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District heating networks will play a prominent role in sector coupling. On the one hand, they can help compensating for fluctuations in renewable power generation. On the other hand, they allow to use waste heat from industrial processes instead of natural gas. However, this new role of district heating will also require new operating modes, deeper insight into the network and, consequently, more sophisticated simulation and optimization tools. Here, we deal with an optimal control problem which is dominated by time-varying delays between heat source and consumers: optimal preheating. The goal is to satisfy a periodic demand with a constant heat supply. This problem is still simple, as no devices like turbines are involved. But it contains already all challenges of simulating dynamic networks and, therefore, represents an ideal benchmark. We present a suitable mathematical model, some illustrative analytic examples, an efficient numerical scheme, and a solution to optimal preheating for a real municipal network. The model is both, accurate enough to predict pressure drop or cooling, but also simple enough to allow for fast numerical solution by a method of characteristics. Automatic differentiation is used for both, computing exact Jacobians within Newton’s method and providing an optimizer with sensitivities.

Laser-induced thermotherapy (LITT) is a minimally invasive method causing tumor destruction due to heat ablation and coagulative effects. Computer simulations can play an important role to assist physicians with the planning and monitoring of the treatment. Our recent study with ex-vivo porcine livers has shown that the vaporization of the water in the tissue must be taken into account when modeling LITT. We extend the model used for simulating LITT to account for vaporization using two different approaches. Results obtained with these new models are then compared with the measurements from the original study.

In this article, we present a numerical solver for simulating district heating networks. The method applies a local time stepping to networks of linear advection equations. Numerical diffusion as well as the computational effort on each edge is reduced significantly. The combination with high order coupling and reconstruction techniques leads to a very efficient scheme.

Laser-induced thermotherapy (LITT) plays an important role in oncology to treat human liver tumors. LITT is a minimally invasive method causing tumor destruction due to heat ablation and coagulative effects of the tissue. Tumor tissue is much more sensitive to heat than normal healthy tissue. The big advantage of the LITT compared to other minimally invasive procedures, such as microwave ablation or radiofrequency therapy, is that the treatment primarily takes place under MRI control, such that patients are exposed to a small radiation dose. The present paper describes the mathematical modeling of laser-induced thermotherapy and shows simulation results for porcine liver.

Laser-induced thermotherapy (LITT) is used to treat liver cancer by inserting a laser applicator into the tumor and applying radiation to heat and destroy it. A mathematical model for the simulation of LITT is compared to experimental results with ex-vivo pig livers.

International audience; During glass tempering, residual stresses are caused by the temperature gradient appearing between the surface and the core of the glass. It is therefore necessary to have an accurate knowledge of the heat transfer occurring during the process to obtain an accurate estimation of the residual stresses. Since glass is a semitransparent material, radiative heat transfer takes place inside the glass in addition to the conductive heat transfer. In this paper, we implemented 1-D thermomechanical models using different methods for the computation of the radiative effects inside the glass: Rosseland approximation, P1 approximation and back ray tracing. Thermal and residual stresses results are compared to experimental results available in the literature to investigate the effects of the different methods on the heat transfer and mechanical behavior. We found that P1 approximation and back ray tracing are in good agreement with the experimental results. Finally, a numerical investigation is done by changing different parameters for which the experimental results are not available.

The purpose of this study was to develop a thermometry software tool for temperature monitoring during laser-induced interstitial thermotherapy (LITT). C++ programming language and several libraries including DICOM Toolkit, Grassroots DICOM library, Insight Segmentation and Registration Toolkit, Visualization Toolkit and Quasar Toolkit were used. The software’s graphical user interface creates windows displaying the temperature map and the coagulation extent in the tissue, determined by the magnetic resonance imaging (MRI) thermometry with the echo planar imaging sequence and a numerical simulation based on the radiation and heat transfer in biological tissues, respectively. The software was evaluated applying the MRI-guided LITT to ex vivo pig liver and simultaneously measuring the temperature through a fiber-optic thermometer as reference. Using the software, the temperature distribution determined by the MRI method was compared with the coagulation extent simulation. An agreement was shown between the MRI temperature map and the simulated coagulation extent. Furthermore, the MRI-based and simulated temperatures agreed with the measured one – a correlation coefficient of 0.9993 and 0.9996 was obtained, respectively. The precision of the MRI temperature amounted to 2.4°C. In conclusion, the software tool developed in the present study can be applied for monitoring and controlling the LITT procedure in ex vivo tissues.

The purpose of the study was to develop a simulation approach for laser-induced thermotherapy (LITT) that is based on mathematical models for radiation transport, heat transport, and tissue damage. The LITT ablation was applied to ex vivo pig liver tissue. Experiments were repeated with different laser powers, i.e., 22-34 W, and flow rates of the cooling water in the applicator system, i.e., 47-92 ml/min. During the procedure, the temperature was measured in the liver sample at different distances to the applicator as well as in the cooling circuit using a fiber optic thermometer. For validation, the simulation results were compared with the results of the laser ablation experiments in the ex vivo pig liver samples. The simulated and measured temperature curves presented a relatively good agreement. The Bland-Altman plot showed an average of temperature differences of -0.13 ∘C and 95%-limits-of-agreement of ±7.11 ∘C. The standard deviation amounted to ±3.63 ∘C. The accuracy of the developed simulation is comparable with the accuracy of the MR thermometry reported in other clinical studies. The simulation showed a significant potential for the application in treatment planning.

This paper aims to prove existence and uniqueness of a solution to the coupling of a nonlinear heat equation with nonlinear boundary conditions with the exact radiative transfer equation, assuming the absorption coefficient k (l) to be piecewise constant and null for small values of the wavelength l as in the paper of N. Siedow, T. Grosan, D. Lochegnies, E. Romero, ""Application of a New Method for Radiative Heat Tranfer to Flat Glass Tempering"", J. Am. Ceram. Soc., 88(8):2181-2187 (2005). An important observation is that for a fixed value of the wavelength l, Planck function is a Lipschitz function with respect to the temperature. Using this fact, we deduce that the solution is at most unique. To prove existence of a solution, we define a fixed point problem related to our initial boundary value problem to which we apply Schauder theorem in a closed convex subset of the Banach separable space L2 (0, t f ; C ( [ 0 , l ] ) ) . We use also Stampacchia truncation method to derive lower and upper bounds on the solution.

Flat glass disks are thermally tempered by air-cooling with two air jets at the centre of their surfaces. Numerical modelling and photoelasticity measurements are proposed to analyze the distribution of the residual stresses through the glass thickness at the centre of the tempered disks. For the modelling, glass properties dependent of the temperature are used for the conductive heat transfer. Radiation is modelled by an improved approximation method. By taking both structural and stress relaxations into account, the transient and residual stresses are computed along the disk thickness. For experimentation, a complete procedure is proposed to access to the stress state in the centre of the disks using a scattered light polariscope. The average distribution of the residual stresses is deduced from stress profile measurements taking four radial orientations at the disk centre into consideration. Comparison between numerical and experimental values is finally discussed for the residual surface and half-thickness stresses at the disk centre.

The mould design for the manufacturing of high-precision glass parts remains a challenging task. This motivates the present study which proposes an optimization technique to identify the mould design that yields the desired glass piece profile at the end of the compression moulding process with an accuracy of the order of 1 μm. The intuitive, yet very efficient method consists in computing at each optimization loop the mismatch between the deformed and desired glass piece geometries and using this information to update the mould design. The deformed glass piece geometry is computed using the commercial finite element package ABAQUS. This package is well suited to model the multistage forming process, the complex rheology of the glass, and the varying mechanical contact between the parts involved. The feasibility of the method is demonstrated in theory by designing the required mould for a convex-concave lens, where an accuracy of the order of 1 μm is achieved.

Achieving correct tempering in thin glass is very important to prevent undesired stress and breakage. Computer simulation can elucidate and control the tempering process. For semitransparent materials like glass, heat transfer by thermal radiation is substantial; for thick glass, it may dominate over convection and conduction. The present paper investigates the tempering of thin glass. A circular glass disk supported by a metallic mold cools down by natural convection. The process can be modeled mathematically by coupling the heat and radiative transfer equation in the glass disk with the heat transfer in the support mold. Even at the glass and support mold interface, radiation exchange must be considered. Mechanical behavior is modeled using the mechanical equilibrium and applying the constitutive law for glass during cooling. For the numerical radiation simulation, the Abaqus® commercial software package was combined with an in-house C code. Based on the differences in temperatures and stresses between simulations that only take surface radiation into account and those that consider surface as well as internal radiation, it has been shown that, even for thin glass, internal radiation cannot be ignored.

