A uniform controllability result for the Keller-Segel system

In this paper we study the controllability of the Keller-Segel system approximating its parabolic-elliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the parabolic-elliptic system when the control is acting on the component of the chemical

SU(2)SU(2)-particle sigma model: Momentum-space quantization of a particle on the sphere S3S^3

We perform the momentum-space quantization of a spin-less particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using a non-canonical method entirely based on symmetry grounds. To achieve this task, non-standard (contact) symmetries are required as already shown in a previous article where the configuration-space quantization was given. The Hilbert space in the momentum space representation turns out to be made of a subset of (oscillatory) solutions of the Helmholtz equation in four dimensions. The most relevant result is the fact that both the scalar product and the generalized Fourier transform between configuration and momentum spaces deviate notably from the naively expected expressions, the former exhibiting now a non-trivial kernel, under a double integral, traced back to the non-trivial topology of the phase space, even though the momentum space as such is flat. In addition, momentum space itself appears directly as the carrier space of an irreducible representation of the symmetry group, and the Fourier transform as the unitary equivalence between two unitary irreducible representations.Comment: 29 pages, 3 figure

Computational analysis of projectile impact resistance on aluminium (a356) curvilinear surface reinforced with carbon nanotubes (cnts) for applications in systems of protection

Computational tests for ballistic impact energy absorption were developed on A356/CNTs composite material with the goal of estimating the improvement of the material’s mechanical properties by the contribution of the CNTs [1]. For the implementation of computational tests on the material exposed to projectile impact, A356/CNTs was configured by means of generalized Hooke’s model for anisotropic materials [1] and Johnson-Cook’s model was used to determine material failure and propagation of energy [2]. A curvilinear surface (semi-spheres on a plaque) with an area of 23x23 cm and thickness of 12 mm was elaborated to represent the composite material. The impact on surface was done with a 9 mm projectile and the surface was developed with 4.5 mm radium semi-spheres. It was used a 0.3% of nanotube insertions on the composite total volume. The results indicated the plaque stopped the impact without drilling. Incidence of damage to wearer, as well as possibility of composite material improvement and the diffusion/dispersion analysis on the curvilinear surface was also done