Direct and inverse problems in thermomechanics

S. Rodt, P.-I. Schneider, L. Zschiedrich, T. Heindel, S. Bounouar, M. Kantner, Th. Koprucki, U. Bandelow, S. Burger, S. Reitzenstein, Chapter 8: Deterministic Quantum Devices for Optical Quantum Communication, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in Solid-State Sciences, Springer, Heidelberg, 2020, pp. 285--359, (Chapter Published), DOI 10.1007/978-3-030-35656-9_8 .
Abstract
Photonic quantum technologies are based on the exchange of information via single photons. The information is typically encoded in the polarization of the photons and security is ensured intrinsically via principles of quantum mechanics such as the no-cloning theorem. Thus, all optical quantum communication networks rely crucially on the availability of suitable quantum-light sources. Such light sources with close to ideal optical and quantum optical properties can be realized by self-assembled semiconductor quantum dots. These high-quality nanocrystals are predestined single-photon emitters due to their quasi zero-dimensional carrier confinement. Still, the development of practical quantum-dot-based sources of single photons and entangled-photon pairs for applications in photonic quantum technology and especially for the quantum-repeater scheme is very demanding and requires highly advanced device concepts and deterministic fabrication technologies. This is mainly explained by their random position and emission energy as well as by the low photon-extraction efficiency in simple planar device configurations.

M. Kantner, Th. Höhne, Th. Koprucki, S. Burger, H.-J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Chapter 7: Multi-Dimensional Modeling and Simulation of Semiconductor Nanophotonic Devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in Solid-State Sciences, Springer, Heidelberg, 2020, pp. 241--283, (Chapter Published), DOI 10.1007/978-3-030-35656-9_7 .
Abstract
Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonicdevices is an important tool in the development of future integrated light sources and quantumdevices. Simulations can guide important technological decisions by revealing performance bottle-necks in new device concepts, contribute to their understanding and help to theoretically exploretheir optimization potential. The efficient implementation of multi-dimensional numerical simulationsfor computer-aided design tasks requires sophisticated numerical methods and modeling tech-niques. We review recent advances in device-scale modeling of quantum dot based single-photonsources and laser diodes by self-consistently coupling the optical Maxwell equations with semi-classical carrier transport models using semi-classical and fully quantum mechanical descriptionsof the optically active region, respectively. For the simulation of realistic devices with complex,multi-dimensional geometries, we have developed a novel hp-adaptive finite element approachfor the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties ofthe photonic structures. For electrically driven devices, we introduced novel discretization andparameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semi-conductors at cryogenic temperature. Our methodical advances are demonstrated on variousapplications, including vertical-cavity surface-emitting lasers, grating couplers and single-photonsources.

L. Ghezzi, D. Hömberg, Ch. Landry, eds., Math for the Digital Factory, 27 of Mathematics in Industry / The European Consortium for Mathematics in Industry, Springer International Publishing AG, Cham, 2017, x+348 pages, (Collection Published), DOI 10.1007/978-3-319-63957-4 .

P. Colli, G. Gilardi, D. Hömberg, E. Rocca, eds., Special Issue dedicated to Jürgen Sprekels on the Occasion of his 65th Birthday, 35, no. 6 of Discrete Contin. Dyn. Syst. Ser. A, American Institute of Mathematical Sciences, Springfield, 2015, 472 pages, (Collection Published).

P. Deuflhard, M. Grötschel, D. Hömberg, U. Horst, J. Kramer, V. Mehrmann, K. Polthier, F. Schmidt, Ch. Schütte, M. Skutella, J. Sprekels, eds., MATHEON -- Mathematics for Key Technologies, 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, 453 pages, (Collection Published).

B. Denkena, D. Hömberg, E. Uhlmann, Mathematik für Werkzeugmaschinen und Fabrikautomatisierung, in: Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt, M. Grötschel, K. Lucas, V. Mehrmann, eds., acatech diskutiert, acatech, Springer, Berlin, Heidelberg, 2008, pp. 279--299, (Chapter Published).

M. Flaschel, H. Yu, N. Reiter, J. Hinrichsen, S. Budday, P. Steinmann, S. Kumar, L. De Lorenzis, Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID, Journal of the Mechanics and Physics of Solids, 180 (2023), pp. 105404/1--105404/23, DOI 10.1016/j.jmps.2023.105404 .

E. Marino, M. Flaschel, S. Kumar, L. De Lorenzis, Automated identification of linear viscoelastic constitutive laws with EUCLID, Mechanics of Materials, 181 (2023), pp. 104643/1--104643/12, DOI 10.1016/j.mechmat.2023.104643 .

D.R.M. Renger, Anisothermal chemical reactions: Onsager--Machlup and macroscopic fluctuation theory, Journal of Physics A: Mathematical and Theoretical, 55 (2022), pp. 315001/1--315001/24, DOI 10.1088/1751-8121/ac7c47 .
Abstract
We study a micro and macroscopic model for chemical reactions with feedback between reactions and temperature of the solute. The first result concerns the quasipotential as the large-deviation rate of the microscopic invariant measure. The second result is an application of modern Onsager-Machlup theory to the pathwise large deviations, in case the system is in detailed balance. The third result is an application of macroscopic fluctuation theory to the reaction flux large deviations, in case the system is in complex balance.

J. Fischer, K. Hopf, M. Kniely, A. Mielke, Global existence analysis of energy-reaction-diffusion systems, SIAM Journal on Mathematical Analysis, 54 (2022), pp. 220--267, DOI 10.1137/20M1387237 .
Abstract
We establish global-in-time existence results for thermodynamically consistent reaction-(cross-)diffusion systems coupled to an equation describing heat transfer. Our main interest is to model species-dependent diffusivities, while at the same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal case lies in the intrinsic presence of cross-diffusion type phenomena like the Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic equilibria, a nonvanishing temperature gradient may drive a concentration flux even in a situation with constant concentrations; likewise, a nonvanishing concentration gradient may drive a heat flux even in a case of spatially constant temperature. We use time discretisation and regularisation techniques and derive a priori estimates based on a suitable entropy and the associated entropy production. Renormalised solutions are used in cases where non-integrable diffusion fluxes or reaction terms appear.

