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A boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions
A boundary control problem for the pure Cahn–Hilliard equations with possibly singular potentialsand dynamic boundary conditions is studied and rst-order necessary conditions for optimality are proved.
Compositional Patterning in Carbon Implanted Titania Nanotubes
Ranging from novel solar cells to smart biosensors, titania nanotube arrays constitute a highly functional material for various applications. A promising route to modify material characteristics while preserving the amorphous nanotube structure is present when applying low-energy ion implantation. In this study, the interplay of phenomenological effects observed upon implantation of low fluences in the unique 3D structure is reported: sputtering versus readsorption and plastic flow, amorphization versus crystallization and compositional patterning. Patterning within the oxygen and carbon subsystem is revealed using transmission electron microscopy. By applying a Cahn–Hilliard approach within the framework of driven alloys, characteristic length scales are derived and it is demonstrated that compositional patterning is expected on free enthalpy grounds, as predicted by density functional theory based ab initio calculations. Hence, an attractive material with increased conductivity for advanced devices is provided. © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH
Interacting particles in an activity landscape
We study interacting active Brownian particles (ABPs) with a space-dependent swim velocity via simulation and theory. We find that, although an equation of state exists, a mechanical equilibrium does not apply to ABPs in activity landscapes. The pressure imbalance originates in the flux of polar order and the gradient of swim velocity across the interface between regions of different activity. An active-passive patch system is mainly controlled by the smallest global density for which the passive patch can be close packed. Below this density a critical point does not exist and the system splits continuously into a dense passive and a dilute active phase with increasing activity. Above this density and for sufficiently high activity the active phase may start to phase separate into a gas and a liquid phase caused by the same mechanism as motility-induced phase separation of ABPs with a homogeneous swim velocity.
Second-order analysis of a boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary condition
In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn-Hilliard equation with possibly singular potentials and dynamic boundary conditions.
Plasma enhanced complete oxidation of ultrathin epitaxial praseodymia films on Si(111)
Praseodymia films have been exposed to oxygen plasma at room temperature after deposition on Si(111) via molecular beam epitaxy. Different parameters as film thickness, exposure time and flux during plasma treatment have been varied to study their influence on the oxygen plasma oxidation process. The surface near regions have been investigated by means of X-ray photoelectron spectroscopy showing that the plasma treatment transforms the stoichiometry of the films from Pr2O3 to PrO2. Closer inspection of the bulk properties of the films by means of synchrotron radiation based X-ray reflectometry and diffraction confirms this transformation if the films are thicker than some critical thickness of 6 nm. The layer distance of these films is extremely small verifying the completeness of the plasma oxidation process. Thinner films, however, cannot be transformed completely. For all films, less oxidized very thin interlayers are detected by these experimental techniques.
Phase Selection in Mn–Si Alloys by Fast Solid-State Reaction with Enhanced Skyrmion Stability
B20-type transition-metal silicides or germanides are noncentrosymmetric materials hosting magnetic skyrmions, which are promising information carriers in spintronic devices. The prerequisite is to prepare thin films on technology-relevant substrates with magnetic skyrmions stabilized at a broad temperature and magnetic-field working window. A canonical example is the B20-MnSi film grown on Si substrates. However, the as-yet unavoidable contamination with MnSi1.7 occurs due to the lower nucleation temperature of this phase. In this work, a simple and efficient method to overcome this problem and prepare single-phase MnSi films on Si substrates is reported. It is based on the millisecond reaction between metallic Mn and Si using flash-lamp annealing (FLA). By controlling the FLA energy density, single-phase MnSi or MnSi1.7 or their mixture can be grown at will. Compared with bulk MnSi, the prepared MnSi films show an increased Curie temperature of up to 41 K. In particular, the magnetic skyrmions are stable over a much wider temperature and magnetic-field range than reported previously. The results constitute a novel phase selection approach for alloys and can help to enhance specific functional properties, such as the stability of magnetic skyrmions. © 2021 The Authors. Advanced Functional Materials published by Wiley-VCH GmbH
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in 2D
We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier-Stokes system with a convective nonlocal Cahn-Hilliard equation in two dimensions of space. We apply recently proved well-posedness and regularity results in order to establish existence of optimal controls as well as first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow.
New Cu-free ti-based composites with residual amorphous matrix
Titanium-based bulk metallic glasses (BMGs) are considered to have potential for biomedical applications because they combine favorable mechanical properties and good biocompatibility. Copper represents the most common alloying element, which provides high amorphization capacity, but reports emphasizing cytotoxic effects of this element have risen concerns about possible effects on human health. A new copper-free alloy with atomic composition Ti42Zr10Pd14Ag26Sn8, in which Cu is completely replaced by Ag, was formulated based on Morinaga’s d-electron alloy design theory. Following this theory, the actual amount of alloying elements, which defines the values of covalent bond strength Bo and d-orbital energy Md, situates the newly designed alloy inside the BMG domain. By mean of centrifugal casting, cylindrical rods with diameters between 2 and 5 mm were fabricated from this new alloy. Differential scanning calorimetry (DSC) and X-rays diffraction (XRD), as well as microstructural analyses using optical and scanning electron microscopy (OM/SEM) revealed an interesting structure characterized by liquid phase-separated formation of crystalline Ag, as well as metastable intermetallic phases embedded in residual amorphous phases.
The more the merrier: effects of macromolecular crowding on the structure and dynamics of biological membranes
Proteins are essential and abundant components of cellular membranes. Being densely packed within the limited surface area, proteins fulfil essential tasks for life, which include transport, signalling and maintenance of cellular homeostasis. The high protein density promotes nonspecific interactions, which affect the dynamics of the membrane-associated processes, but also contribute to higher levels of membrane organization. Here, we provide a comprehensive summary of the most recent findings of diverse effects resulting from high protein densities in both living membranes and reconstituted systems and display why the crowding phenomenon should be considered and assessed when studying cellular pathways. Biochemical, biophysical and computational studies reveal effects of crowding on the translational mobility of proteins and lipids, oligomerization and clustering of integral membrane proteins, and also folding and aggregation of proteins at the lipid membrane interface. The effects of crowding pervade to larger length scales, where interfacial and transmembrane crowding shapes the lipid membrane. Finally, we discuss the design and development of fluorescence-based sensors for macromolecular crowding and the perspectives to use those in application to cellular membranes and suggest some emerging topics in studying crowding at biological interfaces. © 2020 The Authors. The FEBS Journal published by John Wiley & Sons Ltd on behalf of Federation of European Biochemical Societies
Homogenization of a porous intercalation electrode with phase separation
In this work, we derive a new model framework for a porous intercalation electrode with a phase separating active material upon lithium intercalation. We start from a microscopic model consisting of transport equations for lithium ions in an electrolyte phase and intercalated lithium in a solid active phase. Both are coupled through a Neumann--boundary condition modeling the lithium intercalation reaction. The active material phase is considered to be phase separating upon lithium intercalation. We assume that the porous material is a given periodic microstructure and perform analytical homogenization. Effectively, the microscopic model consists of a diffusion and a Cahn--Hilliard equation, whereas the limit model consists of a diffusion and an Allen--Cahn equation. Thus we observe a Cahn--Hilliard to Allen--Cahn transition during the upscaling process. In the sense of gradient flows, the transition goes in hand with a change in the underlying metric structure of the PDE system.