Mathematical methods applied in the study of nonlinear mechanical systems

Contract No. 69 from 02.05.2018

Duration: May 2018- April 2020

Financially supported by Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI

Host Institution: "Alexandru Ioan Cuza" University of Iasi


Principal Investigator: Dr. Ionel-Dumitrel Ghiba

Research Team:

• Conf.dr. Eugen Varvaruca (Senior researcher)


• Conf.dr. Catalin Gales (Senior researcher)


• Asist. dr. Simona Barna (Postdoctoral researcher)


• Asist. dr. Maria Malin (Postdoctoral researcher)


• Master student: Razvan Ceuca

Project Summary:

This project is devoted to advancing the theoretical understanding of some fundamental problems from nonlinear mechanics, as well as to the introduction of new models. The project requires a high degree of mathematical sophistication, technical ability and drive if it is to be moved forward across a wide range of issues as are raised in the proposal. The main tasks of the project given below may be classified into the following four areas: nonlinear shell models; rank-one convexity and polyconvexity in nonlinear elasticity; nonlinear free surface travelling water waves; nonlinear dynamical systems in classical mechanics. This classification will serve to formulate the main objectives and the research methodology of the project and to point out the relevance of our tasks in the framework of applied analysis and nonlinear mechanics.


Objectives:

• Rank-one convexity and polyconvexity in nonlinear elasticity;


• Nonlinear free surface travelling water waves;


• Nonlinear dynamical systems in classical mechanics;


• Nonlinear shell models.

Expected results:

• We shall promote international scientific cooperation and we shall increase the visibility of Romanian research by publishing highly original research papers (a minimum of 8 articles in international ISI journals).

Publications:

• I.D. Ghiba, R.J. Martin, P. Neff. Rank-one convexity implies polyconvexity in isotropic planar incompressible elasticity, Journal de Mathématiques Pures et Appliqués, 116, 88-104, 2018, IF=1.848, SRI=3.767


• R.J. Martin, I.D. Ghiba, P. Neff, A non-ellipticity result, or the impossible taming of the logarithmic strain measure, International Journal of Non-Linear Mechanics, 102, 147-158, 2018, IF=2.163, SRI=1.314


• R.J. Martin, I.D. Ghiba, P. Neff, A polyconvex extension of the logarithmic Hencky strain energy, Analysis and Applications 17: 349-361, 2019. IF=1.21


• A. Constantin, W. Strauss, E. Varvaruca, Large-amplitude steady downstream water waves, under review, 2019-2020.


• S. Nistor, C. Oniciuc, On the uniqueness of complete biconservative surfaces in $\mathbb{R}^3$, Proceedings AMS 147: 1231-1245, 2019. IF=0.813


• C. Lhotka, C. Gales, Charged dust close to outer mean-motion heliosphere, Celestial Mechanics and Dynamical Astronomy 131: UNSP 49, 2019. IF=1.837


• M. Birsan, I.D. Ghiba, R.J. Martin, P. Neff, Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature, Mathematics and Mechanics of Solids, 24: 4000-4019, 2019.


• P. Neff, M. Birsan, I.D. Ghiba, A higher order geometrically nonlinear Cosserat‐shell model with initial curvature effects, PAMM-Proc. Appl. Math. Mech. 19 (1), e201900351, 2019.


• J. Burgos-Garcia, A. Celletti, C. Gales, M. Gidea, W.T. Lam, Hill four-body problem with oblate tertiary: an application to the Sun-Jupiter-Hektor-Skamandrios system, acceptat 2019.


• A. Celletti, C. Gales, C. Lhotka, Resonances in the Earth’s space environment, Communications in Nonlinear Science and Numerical Simulation, Volume 84, May 2020, 105185. (IF=3.967)


• M. Malin, C. Mardare, Estimates for the constant in two nonlinear Korn inequalities, submitted, 2020.


• M. Malin, C. Mardare, A nonlinear Korn inequality in R^n with an explicitly bounded constant, Comptes Rendus Mathematique, accepted, 2020.

Total IF:


Conferences:

• I.D. Ghiba, Rank-one convexity and polyconvexity for some classes of functions, Workshop in analysis, differential equations and mechanics, ICUB and Faculty of Mathematics, University of Bucharest, 9 November, 2018. (cu R. Martin si P. Neff) https://sites.google.com/site/cristianmihaicazacu/mini-workshop-icub-fmi


• E. Varvaruca, Large-amplitude steady gravity water waves with constant vorticity, Analyse, analyse numérique et contrôle des milieux continus, Bucure\c ti, 21-23 mai, 2018. (cu A. Constantin si W. Strauss) https://indico.math.cnrs.fr/event/3053/


• E. Varvaruca, Large-amplitude steady gravity water waves with constant vorticity, Lund Workshop on Fluid Dynamics and Dispersive Equations, University of Lund, Suedia, 25 - 29 iunie, 2018, (cu A. Constantin si W. Strauss) http://delegia.com/app/attendee/default.asp?ProjectId=12468&PageId=72678


• E. Varvaruca, Large-amplitude steady gravity water waves with constant vorticity, 14th Franco-Romanian conference on applied mathematics, 27-31 august, 2018, Bordeaux, Fran\c ta. (cu A. Constantin si W. Strauss) https://france-roumanie.sciencesconf.org/


• C. Gales, On the dynamics of space debris, Outlook in Astronomy, Astrophysics, Space and Planetary Sciences, Cluj-Napoca, 17-19 mai, 2018. http://www.cs.ubbcluj.ro/outlook-in-astronomy-astrophysics-space-and-planetary-sciences-international-conference-17-19-may-2018-cluj-napoca/


• C. Gales, Dynamical effects of tesseral resonances in the LEO region, 2018AMC70 between Mathematics and Astronomy, A Workshop in honor of Andrea Milani Comparetti on the occasion of his 70th birthday, Pisa, 3-5 septembrie, 2018. https://www.dm.unipi.it/webnew/it/content/2018-amc-70-between-mathematics-and-astronomy


• C. Gales, Workshop: Dynamical Systems: from geometry to mechanics, 5-8 February 2019.


• C. Gales, Workshop: Mathematical Models and Methods in Earth and Space Science, 19-22 March 2019


• C. Gales, A portrait of resonances in the space debris problem, The Ninth Congress of Romanian Mathematicians, June 28-July 3, 2019, Galati, Romania.


• C. Gales, XLIV Summer School on Mathematical Physics, Ravello 2-7 September, 2019, with the lecture: On the dynamics of space debris.


• I.D. Ghiba, Well-posedness of nonstandard relaxed models including novel micro-inertia terms, The 2019 EMI International Conference, 3-5 July, 2019.


• C. Gales, I-CELMECH Training School, February 3-7, 2020, Milan, Italy, with the two-hours lecture: Space debris.

Academic visits:

• I.D. Ghiba was guest of Prof. Dr. Mircea Birsan and Prof. dr. Patrizio Neff, Duisburg-Essen University, Germany, September and November, 2019.


• I.D. Ghiba was guest of Prof. Dr. Mircea Birsan and Prof. dr. Patrizio Neff, Duisburg-Essen University, Germany, July 10-August 7, 2018.


• S. Nistor (Barna) was guest of Prof. Stefano Montaldo, University of Cagliari, Italy, 9-16 September 2018.


• I.D. Ghiba was guest of Prof. Dr. Mircea Birsan and Prof. dr. Patrizio Neff, Duisburg-Essen University, Germany, September and November, 2019.

Others:

Scientific reports:

• Scientific report 2018


• Scientific report 2019


• Scientific report 2020-Final report