We present a model for dose calculation in photon radiotherapy based on deterministic transport equations. The model consists of two coupled equations, one for photon and one for electron transport and an equation for the absorbed dose. No assumptions are made with respect to the geometry or the homogeneity of the irradiated medium, so irradiation of any heterogenous medium can be simulated. To get a mathematically simpler model, approximations to the exact equations are presented which keep the essential physical contents of the exact equations, but which can be solved with less numerical effort. The results of dose calculations for simple examples are presented and discussed.

Temperature distributions within semi-transparent materials like glass strongly determine their behavior. It is fundamental to take radiation into account to determine exact temperature distributions. The Rosseland Approximation for radiation is usually an appropriate method, but is only valid with an optically thick glass. In the present paper, we propose an improved approximation that is both efficient and sufficiently accurate even for the semi-transparent region. This new radiation model is used to determine the temperature along the flat glass thickness during tempering. The impact of temperature evaluation on residual stresses is discussed.

In this paper domain decomposition methods for radiative transfer problems including conductive heat transfer are treated. The paper focuses on semi-transparent materials, like glass, and the associated conditions at the interface between the materials. Using asymptotic analysis we derive conditions for the coupling of the radiative transfer equations and a diffusion approximation. Several test casts are treated and a problem appearing in glass manufacturing processes is computed. The results clearly show the advantages of a domain decomposition approach. Accuracy equivalent to the solution of the global radiative transfer solution is achieved, whereas computation time is strongly reduced.

Laser-induced thermotherapy (LITT) is an established minimally invasive percutaneous technique of tumor ablation. Nevertheless, there is a need to predict the effect of laser applications and optimize irradiation planning in LITT. Optical attributes (attenuation, absorption, scattering) change due to thermal denaturation. The work presents the possibility to identify these temperature-dependent parameters from given temperature measurements via an optimal control problem. The solvability of the optimal control problem is analyzed and results of successful implementations are shown.

We consider optimal control-based boundary feedback stabilization of flow problems for incompressible fluids. We follow an analytical approach laid out during the last years in a series of papers by Barbu, Lasiecka, Triggiani, Raymond, and others. They have shown that it is possible to stabilize perturbed flows described by Navier-Stokes equations by designing a stabilizing controller based on a corresponding linear-quadratic optimal control problem. For this purpose, algorithmic advances in solving the associated algebraic Riccati equations are needed and investigated here. The computational complexity of the new algorithms is essentially proportional to the simulation of the forward problem.

We discuss the derivation and investigation of efficient mathematical methods for the solution of optimization and identification problems for radiation dominant processes, which are described by a nonlinear integrodifferential system or diffusive type approximations. These processes are for example relevant in glass production or in the layout of gas turbine combustion chambers. The main focus is on the investigation of optimization algorithms based on the adjoint variables, which are applied to the full radiative heat transfer system as well as to diffusive type approximations. In addition to the optimization we also study new approaches to the reconstruction of the initial temperature from boundary measurements, since its precise knowledge is mandatory for any satisfactory simulation. In particular, we develop a fast, derivative-free method for the solution of the inverse problem, such that we can use many different models for the simulation of the radiative process.

Glass is a man-made material which is used for many thousands of years. It plays an important role in our everydays life, in modern architecture, in science and many other fields.

In a cooling process described by a nonlinear heat equation, we are interested to recover the initial temperature from the temperature measurements that are available on a part of the boundary for some time. Up to now, even for the linear heat equation, this problem usually has been studied as a nonlinear ill-posed operator equation, and regularization methods involving Frechet derivatives have been applied. We propose a fast derivative-free iterative method. Numerical results are presented for the glass cooling process where the nonlinearity appears due to radiation.

The thermal tempering of flat glass in a laboratory facility and an industrial unit with single-jet and multi-jet coolings have been modelled. Firstly the influence of radiation on the transient and residual stresses through the glass thickness was considered. 3D computational fluid dynamic (CFD) models were then developed to analyse the airflow and determine the convective heat transfer at the glass surface during tempering. By coupling these models with 3D finite element models taking both structural and stress relaxation into account, the residual tempering stresses were computed. Photoelastic measurements of the stresses on the surface and through the thickness of the tempered glass plates were used to validate the numerical approach. The homogeneity of the temperature distribution and the residual stresses in the multi-jet configuration were analysed. Finally, a new ultrasonic method to control the residual tempering stresses is proposed. The measurements made on g lass plates tempered using a single-jet configuration were in agreement with the numerical predictions.

This article addresses a new approach for computations of radiative heat transfer in cooling glass. The new solution combines meshfree finite pointset method (FPM) and models of radiative heat transfer in semi-transparent media. This allows to exploit the advantages of particle methods, like their natural capacity to follow changes of deforming geometries, and to reconstruct time evolution of temperature fields due to conduction and radiation effects. Special attention is paid to the radiation as a dominant mechanism of heat transport in high temperatures in semi-transparent materials (e.g. glass). The paper begins with a brief presentation of FPM. It is followed by a discussion of mathematical models of radiation used in computations. The closing part gives a concise review of results of numerical simulations.

This communication discusses the possibility of identifying the shear and structure relaxation functions in inorganic glass by means of a single, simple, and non-intrusive experiment. The latter consists of measuring the thickness variation over time of a glass plate cooled symmetrically from both sides from a temperature above the glass transition temperature down to room temperature. Results with “artificially” created experimental observations suggest that in spite of its simplicity, the thickness variation curve contains sufficient information to identify uniquely the relaxation function parameters using the Levenberg–Marquardt method.

Hypothesis: Cochlear fluid pharmacokinetics can be better represented by three-dimensional (3D) finite-element simulations of drug dispersal. Background: Local drug deliveries to the round window membrane are increasingly being used to treat inner ear disorders. Crucial to the development of safe therapies is knowledge of drug distribution in the inner ear with different delivery methods. Computer simulations allow application protocols and drug delivery systems to be evaluated, and may permit animal studies to be extrapolated to the larger cochlea of the human. Methods: A finite-element 3D model of the cochlea was constructed based on geometric dimensions of the guinea pig cochlea. Drug propagation along and between compartments was described by passive diffusion. To demonstrate the potential value of the model, methylprednisolone distribution in the cochlea was calculated for two clinically relevant application protocols using pharmacokinetic parameters derived from a prior one-dimensional (1D) model. In addition, a simplified geometry was used to compare results from 3D with 1D simulations. Results: For the simplified geometry, calculated concentration profiles with distance were in excellent agreement between the 1D and the 3D models. Different drug delivery strategies produce very different concentration time courses, peak concentrations and basal-apical concentration gradients of drug. In addition, 3D computations demonstrate the existence of substantial gradients across the scalae in the basal turn. Conclusion: The 3D model clearly shows the presence of drug gradients across the basal scalae of guinea pigs, demonstrating the necessity of a 3D approach to predict drug movements across and between scalae with larger cross-sectional areas, such as the human, with accuracy. This is the first model to incorporate the volume of the spiral ligament and to calculate diffusion through this structure. Further development of the 3D model will have to incorporate a more accurate geometry of the entire inner ear and incorporate more of the specific processes that contribute to drug removal from the inner ear fluids. Appropriate computer models may assist in both drug and drug delivery system design and can thus accelerate the development of a rationale-based local drug delivery to the inner ear and its successful establishment in clinical practice.

Laser labelling inside glass induces micro-cracks by high energy densities in the focus. The micro-cracks reduce the mechanical stability of glass. Light scattering allows the observer to perceive the cracks as white pixels. Coloured marking of glass in this manner is not possible. Coloured marking inside glass by changing the oxidation state of the metal ions locally in the focus does not weaken the mechanical properties of the glass. Two kind of glass systems, lime-natron-silicate and borosilicate with 0.5 % mass-content of doping are investigated. The simultaneous presence of donators and acceptors allows a transition of electrons between polyvalent ions, and can lead to permanent colour-centres inside the glass, due to the fact that the absorption of the polyvalent ions is changed by the laser-induced conversion process. For this purpose a 3 ω Nd:YAG (wavelength λL = 355 nm, pulse duration t = 10 to 80 ns) and a Ti:Sapphire solid-state laser (wavelength λL = 810 nm, pulse duration t = 200 fs) are used. The radiation parameters and the chemical composition of the glass (mainly doping) are the dominant factors to generate coloured marking. The transmittance as a function of the fluence and the change of the absorption coefficient is measured and gives a statement of the colourshade. Further the difference between lime-natron-silicate and borosilicate glass (same doping variety) is examined. Actually mauve, yellow, red-brown an grey colouring can be produced. Cracks in the microstructure of glass can also be the cause for brown colour-centres generating.

