TUM-ParticleTyper 2: automated quantitative analysis of (microplastic) particles and fibers down to 1 [Formula: see text]m by Raman microspectroscopy.

Accurate quantification of small microplastics in environmental and food samples is a prerequisite for studying their potential hazard. Knowledge of numbers, size distributions and polymer type for particles and fibers is particularly relevant in this respect. Raman microspectroscopy can identify particles down to 1 [Formula: see text]m in diameter.

Speed-up hyperspheres homotopic path tracking algorithm for PWL circuits simulations.

In the present work, we introduce an improved version of the hyperspheres path tracking method adapted for piecewise linear (PWL) circuits. This enhanced version takes advantage of the PWL characteristics from the homotopic curve, achieving faster path tracking and improving the performance of the homotopy continuation method (HCM). Faster computing time allows the study of complex circuits with higher complexity; the proposed method also decrease, significantly, the probability of having a diverging problem when using the Newton-Raphson method because it is applied just twice per linear region on the homotopic path.

Modified hyperspheres algorithm to trace homotopy curves of nonlinear circuits composed by piecewise linear modelled devices.

We present a homotopy continuation method (HCM) for finding multiple operating points of nonlinear circuits composed of devices modelled by using piecewise linear (PWL) representations. We propose an adaptation of the modified spheres path tracking algorithm to trace the homotopy trajectories of PWL circuits. In order to assess the benefits of this proposal, four nonlinear circuits composed of piecewise linear modelled devices are analysed to determine their multiple operating points.