulations. References U. Ledzewicz, H. Maurer, and H. Schattler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy, Mathematical Biosciences and Engineering , 8 , 2011, 307--328. doi:10.3934/mbe.2011.8.307 U. Ledzewicz, H. Maurer, H. Schattler, On optimal delivery of combination therapy for tumors, Mathematical Biosciences , 22 , 2009, 13--26. doi:10.1016/j.mbs.2009.08.004 H. Maurer, C. Buskens, J.-H. R. Kim, Y. Kaya, Optimization methods for the verification of second-order sufficient conditions for bang-bang controls. Optimal Control Applications and Methods , 26 , 2005, 129--156. doi:10.1002/oca.756 A. W. Merz, Optimal aircraft collision avoidance. Proceedings of the Joint Automatic Control Conf. , Paper 15-3, pages 449--454, 1973. A. W. Merz, Optimal evasive manoeuvres in maritime collision avoidance. Navigation , 20 (2), 1973, 144--152. T. Tarnopolskaya, and N. L. Fulton, Optimal cooperative collision avoidance strategy for coplanar encounter: Merz's solution revisited, J. Optim. Theory Appl. , 140 (2), 2009, 355--375. doi:10.1007/s10957-008-9452-9 T. Tarnopolskaya, and N. L. Fulton, Parametric behavior of the optimal control solution for collision avoidance in a close proximity encounter, In R. S. Andersson et al., editors, 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation , pages 425--431, 2009. http://www.mssanz.org.au/modsim09/A7/tarnopolskaya_A7.pdf T. Tarnopolskaya, and N. L. Fulton, Synthesis of optimal control for cooperative collision avoidance for aircraft (ships) with unequal turn capabilities, J. Optim. Theory Appl. , 144 (2), 2010, 367--390. doi:10.1007/s10957-009-9597-1 T. Tarnopolskaya, and N. L. Fulton, Dispersal Curves for Optimal Collision Avoidance in a Close Proximity Encounter: a Case of Participants with Unequal Turn Rates, Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2010 , WCE 2010, pages 1789--1794. IAENG, 2010. http://www.iaeng.org/publication/WCE2010/WCE2010_pp1789-1794.pdf T. Tarnopolskaya, and N. L. Fulton, Non-unique Optimal Collision Avoidance Strategies for Coplanar Encounter of Participants with Unequal Turn Capabilities, IAENG International Journal of Applied Mathematics , 40 (4), 2010, 289--296. http://www.iaeng.org/IJAM/issues_v40/issue_4/IJAM_40_4_10.pdf T. Tarnopolskaya, and N. L. Fulton, Synthesis of Optimal Control for Cooperative Collision Avoidance in a Close Proximity Encounter: Special Cases, Proceedings of the 18th World Congress of the International Federation of Automatic Control (IFAC) , Milan (Italy), August 28--September 2, 2011, 18 (1), 9775--9781. T. Tarnopolskaya, N. L. Fulton, and H. Maurer, Synthesis of optimal bang-bang control for cooperative collision avoidance for aircraft (ships) with unequal linear speeds. J. Optim. Theory Appl. , to appear, 2012.

Editorial

This special issue of the European Journal of Applied Mathematics is devoted to the ‘Liquid Crystal Theory and Modelling: Discussion Meeting’ that was held in Oxford on the 29th-30th October 2009. This international, interdisciplinary meeting was organised jointly by Dr Apala Majumdar (University of Oxford) and Prof. Nigel Mottram (University of Strathclyde) and was funded by OCCAM (Oxford Centre for Collaborative Applied Mathematics), the London Mathematical Society, Taylor and Francis and Cambridge University Press.

