This paper presents the integration and channel characterization of a highly integrated dual-band digital beamforming space-borne synthetic aperture radar (SAR) receiver. The proposed SAR sensor is a low-cost, lightweight, low-power consumption, and dual-band (X/Ka) dual-polarized module ready for the next-generation space-borne SAR missions. In previous works, by the authors, the design and experimental characterization of each sub-system was already presented and discussed. This work expands upon the previous characterization by providing an exhaustive experimental assessment of the fully integrated system. As it will be shown, the proposed tests were used to validate all the instrument channels in a set-up where the SAR sensor was illuminated by an external source minim the ground reflected waves. Test results demonstrate how the system channels are properly operating allowing the reception of the input signals and their processing in the digital domain. The possibility to easily implement a calibration procedure has also been validated to equalize, in the digital domain, the unavoidable amplitude differences between the different channels.

Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to turbulence is achieved via the broadening or narrowing of the basin of attraction of the laminar flow. In this paper, a novel methodology to assess the robustness of the laminar flow and the efficiency of control strategies is introduced. It relies on the statistical sampling of the phase-space neighbourhood around the laminar flow in order to assess the transition probability of perturbations as a function of their energy. This approach is applied to a canonical flow (plane Couette flow) and provides invaluable insight: in the presence of the chosen control, transition is significantly suppressed whereas plausible scalar indicators of the nonlinear stability of the flow, such as the edge-state energy, do not provide conclusive predictions. The methodology presented here in the context of transition to turbulence is applicable to any nonlinear system displaying finite-amplitude instability.

The Northeast Greenland Ice Stream (NEGIS) is an important dynamic component for the total mass balance of the Greenland ice sheet, as it reaches up to the central divide and drains 12% of the ice sheet. The geometric boundary conditions and in particular the nature of the subglacial bed of the NEGIS are essential to understand its ice flow dynamics. We present a record of more than 8000 km of radar survey lines of multi-channel, ultra-wideband radio echo sounding data covering an area of 24 000 km2, centered on the drill site for the East Greenland Ice-core Project (EGRIP), in the upper part of the NEGIS catchment. Our data yield a new detailed model of ice-thickness distribution and basal topography in the region. The enhanced resolution of our bed topography model shows features which we interpret to be caused by erosional activity, potentially over several glacial–interglacial cycles. Off-nadir reflections from the ice–bed interface in the center of the ice stream indicate a streamlined bed with elongated subglacial landforms. Our new bed topography model will help to improve the basal boundary conditions of NEGIS prescribed for ice flow models and thus foster an improved understanding of the ice-dynamic setting.

In order to reduce the time spent on tolerance analysis, it is necessary to correctly identify and prioritize the key characteristics of the product. For multiple-state mechanisms, a systematic procedure for doing this is lacking. We present a new complexity metric for multiple-state mechanisms based on the product behavior, describing the impact of geometrical variation. The sequence of the structural state transitions is linked to the product composition, enabling a clear prioritization of variation-critical states and interfaces. The approach is applied on an industrial case and verified based on a comparison with the company-specified priority tolerance calculations.

Increasing fluorination of organosilyl nitrile solvents improves ionic conductivities of lithium salt electrolytes, resulting from higher values of salt dissociation. Ionic conductivities at 298 K range from 1.5 to 3.2 mS/cm for LiPF6 salt concentrations at 0.6 or 0.7 M. The authors also report on solvent blend electrolytes where the fluoroorganosilyl (FOS) nitrile solvent is mixed with ethylene carbonate and diethyl carbonate. Ionic conductivities of the FOS solvent/carbonate blend electrolytes increase achieving ionic conductivities at 298 K of 5.5–6.3 mS/cm and salt dissociation values ranging from 0.42 to 0.45. Salt dissociation generally decreases with increasing temperature.

Numerical simulations of quasi-static magnetoconvection with a vertical magnetic field are carried out up to a Chandrasekhar number of $Q=10^{8}$ over a broad range of Rayleigh numbers $Ra$ . Three magnetoconvection regimes are identified: two of the regimes are magnetically constrained in the sense that a leading-order balance exists between the Lorentz and buoyancy forces, whereas the third regime is characterized by unbalanced dynamics that is similar to non-magnetic convection. Each regime is distinguished by flow morphology, momentum and heat equation balances, and heat transport behaviour. One of the magnetically constrained regimes appears to represent an ‘ultimate’ magnetoconvection regime in the dual limit of asymptotically large buoyancy forcing and magnetic field strength; this regime is characterized by an interconnected network of anisotropic, spatially localized fluid columns aligned with the direction of the imposed magnetic field that remain quasi-laminar despite having large flow speeds. As for non-magnetic convection, heat transport is controlled primarily by the thermal boundary layer. Empirically, the scaling of the heat transport and flow speeds with $Ra$ appear to be independent of the thermal Prandtl number within the magnetically constrained, high- $Q$ regimes.

