Browsing by Subject "Periodic systems"

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Open Access
Identification of a vertical hopping robot model via harmonic transfer functions
(Sage Publications Ltd., 2016) Uyanık, İ.; Ankaralı, M. M.; Cowan, N. J.; Saranlı U.; Morgül, Ö.
A common approach to understanding and controlling robotic legged locomotion is the construction and analysis of simplified mathematical models that capture essential features of locomotor behaviours. However, the representational power of such simple mathematical models is inevitably limited due to the non-linear and complex nature of biological locomotor systems. Attempting to identify and explicitly incorporate key non-linearities into the model is challenging, increases complexity, and decreases the analytic utility of the resulting models. In this paper, we adopt a data-driven approach, with the goal of furnishing an input–output representation of a locomotor system. Our method is based on approximating the hybrid dynamics of a legged locomotion model around its limit cycle as a Linear Time Periodic (LTP) system. Perturbing inputs to the locomotor system with small chirp signals yield the input–output data necessary for the application of LTP system identification techniques, allowing us to estimate harmonic transfer functions (HTFs) associated with the local LTP approximation to the system dynamics around the limit cycle. We compare actual system responses with responses predicted by the HTF, providing evidence that data-driven system identification methods can be used to construct models for locomotor behaviours.
Embargo
On the identification and finite element treatment of macroscopic stress in Kohn–Sham density functional theory
(Elsevier BV, 2024-12-14) Temizer, İlker
The macroscopic stress formulation for periodic systems in Kohn–Sham density functional theory is critically examined. The identification of the stress through the partial variation of the energy with respect to cell deformation is cast in a strictly large deformation context. The nature of the non-uniqueness in the stress expression which emanates from this variation is extensively discussed. The possible lack of symmetry in this expression is highlighted and the conditions under which different expressions deliver the same tensorial value are derived. These observations are demonstrated through a finite element framework that is validated towards energy, force and stress calculations.