Irrelevance of the fractal dimension term in the fractal attrition equation

The modified Fractal Attrition Equation (mFAE) models the casualties produced by Map Aware Non-uniform Automata (MANA), an agent based combat modelling distillation, at each MANA time step. The mFAE has three important differences from the simple early twentieth century models of casualties that used only the numbers on each side to make predictions. Firstly, only those agents within range of the enemy may inflict casualties. Secondly, the detection range is assumed to be greater than the range of weapons and a fitting factor assumed to represent the gap between these two ranges, is introduced. This builds in one of the assumptions of Network Centric Warfare, that you will be able to see your enemies before they can shoot at you. Thirdly, and novelly, a fractal dimension is introduced. We postulate that the important part of the information used in calculating the fractal dimension has already been incorporated into the model through the consideration of range. We test this hypothesis by comparing the outcomes of the mFAE with and without the fractal term on three scenarios: that used by the developers of the mFAE; best practice MANA tactics from the literature; and a rout scenario. When the two models are scaled to fit the MANA casualties there is no significant difference in fit. We conclude that the fractal term in the mFAE is redundant. References J. V. Chase, Sea fights, a mathematical investigation of the effect of superiority of force in. RG 8, Box 109, XTAV(1902), Naval War College Archives. F. W. Lanchester, Aircraft in warfare: the dawn of the fourth arm---No. V, The principle of concentration, Engineering 98: 422--423, (1914). http://www.archive.org/details/aircraftinwarfar00lancrich N. J. MacKay, Lanchester combat models, Mathematics Today, 42, pp.170--173, 2006. http://arXiv.org/abs/math/0606300v1 T. W. Lucas and T. Turkes Fitting Lanchester models to the battles of Kursk and Ardennes. Nav Res Log 51: 95--116 (2004). G. C. McIntosh and M. K. Lauren, Incorporating fractal concepts into equations of attrition for military conflicts, Journal of the Operational Research Society, 2(59): 703--713, (2008). doi:10.1057/palgrave.jors.2602383 M. K. Lauren Firepower concentration in cellular automaton combat models---an alternative to Lanchester, Journal of the Operational Research Society, 53: 672--679, (2002). doi:10.1057/palgrave.jors.2601355 M. K. Lauren, J. M. Smith, J. Moffat and N. D. Perry Using the fractal attrition equation to construct a metamodel of the MANA cellular automaton combat model, The Technical Cooperation Program, Joint Systems and Analysis Group, Technical Panel 3, November 2005. G. C. McIntosh, D. P. Galligan, M. A. Anderson and M. K. Lauren, MANA (Map Aware Non-uniform Automata) Version 4 User Manual, DTA Technical Note 2007/3 NR 1465. http://arxiv.org/abs/nlin/0607051v1 J. Moffat, J. Smith and S. Witty, Emergent behaviour: Theory and experimentation using the mana model, Journal of Applied Mathematics and Decision Sciences---JAMDS , 2006, pp.1--14, 2006. doi:10.1155/JAMDS/2006/54846 D. R. Shine, An Exploratory Study of the Army-as-a-System Core Skills: Comparing the Effectiveness of Warfighting Tactics Using MANA, DSTO-TR-1663, (2005), DSTO (Australia). P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys Rev Lett 50(5): 346--349 (1983). doi:10.1103/PhysRevLett.50.346 J. G. Eisenhauer, Regression through the Origin, Teaching Statistics, 25(3): 76--80, (2003).

Annual Index

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 91, Issue 12 p. 1005-1008 Annual Index Annual Index First published: 08 November 2011 https://doi.org/10.1002/zamm.201190024AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume91, Issue12December 2011Pages 1005-1008 RelatedInformation

Anisotropic second-order models and associated fundamental diagrams

According to Banks [Investigation of some characteristics of congested flow. Transportation Research Record, 1999], traffic heterogeneity explains the data scattering on the flow–density plane and positive transferences within the congested phase (a transference is a line connecting adjacent points in the time series). This heterogeneity results from a traffic mixture, made up of various vehicles and drivers, or different traffic conditions such as meteorological conditions. This paper only deals with traffic mixture and more particularly with vehicle classes such as passenger car and truck, which are correlated to the vehicle length. When considering a macroscopic model, the mean vehicle length, which is measured by sensors, is associated with the truck percentage. Then the Generic Second Order Model (GSOM) by Lebacque [Lebacque, J.P., Mammar, S., Haj-Salem, H., 2007a. Generic second-order traffic flow modeling. In: Proceedings of the 17th International Symposium on Transportation and Traffic Theory, London, 23–25 July 2007, 749–770.] provides a rigorous mathematical framework for traffic heterogeneity modeling. The added value in this paper is that admissible invariants which characterize generic fundamental diagrams, possibly depending on the mean vehicle length, are interpreted and debated. Aw–Rascle–Zhang’s [Aw, A., Rascle, M., 2000. Resurrection of second-order models of traffic flow. SIAM Journal of Applied Mathematics, 60 (3), 916–938; Zhang, H.M., 2002. A non equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B, 36, 275–290.] and Colombo’s [Colombo, R.M., 2002. A 2×2 hyperbolic traffic flow model. Mathematical and Computer Modeling, 35, 683–688.] anisotropic models are deeply analyzed from a traffic point of view. At last an extended GSOM equation system provides a full parameterization of fundamental diagrams which is needed to traffic heterogeneity modeling.

