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Nonlinear phenomena are phenomena, which, in contrast to a linear system, cannot be explained by a mathematical relationship of proportionality (that is, a linear relationship between two variables). For example, the spread of an infectious disease is most often exponential, rather than linear, with time.
Multiple parameter estimation techniques are employed to empirically validate theoretical propositions regarding complex systems by discerning relevant free parameters from often scarce experimental data. In this tutorial, the authors provide a beginner’s guide to parameter estimation via adjoint optimization, and show its efficiency in prototypical problems across different fields of physics.
Controlling phase transitions in solids is crucial for many applications. Ultrafast laser pulses have now been shown to enable the energy-efficient generation of structural fluctuations in VO2 by harnessing the correlated disorder in the material.
Linear topological systems can be characterized using invariants such as the Chern number. This concept can be extended to the nonlinear regime, giving rise to nonlinearity-induced topological phase transitions.
Bifurcation of exceptional points (EPs) could offer applications in metrology by amplifying sensitivity. The authors find that introducing experimentally nonlinearity can bifurcate the EP degeneracy lifting yielding an elevenfold sensitivity enhancement and a chaotic dynamics near the EP compared to the conventional EP-based approach in the linear regime.
Stable regions in four-dimensional phase space have been observed by following the motion of accelerated proton beams subject to nonlinear forces. This provides insights into the physics of dynamical systems and may lead to improved accelerator designs.
Ageing is a non-linear, irreversible process that defines many properties of glassy materials. Now, it is shown that the so-called material-time formalism can describe ageing in terms of equilibrium-like properties.
Predicting the large-scale behaviour of complex systems is challenging because of their underlying nonlinear dynamics. Theoretical evidence now verifies that many complex systems can be simplified and still provide an insightful description of the phenomena of interest.
