Evolutionary-based sparse regression for the experimental identification of duffing oscillator

In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms as part of the ordinary differential equation of the system. Correct identification of this nonlinear system using sparse identification is hugely dependent on selecting the correct form of nonlinearity included in the function library. Consequently, in this work, the evolutionary-based sparse identification is replacing the need for user knowledge when constructing the library in sparse identification. Constructing the library based on the data-driven evolutionary approach is an effective way to extend the space of nonlinear functions, allowing for the sparse regression to be applied on an extensive space of functions. The results show that the method provides an effective algorithm for the purpose of unveiling the physical nature of the Duffing oscillator. In addition, the robustness of the identification algorithm is investigated for various levels of noise in simulation. The proposed method has possible applications to other nonlinear dynamic systems in mechatronics, robotics, and electronics

Long-range forces in controlled systems

This thesis investigates new phenomena due to long-range forces and their effects on different multi-DOFs systems. In particular the systems considered are metamaterials, i.e. materials with long-range connections. The long-range connections characterizing metamaterials are part of the more general framework of non-local elasticity. In the theory of non-local elasticity, the connections between non-adjacent particles can assume different configurations, namely one-to-all, all-to-all, all-to-all-limited, random-sparse and all-to-all-twin. In this study three aspects of the long-range interactions are investigated, and two models of non-local elasticity are considered: all-to-all and random-sparse. The first topic considers an all-to-all connections topology and formalizes the mathematical models to study wave propagation in long-range 1D metamaterials. Closed forms of the dispersion equation are disclosed, and a propagation map synthesizes the properties of these materials which unveil wave-stopping, negative group velocity, instability and non-local effects. This investigation defines how long-range interactions in elastic metamaterials can produce a variety of new effects in wave propagation. The second one considers an all-to-all connections topology and aims to define an optimal design of the long-range actions in terms of spatial and intensity distribution to obtain a passive control of the propagation behavior which may produces exotic effects. A phenomenon of frequency filtering in a confined region of a 1D metamaterial is obtained and the optimization process guarantees this is the best obtainable result for a specific set of control parameters. The third one considers a random-sparse connections topology and provides a new definition of long-range force, based on the concept of small-world network. The small-world model, born in the field of social networks, is suitably applied to a regular lattice by the introduction of additional, randomly selected, elastic connections between different points. These connections modify the waves propagation within the structure and the system exhibits a much higher propagation speed and synchronization. This result is one of the remarkable characteristics of the defined long-range connections topology that can be applied to metamaterials as well as other multi-DOFs systems. Qualitative experimental results are presented, and a preliminary set-up is illustrated. To summarize, this thesis highlights non-local elastic structures which display unusual propagation behaviors; moreover, it proposes a control approach that produces a frequency filtering material and shows the fast propagation of energy within a random-sparse connected material

Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations

In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equations. Our approach is non-intrusive and we use the existing fluid dynamics solver NaSt3DGPF to solve the incompressible two-phase Navier-Stokes equation for each given realization. We are able to empirically show that the resulting kernel-based stochastic collocation is highly competitive in this setting and even outperforms some other standard methods

A framework for quantification and physical modeling of cell mixing applied to oscillator synchronization in vertebrate somitogenesis

In development and disease, cells move as they exchange signals. One example is found in vertebrate development, during which the timing of segment formation is set by a ‘segmentation clock’, in which oscillating gene expression is synchronized across a population of cells by Delta-Notch signaling. Delta-Notch signaling requires local cell-cell contact, but in the zebrafish embryonic tailbud, oscillating cells move rapidly, exchanging neighbors. Previous theoretical studies proposed that this relative movement or cell mixing might alter signaling and thereby enhance synchronization. However, it remains unclear whether the mixing timescale in the tissue is in the right range for this effect, because a framework to reliably measure the mixing timescale and compare it with signaling timescale is lacking. Here, we develop such a framework using a quantitative description of cell mixing without the need for an external reference frame and constructing a physical model of cell movement based on the data. Numerical simulations show that mixing with experimentally observed statistics enhances synchronization of coupled phase oscillators, suggesting that mixing in the tailbud is fast enough to affect the coherence of rhythmic gene expression. Our approach will find general application in analyzing the relative movements of communicating cells during development and disease.Fil: Uriu, Koichiro. Kanazawa University; JapónFil: Bhavna, Rajasekaran. Max Planck Institute of Molecular Cell Biology and Genetics; Alemania. Max Planck Institute for the Physics of Complex Systems; AlemaniaFil: Oates, Andrew C.. Francis Crick Institute; Reino Unido. University College London; Reino UnidoFil: Morelli, Luis Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación en Biomedicina de Buenos Aires - Instituto Partner de la Sociedad Max Planck; Argentina. Max Planck Institute for Molecular Physiology; Alemania. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin