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Semi-insulating Gallium Arsenide (SI-GaAs) samples experimentally show, under high electric fields and even at room temperature, negative differential conductivity in N-shaped form (NNDC). Since the most consolidated model for n-GaAs, namely, "the model", proposed by E. Schöll was not capable to generate the NNDC curve for SI-GaAs, in this work we have proposed an alternative model. The model proposed, "the two-valley model" is based on the minimal set of generation-recombination equations for two valleys inside of the conduction band, and an equation for the drift velocity as a function of the applied electric field, that covers the physical properties of the nonlinear electrical conduction of the SI-GaAs system. The "two-valley model" was capable to generate theoretically the NNDC region for the first time, and with that, we were able to build a high resolution parameter-space of the periodicity (PSP) using a Periodicity-Detection (PD) routine. In the parameter-space were observed self-organized periodic structures immersed in chaotic regions. The complex regions are presented in a "shrimp" shape rotated around a focal point, which forms in large-scale a "snail shell" shape, with intricate connections between different "shrimps". The knowledge of detailed information on parameter spaces is crucial to localize wide regions of smooth and continuous chaos.

A thin-walled tube with a predesigned spiral structure, named as the sinusoidal spiral tube (SST), was proposed to improve the energy absorption performance of the traditional circular straight tube and sinusoidal corrugation tube (SCT). A prototype of the SST was fabricated through additive manufacturing and its mechanical properties were tested. The numerical results were consistent with the tests. The effect of geometric features involving amplitude and pitch on energy absorption has been investigated through a series of numerical simulations. The results showed that there are six representative deformation modes and these modes transformed clearly under the action of amplitude and number of turns. On the other hand, the initial peak force was significantly reduced by 53.57–85.34% compared to the straight tube. The stability of plateau force was greatly improved by the spiral structure. The specific energy absorption increased by more than 15% compared to the SCTs under pinned–pinned and fixed–fixed boundary conditions, attributed to the transformation of the deformation mode and the increased number of folded lobes in the straight part. Last but not least, a theoretical model was proposed to predict the mean crushing force of the novel structure under free–free boundary conditions. It showed a good agreement with the numerical results.

We propose a new theory to explain the formation of spiral arms and of all types of outer rings in barred galaxies. We have extended and applied the technique used in celestial mechanics to compute transfer orbits. Thus, our theory is based on the chaotic orbital motion driven by the invariant manifolds associated to the periodic orbits around the hyperbolic equilibrium points. In particular, spiral arms and outer rings are related to the presence of heteroclinic or homoclinic orbits. Thus, R₁ rings are associated to the presence of heteroclinic orbits, while R₁R₂ rings are associated to the presence of homoclinic orbits. Spiral arms and R₂ rings, however, appear when there exist neither heteroclinic nor homoclinic orbits. We examine the parameter space of three realistic, yet simple, barred galaxy models and discuss the formation of the different morphologies according to the properties of the galaxy model. The different morphologies arise from differences in the dynamical parameters of the galaxy.