Unsteady spatially localized states such as puffs, slugs or spots play an important role in transition to turbulence. In plane Couette flow, steady versions of these states are found on two intertwined solution branches describing homoclinic snaking (Schneider et al., Phys. Rev. Lett., vol. 104, 2010, 104501). These branches can be used to generate a number of spatially localized initial conditions whose transition can be investigated. From the low Reynolds numbers where homoclinic snaking is first observed ( $Re<175$ ) to transitional ones ( $Re\approx 325$ ), these spatially localized states traverse various regimes where their relaminarization time and dynamics are affected by the dynamical structure of phase space. These regimes are reported and characterized in this paper for a $4\unicode[STIX]{x03C0}$ -periodic domain in the streamwise direction as a function of the two remaining variables: the Reynolds number and the width of the localized pattern. Close to the snaking, localized states are attracted by spatially localized periodic orbits before relaminarizing. At larger values of the Reynolds number, the flow enters a chaotic transient of variable duration before relaminarizing. Very long chaotic transients ( $t>10^{4}$ ) can be observed without difficulty for relatively low values of the Reynolds number ( $Re\approx 250$ ).

Increasing the number of quantum bits while preserving precise control of their quantum electronic properties is a significant challenge in materials design for the development of semiconductor quantum computing devices. Semiconductor heterostructures can host multiple quantum dots that are electrostatically defined by voltages applied to an array of metallic nanoelectrodes. The structural distortion of multiple-quantum-dot devices due to elastic stress associated with the electrodes has been difficult to predict because of the large micrometer-scale overall sizes of the devices, the complex spatial arrangement of the electrodes, and the sensitive dependence of the magnitude and spatial variation of the stress on processing conditions. Synchrotron X-ray nanobeam Bragg diffraction studies of a GaAs/AlGaAs heterostructure reveal the magnitude and nanoscale variation of these distortions. Investigations of individual linear electrodes reveal lattice tilts consistent with a 28-MPa compressive residual stress in the electrodes. The angular magnitude of the tilts varies by up to 20% over distances of less than 200 nm along the length of the electrodes, consistent with heterogeneity in the metal residual stress. A similar variation of the crystal tilt is observed in multiple-quantum-dot devices, due to a combination of the variation of the stress and the complex electrode arrangement. The heterogeneity in particular can lead to significant challenges in the scaling of multiple-quantum-dot devices due to differences between the charging energies of dots and uncertainty in the potential energy landscape. Alternatively, if incorporated in design, stress presents a new degree of freedom in device fabrication.

Rayleigh–Bénard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of atmospheric convection is the buoyancy source provided by the condensation of water vapour, but the presence of radiation, compressibility, liquid water and ice further complicate the system and our understanding of it. In this paper we present an idealized model of moist convection by taking the Boussinesq limit of the ideal-gas equations and adding a condensate that obeys a simplified Clausius–Clapeyron relation. The system allows moist convection to be explored at a fundamental level and reduces to the classical Rayleigh–Bénard model if the latent heat of condensation is taken to be zero. The model has an exact, Rayleigh-number-independent ‘drizzle’ solution in which the diffusion of water vapour from a saturated lower surface is balanced by condensation, with the temperature field (and so the saturation value of the moisture) determined self-consistently by the heat released in the condensation. This state is the moist analogue of the conductive solution in the classical problem. We numerically determine the linear stability properties of this solution as a function of Rayleigh number and a non-dimensional latent-heat parameter. We also present some two-dimensional, time-dependent, nonlinear solutions at various values of Rayleigh number and the non-dimensional condensational parameters. At sufficiently low Rayleigh number the system converges to the drizzle solution, and we find no evidence that two-dimensional self-sustained convection can occur when that solution is stable. The flow transitions from steady to turbulent as the Rayleigh number or the effects of condensation are increased, with plumes triggered by gravity waves emanating from other plumes. The interior dries as the level of turbulence increases, because the plumes entrain more dry air and because the saturated boundary layer at the top becomes thinner. The flow develops a broad relative humidity minimum in the domain interior, only weakly dependent on Rayleigh number when that is high.

