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[CT031]

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : In this paper, the recovery of the diffusion coefficient from the final time-measured data is carried out using the quasi-solution approach. The inverse coefficient problem is formulated as a minimization problem using an objective functional. The existence of the minimizer is proved, then the necessary optimality condition is derived, and by using that condition, the stability results are proved. To illustrate the efficiency of this method, numerical results are investigated using the conjugate gradient method.
Classification : 35G16, 35R30, 49K35, 49K20
Author(s) :
- NAVANEETHA KRISHNAN M (CENTRAL UNIVERSITY OF TAMIL NADU, THIRUVARUR - 610005)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : Recent results on the dynamics of beams under self-weight imply the existence of dynamic compression in ultra-large marine structures, possibly causing the coexistence of compressive and anti-compressive vibration modes. This results in a harmonic phase-transition as the mode-shapes flip qualitatively, leading to extreme curvatures and numerical instability. For this talk we'll present sharp estimates for the bottom tensions required for the safe operation of marine risers through an analogy with quantum systems with turning points.
Classification : 35Gxx, 35Pxx, 35Qxx
Author(s) :
- Arthur Bizzi (IMPA)
- Arthur Bizzi (IMPA)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : Recent results imply the coexistence of compressive and anti-compressive vibration modes for massive Rayleigh beams, leading to a harmonic phase-transition within the structure. As a result, the underlying wave operators switch between causal and anti-causal, a phenomenon which is entirely absent from the usual Euler-Bernoulli simplification. For this talk, we'll discuss the wide-ranging implications of this for the control of flexible structures, specially the partial loss of controllabity and observability.
Classification : 35Gxx, 35Pxx, 35Qxx
Author(s) :
- Arthur Bizzi (IMPA)
- Arthur Bizzi (IMPA)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : The Helmholtz-Hodge decomposition is a fundamental tool in the study of vector fields and has many applications. In this talk, we will focus on the case of polynomial vector fields. First, we will introduce results on the general properties and methods for finding a decomposition. As an application, we will explain the relationship between the Helmholtz-Hodge decomposition and the construction of Lyapunov functions.
Classification : 37B25, 31B99
Author(s) :
- Tomoharu Suda (RIKEN)
- Tomoharu Suda (Keio University)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : Koopman operator methods along with the associated numerical algorithms have provided a powerful methodology for the data-driven study of nonlinear dynamical systems. In this talk, we will give a brief outline of how the Koopman group of operators can be generalized beyond function spaces to the space of sections of various vector bundles over the state space. We describe their relationship with the standard Koopman operator on functions as well as describe the new spectral invariants produced by these generalized operators. We then demonstrate how the recently developed spectral exterior calculus framework can be utilized to compute the spectral properties of the generator of the induced operator on sections of the cotangent bundle. We conclude with some applications of the algorithm to some well-known dynamical systems.
Classification : 37C30
Author(s) :
- Allan M. Avila (AIMdyn Inc.)