Entire slice regular functions

Entire functions in one complex variable are extremely relevant in several areas ranging from the study of convolution equations to special functions. An analog of entire functions in the quaternionic setting can be defined in the slice regular setting, a framework which includes polynomials and power series of the quaternionic variable. In the first chapters of this work we introduce and discuss the algebra and the analysis of slice regular functions. In addition to offering a self-contained introduction to the theory of slice-regular functions, these chapters also contain a few new results (for example we complete the discussion on lower bounds for slice regular functions initiated with the Ehrenpreis-Malgrange, by adding a brand new Cartan-type theorem). The core of the work is Chapter 5, where we study the growth of entire slice regular functions, and we show how such growth is related to the coefficients of the power series expansions that these functions have. It should be noted that the proofs we offer are not simple reconstructions of the holomorphic case. Indeed, the non-commutative setting creates a series of non-trivial problems. Also the counting of the zeros is not trivial because of the presence of spherical zeros which have infinite cardinality. We prove the analog of Jensen and Carath\'eodory theorems in this setting

Orbit design for future SpaceChip swarm missions

The effect of solar radiation pressure and atmospheric drag on the orbital dynamics of satellites-on-a-chip (SpaceChips) is exploited to design long-lived orbits about the Earth. The orbit energy gain due to asymmetric solar radiation pressure, considering the Earth shadow, is used to balance the energy loss due to atmospheric drag. Future missions for a swarm of SpaceChips are proposed, where a number of small devices are released from a conventional spacecraft to perform spatially distributed measurements of the conditions in the ionosphere and exosphere. It is shown that the orbit lifetime can be extended and indeed selected through solar radiation pressure and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag

Orbital dynamics of earth-orbiting 'smart dust' spacecraft under the effects of solar radiation pressure and aerodynamic drag

This paper investigates how the perturbations due to asymmetric solar radiation pressure, in presence of Earth's shadow, and atmospheric drag can be balanced to obtain long-lived Earth centered orbits for swarms of SpaceChips, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where a Sun-synchronous apse-line precession is achieved passively. The long-term evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Therefore, long-lived orbits can be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the short life-time of high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the end-of life decay of SpaceChips, thus preventing long-lived orbit debris

Nonlinear elasticity of monolayer graphene

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior of one-atom thick carbon sheets and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.Comment: 4 page

On the first Gaussian map for Prym-canonical line bundles

We prove by degeneration to Prym-canonical binary curves that the first Gaussian map of the Prym canonical line bundle $\omega_C \otimes A$ is surjective for the general point [C,A] of R_g if g >11, while it is injective if g < 12.Comment: To appear in Geometriae Dedicata. arXiv admin note: text overlap with arXiv:1105.447

Orbit control of high area-to-mass ratio spacecraft using electrochromic coating

This paper presents a novel method for the orbit control of high area-to-mass ratio spacecraft, such as spacecraft-on-a-chip, future „smart dust‟ devices and inflatable spacecraft. By changing the reflectivity coefficient of an electrochromic coating of the spacecraft, the perturbing effect of solar radiation pressure (SRP) is exploited to enable long-lived orbits and to control formations, without the need for propellant consumption or active pointing. The spacecraft is coated with a thin film of an electrochromic material that changes its reflectivity coefficient when a small current is applied. The change of reflectance alters the fraction of the radiation pressure force that is transmitted to the satellite, and hence has a direct effect on the spacecraft orbit evolution. The orbital element space is analysed to identify orbits which can be stabilised with electrochromic orbit control. A closed-loop feedback control method using an artificial potential field approach is introduced to stabilise these otherwise unsteady orbits. The stability of this solution is analysed and verified through numerical simulation. Finally, a test case is simulated in which the control method is used to perform orbital manoeuvres for a spacecraft formation

Orbit evolution, maintenance and disposal of SpaceChip swarms

The combined effect of solar radiation pressure and atmospheric drag is investigated for future mission conceptsfor swarms of satellites-on-a-chip (SpaceChips). The natural evolution of the swarm is exploited to perform spatially distributed measurements of the upper layers of the atmosphere. The energy gain from asymmetric solar radiation pressure can be used to balance the energy dissipation from atmospheric drag. An algorithm for long-term orbit control is then designed, based on changing the reflectivity coefficient of the SpaceChips. The subsequent modulation of the solar radiation pressure allows stabilisation of the swarm in the orbital element phase space. It is shown that the normally short orbit lifetime for such devices can be extended through the interaction of solar radiation pressure and atmospheric drag and indeed selected and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag