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Tuning the bandgap in ternary III-V semiconductors via modification of the composition or the strain in the material is a major approach for the design of optoelectronic materials. Experimental approaches screening a large range of possible target structures are hampered by the tremendous effort to optimize the material synthesis for every target structure. We present an approach based on density functional theory efficiently capable of providing the bandgap as a function of composition and strain. Using a specific density functional designed for accurate bandgap computation (TB09) together with a band unfolding procedure and special quasirandom structures, we develop a computational protocol efficiently able to predict bandgaps. The approach's accuracy is validated by comparison to selected experimental data. We thus map the phase space of composition and strain (we call this the ``bandgap phase diagram'') for several important III-V compound semiconductors: GaAsP, GaAsN, GaPSb, GaAsSb, GaPBi, and GaAsBi. We show the application of these diagrams for identifying the most promising materials for device design. Furthermore, our computational protocol can easily be generalized to explore the vast chemical space of III-V materials with all other possible combinations of III- and V-elements., Comment: 13 pages, 7 figures, GitHub (https://bmondal94.github.io/Bandgap-Phase-Diagram/)

In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body surrounded by a liquid in a rectangular domain is deformed by the flow which can be controlled by the Dirichlet boundary condition at the inlet. On the walls along the channel homogeneous Dirichlet boundary conditions and on the outflow boundary do-nothing conditions are prescribed. We recall existence results for the nonlinear system from that reference and analyze the control to state mapping generalizing the results of [Wollner and Wick, J. Math. Fluid Mech., 21, 2019] to the setting of the nonlinear Navier-Stokes equation for the fluid and the situation of mixed boundary conditions in a domain with corners.

In this paper we discuss existence, uniqueness and some properties of a class of solitons to the anisotropic mean curvature flow, i.e., graphical translators, either in the plane or under an assumption of cylindrical symmetry on the anisotropy and the mobility. In these cases, the equation becomes an ordinary differential equation, and this allows to find explicitly the translators and describe their main features., Comment: 15 pages

We consider the anisotropic mean curvature flow of entire Lipschitz graphs. We prove existence and uniqueness of expanding self-similar solutions which are asymptotic to a prescribed cone, and we characterize the long time behavior of solutions, after suitable rescaling, when the initial datum is a sublinear perturbation of a cone. In the case of regular anisotropies, we prove the stability of self-similar solutions asymptotic to strictly mean convex cones, with respect to perturbations vanishing at infinity. We also show the stability of hyperplanes, with a proof which is novel also for the isotropic mean curvature flow.

In this paper we combine an approach based on Runge-Kutta Nets considered in [Benning et al., J. Comput. Dynamics, 9, 2019] and a technique on augmenting the input space in [Dupont et al., NeurIPS, 2019] to obtain network architectures which show a better numerical performance for deep neural networks in point and image classification problems. The approach is illustrated with several examples implemented in PyTorch.

In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show exponential stabilization to nonstationary trajectories. Based on a Moreau-Yosida approximation, a feedback operator is established using a finite (and uniform in the approximation index) number of actuators leading to exponential decay of given rate of the state variable. Several numerical examples are presented addressing smooth and nonsmooth obstacle functions., Comment: 55 subfigures

This paper proves error estimates for $H^2$ conforming finite elements for equations which model the flow of surfaces by different powers of the mean curvature (this includes mean curvature flow). for an adapted scheme originally proposed in [17] for the inverse mean curvature flow. The scheme is based on a known regularization procedure and produces different kinds of errors, a regularization error, a finite element discretization error for the regularized problems and a full error. While in the literature and own previous work different aspects of the aforementioned error types are treated, here, we solely and for the first time focus on the finite element discretization error in the $W^{2,\mu}$ norm for the regularized equation analyzing also the dependencies from the regularization parameter.

We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that, if the maximal time is finite, then either the length of one of the curves goes to zero or the $L^2$ norm of the anisotropic curvature blows up., Comment: 39 pages, 1 figure

We demonstrate the full thermoelectric and structural characterization of individual bismuth-based (Bi-based) core/shell nanowires. The influence of strain on the temperature dependence of the electrical conductivity, the absolute Seebeck coefficient and the thermal conductivity of bismuth/titanium dioxide ($\text{Bi}/\text{TiO}_{2}$) nanowires with different diameters is investigated and compared to bismuth (Bi) and bismuth/tellurium (Bi/Te) nanowires and bismuth bulk. Scattering at surfaces, crystal defects and interfaces between the core and the shell reduces the electrical conductivity to less than $5\,\%$ and the thermal conductivity to less than $25\,\%$ to $50\,\%$ of the bulk value at room temperature. On behalf of a compressive strain, $\text{Bi}/\text{TiO}_{2}$ core/shell nanowires show a decreasing electrical conductivity with decreasing temperature opposed to that of Bi and Bi/Te nanowires. We find that the compressive strain induced by the $\text{TiO}_{2}$ shell can lead to a band opening of bismuth increasing the absolute Seebeck coefficient by $10\,\%$ to $30\,\%$ compared to bulk at room temperature. In the semiconducting state, the activation energy is determined to $\left|41.3\pm0.2\right|\,\text{meV}$. We show that if the strain exceeds the elastic limit the semimetallic state is recovered due to the lattice relaxation.

In this contribution we present a local discontinuous Galerkin (LDG) pressure-correction scheme for the incompressible Navier-Stokes equations. The scheme does not need penalty parameters and satisfies the discrete continuity equation exactly. The scheme is especially suitable for two-phase flow when used with a piecewise-linear interface construction (PLIC) volume-of-fluid (VoF) method and cut-cell quadratures., Comment: 8 pages, 5 figures, to be published in the proceedings of "Finite Volumes for Complex Applications IX" (FVCA9)

The Monge-Amp\`{e}re equation arises in the theory of optimal transport. When more complicated cost functions are involved in the optimal transportation problem, which are motivated e.g. from economics, the corresponding equation for the optimal transportation map becomes a Monge-Amp\`{e}re type equation. Such Monge-Amp\`{e}re type equations are a topic of current research from the viewpoint of mathematical analysis. From the numerical point of view there is a lot of current research for the Monge-Amp\`{e}re equation itself and rarely for the more general Monge-Amp\`{e}re type equation. Introducing the notion of discrete $Q$-convexity as well as specifically designed barrier functions this purely theoretical paper extends the very recently studied two-scale method approximation of the Monge-Amp\`{e}re itself \cite{NochettoNtogkasZhang2018} to the more general Monge-Amp\`{e}re type equation as it arises e.g. in \cite{PhillippisFigalli2013} in the context of Sobolev regularity.

In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order sufficient conditions relying on the Goh transform. The appendix provides an example illustrating the applicability of our results., Comment: This is the second part of a work on optimality conditions for a control problem of a semilinear heat equation. More precisely, the full version, available arXiv:1906.00237, has been divided in two, resulting in arXiv:1906.00237v2 (that corresponds to Part I) and the current manuscript (which is Part II)

In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with respect to the space variable. The control is multidimensional. The cost functional is of a tracking type and contains a linear term in the control variables. We derive second order necessary conditions relying on the concept of alternative costates and quasi-radial critical directions. The appendix provides an example illustrating the applicability of our results., Comment: This is the first part of a work on optimality conditions for a control problem of a semilinear heat equation. More precisely, the full version, available at arXiv:1906.00237v1, has been divided in two, resulting in the current manuscript (that corresponds to Part I) and arXiv:1909.05056 (which is Part II)