A.F.M. TER Elst, A. Linke, J. Rehberg, On the numerical range of sectorial forms, Pure and Applied Functional Analysis, 7 (2022), pp. 1931--1940.
Abstract
We provide a sharp and optimal generic bound for the angle of the sectorial form associated to a non-symmetric second-order elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper H^∞-angle for the H^∞-calculus on L_p for all p ∈ (1, ∞) if the coefficients are real valued.

D. Hömberg, K. Krumbiegel, N. Togobytska, Optimal control of multiphase steel production, Journal of Mathematics in Industry, 9 (2019), pp. 1--32, DOI 10.1186/s13362-019-0063-x .
Abstract
An optimal control problem for the production of multiphase steel is investigated, where the state equations are a semilinear heat equation and an ordinary differential equation, which describes the evolution of the ferrite phase fraction. The optimal control problem is analyzed and the first-order necessary and second-order sufficient optimality conditions are derived. For the numerical solution of the control problem reduced sequential quadratic programming (rSQP) method with a primal-dual active set strategy (PDAS) was applied. The numerical results were presented for the optimal control of a cooling line for production of hot rolled Mo-Mn dual phase steel.

D. Hömberg, S. Lu, M. Yamamoto, Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data, Journal of Differential Equations, 266 (2019), pp. 7525--7544, DOI 10.1016/j.jde.2018.12.004 .
Abstract
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 heat source inverse problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement.

G. Lazzaroni, R. Rossi, M. Thomas, R. Toader, Rate-independent damage in thermo-viscoelastic materials with inertia, Journal of Dynamics and Differential Equations, 30 (2018), pp. 1311--1364, DOI 10.1007/s10884-018-9666-y .
Abstract
We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is independent of temperature.

CH. Heinemann, Ch. Kraus, E. Rocca, R. Rossi, A temperature-dependent phase-field model for phase separation and damage, Archive for Rational Mechanics and Analysis, 225 (2017), pp. 177--247.
Abstract
In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature (cf., e.g., [C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321--359] and [C. Heinemann, C. Kraus: Existence results for diffuse interface models describing phase separation and damage. European J. Appl. Math. 24 (2013), 179--211]), we encompass in the model thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More in particular, we prove the existence of "entropic weak solutions", resorting to a solvability concept first introduced in [E. Feireisl: Mathematical theory of compressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53 (2007), 461--490] in the framework of Fourier-Navier-Stokes systems and then recently employed in [E. Feireisl, H. Petzeltová, E. Rocca: Existence of solutions to a phase transition model with microscopic movements. Math. Methods Appl. Sci. 32 (2009), 1345--1369], [E. Rocca, R. Rossi: "Entropic" solutions to a thermodynamically consistent PDE system for phase transitions and damage. SIAM J. Math. Anal., 47 (2015), 2519--2586] for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.

D. Hömberg, F.S. Patacchini, K. Sakamoto, J. Zimmer, A revisited Johnson--Mehl--Avrami--Kolmogorov model and the evolution of grain-size distributions in steel, IMA Journal of Applied Mathematics, 82 (2017), pp. 763--780, DOI 10.1093/imamat/hxx012 .
Abstract
The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker-Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studies are given and confirm expected properties qualitatively. As a preparation for future work on parameter identification, a strategy is presented for the comparison of volume distributions with area distributions experimentally gained from polished micrograph sections.

Y. Guo, D. Hömberg, G. Hu, J. Li, H. Liu, A time domain sampling method for inverse acoustic scattering problems, Journal of Computational Physics, 314 (2016), pp. 647--660.
Abstract
This work concerns the inverse scattering problems of imaging unknown/inaccessible scatterers by transient acoustic near-field measurements. Based on the analysis of the migration method, we propose efficient and effective sampling schemes for imaging small and extended scatterers from knowledge of time-dependent scattered data due to incident impulsive point sources. Though the inverse scattering problems are known to be nonlinear and ill-posed, the proposed imaging algorithms are totally “direct” involving only integral calculations on the measurement surface. Theoretical justifications are presented and numerical experiments are conducted to demonstrate the effectiveness and robustness of our methods. In particular, the proposed static imaging functionals enhance the performance of the total focusing method (TFM) and the dynamic imaging functionals show analogous behavior to the time reversal inversion but without solving time-dependent wave equations.

K. Sturm, M. Hintermüller, D. Hömberg, Distortion compensation as a shape optimisation problem for a sharp interface model, Computational Optimization and Applications. An International Journal, 64 (2016), pp. 557--588.
Abstract
We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.

D. Hömberg, Q. Liu, J. Montalvo-Urquizo, D. Nadolski, Th. Petzold, A. Schmidt, A. Schulz, Simulation of multi-frequency-induction-hardening including phase transitions and mechanical effects, Finite Elements in Analysis and Design, 121 (2016), pp. 86--100.
Abstract
Induction hardening is a well known method for the heat treatment of steel components. With the concept of multi-frequency hardening, where currents with two different frequency components are provided on a single inductor coil, it is possible to optimize the hardening zone to follow a given contour, e.g. of a gear. In this article, we consider the simulation of multi-frequency induction hardening in 3D. The equations to solve are the vector potential formulation of Maxwell's equations describing the electromagnetic fields, the balance of momentum to determine internal stresses and deformations arising from thermoelasticity and transformation induced plasticity, a rate law to determine the distribution of different phases and the heat equation to determine the temperature distribution in the workpiece. The equations are solved using adaptive finite element methods. The simulation results are compared to experiments for discs and for gears. A very good agreement for the hardening profile and the temperature is observed. It is also possible to predict the distribution of residual stresses after the heat treatment.

G. Hu, M. Yamamoto, Hölder stability estimate of the Robin coefficient in corrosion detection problems with a single boundary measurement, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 31 (2015), pp. 115009/1--115009/20.

TH. Petzold, D. Hömberg, D. Nadolski, A. Schulz, H. Stiele, Adaptive Finite-Elemente-Simulation des Mehrfrequenz-Induktionshärtens, HTM Journal for Heat Treatment and Materials, 70 (2015), pp. 33--39.

