This paper describes an electrostatic field-assisted assembly technique combined with an electrospinning process used to position and align individual nanofibres (NFs) on a tapered and grounded wheel-like bobbin. The bobbin is able to wind a continuously as-spun nanofibre at its tip-like edge. The alignment approach has resulted in polyethylene oxide-based NFs with diameters ranging from 100-300 nm and lengths of up to hundreds of microns. The results demonstrate the effectiveness of this new approach for assembling NFs in parallel arrays while being able to control the average separation between the fibres.

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In this letter, we report on a technique for the hierarchical assembly of nanofibers into crossbar nanostructures. An electrospinning process is used to create polymer-based nanofibers with diameters ranging from 10–180 nm and lengths of up to several centimeters. By controlling the electrostatic field and the polymer rheology, the nanofibers can be assembled into parallel periodic arrays. We also propose a theoretical model for the process.

The shape evolution of small droplets attached to a conducting surface and subjected to relatively strong electric fields is studied both experimentally and numerically. The problem is motivated by the phenomena characteristic of the electrospinning of nanofibres. Three different scenarios of droplet shape evolution are distinguished, based on numerical solution of the Stokes equations for perfectly conducting droplets. (i) In sufficiently weak (subcritical) electric fields the droplets are stretched by the electric Maxwell stresses and acquire steady-state shapes where equilibrium is achieved by means of the surface tension. (ii) In stronger (supercritical) electric fields the Maxwell stresses overcome the surface tension, and jetting is initiated from the droplet tip if the static (initial) contact angle of the droplet with the conducting electrode is $\alpha_{s}\,{<}\,0.8\pi $; in this case the jet base acquires a quasi-steady, nearly conical shape with vertical semi-angle $\beta \,{\leq}\, 30^{\circ}$, which is significantly smaller than that of the Taylor cone ($\beta_{T}\,{=}\,49.3^{\circ}$). (iii) In supercritical electric fields acting on droplets with contact angle in the range $0.8\pi \,{<}\,\alpha_{s}\,{<}\,\pi $ there is no jetting and almost the whole droplet jumps off, similar to the gravity or drop-on-demand dripping. The droplet–jet transitional region and the jet region proper are studied in detail for the second case, using the quasi-one-dimensional equations with inertial effects and such additional features as the dielectric properties of the liquid (leaky dielectrics) taken into account. The flow in the transitional and jet region is matched to that in the droplet. By this means, the current–voltage characteristic $I\,{=}\,I(U)$ and the volumetric flow rate $Q$ in electrospun viscous jets are predicted, given the potential difference applied. The predicted dependence $I\,{=}\,I(U)$ is nonlinear due to the convective mechanism of charge redistribution superimposed on the conductive (ohmic) one. For $U\,{=}\,O(10kV)$ and fluid conductivity $\sigma \,{=}\,10^{-4}$ S m$^{-1}$, realistic current values $I\,{=}\,O(10^{2}nA)$ were predicted.

Spacecraft relative motion planning is concerned with the design and execution of maneuvers relative to a nominal target. These types of maneuvers are frequently utilized in missions such as rendezvous and docking, satellite inspection and formation flight where exclusion zones representing spacecraft or other obstacles must be avoided. The presence of these exclusion zones leads to non-linear and non-convex constraints which must be satisfied. In this paper, a novel approach to spacecraft relative motion planning with obstacle avoidance and thrust constraints is developed. This approach is based on a graph search applied to a virtual net of closed (periodic) natural motion trajectories, where the natural motion trajectories represent virtual net nodes (vertices), and adjacency and connection information is determined by conditions defined in terms of safe, positively-invariant tubes built around each trajectory. These conditions guarantee that transitions from one natural motion trajectory to another natural motion trajectory can be completed without constraint violations. The proposed approach improves the flexibility of a previous approach based on the use of forced equilibria, and has other advantages in terms of reduced fuel consumption and passive safety. The resulting maneuvers, if planned on-board, can be executed directly or, if planned off-board, can be used to warm start trajectory optimizers to generate further improvements. Nomenclature A, A c , ¯ A = Discrete-time, continuous-time and closed-loop dynamics matrices B = Discrete-time input matrix e = State error J = Trajectory cost k = Discrete-time instant (integer) K = State-feedback gain matrix P = Positive-definite ellipsoidal shape matrix u = Control vector u max = Maximum allowable control X = Spacecraft state vector consisting of relative positions and velocities, x, y, z, ˙ x, ˙ y, ˙ z X n = State vector along a natural motion trajectory X ni = State vector along natural motion trajectory N i δ = Integer corresponding to initial controller reference point along a natural motion trajectory ∆T = Discrete-time update period Ξ, Ξ w = Unweighted and weighted connection arrays Π, Π w = Unweighted and weighted adjacency matrices ρ s k = Ellipsoidal scale factors for safe sets ρ k = Ellipsoidal scale factors used to generate safe, positively-invariant tubes ρ u , ρ Oi,k = Maximum possible ellipsoidal scale factors considering control constraints, or the ith exclusion zone constraint B(Z, γ) = Ball of radius γ centered at state vector Z E k,N = Ellipsoidal set centered at X n (k) along natural motion trajectory N with scale factor ρ k E s k,N = Safe ellipsoidal set centered at X n (k) along natural motion trajectory N with scale factor ρ s k N = Set of state vectors corresponding to a closed natural motion trajectory O(s i , S i) = Ellipsoidal exclusion zone centered at point s i with shape matrix S i T s N = Safe tube for natural motion trajectory N T N = Safe, positively invariant tube for natural motion trajectory N R = Set of real numbers Z = Set ...