In this paper we introduce a derivative-free, iterative method for solving nonlinear ill-posed problems \(Fx=y\), where instead of \(y\) noisy data \(y_\delta\) with \(|| y-y_\delta ||\leq \delta\) are given and \(F:D(F)\subseteq X \rightarrow Y\) is a nonlinear operator between Hilbert spaces \(X\) and \(Y\). This method is defined by splitting the operator \(F\) into a linear part \(A\) and a nonlinear part \(G\), such that \(F=A+G\). Then iterations are organized as \(A u_{k+1}=y_\delta-Gu_k\). In the context of ill-posed problems we consider the situation when \(A\) does not have a bounded inverse, thus each iteration needs to be regularized. Under some conditions on the operators \(A\) and \(G\) we study the behavior of the iteration error. We obtain its stability with respect to the iteration number \(k\) as well as the optimal convergence rate with respect to the noise level \(\delta\), provided that the solution satisfies a generalized source condition. As an example, we consider an inverse problem of initial temperature reconstruction for a nonlinear heat equation, where the nonlinearity appears due to radiation effects. The obtained iteration error in the numerical results has the theoretically expected behavior. The theoretical assumptions are illustrated by a computational experiment.

The local delivery of drugs to the cochlea is a promising alternative to systemic treatment of inner ear disorders. Whilst new drugs are being developed for this purpose, it is important to determine the time course and total dose required for the various target regions within the inner ear. Due to the small fluid spaces of the inner ear and the resulting experimental and analytical difficulties, many animal studies have only obtained one sample per animal. This results in limited information about drug time courses at specific locations in the inner ear. We show here how computer models considering general pharmacokinetic principles and inner ear geometry are used for application of the 3R-principle in animal research while avoiding experimental sampling artefacts. This can be achieved by: (1) careful planning and interpretation of experiments to study pharmacokinetics in the inner ear, (2) optimising volume sampling techniques, (3) facilitating the use of advantageous, continuous sampling methods like microdialysis and (4) developing a 3D-model that will permit consideration of the complex geometry of the inner ear when transferring results from one species to another.

Tracer particles in high-viscosity fluids, such as polymer or glass melts, exhibit complex kinematics during mixing processes. At first glance, this is surprising because high viscosities are usually associated with “simple” flows. Nevertheless, a more thorough analysis shows that deterministic chaos is at work and that this is synonymous with good mixing.

The technological control of all subprocesses in glass making (melting, hot forming, annealing) requires a correct description of the heat transport within the glass and the heat transfer between glass and vessels (crucibles, tanks), molds, or cooling equipment (lehrs, vans). Especially in hot forming, the heat transfer from the glass into the molds is of decisive importance. The heat balance of the glass-mold system has considerable influence on the process control and, finally, on the product quality.

Laser-induced thermotherapy (LITT) is an established minimally invasive percutaneous technique of tumor ablation. Nevertheless, there is a need to predict the effect of laser applications and optimizing irradiation planning in LITT. Optical attributes (absorption, scattering) change due to thermal denaturation. The work presents the possibility to identify these temperature dependent parameters from given temperature measurements via an optimal control problem. The solvability of the optimal control problem is analyzed and results of successful implementations are shown.

In this paper we propose a derivative-free iterative method for the approximate solution of a nonlinear inverse problem Fx = y. In this method the iterations are defined as Gxk+1 = Gxk + (Sy − SFxk), where G is an easily invertible operator and S is an operator from a data space to a solution space. We give general suggestions for the choice of operators G and S and show a practically relevant example of an inverse problem where such a method is succesfully applied. We carry out analysis of the proposed method for linear inverse problems. Using the recently introduced balancing principle we construct a stopping rule. Under reasonable assumptions, we show that this stopping rule leads to the regularization algorithm. Numerical results for a test example show its satisfactory behavior.