R. Rossi, M. Thomas, From an adhesive to a brittle delamination model in thermo-visco-elasticity, ESAIM. Control, Optimisation and Calculus of Variations, 21 (2015), pp. 1--59.
Abstract
We address the analysis of a model for brittle delamination of two visco-elastic bodies, bonded along a prescribed surface. The model also encompasses thermal effects in the bulk. The related PDE system for the displacements, the absolute temperature, and the delamination variable has a highly nonlinear character. On the contact surface, it features frictionless Signorini conditions and a nonconvex, brittle constraint acting as a transmission condition for the displacements. We prove the existence of (weak/energetic) solutions to the associated Cauchy problem, by approximating it in two steps with suitably regularized problems. We perform the two consecutive passages to the limit via refined variational convergence techniques.

CH. Heinemann, E. Rocca, Damage processes in thermoviscoelastic materials with damage-dependent thermal expansion coefficients, Mathematical Methods in the Applied Sciences, 38 (2015), pp. 4587--4612.
Abstract
In this paper we prove existence of global in time weak solutions for a highly nonlinear PDE system arising in the context of damage phenomena in thermoviscoelastic materials. The main novelty of the present contribution with respect to the ones already present in the literature consists in the possibility of taking into account a damage-dependent thermal expansion coefficient. This term implies the presence of nonlinear couplings in the PDE system, which make the analysis more challenging.

D. Hömberg, Th. Petzold, E. Rocca, Analysis and simulations of multifrequency induction hardening, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 22 (2015), pp. 84--97.
Abstract
We study a model for induction hardening of steel. The related differential system consists of a time domain vector potential formulation of the Maxwell's equations coupled with an internal energy balance and an ODE for the volume fraction of austenite, the high temperature phase in steel. We first solve the initial boundary value problem associated by means of a Schauder fixed point argument coupled with suitable a-priori estimates and regularity results. Moreover, we prove a stability estimate entailing, in particular, uniqueness of solutions for our Cauchy problem. We conclude with some finite element simulations for the coupled system.

W. Bleck, D. Hömberg, U. Prahl, P. Suwanpinij, N. Togobytska, Optimal control of a cooling line for production of hot rolled dual phase steel, Steel Research International, 85 (2014), pp. 1328--1333.
Abstract
In this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg.

D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Parameter identification in non-isothermal nucleation and growth processes, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 30 (2014), pp. 035003/1--035003/24.
Abstract
We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.

K. Chełminski, D. Hömberg, O. Rott, On a thermomechanical milling model, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 12 (2011), pp. 615--632.
Abstract
This paper deals with a new mathematical model to characterize the interaction between machine and workpiece in a milling process. The model consists of a harmonic oscillator equation for the dynamics of the cutter and a linear thermoelastic workpiece model. The coupling through the cutting force adds delay terms and further nonlinear effects. After a short derivation of the governing equations it is shown that the complete system admits a unique weak solution. A numerical solution strategy is outlined and complemented by numerical simulations of stable and unstable cutting conditions.

A. Fasano, D. Hömberg, D. Naumov, On a mathematical model for laser-induced thermotherapy, Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems. Elsevier Science Inc., New York, NY. English, English abstracts., 34 (2010), pp. 3831--3840.
Abstract
We study a mathematical model for laser-induced thermotherapy, a minimally invasive cancer treatment. The model consists of a diffusion approximation of the radiation transport equation coupled to a bio-heat equation and a model to describe the evolution of the coagulated zone. Special emphasis is laid on a refined model of the applicator device, accounting for the effect of coolant flow inside. Comparisons between experiment and simulations show that the model is able to predict the experimentally achieved temperatures reasonably well.

A. Fasano, D. Hömberg, L. Panizzi, A mathematical model for case hardening of steel, Mathematical Models & Methods in Applied Sciences, 19 (2009), pp. 2101--2126.
Abstract
A mathematical model for the case hardening of steel is presented. Carbon is dissolved in the surface layer of a low-carbon steel part at a temperature sufficient to render the steel austenitic, followed by quenching to form a martensitic microstructure. The model consists of a nonlinear evolution equation for the temperature, coupled with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations to describe the evolution of phase fractions. We investigate questions of existence and uniqueness of a solution and finally present some numerical simulations.

D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, Materialwissenschaft und Werkstofftechnik, 40 (2009), pp. 438--442.
Abstract
The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control.

D. Hömberg, N. Togobytska, M. Yamamoto, On the evaluation of dilatometer experiments, Applicable Analysis. An International Journal, 88 (2009), pp. 669--681.
Abstract
The goal of this paper is a mathematical investigation of dilatometer experiments to measure the kinetics of solid-solid phase transitions in steel upon cooling from the high temperature phase. Usually, the data are only used for measuring the start and end temperature of the phase transition. In the case of several coexisting product phases, lavish microscopic investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, we show that the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data and present some numerical identification results.

K. Chełminski, D. Hömberg, D. Kern, On a thermomechanical model of phase transitions in steel, Advances in Mathematical Sciences and Applications, 18 (2008), pp. 119--140.

P. Suwanpinij, N. Togobytska, Ch. Keul, W. Weiss, U. Prahl, D. Hömberg, W. Bleck, Phase transformation modeling and parameter identification from dilatometric investigations, Steel Research International, 79 (2008), pp. 793--799.
Abstract
The goal of this paper is to propose a new approach towards the evaluation of dilatometric results, which are often employed to analyse the phase transformation kinetics in steel, especially in terms of continuous cooling transformation (CCT) diagram. A simple task of dilatometry is deriving the start and end temperatures of the phase transformation. It can yield phase transformation kinetics provided that plenty metallographic investigations are performed, whose analysis is complicated especially in case of several coexisting product phases. The new method is based on the numerical solution of a thermomechanical identification problem. It is expected that the phase transformation kinetics can be derived by this approach with less metallographic tasks. The first results are remarkably promising although further investigations are required for the numerical simulations.

H. Alder, D. Hömberg, W. Weiss, Simulationsbasierte Regelung der Laserhärtung von Stahl, HTM Zeitschrift für Werkstoffe. Wärmebehandlung. Fertigung, 61 (2006), pp. 103--108.

D. Hömberg, W. Weiss, PID control of laser surface hardening of steel, IEEE Transactions on Control Systems Technology, 14 (2006), pp. 896--904.

D. Hömberg, A. Khludnev, A thermoelastic contact problem with a phase transition, IMA Journal of Applied Mathematics, 71 (2006), pp. 479--495.

D. Hömberg, M. Yamamoto, On an inverse problem related to laser material treatments, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 22 (2006), pp. 1855--1867.

D. Hömberg, A mathematical model for induction hardening including mechanical effects, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 5 (2004), pp. 55--90.

D. Hömberg, S. Volkwein, Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition, Mathematical and Computer Modelling, 38 (2003), pp. 1003-1028.

K. Hopf, Global existence analysis of energy-reaction-diffusion systems, in: Report 29: Variational Methods for Evolution (hybrid meeting), A. Mielke, M. Peletier, D. Slepcev, eds., 17 of Oberwolfach Reports, European Mathematical Society Publishing House, Zurich, 2021, pp. 1418--1421, DOI 10.4171/OWR/2020/29 .

L. Capone, Th. Petzold, D. Hömberg, D. Ivanov, A novel integrated tool for parametric geometry generation and simulation for induction hardening of gears, in: Heat Treat 2017: Proceedings of the 29th AMS Heat Treating Society Conference, October 24--26, 2017, Columbus, Ohio, USA, ASM International, Materials Park, Ohio, 2017, pp. 234--242.

P. Das, J.I. Asperheim, B. Grande, Th. Petzold, D. Hömberg, Simulation of temperature profile in longitudinal welded tubes during high-frequency induction (HFI) welding, in: Heat Treat 2017: Proceedings of the 29th AMS Heat Treating Society Conference, October 24--26, 2017, Columbus, Ohio, USA, ASM International, Materials Park, Ohio, 2017, pp. 534--538.

G. Lazzaroni, R. Rossi, M. Thomas, R. Toader, Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics, in: MURPHYS-HSFS-2014: 7th International Workshop on MUlti-Rate Processes and HYSteresis (MURPHYS) & 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS), O. Klein, M. Dimian, P. Gurevich, D. Knees, D. Rachinskii, S. Tikhomirov, eds., 727 of Journal of Physics: Conference Series, IOP Publishing, 2016, pp. 012009/1--012009/20.
Abstract
This note deals with the analysis of a model for partial damage, where the rate-independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from [Roubíček M2AS'09, SIAM'10] with the methods from Lazzaroni/Rossi/Thomas/Toader [WIAS Preprint 2025]. The present analysis encompasses, differently from [Roubíček SIAM'10], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [WIAS Preprint 2025], a nonconstant heat capacity and a time-dependent Dirichlet loading.

Q. Liu, Th. Petzold, D. Nadolski, R. Pulch, Simulation of thermomechanical behavior subjected to induction hardening, in: Scientific Computing in Electrical Engineering, SCEE 2014, Wuppertal, Germany, July 2014, A. Bartel, M. Clemens, M. Günther, E.J.W. TER Maten, eds., 23 of Mathematics in Industry, Springer International Publishing Switzerland, Cham, 2016, pp. 133--142.

C. Carstensen, M. Hintermüller, D. Hömberg, F. Tröltzsch, C -- Production, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 151--153.

M. Hintermüller, D. Hömberg, O. Klein, J. Sprekels, F. Tröltzsch, C4 -- PDE-constrained optimization with industrial applications, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 207--222.

D. Hömberg, E. Rocca, Th. Petzold, Multi-frequency induction hardening -- A challenge for industrial mathematics, in: The Impact of Applications on Mathematics -- Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 257--264.

D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Nucleation rate identification in binary phase transition, in: The Impact of Applications on Mathematics -- Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 227--243.

P. Krejčí, E. Rocca, J. Sprekels, Liquid-solid phase transitions in a deformable container, in: Continuous Media with Microstructure, B. Albers, ed., Springer, Berlin/Heidelberg, 2010, pp. 285-300.

L. Panizzi, A. Fasano, D. Hömberg, Modeling, analysis and simulations of case hardening of steel, in: Progress in Industrial Mathematics at ECMI 2008, A. Fitt, J. Norbury, H. Ockendon, E. Wilson, eds., 15 of Mathematics in Industry, Springer, Berlin et al., 2010, pp. 965--970.

D. Hömberg, O. Rott, Modeling, analysis and stability of milling processes including workpiece effects, in: Progress in Industrial Mathematics at ECMI 2008, A. Fitt, J. Norbury, H. Ockendon, E. Wilson, eds., 15 of Mathematics in Industry, Springer, Berlin et al., 2010, pp. 493--498.

O. Rott, P. Rasper, D. Hömberg, E. Uhlmann, A milling model with thermal effects including the dynamics of machine and work piece, B. Denkena, ed., Proceedings, 1st International Conference on Process Machine Interactions, Hannover, September 3--4, 2008, PZH Produktionstechnisches Zentrum GmbH, Garbsen, 2008, pp. 369--378.
Abstract
This paper deals with the development of a new mathematical model that characterizes the structure-process interaction for a complex milling system. The structure is divided into a work piece and a machine part, which are represented by different models. While the machine dynamics is characterized by a standard multi-body system, the work piece is described as a linear thermo-elastic continuum. The coupling of both parts is carried out by an empirical process model permitting an estimate of heat and coupling forces occurring during milling. This work reports the derivation of the governing equations emphasizing the coupling and summarizes the numerical algorithms being applied to solve the coupled equation system. The results of numerical simulations that show the dynamics of the complex thermo-mechanical system are presented at the end.

D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, in: Proceedings of the 2nd International Conference on Distortion Engineering -- IDE 2008, 17--19 September 2008, Bremen, Germany, H.-W. Zoch, Th. Lübben, eds., IWT, Bremen, 2008, pp. 201--209.

D. Hömberg, D. Kern, W. Weiss, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, in: Distortion Engineering -- Verzugsbeherrschung in der Fertigung III --, 3 of Sonderforschungsbereich 570, Universität Bremen, Kolloquium, 2006, pp. 39--55.

M. Anthonissen, D. Hömberg, W. Weiss, Real-time control of surface remelting, in: Progress in Industrial Mathematics at ECMI 2004, A. Di Bucchianico, R.M.M. Mattheij, M.A. Peletier, eds., 8 of Mathematics in Industry, Springer, 2005, pp. 356--360.

D. Hömberg, S. Volkwein, W. Weiss, Optimal control strategies for the surface hardening of steel, in: Proceedings of the 2nd International Conference on Thermal Process Modelling and Computer Simulation, S. Denis, P. Archambault, J.-M. Bergheau, R. Fortunier, eds., 120 of J. Physique IV, EDP Sciences, 2004, pp. 325--335.

TH. Eiter, L. Schmeller, Weak solutions to a model for phase separation coupled with finite-strain viscoelasticity subject to external distortion, Preprint no. 3130, WIAS, Berlin, 2024, DOI 10.20347/WIAS.PREPRINT.3130 .
Abstract, PDF (376 kByte)
We study the coupling of a viscoelastic deformation governed by a Kelvin--Voigt model at equilibrium, based on the concept of second-grade nonsimple materials, with a plastic deformation due to volumetric swelling, described via a phase-field variable subject to a Cahn--Hilliard model expressed in a Lagrangian frame. Such models can be used to describe the time evolution of hydrogels in terms of phase separation within a deformable substrate. The equations are mainly coupled via a multiplicative decomposition of the deformation gradient into both contributions and via a Korteweg term in the Eulerian frame. To treat time-dependent Dirichlet conditions for the deformation, an auxiliary variable with fixed boundary values is introduced, which results in another multiplicative structure. Imposing suitable growth conditions on the elastic and viscous potentials, we construct weak solutions to this quasistatic model as the limit of time-discrete solutions to incremental minimization problems. The limit passage is possible due to additional regularity induced by the hyperelastic and viscous stresses.

D. Hömberg, O. Rott, K. Sturm, Discretisation and error analysis for a mathematical model of milling processes, Preprint no. 2364, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2364 .
Abstract, PDF (565 kByte)
We investigate a mathematical model for milling where the cutting tool dynamics is considered together with an elastic workpiece model. Both are coupled by the cutting forces consisting of two dynamic components representing vibrations of the tool and of the workpiece, respectively, at the present and previous tooth periods. We develop a numerical solution algorithm and derive error estimates both for the semi-discrete and the fully discrete numerical scheme. Numerical computations in the last section support the analytically derived error estimates.

O. Kastner, G.J. Ackland, G. Eggeler, W. Weiss, A molecular dynamics view of hysteresis and functional fatigue in martensitic transformations, Preprint no. 1497, WIAS, Berlin, 2010, DOI 10.20347/WIAS.PREPRINT.1497 .
Abstract, Postscript (16 MByte), PDF (4977 kByte)
Shape memory alloys (SMA) exhibit a number of features which are not easily explained by equilibrium thermodynamics, including hysteresis in the phase transformation and ?reverse? shape memory in the high symmetry phase. Processing can change these features: repeated cycling can ?train? the reverse shape memory effect, while changing the amount of hysteresis and other functional properties. These effects are likely to be due to creation of persistent localised defects, which are impossible to study using non-atomistic methods. Here we present a molecular dynamics simulation study of this behaviour. To ensure the largest possible system size, we use a two dimensional binary Lennard-Jones model, which represents a reliable qualitative model system for martensite/austenite transformations. The evolution of the defect structure and its excess energy is investigated in simulations of cyclic transformation/ reverse transformation processes with 160,000 atoms. The simulations show that the transformation proceeds by non-diffusive nucleation and growth processes and produces distinct microstructure. Upon transformation, lattice defects are generated which affect subsequent transformations and vary the potential energy landscape of the sample. Some of the defects persist through the transformation, providing nucleation centres for subsequent cycles. Such defects may provide a memory of previous structures, and thereby may be the basis of a reversible shape memory effect.

O. Rott, E. Jarlebring, An iterative method for the multipliers of periodic delay-differential equations and the analysis of a PDE milling model, Preprint no. 1470, WIAS, Berlin, 2009, DOI 10.20347/WIAS.PREPRINT.1470 .
Abstract, Postscript (670 kByte), PDF (189 kByte)
Locally convergent iterative schemes have turned out to be very useful in the analysis of the characteristic roots of delay-differential equations (DDEs) with constant coefficients. In this work we present a locally convergent iterative scheme for the characteristic multipliers of periodic-coefficient DDEs. The method is an adaption of an iterative method called residual inverse iteration. The possibility to use this method stems from an observation that the characteristic matrix can be expressed with the fundamental solution of a differential equation. We apply the method to a coupled milling model containing a partial and an ordinary differential equation. The conclusion of the numerical results is that the stability diagram of the coupled model differs significantly from the combined stability diagrams for each subsystem.

D. Hömberg, A. Steinbrecher, T. Stykel, Optimal control of robot-guided laser material treatment, Preprint no. 1405, WIAS, Berlin, 2009, DOI 10.20347/WIAS.PREPRINT.1405 .
Abstract, Postscript (10 MByte), PDF (2216 kByte)
In this article we will consider the optimal control of robot guided laser material treatments, where the discrete multibody system model of a robot is coupled with a PDE model of the laser treatment. We will present and discuss several optimization approaches of such optimal control problems and its properties in view of a robust and suitable numerical solution. We will illustrate the approaches in an application to the surface hardening of steel.

W. Dreyer, D. Hömberg, Th. Petzold, A model for the austenite-ferrite phase transition in steel including misfit stress, Preprint no. 1310, WIAS, Berlin, 2008, DOI 10.20347/WIAS.PREPRINT.1310 .
Abstract, Postscript (730 kByte), PDF (445 kByte)
We present a thermodynamically consistent model to describe the austenite-ferrite phase transition in steel. We consider the influence of the mechanical displacement field due to eigenstrains caused by volumetric expansion. The model equations are derived in a systematical framework. They are based on the conservation laws for mass and momentum and the second law of thermodynamics. By means of numerical computations for a simplified interface controlled model, we examine the influence of the mechanical contributions to the transformation kinetics and the equilibrium states.

