Simulation der Strahlhärtung von Stahl mit WIAS-SHarP

Die Software WIAS-SHarP zur Simulation der Oberflaechenhaertung von Stahl mit Laser- und Elektronenstrahl wurde im Rahmen eines zweijaehrigen interdisziplinaeren Forschungsprojektes entwickelt. Das zugrunde liegende mathematische Modell besteht aus einem System gewoehnlicher Differentialgleichungen zur Beschreibung der Gefuegeumwandlungen, gekoppelt mit einer nichtlinearen Waermeleitungsgleichung sowie Komponenten zur Beschreibung der Energieeinkopplung. Um eine moeglichst breite Anwendbarkeit der Software zu gewaehrleisten, wurden werkstoffspezifische Kennwerte zum Umwandlungsverhalten fuer eine grosse Anzahl praxisrelevanter Staehle bereitgestellt. Zur Modellverifikation wurden experimentelle Untersuchungen bei beteiligten Industriepartnern durchgefuehrt und mit den entsprechenden Simulationsrechnungen verglichen

Dynamics of an asymmetric bilayer lipid membrane in a viscous solvent

Bilayer lipid membranes (BLMs) are an essential component of many biological systems, forming a functional barrier between the cell and the surrounding environment. When the membrane relaxes from a structural perturbation, the dynamics of the relaxation depends on the bilayer structure. We present a model of a BLM in a viscous solvent, including an explicit description of a 'thick' membrane, where the fluctuations in the thickness of a monolayer leaflet are coupled to changes in the lipid density within that monolayer. We find dispersion relations describing three intuitive forms of bilayer motion, including a mode describing motion of the intermonolayer surface not noted previously in the literature. Two intrinsic length scales emerge that help characterise the dynamics; the well known Saffman-Delbruck length and another, $\ell_r$, resulting from the intermonolayer friction. The framework also allows for asymmetry in the BLM parameters between the monolayer leaflets, which is found to couple dynamic modes of bilayer motion

Outcome Prediction of Consciousness Disorders in the Acute Stage Based on a Complementary Motor Behavioural Tool.

Attaining an accurate diagnosis in the acute phase for severely brain-damaged patients presenting Disorders of Consciousness (DOC) is crucial for prognostic validity; such a diagnosis determines further medical management, in terms of therapeutic choices and end-of-life decisions. However, DOC evaluation based on validated scales, such as the Revised Coma Recovery Scale (CRS-R), can lead to an underestimation of consciousness and to frequent misdiagnoses particularly in cases of cognitive motor dissociation due to other aetiologies. The purpose of this study is to determine the clinical signs that lead to a more accurate consciousness assessment allowing more reliable outcome prediction. From the Unit of Acute Neurorehabilitation (University Hospital, Lausanne, Switzerland) between 2011 and 2014, we enrolled 33 DOC patients with a DOC diagnosis according to the CRS-R that had been established within 28 days of brain damage. The first CRS-R assessment established the initial diagnosis of Unresponsive Wakefulness Syndrome (UWS) in 20 patients and a Minimally Consciousness State (MCS) in the remaining13 patients. We clinically evaluated the patients over time using the CRS-R scale and concurrently from the beginning with complementary clinical items of a new observational Motor Behaviour Tool (MBT). Primary endpoint was outcome at unit discharge distinguishing two main classes of patients (DOC patients having emerged from DOC and those remaining in DOC) and 6 subclasses detailing the outcome of UWS and MCS patients, respectively. Based on CRS-R and MBT scores assessed separately and jointly, statistical testing was performed in the acute phase using a non-parametric Mann-Whitney U test; longitudinal CRS-R data were modelled with a Generalized Linear Model. Fifty-five per cent of the UWS patients and 77% of the MCS patients had emerged from DOC. First, statistical prediction of the first CRS-R scores did not permit outcome differentiation between classes; longitudinal regression modelling of the CRS-R data identified distinct outcome evolution, but not earlier than 19 days. Second, the MBT yielded a significant outcome predictability in the acute phase (p<0.02, sensitivity>0.81). Third, a statistical comparison of the CRS-R subscales weighted by MBT became significantly predictive for DOC outcome (p<0.02). The association of MBT and CRS-R scoring improves significantly the evaluation of consciousness and the predictability of outcome in the acute phase. Subtle motor behaviour assessment provides accurate insight into the amount and the content of consciousness even in the case of cognitive motor dissociation

Weak Solutions to a Nonuniformly Elliptic PDE System in the Harmonic Regime

We study the existence of weak solutions to a nonlinear strongly coupled parabolic–elliptic PDEs arising in the heating induction-conduction process of steel hardening. In this setting, our major concern is to consider the case when the electric conductivity is nonuniformly elliptic which, together with a right hand side in L1 in the energy balance equation, yields to a difficult theoretical situation. The existence result gives a weak solution to a similar PDEs system where the energy balance equation has been perturbed by a measure term.Ministerio de Economía y Competitividad MTM2010-16401Junta de Andalucía FQM-31

Real-time control of surface remelting

We consider a model for laser surface remelting, a process to improve the surface quality of steel components. The mathematical model consists of the two-dimensional heat equation for temperature and an ordinary differential equation for the liquid phase. The equations are coupled via source terms. We study the efficient numerical simulation using adaptive grids, which are especially well-suited for problems with moving heat sources. To account for the local high activity due to the heat source, we introduce local uniform grids and couple the solutions on the global coarse and local fine grids using the local defect correction (LDC) technique

Optimal control strategies for the surface hardening of steel

We discuss control strategies for the surface hardening of steel with laser or electron beam. The goal is to acchieve a prescribed hardening depth avoiding surface melting. Our mathematical model consists of a system of ODEs for the phase volume fractions coupled with the heat equation. The system is solved semi-implicitely using the finite element method. For the optimal control we discuss two approaches: model reduction using POD (Proper Orthogonal Decomposition) and a feedback control of temperature. The numerical results prove that it is not sufficient to control the surface temperature in order to obtain a uniform hardening depth. Instead the best strategy should be to compute the optimal temperature in the hot spot of the beam by solving the control problem and use this temperature as the set-point for the pyrometer control of the real process

Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data

We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic inverse heat source problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement. © 201