Non-linear Systems
Non-linear physics is the study of systems where the output is not directly proportional to the input. Unlike linear systems, which follow simple, predictable relationships, non-linear systems exhibit complex behaviours that can be chaotic, unpredictable, and counterintuitive. These systems are governed by non-linear equations, which often involve higher-degree polynomials or non-polynomial functions.
In non-linear physics, non-linear processes can lead to complex equilibrium states and dynamics. These include phenomena such as instabilities and chaotic equilibrium phase diagrams. Instabilities occur when small perturbations grow over time, leading to significant changes in the system's behaviour. Chaotic dynamics, on the other hand, are characterized by sensitive dependence on initial conditions, where tiny differences can result in vastly different outcomes.
An example of non-linear process, first modelled in our lab, is the Red Blood Cell density separation. This process is useful in biophysical research to separate cohorts of cells with different age. Blood density separation involves the use of density gradient mediums, such as nanoparticles suspensions, to isolate blood cells based on their densities. The separation process is influenced by non-linear dynamics, where the interactions between blood components and the gradient medium can lead to band patterns, whose exact structure are non-linear functions of the volume fraction and density distribution. These states can exhibit instabilities and chaotic behaviour, affecting the efficiency and outcome of the separation process.
Understanding these non-linear behaviours is crucial for optimizing separation techniques and improving the accuracy of isolating specific cell populations.
Figure adapted from F. Maurer et al., ArXiv, 2024 https://doi.org/10.48550/arXiv.2407.07676