Similarity, Symmetry and Group Theoretical Methods in Mechanics - CURRENTLY NOT SCHEDULED

Invited Lecturers

George Bluman (University of British Columbia, Vancouver, Canada)
6 lectures on: These five lectures will give an overview of recent developments by George Bluman and his collaborators in the field of symmetries anddifferential equations. •General introduction giving an extensive overview of topics to be covered. •Review of local symmetries - point, contact, higher-order. •Construction of conservation laws (CLs) - direct method to find them, connections with Noether’s theorem. •Use of symmetries to construct new conservation laws from known CLs. •How to systematically find trees of equivalent but nonlocally related PDE systems for a given PDE system through the use of CLs, point symmetries and subsystems. •How to systematically find nonlocal symmetries and nonlocal conservation laws for a given PDE system. •The multidimensional situation. •All topics will be illustrated through numerous examples.

Jean Francois Ganghoffer (Université de Lorraine, Nancy, France)
6 lectures on: Symmetry methods in continuum solid mechanics of materials. •Symmetries in the Lagrangian formulation of field theories. •Symmetries in continuum solid mechanics (nonlinear elasticity). •Invariance relations in nonlinear elasticity, path independent integrals. •Eshelbian mechanics. •Applications of Lie symmetries in elastoviscoplasticity: construction of invariance relations and master responses.

Ivailo Mladenov (Bulgarian Academy of Sciences, Sofia, Bulgaria)
5 lectures on: The Many Faces of Elastica. •Geometrical background. •Intrinsic equations. •Symmetries. The generalized elastica. •Membrane shapes, Hele-Shaw cells. •Explicit solutions of the shape equation.

Andreas Müller (Shanghai Jiao Tong University Joint Institute, China)
6 lectures on: Group Theoretical Approaches to the Mobility and Singularities of Mechanisms. •Analytic varieties and mobility concepts. •Non-smooth kinematic phenomena. •Higher-order local analysis. •Generic statements. •Open problems and alternative routes.

Martin Oberlack (Technical University, Darmstadt, Germany)
6 lectures on: Symmetry Methods in Fluid Mechanics and Turbulence Theory. •Symmetries of Euler and Navier-Stokes equations in 3D. •Conservation laws of Euler and Navier-Stokes equations in 3D. •Symmetries and conservation laws of Euler and Navier-Stokes equations in reduced dimensions. •The three fundamental statistical approaches to turbulence: Lundgren-Monin-Novikov pdf equations, the Friedmann-Keller moment equations and the Hopf functional equation. •Counterpart of classical symmetries of Euler and Navier- Stokes for turbulence statistics. •New statistical symmetries of turbulence with no classical counterpart. •Symmetry invariant solutions as turbulent scaling laws derived from classical and new statistical symmetries.

Jan J. Slawianowski (University of Warsaw, Poland)
6 lectures on: Mechanical Systems with Affine and Unitary Degrees of Freedom. •Hamiltonian and quantum systems on Lie groups and homogeneous spaces. •Rigid body and affinely-rigid body. •Affinely-invariant dynamics of affinely-rigid body. •Micromorphic mechanics and its affine generalization. •Born-Infeld theory and the mechanics of shells. •D’Alembert and Vakonomic variational principles.

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