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Abstract Full-disk measurements of the solar magnetic field by the Helioseismic and Magnetic Imager (HMI) are often used for magnetic field extrapolations, but its limited spatial and spectral resolution can lead to significant errors. We compare HMI data with observations of NOAA 12104 by the Hinode Spectropolarimeter (SP) to derive a scaling curve for the magnetic field strength,B. The SP data in the Feilines at 630 nm were inverted with the SIR code. We find that the Milne–Eddington inversion of HMI underestimatesBand the line-of-sight flux, Φ, in all granulation surroundings by an average factor of 4.5 in plage and 9.2 in the quiet Sun in comparison to the SP. The deviation is inversely proportional to the magnetic fill factor,f, in the SP results. We derived a correction curve to match the HMIBwith the effective fluxBfin the SP data that scaled HMIBup by 1.3 on average. A comparison of non-force-free field extrapolations over a larger field of view without and with the correction revealed minor changes in connectivity and a proportional scaling of electric currents and Lorentz force (∝B∼ 1.3) and free energy (∝B² ∼ 2). Magnetic field extrapolations of HMI vector data with large areas of plage and quiet Sun will underestimate the photospheric magnetic field strength by a factor of 5–10 and the coronal magnetic flux by at least a factor of 2. An HMI inversion including a fill factor would mitigate the problem. 

Context.Erupting magnetic flux ropes (MFRs) are believed to play a crucial role in producing solar flares. However, the formation of erupting MFRs in complex coronal magnetic configurations and the role of their subsequent evolution in the flaring events are not fully understood. Aims.We perform a magnetohydrodynamic (MHD) simulation of active region NOAA 12241 to understand the formation of a rising magnetic flux rope during the onset of an M6.9 flare on 2014 December 18 around 21:41 UT (SOL2014-12- 18T21:41M6.9), which was followed by the appearance of parallel flare ribbons. Methods.The MHD simulation was initialised with an extrapolated non-force-free magnetic field generated from the photospheric vector magnetogram of the active region taken a few minutes before the flare. Results.The initial magnetic field topology displays a pre-existing sheared arcade enveloping the polarity inversion line. The simulated dynamics exhibit the movement of the oppositely directed legs of the sheared arcade field lines towards each other due to the converging Lorentz force, resulting in the onset of tether-cutting magnetic reconnection that produces an underlying flare arcade and flare ribbons. Concurrently, a magnetic flux rope above the flare arcade develops inside the sheared arcade and shows a rising motion. The flux rope is found to be formed in a torus-unstable region, thereby explaining its eruptive nature. Interestingly, the location and rise of the rope are in good agreement with the corresponding observations seen in extreme-ultraviolet channels of the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). Furthermore, the foot points of the simulation’s flare arcade match well with the location of the observed parallel ribbons of the flare. Conclusions.The presented simulation supports the development of the MFR by the tether-cutting magnetic reconnection inside the sheared coronal arcade during flare onset. The MFR is then found to extend along the polarity inversion line (PIL) through slip-running reconnection. The MFR’s eruptive nature is ascribed both to its formation in the torus-unstable region and also to the runaway tether-cutting reconnection. 

Context. The inverse Evershed flow (IEF) is a mass motion towards sunspots at chromospheric heights. Aims. We combined high-resolution observations of NOAA 12418 from the Dunn Solar Telescope and vector magnetic field measurements from the Helioseismic and Magnetic Imager (HMI) to determine the driver of the IEF. Methods. We derived chromospheric line-of-sight (LOS) velocities from spectra of H α and Ca  II IR. The HMI data were used in a non-force-free magnetic field extrapolation to track closed field lines near the sunspot in the active region. We determined their length and height, located their inner and outer foot points, and derived flow velocities along them. Results. The magnetic field lines related to the IEF reach on average a height of 3 megameter (Mm) over a length of 13 Mm. The inner (outer) foot points are located at 1.2 (1.9) sunspot radii. The average field strength difference Δ B between inner and outer foot points is +400 G. The temperature difference Δ T is anti-correlated with Δ B with an average value of −100 K. The pressure difference Δ p is dominated by Δ B and is primarily positive with a driving force towards the inner foot points of 1.7 kPa on average. The velocities predicted from Δ p reproduce the LOS velocities of 2–10 km s −1 with a square-root dependence. Conclusions. We find that the IEF is driven along magnetic field lines connecting network elements with the outer penumbra by a gas pressure difference that results from a difference in field strength as predicted by the classical siphon flow scenario. 

Studies of cell-extracellular matrix (ECM) interactions within fibrous systems such as collagen or fibrin are challenging, particularly if peri-cellular stiffness cannot be monitored. Here we present our light-based method for non-invasive patterning of molecular crosslinking combined with multi-axes optical tweezers active microrheology to map ECM stiffness landscapes. This method allows us to generate prescribed stiffness gradients and associated anisotropies, which model stiffness of the natural peri-cellular ECM. Patterned crosslinking induces strain hardening and measured stiffness gradients are in agreement with predicted strain fields. Migratory cells respond to these gradients as assessed by change in F-actin distribution and morphological properties. 

In the first part of the review, we observed that there exists a significant gap between the predictive and prescriptive models pertaining to crash risk prediction and minimization, respectively. In this part, we review and categorize the optimization/ prescriptive analytic models that focus on minimizing crash risk. Although the majority of works in this segment of the literature are related to the hazardous materials (hazmat) trucking problems, we show that (with some exceptions) many can also be utilized in non-hazmat scenarios. In an effort to highlight the effect of crash risk prediction model on the accumulated risk obtained from the prescriptive model, we present a simulated example where we utilize four risk indicators (obtained from logistic regression, Poisson regression, XGBoost, and neural network) in the k-shortest path algorithm. From our example, we demonstrate two major designed takeaways: (a) the shortest path may not always result in the lowest crash risk, and (b) a similarity in overall predictive performance may not always translate to similar outcomes from the prescriptive models. Based on the review and example, we highlight several avenues for future research.