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- ItemA boundary control problem for the pure Cahn–Hilliard equation with dynamic boundary conditions(Berlin ; Boston, Mass. : de Gruyter, 2015) Colli, Pierluigi; Gilardi, Gianni; Sprekels, JürgenA 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.
- ItemPlasma enhanced complete oxidation of ultrathin epitaxial praseodymia films on Si(111)(Basel : MDPI, 2015) Kuschel, Olga; Dieck, Florian; Wilkens, Henrik; Gevers, Sebastian; Rodewald, Jari; Otte, Christian; Zoellner, Marvin Hartwig; Niu, Gang; Schroeder, Thomas; Wollschläger, JoachimPraseodymia 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.
- ItemNew Cu-free ti-based composites with residual amorphous matrix(Basel : MDPI, 2016) Nicoara, Mircea; Locovei, Cosmin; Serban, Viorel Aurel; Parthiban, R.; Calin, Mariana; Stoica, MihaiTitanium-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.
- ItemOn an application of Tikhonovs fixed point theorem to a nonlocal Cahn-Hilliard type system modeling phase separation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Colli, Pierluigi; Gilardi, Gianni; Sprekels, JürgenThis paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006) 105-118. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter p and the chemical potential my. Singular contributions to the local free energy in the form of logarithmic or ouble-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonovs fixed point theorem in a rather unusual separable and reflexive Banach space.
- ItemOn the Cahn-Hilliard equation with dynamic boundary conditions and a dominating boundary potential(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Colli, Pierluigi; Gilardi, Gianni; Sprekels, JürgenThe Cahn-Hilliard and viscous Cahn-Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved.
- ItemExistence of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Heinemann, Christian; Kraus, ChristianeThe Cahn-Hilliard model is a typical phase field approach for describing phase separation and coarsening phenomena in alloys. This model has been generalized to the so-called Cahn-Larché system by combining it with elasticity to capture non-neglecting deformation phenomena, which occurs during phase separation in the material. Evolving microstructures such as phase separation and coarsening processes have a strong influence on damage initiation and propagation in alloys. We develop the existing framework of Cahn-Hilliard and Cahn-Larché systems by coupling these systems with a unidirectional evolution inclusion for an internal variable, describing damage processes. After establishing a weak notion of the corresponding evolutionary system, we prove existence of weak solutions for rate-dependent damage processes under certain growth conditions of the energy functional
- ItemA degenerating Cahn-Hilliard system coupled with complete damage processes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Heinemann, Christian; Kraus, ChristianeComplete damage in elastic solids appears when the material looses all its integrity due to high exposure. In the case of alloys, the situation is quite involved since spinodal decomposition and coarsening also occur at sufficiently low temperatures which may lead locally to high stress peaks. Experimental observations on solder alloys reveal void and crack growth especially at phase boundaries. In this work, we investigate analytically a degenerating PDE system with a time-depending domain for phase separation and complete damage processes under time-varying Dirichlet boundary conditions. The evolution of the system is described by a degenerating parabolic differential equation of fourth order for the concentration, a doubly nonlinear differential inclusion for the damage process and a degenerating quasi-static balance equation for the displacement field. All these equations are strongly nonlinearly coupled....
- ItemExistence of weak solutions for the Cahn-Hilliard reaction model including elastic effects and damage(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Kraus, Christiane; Roggensack, ArneIn this paper, we introduce and study analytically a vectorial Cahn-Hilliard reaction model coupled with rate-dependent damage processes. The recently proposed Cahn-Hilliard reaction model can e.g. be used to describe the behavior of electrodes of lithium-ion batteries as it includes both the intercalation reactions at the surfaces and the separation into different phases. The coupling with the damage process allows considering simultaneously the evolution of a damage field, a second important physical effect occurring during the charging or discharging of lithium-ion batteries. Mathematically, this is realized by a Cahn-Larché system with a non-linear Newton boundary condition for the chemical potential and a doubly non-linear differential inclusion for the damage evolution. We show that this system possesses an underlying generalized gradient structure which incorporates the non-linear Newton boundary condition. Using this gradient structure and techniques from the field of convex analysis we are able to prove constructively the existence of weak solutions of the coupled PDE system.
- ItemExistence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Heinemann, Christian; Kraus, ChristianeIn this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed boundary conditions for the displacement variable. The main aim of this work is to establish existence of weak solutions for the introduced hyperbolic-parabolic system. To this end, we first adopt the notion of weak solutions introduced in [HK11]. Then we prove existence of weak solutions by means of regularization, time-discretization and different variational techniques.
- ItemA boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Colli, Pierluigi; Gilardi, Gianni; Sprekels, JürgenA boundary control problem for the pure Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.