Book Review: Ciro D'Apice, Simone Göttlich, Michael Herty, and Benedetto Piccoli, Modeling, Simulation, and Optimization of Supply Chains. A Continuous Approach. Cambridge University Press, SIAM Philadelphia 2010

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 91, Issue 8 p. 686-686 Book Review Book Review: Ciro D'Apice, Simone Göttlich, Michael Herty, and Benedetto Piccoli, Modeling, Simulation, and Optimization of Supply Chains. A Continuous Approach. Cambridge University Press, SIAM Philadelphia 2010 Christian Wieners, Christian Wieners KarlsruheSearch for more papers by this author Christian Wieners, Christian Wieners KarlsruheSearch for more papers by this author First published: 06 July 2011 https://doi.org/10.1002/zamm.201190018AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume91, Issue8August 2011Pages 686-686 RelatedInformation

Special Issue: 2020 visions of applied mathematics

Journal Article Special Issue: 2020 visions of applied mathematics Get access Alan Champneys, Alan Champneys Department of Engineering Mathematics, University of Bristol Search for other works by this author on: Oxford Academic Google Scholar Fordyce Davidson Fordyce Davidson Division of Mathematics, University of Dundee Search for other works by this author on: Oxford Academic Google Scholar IMA Journal of Applied Mathematics, Volume 76, Issue 3, June 2011, Pages 351–352, https://doi.org/10.1093/imamat/hxr026 Published: 01 June 2011

Book Review: J. N. Reddy and D. K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics, Ed. 3, CRC Press, Taylor & Francis Group, Boca Raton, 2010

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 91, Issue 5 p. 385-385 Book Review Book Review: J. N. Reddy and D. K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics, Ed. 3, CRC Press, Taylor & Francis Group, Boca Raton, 2010 B. Platzer, B. Platzer ChemnitzSearch for more papers by this author B. Platzer, B. Platzer ChemnitzSearch for more papers by this author First published: 31 March 2011 https://doi.org/10.1002/zamm.201190011Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume91, Issue5May 2011Pages 385-385 RelatedInformation

Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces

The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58^(5), 787–792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are illustrated by an example.

Annual Index

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 90, Issue 12 p. 1005-1008 Annual Index Annual Index First published: 17 November 2010 https://doi.org/10.1002/zamm.201090015AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume90, Issue12December 2010Pages 1005-1008 RelatedInformation

Editorial

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 90, Issue 12 p. 910-910 Editorial Editorial Holm Altenbach, Holm Altenbach Halle (Saale)Search for more papers by this author Holm Altenbach, Holm Altenbach Halle (Saale)Search for more papers by this author First published: 17 November 2010 https://doi.org/10.1002/zamm.201009022AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume90, Issue12December 2010Pages 910-910 RelatedInformation

Special Issue: On the Occasion of Zenon Mróz' 80th Birthday, Part II

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 90, Issue 10-11 Cover Picture Special Issue: On the Occasion of Zenon Mróz' 80th Birthday, Part II First published: 07 October 2010 https://doi.org/10.1002/zamm.201090014AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract See G. Sagar and E. Stein, Contributions on the theory and computation of mono- and poly-crystalline cyclic martensitic phase transformations, ZAMM 90 (2010) 9, p. 656 Volume90, Issue10-11Special Issue: “On the Occasion of Zenon Mróz' 80th Birthday”, Part IIOctober 2010 RelatedInformation

Modified hybrid algorithm for a family of quasi- [formula omitted]-asymptotically nonexpansive mappings

The purpose of this paper is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi- ϕ -asymptotically nonexpansive mappings. The method of the proof is different from the original one. Our results improve and extend the corresponding results announced by H.Y. Zhou, G.L. Gao, B. Tan [H.Y. Zhou, G.L. Gao, B. Tan, Convergence theorems of a Modified hybrid algorithm for a family of quasi- ϕ -asymptotically nonexpansive mappings, Journal of Applied Mathematics and Computing, doi: 10.1007/s12190-009-0263-4], [Yasunori Kimura, Wataru Takahashi, On a hybrid method for a family of relatively nonexpensive mappings in a Banach space, J. Math. Anal. Appl. 357 (2009) 356-363] and some others.

Special Issue: On the Occasion of Zenon Mróz' 80th Birthday, Part I

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 90, Issue 9 Cover Picture Special Issue: On the Occasion of Zenon Mróz' 80th Birthday, Part I First published: 26 August 2010 https://doi.org/10.1002/zamm.201090013AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Graphical Abstract See G. Sagar and E. Stein, Contributions on the theory and computation of mono- and poly-crystalline cyclic martensitic phase transformations, ZAMM 90 (2010) 9, p. 656 Volume90, Issue9Special Issue: “On the Occasion of Zenon Mróz' 80th Birthday”, Part ISeptember 2010 RelatedInformation

Special Issue: Phase Transition in Deformable Solids

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 90, Issue 7-8 Cover Picture Special Issue: Phase Transition in Deformable Solids First published: 09 June 2010 https://doi.org/10.1002/zamm.201090012AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Graphical Abstract See R. Ostwald, T. Bartel, and A. Menzel: A computational micro-sphere model applied to the simulation of phase-transformations, ZAMM 90 (2010), 7–8, p. 615, Fig. 9 and p. 617, Fig. 13b Volume90, Issue7-8Special Issue: Phase Transition in Deformable SolidsJuly 2010 RelatedInformation

The large-time development of the solution to an initial-value problem for the Korteweg-de Vries-Burgers equation: I. Initial data has a discontinuous compressive step

Journal Article The large-time development of the solution to an initial-value problem for the Korteweg-de Vries-Burgers equation: I. Initial data has a discontinuous compressive step Get access J. A. Leach J. A. Leach School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Search for other works by this author on: Oxford Academic Google Scholar IMA Journal of Applied Mathematics, Volume 75, Issue 5, October 2010, Pages 732–776, https://doi.org/10.1093/imamat/hxq032 Published: 07 June 2010 Article history Received: 28 November 2008 Revision received: 10 August 2009 Accepted: 15 April 2010 Published: 07 June 2010

Message from the retiring Editor-in-Chief

As all of you see, the Japan Journal of Industrial and Applied Mathematics (JJIAM) has already twenty-six years of history, Vol. 1 to Vol. 26, inclusive of the first seven yearswhile the journalwas entitled the Japan Journal of Applied Mathematics (JJAM). The late Professor Yamaguti Masaya, the very founder of JJAM, served the initial thirteen years (Vol. 1 through Vol. 13) as Editor-in-Chief with three collaborating editors listed as “the founding editors” inside the front cover of each issue of the Journal. I served the following thirteen years (Vol. 14 through Vol. 26) as Editor-in-Chief, but I introduced theArea Editors systemwith three area editors who substantially supported the editorial works with their associate editors. I am certainly indebted to all those area editors and associate editors. I would thank also the liaison editors-at-large from the Japan Society for Industrial and AppliedMathematics who constantly attended the regular editorial meetings and gave us valuable advices. The invaluable advices given from time to time by “Advisors” should also cordially be acknowledged. In summary, I have been more than happy that I could collaborate with all these people. During all the twenty-six years, i.e. from Vol. 1 through Vol. 26, “Kinokuniya” has been responsible for the publication of the Journal, which will be taken over by “Springer Japan” beginning with Vol. 27. Taking this opportunity, I have resigned from the position of Editor-in-Chief of JJIAM, which will be succeeded by Professor Mimura Masayasu. Under the leadership of the new Editor-in-Chief, JJIAM will, I hope, develop further to an internationally and interdisciplinarily better recognized scientific medium in the world of industrial and applied mathematics.

Paul Heinz Müller. 23. August 1924 – 10. Mai 2009

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 89, Issue 12 p. 1002-1004 Nachruf Paul Heinz Müller. 23. August 1924 – 10. Mai 2009 Rolf Kühne, Rolf KühneSearch for more papers by this authorGert Maibaum, Gert MaibaumSearch for more papers by this authorVolker Nollau, Volker NollauSearch for more papers by this authorThomas Riedrich, Thomas RiedrichSearch for more papers by this authorDietrich Stoyan, Dietrich StoyanSearch for more papers by this author Rolf Kühne, Rolf KühneSearch for more papers by this authorGert Maibaum, Gert MaibaumSearch for more papers by this authorVolker Nollau, Volker NollauSearch for more papers by this authorThomas Riedrich, Thomas RiedrichSearch for more papers by this authorDietrich Stoyan, Dietrich StoyanSearch for more papers by this author First published: 17 November 2009 https://doi.org/10.1002/zamm.200990023AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume89, Issue12December 2009Pages 1002-1004 RelatedInformation

Cover Picture: ZAMM 11/2009

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikVolume 89, Issue 11 Cover Picture Cover Picture: ZAMM 11/2009 First published: 23 October 2009 https://doi.org/10.1002/zamm.200990020AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume89, Issue11November 2009 RelatedInformation