M. Kniely, A thermodynamically correct framework for electro-energy-reaction-diffusion systems, 22nd ECMI Conference on Industrial and Applied Mathematics, June 26 - 30, 2023, Wrocław University of Science and Technology, Poland, June 30, 2023.

M. Kniely, On a thermodynamically consistent electro-energy-reaction-diffusion system, 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2023), Session 14 ``Applied Analysis'', May 30 - June 2, 2023, Technische Universität Dresden, June 1, 2023.

TH. Eiter, On the resolvent problems associated with rotating viscous flow, DMV Annual Meeting 2022, Section 09 ``Applied Analysis and Partial Differential Equations", September 12 - 16, 2022, Freie Universität Berlin, September 14, 2022.

TH. Eiter, On uniform resolvent estimates associated with time-periodic rotating viscous flow, Mathematical Fluid Mechanics in 2022 (Hybrid Event), August 22 - 26, 2022, Czech Academy of Sciences, Prague, Czech Republic, August 24, 2022.

M. Landstorfer, M. Eigel, M. Heida, A. Selahi, Recovery of battery ageing dynamics with multiple timescales (online poster), MATH+ Day 2021 (Online Event), Technische Universität Berlin, November 5, 2021.

K. Hopf, Global existence analysis of energy-reaction-diffusion systems, Workshop ``Variational Methods for Evolution'', September 13 - 19, 2020, Mathematisches Forschungsinstitut Oberwolfach, September 15, 2020.

M.J. Arenas Jaén, Modelling, simulation and optimization of inductive pre-heating for thermal cutting of steel plates, The 20th European Conference on Mathematics for Industry (ECMI 2018), Minisymposium 27 ``MSO for Steel Production and Manufacturing'', June 18 - 22, 2018, Budapest, Hungary, June 19, 2018.

TH. Petzold, The MIMESIS project -- An example for an interdisciplinary research project, Leibniz-Kolleg for Young Researchers: Chances and Challenges of Interdisciplinary Research, Thematic Workshop ``Models and Modelling'', November 9 - 11, 2016, Leibniz-Gemeinschaft, Berlin, November 9, 2016.

D. Hömberg, Analysis and simulation of Joule heating problems, Mathematisches Kolloquium, Bergische Universität Wuppertal, Fachgruppe Mathematik und Informatik, June 21, 2016.

D. Hömberg, Math for steel production and manufacturing, MACSI10 -- Empowering Industrial Mathematical and Statistical Modelling for the Future, December 8 - 9, 2016, University of Limerick, Ireland, December 9, 2016.

M. Heida, Modeling of fluid interfaces, Jahrestagung der Deutschen Mathematiker-Vereinigung, Minisymposium ``Mathematics of Fluid Interfaces'', September 21 - 25, 2015, Universität Hamburg, Fakultät für Mathematik, Informatik und Naturwissenschaften, Hamburg, September 23, 2015.

CH. Heinemann, Damage processes in thermoviscoelastic materials with damage-dependent thermal expansion coefficients, 3rd Workshop of the GAMM Activity Group Analysis of Partial differential Equations, September 30 - October 2, 2015, Universität Kassel, Institut für Mathematik, October 1, 2015.

D. Hömberg, Nucleation, growth, and grain size evolution in multiphase materials, INdAM Workshop ``Special Materials in Complex Systems -- SMaCS 2015'', May 18 - 22, 2015, Rome, Italy, May 21, 2015.

D. Hömberg, Optimal coefficient control for semilinear parabolic equations, Fudan University, School of Mathematical Sciences, Shanghai, China, March 10, 2015.

TH. Petzold, Adaptive Finite-Elemente-Simulation des Mehrfrequenz-Induktionshärtens in 3D, Härterei-Kongress, October 22 - 24, 2014, Köln, October 23, 2014.

TH. Petzold, Finite element simulations and experiments for multifrequency induction hardening, IUTAM Symposium on Thermomechanical-Electromagnetic Coupling in Solids: Microstructural and Stability Aspect, June 16 - 18, 2014, Paris, France, June 18, 2014.

TH. Petzold, Modelling and simulation of multi-frequency induction hardening of steel parts, 7th International Scientific Colloquium ``Modelling for Electromagnetic Processing'' (MEP 2014), September 16 - 19, 2014, Leibniz Universität Hannover, September 19, 2014.

TH. Petzold, Modelling and simulation of multifrequency induction hardening for gear components, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium ``Recent Trends in Modelling, Analysis, and Simulation of Induction Heat Treatments'', June 9 - 13, 2014, Taormina, Italy, June 13, 2014.

M. Thomas, Rate-independent systems with viscosity and inertia: Existence and evolutionary Gamma-convergence, Workshop ``Variational Methods for Evolution'', December 14 - 20, 2014, Mathematisches Forschungsinstitut Oberwolfach, December 18, 2014.

M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials, 7th International Workshop on Multi-Rate Processes & Hysteresis, 2nd International Workshop on Hysteresis and Slow-Fast Systems (MURPHYS-HSFS-2014), April 7 - 11, 2014, WIAS Berlin, April 8, 2014.

M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials with inertia, International Workshop ``Variational Modeling in Solid Mechanics'', September 22 - 24, 2014, University of Udine, Department of Mathematics and Informatics, Italy, September 23, 2014.

M. Thomas, Rate-independent, partial damage in thermo-viscoelastic materials with inertia, Oberseminar ``Analysis und Angewandte Mathematik'', Universität Kassel, Institut für Mathematik, December 1, 2014.

D. Hömberg, Modelling, simulation and control of surface heat treatments, Norwegian University of Science and Technology, Department of Physics, Trondheim, October 31, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Workshop ``Recent Developments and Challenges in Interface and Free Boundary Problems'', March 25 - 28, 2014, University of Warwick, UK, March 26, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hot-rolling, June 9 - 13, 2014, Taormina, Italy, June 9, 2014.

D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Wrocław University of Technology, Institute of Mathematics and Computer Science, Poland, July 1, 2014.

D. Hömberg, Oberflächenbearbeitung mit Mathematik, Opel Innovation Day, Rüsselsheim, November 7, 2014.

D. Hömberg, Optimal control and shape design problems in thermomechanics, BMS-WIAS Summer School ``Applied Analysis for Materials'', August 25 - September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 1, 2014.