The quasi-geostrophic dynamo model (QGDM) is a multiscale, fully nonlinear Cartesian dynamo model that is valid in the asymptotic limit of low Rossby number. In the additional limit of small magnetic Prandtl number investigated here, the QGDM is a self-consistent, asymptotically exact form of an $\unicode[STIX]{x1D6FC}^{2}$ large-scale dynamo. This article explores methods for simulating the multiscale QGDM and investigates how convection is altered by the magnetic field in the planetary regime of small Rossby number and small magnetic Prandtl number. At present, this combination is beyond the reach of direct numerical simulations. We use a simplified class of solutions whose horizontal structure is restricted to a periodic hexagonal lattice characterized by a single horizontal wavenumber (single mode). In contrast with previous kinematic investigations of the QGDM, the Lorentz force is included to study saturated, self-consistent dynamos. Two methodologies are used to assess handling of the multiple time scales of the QGDM: a stiff, common-in-time approach where all time scales are converted to a single time variable and a heterogeneous multiscale modelling approach employing fast time averaging on the Reynolds, magnetic and buoyancy eddy fluxes that feed back onto the slow scales. These strategies produce consistent results and each illustrates self-similar dynamics as the time-averaging window is increased. The properties of the convection are significantly altered by the dynamo-generated magnetic field. All solutions show a decrease in the overall heat transfer efficiency as compared to non-magnetic convection, suggesting that a change in length scale or flow planform plays a critical role in the enhanced heat transfer efficiency observed in previous dynamo studies. All dynamo solutions show a trend of increasing ohmic dissipation relative to viscous dissipation as the buoyancy forcing is increased.

This article describes a formal proof of the Kepler conjecture on dense sphere packings in a combination of the HOL Light and Isabelle proof assistants. This paper constitutes the official published account of the now completed Flyspeck project.

We consider dynamo action driven by three-dimensional rotating anelastic convection in a spherical shell. Motivated by the behaviour of the solar dynamo, we examine the interaction of hydromagnetic modes with different symmetries and demonstrate how complicated interactions between convection, differential rotation and magnetic fields may lead to modulation of the basic cycle. For some parameters, type 1 modulation occurs by the transfer of energy between modes of different symmetries with little change in the overall amplitude; for other parameters, the modulation is of type 2, where the amplitude is significantly affected (leading to grand minima in activity) without significant changes in symmetry. Most importantly, we identify the presence of ‘supermodulation’ in the solutions, where the activity switches chaotically between type 1 and type 2 modulation; this is believed to be an important process in solar activity.

The effects of large-scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of direct numerical simulations, systematically varying the nature of the mechanical force in time. We find that the statistically stationary solutions of these flows depend on the nature of the forcing mechanism. Rapidly enough rotating flows with a forcing that has a persistent direction relative to the axis of rotation bifurcate from a non-helical state to a helical state despite the fact that the forcing is non-helical. We demonstrate that the nature of the mechanical force in time and the emergence of helicity have direct implications for the cascade dynamics of these flows, determining the anisotropy in the flow, the energy condensation at large scales and the power-law energy spectra that are consistent with previous findings and phenomenologies under strong and weak turbulence.

Motivated by recent advances in direct statistical simulation (DSS) of astrophysical phenomena such as out-of-equilibrium jets, we perform a direct numerical simulation (DNS) of the helical magnetorotational instability (HMRI) under the generalised quasilinear approximation (GQL). This approximation generalises the quasilinear approximation (QL) to include the self-consistent interaction of large-scale modes, interpolating between fully nonlinear DNS and QL DNS whilst still remaining formally linear in the small scales. In this paper we address whether GQL can more accurately describe low-order statistics of axisymmetric HMRI when compared with QL by performing DNS under various degrees of GQL approximation. We utilise various diagnostics, such as energy spectra in addition to first and second cumulants, for calculations performed for a range of Reynolds and Hartmann numbers (describing rotation and imposed magnetic field strength respectively). We find that GQL performs significantly better than QL in describing the statistics of the HMRI even when relatively few large-scale modes are kept in the formalism. We conclude that DSS based on GQL (GCE2) will be significantly more accurate than that based on QL (CE2).

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ( $T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$ , flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$ , below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$ .