Meta-structures that display axial-twist coupling can be achieved through the emerging kinematics in Kresling origami patterns. A central challenge in these structures is understanding their nonlinear mechanical behaviour, specifically their equilibrium branches and bifurcation diagrams. This involves identifying relationships between desired responses and the geometric variables that define the design space, including the Kresling polygon count, initial twist angle, height, radius, and crease lengths. As the number of constituent units increases in an n-layer chain, we track complex equilibrium branches extending into the post-critical regime under successive instabilities, including branch-point bifurcations and limit-point instabilities. This work begins by establishing the relationship between the geometric design variables and the response curves of the assembled chain by modelling the crease lines as axial-load-carrying elements. Subsequently, equilibrium branches and instabilities are systematically investigated via continuation and bifurcation analysis, beginning with the single-layer system and progressively extending to two- and three-layer configurations. Finally, a generalisation strategy is proposed to extend these findings to an n-layer Kresling chain. This strategy enables the predictive construction of equilibrium paths and the inverse design of multi-layer meta-structures, using prescribed critical points to control post-critical behaviour. It provides a foundation for the inverse design and optimisation of architected mechanical metamaterials with programmable responses.

A time-reversal characteristic-mode decomposition is developed for reciprocal lossy electromagnetic structures. The formulation is built on a transmit--receive interpretation of reciprocity: the far-field pattern radiated by a mode determines the time-reversed incident field that is optimally matched to couple energy back into that same mode. This physical picture leads to an antilinear characteristic-mode equation whose solutions remain radiation-power orthogonal even in the presence of material loss, lossy loading, or matched absorption. As a result, the modal expansion coefficients directly represent the radiated-power contributions of the corresponding modes and avoid the singular biorthogonal normalization that may arise in nonnormal classical characteristic-mode expansions. Equivalent formulations are derived in the scattering-operator, T-matrix, and method-of-moments (MoM) frameworks, thereby connecting external wave-channel descriptions with current-space and port-excitation descriptions. The proposed modes reduce to classical characteristic modes in the lossless limit. Numerical examples involving a lossy two-sphere system and a loaded folded antenna demonstrate the radiation-power orthogonality, modal-expansion stability, and power interpretability of the proposed decomposition near exceptional points, where classical characteristic-mode expansions become singular or lose their radiated-power meaning.

Thermomagnetic generators (TMGs) are devices that convert waste heat to electricity through a change in magnetization of a solid material. This causes a changing flux through a coil, which induces an electromotive force per Faraday's law. However, the influence of the coil on the performance of the TMG has not been investigated and existing TMG prototypes merely utilize some coil, not the optimal coil for a given device. In this work we present an analytical and numerical model of a TMG that calculates power by explicitly coupling the TMGs magnetic and electric circuits and use this to analyze the influence of the coil on the TMG performance. We show that analytically TMG power has a linear dependence on coil volume, independent of the specific combination of wire radius and coil turns. The model is validated with experimental data, and finally used to study prototype TMGs presented in literature, where we show that the power of these literature TMGs can be increased by a factor of 10-400 times, had larger coils been used in the prototypes.