J. Sprekels, Prandtl--Ishlinskii operators and elastoplasticity, Spring School on ``Rate-independent Evolutions and Hysteresis Modelling'', May 27 - 31, 2013, Politecnico di Milano, Università degli Studi di Milano, Italy.

D. Kern, Analysis and simulation of a thermomechanical model of phase transitions in steel, Universität Bremen, SFB 570 ``Distortion Engineering'', February 2, 2011.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 9. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', Siegen, April 6, 2011.

N. Togobytska, Simulation, optimisation and control of microstructure evolution and mechanical properties during hot rolling of multiphase steels, 10. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', Freiberg, November 8, 2011.

D. Hömberg, Optimal control problems in thermomechanics, Schwerpunktskolloquium ``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, January 20, 2011.

N. Togobytska, An inverse problem for laser-induced thermotherapy arising in tumor tissue imaging, Chemnitz Symposium on Inverse Problems 2010, September 23 - 24, 2010, September 24, 2010.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 8. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', Aachen, November 10, 2010.

D. Hömberg, Modelling, simulation and control of phase transformations in steel, Nippon Steel Corporation, Chiba, Japan, September 10, 2010.

D. Hömberg, Multiphase steels, heat treatment and distortion --- Mathematical challenges in steel production and manufacturing, Summer School ``High Performance Computing'' (organizer: TU Ilmenau), September 29 - October 2, 2010, Upstalsboom Hotel Friedrichshain, Berlin, September 30, 2010.

D. Kern, Optimal control of a thermomechanical model including transformation induced plasticity, SIAM Conference on Control and its Applications, July 6 - 8, 2009, Denver, USA, July 8, 2009.

N. Togobytska, Parameter identification for the phase transformations in steel, Conference on Applied Inverse Problems 2009, July 20 - 24, 2009, University of Vienna, Austria, July 21, 2009.

N. Togobytska, Parameter identification from dilatometric investigations, SIAM Conference on Control and its Applications, July 6 - 8, 2009, Denver, USA, July 8, 2009.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, 8. Kolloquium zum DFG SPP 1204 ``Algorithmen zur schnellen, werkstoffgerechten Prozesskettengestaltung und -analyse in der Umformtechnik'', WIAS Berlin, June 23, 2009.

D. Hömberg, Coupling of process, machine, and work-piece in production processes --- A challenge for industrial mathematics, Workshop ``Industrial Mathematics and its Practice'', February 23 - 24, 2009, University of Tokyo, Japan, February 23, 2009.

D. Hömberg, Die Wärmebehandlung von Stahl --- Thermomechanische Modellierung, Simulation und Optimierung, Technische Universität Dortmund, Fakultät Maschinenbau, January 22, 2009.

D. Hömberg, Direct and inverse problems related to phase transitions and distortion in modern multi-phase steels, Workshop ``Mathematical Models and Analytical Problems for Special Materials'', July 9 - 11, 2009, Università degli Studi di Brescia, Italy, July 9, 2009.

D. Hömberg, Distortion compensation --- An optimal control approach, 24th IFIP TC 7 Conference on System Modelling and Optimization, July 27 - 31, 2009, Buenos Aires, Argentina, July 27, 2009.

D. Hömberg, Interactions between machine, work-piece, and process dynamics in milling machines, SIAM Conference on Mathematics for Industry: Challenges and Frontiers (MI09), October 9 - 10, 2009, San Francisco, USA, October 9, 2009.

D. Hömberg, Optimal control of heat treatments and stability of milling processes --- Two case studies from industrial mathematics, Worcester Polytechnic Institute, Mechanical Engineering Department, USA, October 7, 2009.

D. Hömberg, The mathematics of distortion, University of Delaware, Department of Mathematical Sciences, Newark, USA, October 6, 2009.

O. Rott, A milling model with thermal effects including the dynamics of machine and workpiece, 1st International Conference on Process Machine Interactions (PMI 2008), September 3 - 4, 2008, Leibniz Universität Hannover, September 3, 2008.

O. Rott, Modeling, analysis and stability of milling processes including workpiece effects, The European Consortium for Mathematics in Industry (ECMI 2008), June 30 - July 4, 2008, University College, London, UK, July 3, 2008.

O. Rott, Numerical solution of a milling model including thermoelastic workpiece effects, Universität Dortmund, Fachbereich für Mathematik, June 23, 2008.

O. Rott, Parameter für ein MKS-Modell einer Fräsmaschine, DFG SPP 1180 Workshop ``Parameteridentifikation bei Werkzeugmaschinen'', February 21 - 22, 2008, WIAS Berlin, February 22, 2008.

O. Rott, Semiimplizite Zeitintegration eines gekoppelten Systems aus partiellen und gewöhnlichen Differentialgleichungen mit Retardierung, DFG SPP 1180 Workshop ``Modellierungstechnologien'', May 29 - 30, 2008, Dresden, May 30, 2008.

N. Togobytska, On the evaluation of the dilatometer experiments, Chemnitz Symposium on Inverse Problems 2008, September 25 - 26, 2008, September 25, 2008.

N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Antragskolloquium zum DFG Schwerpunktprogramm 1204/2, Bonn, May 20, 2008.

W. Bleck, D. Hömberg, Ch. Keul, U. Prahl, P. Suwanpinij, N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Workshop ``MEFORM 2008: Simulation von Umformprozessen'', Freiberg, March 26 - 28, 2008.

D. Hömberg, Modellierung und Optimierung der Gefügeumwandlung in niedrig legierten Stählen und Anwendungen, Salzgitter Mannesmann Forschung GmbH, February 19, 2008.

D. Hömberg, On a mathematical model for high-speed milling including the dynamics of machine and work-piece, Conference ``Direct, Inverse and Control Problems for PDE's'' (DICOP 08), September 22 - 26, 2008, Cortona, Italy, September 26, 2008.

D. Hömberg, Prozesskette Stahl, Workshop of scshape Matheon with Siemens AG (Industry Sector) in cooperation with Center of Knowledge Interchange (CKI) of Technische Universität (TU) Berlin and Siemens AG, TU Berlin, September 29, 2008.

