Ultrafast and long-range self-transport of droplets on multi-bioinspired surface with periodic gradient structure

Droplet self-transport is crucial in various fields ranging from physics to biochemistry. Despite extensive progress, existing systems for droplet self-transport still perform at low transport velocity or limited transport range. Here, a multi-bioinspired surface comprising two-dimensional gradient structures is proposed innovatively, which integrates the heterogeneous wettability with the shape gradient morphology. Droplet transport behaviors are systematically investigated from experiment, theory, and simulation. The fabricated structure achieves the ultrafast (over ~ 450 mm/s) and long-range (over ~ 200 mm) self-transport of droplets. Moreover, the fantastic scalability of this structure enables it to pump numerous multi-scale droplets from one site to the preset region with ultralow loss. Drawing inspirations, two systems have been designed to complete complex tasks on open surface. This work provides a reliable droplet manipulation strategy for various applications, such as water collection, microfluidics, and biomedicine, etc.

Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion, vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al., Nucl. Fusion, vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion, vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al., Nucl. Fusion, vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids, vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas, vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria. Part 2. Applications

The shape gradient is a local sensitivity function defined on the surface of an object which provides the change in a characteristic quantity, or figure of merit, associated with a perturbation to the shape of the object. The shape gradient can be used for gradient-based optimization, sensitivity analysis and tolerance calculations. However, it is generally expensive to compute from finite-difference derivatives for shapes that are described by many parameters, as is the case for typical stellarator geometry. In an accompanying work (Antonsen, Paul & Landreman J. Plasma Phys., vol. 85 (2), 2019), generalized self-adjointness relations are obtained for magnetohydrodynamic (MHD) equilibria. These describe the relation between perturbed equilibria due to changes in the rotational transform or toroidal current profiles, displacements of the plasma boundary, modifications of currents in the vacuum region or the addition of bulk forces. These are applied to efficiently compute the shape gradient of functions of MHD equilibria with an adjoint approach. In this way, the shape derivative with respect to any perturbation applied to the plasma boundary or coil shapes can be computed with only one additional MHD equilibrium solution. We demonstrate that this approach is applicable for several figures of merit of interest for stellarator configuration optimization: the magnetic well, the magnetic ripple on axis, the departure from quasisymmetry, the effective ripple in the low-collisionality $1/\unicode[STIX]{x1D708}$ regime $(\unicode[STIX]{x1D716}_{\text{eff}}^{3/2})$ (Nemov et al. Phys. Plasmas, vol. 6 (12), 1999, pp. 4622–4632) and several finite-collisionality neoclassical quantities. Numerical verification of this method is demonstrated for the magnetic well figure of merit with the VMEC code (Hirshman & Whitson Phys. Fluids, vol. 26 (12), 1983, p. 3553) and for the magnetic ripple with modification of the ANIMEC code (Cooper et al. Comput. Phys. Commun., vol. 72 (1), 1992, pp. 1–13). Comparisons with the direct approach demonstrate that, in order to obtain agreement within several per cent, the adjoint approach provides a factor of $O(10^{3})$ in computational savings.

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of$O(N)$, where$N$is the number of parameters used to describe the outer flux surface or coil shapes.

On Factors Affecting Subharmonic-aided Pressure Estimation (SHAPE)

Subharmonic-aided pressure estimation (SHAPE) estimates hydrostatic pressure using the inverse relationship with subharmonic amplitude variations of ultrasound contrast agents (UCAs). We studied the impact of varying incident acoustic outputs (IAO), UCA concentration, and hematocrit on SHAPE. A Logiq 9 scanner with a 4C curvilinear probe (GE, Milwaukee, Wisconsin) was used with Sonazoid (GE Healthcare, Oslo, Norway) transmitting at 2.5 MHz and receiving at 1.25 MHz. An improved IAO selection algorithm provided improved correlations ( r from −0.85 to −0.95 vs. −0.39 to −0.98). There was no significant change in SHAPE gradient as the pressure increased from 10 to 40 mmHg and hematocrit concentration was tripled from 1.8 to 4.5 mL/L (Δ0.00-0.01 dB, p = 0.18), and as UCA concentration was increased from 0.2 to 1.2 mL/L (Δ0.02-0.05 dB, p = 0.75). The results for the correlation between the SHAPE gradient and hematocrit values for patients ( N = 100) in an ongoing clinical trial were also calculated showing a poor correlation value of 0.14. Overall, the SHAPE gradient is independent of hematocrit and UCA concentration. An improved algorithm for IAO selection will make SHAPE more accurate.