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Abstract We show that the quasiparticle kinetic theory for quantum and classical Calogero models reduces to the free-streaming Boltzmann equation. We reconcile this simple emergent behaviour with the strongly interacting character of the model by developing a Bethe–Lax correspondence in the classical case. This demonstrates explicitly that the freely propagating degrees of freedom are not bare particles, but rather quasiparticles corresponding to eigenvectors of the Lax matrix. We apply the resulting kinetic theory to classical Calogero particles in external trapping potentials and find excellent agreement with numerical simulations in all cases, both for harmonic traps that preserve integrability and exhibit perfect revivals, and for anharmonic traps that break microscopic integrability. Our framework also yields a simple description of multi-soliton solutions in a harmonic trap, with solitons corresponding to sharp peaks in the quasiparticle density. Extensions to quantum systems of Calogero particles are discussed.
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A New Analytical Approach for Bistable Composites
Structures with adaptive capabilities offer many potentials to achieve future needs in efficiency, reliability, and intelligence. To this end, bistable CFRP (Carbon Fibre Reinforced Polymers) composites with asymmetric fiber layout are a promising concept that has shown shape morphing capabilities that adapt to the changes in the environment such as external forces and moments. This adaptability opens them to endless application potentials, ranging from small micro-switches to large airfoil sections in airplane wings or wind turbine blades. To harness this potential, it is essential to predict these composites’ physical shapes and behavior accurately. To this end, Hyer and Dano devised the first analytical model based on the concepts of Classical Lamination Theory, and this model has become the cornerstone of almost all subsequent studies. However, this theory uses Kirchoff’s theory of thin plates that are limited by several assumptions. As a result, Hyer’s theory can predict the overall shape of these laminates but lacks accuracy. A reason for this model’s underperformance is that it ignores the inter-laminar stresses and strains, but such stresses/strains play a vital role in the balance of the overall stress field and are found significantly higher near the free edges. To overcome these fundamental limitations, we propose a new analytical approach by combining the Reissner-Mindlin theory with concepts from the Classical Lamination Theory. This new model introduces in-plane rotations as two additional degrees of freedom. Thus, it has five independent variables compared to only three in Hyer and Dano’s model and its derivatives. Hence, we have a more complex but more accurate model. This paper outlines our new analytical approach by 1) introducing these two additional degrees of freedom; 2) selecting appropriate polynomial approximations; 3) formulating inter-laminar stresses that are functions of these added rotations; and 4) incorporating these inter-laminar stresses in the potential energy equation. By comparing this model’s prediction with the finite element simulation results, we found the new model slightly under predicts the laminate deformation, but the overall accuracy is promising, as evidenced by high R-squared correlation.
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- Award ID(s):
- 1760943
- PAR ID:
- 10351421
- Date Published:
- Journal Name:
- Proceedings of the ASME 2021 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
- Page Range / eLocation ID:
- V001T07A010
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/SMASIS2021-68224