D. Hömberg, Solid-solid phase transitions --- Analysis, optimal control and industrial application, Warsaw University of Technology, Faculty of Mathematics and Information Science, Poland, February 14, 2008.

D. Hömberg, The heat treatment of steel --- A mathematical control problem, 2nd International Conference on Distortion Engineering 2008, September 17 - 19, 2008, Bremen, September 19, 2008.

D. Kern, Optimal control of a thermo-mechanical model of phase transitions in steel, 13th Czech-French-German Conference on Optimization, September 17 - 21, 2007, Heidelberg, September 20, 2007.

W. Weiss, Control of laser surface hardening, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 19, 2007.

W. Weiss, Simulationsbasierte Regelung der Laserhärtung von Stahl, Ruhr-Universität Bochum, Institut für Werkstoffe, May 30, 2007.

D. Hömberg, D. Kern, Optimal control of a thermomechanical model of phase transitions in steel, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 19, 2007.

D. Hömberg, Mathematics for steel production and manufacturing, Nippon Steel, Kimitsu, Japan, March 1, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Universidad de Cádiz, Departamento de Matemáticas, Puerto Real, Spain, January 15, 2007.

D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Fudan University, Department of Mathematics, Shanghai, China, March 5, 2007.

D. Hömberg, Phase transition models for multiphase steels, Industrial and Interdisciplinary Workshop ``Problems Related to the Manufacture of Multiphase Steels'', University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, November 2, 2007.

D. Hömberg, Solid-solid phase transitions in steel --- modeling, simulation and optimal control, Universitá di Pavia, Dipartimento di Matematica, Italy, March 27, 2007.

D. Hömberg, Thermomechanical phase transition models --- analysis, optimal control and industrial applications, University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, October 11, 2007.

D. Hömberg, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, Universität Bremen, SFB 570 ``Distortion Engineering'', March 2, 2006.

D. Hömberg, Modellierung, Simulation und Optimierung der Wärmebehandlung von Stahl, Endress+Hauser Flowtec AG, Reinach, Switzerland, May 15, 2006.

D. Hömberg, Optimal control of a thermomechanical phase transition model, 12th IEEE International Conference on Methods and Models in Automation and Robotics, August 28 - 31, 2006, Miedzyzdroje, Poland, August 29, 2006.

D. Hömberg, Optimal control of thermomechanical phase transitions, Workshop ``Inverse and Control Problems for PDE's'', March 13 - 17, 2006, Rome, Italy, March 13, 2006.

D. Hömberg, Phasenübergänge in Stahl, Summer School ``Simulation und Anwendungen von Mikrostrukturen'', August 14 - 18, 2006, Föhr.

D. Hömberg, Thermomechanical models of phase transitions --- modelling, control and industrial applications, Escuela Politécnica Nacional, Departamento de Matématica, Quito, Ecuador, November 13, 2006.

D. Hömberg, A thermomechanical phase transition model for the surface hardening of steel, International Conference ``Free Boundary Problems: Theory and Applications'', June 7 - 12, 2005, Coimbra, Portugal, June 11, 2005.

D. Hömberg, Control of laser material treatments, SIAM Conference on Mathematics for Industry, October 24 - 26, 2005, Detroit Marriott Renaissance Center, USA, October 25, 2005.

D. Hömberg, Die Laserhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Universität Bayreuth, Mathematisches Institut, June 30, 2005.

D. Hömberg, Entwicklung eines Prognosetools zur Identifizierung von stabilen Fräsprozessen, DFG SPP 1180, Garbsen, May 19, 2005.

D. Hömberg, Laser material treatments --- modeling, simulation, and optimal control, Michigan State University, Department of Mathematics, East Lansing, USA, October 27, 2005.

D. Hömberg, Modelling, simulation and control of laser material treatments, Scuola Normale Superiore, Pisa, Italy, November 22, 2005.

D. Hömberg, On a thermomechanical model of surface heat treatments, EQUADIFF 11 International conference on differential equations, July 25 - 29, 2005, Comenius University, Bratislava, Slovakia, July 28, 2005.

D. Hömberg, Optimal control of solid-solid phase transitions including mechanical effects, Workshop ``Optimal Control of Coupled Systems of PDE'', April 17 - 23, 2005, Mathematisches Forschungsinstitut Oberwolfach, April 22, 2005.

D. Hömberg, Von der Stahlhärtung bis zur Krebstherapie --- Simulations- und Optimierungsaufgaben in Lehre und Forschung, FEMLAB Konferenz 2005, November 3 - 4, 2005, Frankfurt am Main, November 3, 2005.

D. Hömberg, Modellierung, Analysis und optimale Steuerung der Lasermaterialbearbeitung, Kolloquium der Angewandten Mathematik, Universität Münster, December 3, 2004.

D. Hömberg, Modelling, simulation and control issues in laser-induced thermotherapy, 13-th European Conference on Mathematics for Industry (ECMI 2004), June 21 - 25, 2004, Eindhoven University of Technology, Eindhoven, Netherlands, June 22, 2004.

D. Hömberg, On a thermomechanical model of phase transitions in steel, INdAM Workshop ``Dissipative Models in Phase Transitions'', September 5 - 11, 2004, Cortona, Italy, September 10, 2004.

D. Hömberg, On a thermomechanical model of surface heat treatments, University of Tokyo, Department of Mathematical Sciences, Japan, October 14, 2004.

D. Hömberg, Optimal control of laser surface hardening, University of Chiba, Department of Mathematics and Informatics, Japan, October 19, 2004.

D. Hömberg, Simulation und Optimierung der Lasermaterialbearbeitung, Seminar des Forschungsschwerpunktes Photonik, Technische Universität Berlin, Optisches Institut, June 18, 2004.

D. Hömberg, Thermoelastische Phasenübergänge in Stahl, Humboldt-Universität zu Berlin, Institut für Mathematik, May 13, 2004.

D. Hömberg, Widerstandsschweißen und Oberflächenhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Colloquium of Sfb 393, Technische Universität Chemnitz, Institut für Mathematik, February 13, 2004.

D. Hömberg, A mathematical model for capacitor resistance welding, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7 - 11, 2003, Sydney, Australia, July 10, 2003.