Virtual Testing of Experimental Continuation

We present a critical advance in experimental testing of nonlinear structures. Traditional quasi-static experimental methods control the displacement or force at one or more load-introduction points on a structure. This approach is unable to traverse limit points in the control parameter, as the immediate equilibrium beyond these points is statically unstable, causing the structure to snap to another equilibrium. As a result, unstable equilibria---observed numerically---are yet to be verified experimentally. Based on previous experimental work, and a virtual testing environment developed herein, we propose a new experimental continuation method that can path-follow along unstable equilibria and traverse limit points. To support these developments, we provide insightful analogies between a fundamental building block of our technique---shape control---and analysis concepts such as the principle of virtual work and Galerkin's method. The proposed testing method will enable the validation of an emerging class of nonlinear structures that exploit instabilities for novel functionality

A physics-based compact model of SiC power MOSFETs

The presented compact model of SiC power MOSFETs is based on a thorough consideration of the physical phenomena which are important for the device characteristics and its electrothermal behavior. The model includes descriptions of the dependence of channel charge and electron mobility on the charge of interface traps and a simple but effective calculation of the voltage-dependent drain resistance. Comparisons with both physical 2-D device simulations and experiments validate the correctness of the modeling approach and the accuracy of the results

Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in Nf=3N_{\rm f}=3 QCD

Using a finite volume Gradient Flow (GF) renormalization scheme with Schr\"odinger Functional (SF) boundary conditions, we compute the non-perturbative running coupling in the range $2.2 \lesssim {\bar g}_\mathrm{GF}^2(L) \lesssim 13$. Careful continuum extrapolations turn out to be crucial to reach our high accuracy. The running of the coupling is always between one-loop and two-loop and very close to one-loop in the region of $200\,{\rm MeV} \lesssim \mu=1/L \lesssim 4\,{\rm GeV}$. While there is no convincing contact to two-loop running, we match non-perturbatively to the SF coupling with background field. In this case we know the $\mu$ dependence up to $\sim 100\,{\rm GeV}$ and can thus connect to the $\Lambda$-parameter.Comment: 34 pages, LaTe

A status update on the determination of ΛMS‾Nf=3{\Lambda}_{\overline{\rm MS}}^{N_{\rm f}=3} by the ALPHA collaboration

The ALPHA collaboration aims to determine $\alpha_s(m_Z)$ with a total error below the percent level. A further step towards this goal can be taken by combining results from the recent simulations of 2+1-flavour QCD by the CLS initiative with a number of tools developed over the years: renormalized couplings in finite volume schemes, recursive finite size techniques, two-loop renormalized perturbation theory and the (improved) gradient flow on the lattice. We sketch the strategy, which involves both the standard SF coupling in the high energy regime and a gradient flow coupling at low energies. This implies the need for matching both schemes at an intermediate switching scale, $L_{\rm swi}$, which we choose roughly in the range 2-4 GeV. In this contribution we present a preliminary result for this matching procedure, and we then focus on our almost final results for the scale evolution of the SF coupling from $L_{\rm swi}$ towards the perturbative regime, where we extract the $N_{\rm f} = 3$ ${\Lambda}$-parameter, ${\Lambda}_{\overline{\rm MS}}^{N_{\rm f}=3}$, in units of $L_{\rm swi}$ . Connecting $L_{\rm swi}$ and thus the ${\Lambda}$-parameter to a hadronic scale such as $F_K$ requires 2 further ingredients: first, the connection of $L_{\rm swi}$ to $L_{\rm max}$ using a few steps with the step-scaling function of the gradient flow coupling, and, second, the continuum extrapolation of $L_{\rm max} F_K$.Comment: 7 pages, 4 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe, Japa

Engineering muscle networks in 3D gelatin methacryloyl hydrogels: influence of mechanical stiffness and geometrical confinement

In this work, the influence of mechanical stiffness and geometrical confinement on the 3D culture of myoblast-laden gelatin methacryloyl (GelMA) photo-crosslinkable hydrogels was evaluated in terms of in vitro myogenesis. We formulated a set of cell-laden GelMA hydrogels with a compressive modulus in the range 1÷17 kPa, obtained by varying GelMA concentration and degree of cross-linking. C2C12 myoblasts were chosen as the cell model, to investigate the supportiveness of different GelMA hydrogels on myotube formation up to 2 weeks. Results showed that the hydrogels with a stiffness in the range 1÷3 kPa provided enhanced support to C2C12 differentiation in terms of myotube number, rate of formation and space distribution. Finally, we studied the influence of geometrical confinement on myotube orientation by confining cells within thin hydrogel slabs having different cross-sections: i) 2000×2000 m, ii) 1000×1000 m and iii) 500×500 m. The obtained results showed that by reducing the cross-section—i.e., by increasing the level of confinement—myotubes were more likely restrained and formed aligned myostructures that better mimicked the native morphology of skeletal muscle

Nudging axially compressed cylindrical panels towards imperfection insensitivity

Curved shell structures are known for their excellent load-carrying capability and are commonly used in thin-walled constructions. Although theoretically able to withstand greater buckling loads than flat structures, shell structures are notoriously sensitive to imperfections owing to their postbuckling behavior often being governed by subcritical bifurcations. Thus, shell structures often buckle at significantly lower loads than those predicted numerically and the ensuing dynamic snap to another equilibrium can lead to permanent damage. Furthermore, the strong sensitivity to initial imperfections, as well as their stochastic nature, limits the predictive capability of current stability analyses. Our objective here is to convert the subcritical nature of the buckling event to a supercritical one, thereby improving the reliability of numerical predictions and mitigating the possibility of catastrophic failure. We explore the elastically nonlinear postbuckling response of axially compressed cylindrical panels using numerical continuation techniques. These analyses show that axially compressed panels exhibit a highly nonlinear and complex postbuckling behavior with many entangled postbuckled equilibrium curves. We unveil isolated regions of stable equilibria in otherwise unstable postbuckled regimes, which often possess greater load-carrying capacity. By modifying the initial geometry of the panel in a targeted - rather than stochastic - and imperceptible manner, the postbuckling behavior of these shells can be tailored without a significant increase in mass. These findings provide new insight into the buckling and postbuckling behavior of shell structures and opportunities for modifying and controlling their postbuckling response for enhanced efficiency and functionality.</p