Optimal control of semiconductor melts by traveling magnetic fields

In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heater-magnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heater-magnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solid-liquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solid-liquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization

Mindlin-Reissner-Platte: Einige Elemente, Fehlerschätzer und Ergebnisse

Some problems and results in connection with error estimators for modern elements of the Mindlin Reissner equation for plates are discussed

Optimal control of semiconductor melts by traveling magnetic fields

In this paper, the optimal control of traveling magnetic fields in a process of crystal growth from the melt of semiconductor materials is considered. As controls, the phase shifts of the voltage in the coils of a heater-magnet module are employed to generate Lorentz forces for stirring the crystal melt in an optimal way. By the use of a new industrial heater-magnet module, the Lorentz forces have a stronger impact on the melt than in earlier technologies. It is known from experiments that during the growth process temperature oscillations with respect to time occur in the neighborhood of the solid-liquid interface. These oscillations may strongly influence the quality of the growing single crystal. As it seems to be impossible to suppress them completely, the main goal of optimization has to be less ambitious, namely, one tries to achieve oscillations that have a small amplitude and a frequency which is sufficiently high such that the solid-liquid interface does not have enough time to react to the oscillations. In our approach, we control the oscillations at a finite number of selected points in the neighborhood of the solidification front. The system dynamics is modeled by a coupled system of partial differential equations that account for instationary heat condution, turbulent melt flow, and magnetic field. We report on numerical methods for solving this system and for the optimization of the whole process. Different objective functionals are tested to reach the goal of optimization

Influence of molecular weight of polycation polydimethyldiallylammonium and carbon nanotube content on electric conductivity of layer-by-layer films

For biological and engineering applications, nm-thin films with high electrical conductivity and tunable sheet resistance are desirable. Multilayers of polydimethyldiallylammonium chloride (PDADMA) with two different molecular weights (322 and 44.3 kDa) and oxidized carbon nanotubes (CNTs) were constructed using the layer-by-layer technique. The surface coverage of the CNTs was monitored with a selected visible near infrared absorption peak. Both the film thickness and the surface coverage of the CNTs increased linearly with the number of CNT/PDADMA bilayers deposited (film thickness up to 80 nm). Atomic force microscopy images showed a predominantly surface-parallel orientation of CNTs. Ohmic behavior with constant electrical conductivity of each CNT/PDADMA film and conductivity up to 4 · 103 S/m was found. A change in PDADMA molecular weight by almost a factor of ten has no effect on the film thickness and electrical conductivity, only the film/air roughness is reduced. However, increasing CNT concentration in the deposition dispersion from 0.15 up to 0.25 mg/ml results in an increased thickness of a CNT/PDADMA bilayer (by a factor of three). The increased bilayer thickness is accompanied by a decreased electrical conductivity (by a factor of four). The decreased conductivity is attributed to the increased monomer/CNT ratio

Learning Interacting Theories from Data

One challenge of physics is to explain how collective properties arise from microscopic interactions. Indeed, interactions form the building blocks of almost all physical theories and are described by polynomial terms in the action. The traditional approach is to derive these terms from elementary processes and then use the resulting model to make predictions for the entire system. But what if the underlying processes are unknown? Can we reverse the approach and learn the microscopic action by observing the entire system? We use invertible neural networks (INNs) to first learn the observed data distribution. By the choice of a suitable nonlinearity for the neuronal activation function, we are then able to compute the action from the weights of the trained model; a diagrammatic language expresses the change of the action from layer to layer. This process uncovers how the network hierarchically constructs interactions via nonlinear transformations of pairwise relations. We test this approach on simulated data sets of interacting theories. The network consistently reproduces a broad class of unimodal distributions; outside this class, it finds effective theories that approximate the data statistics up to the third cumulant. We explicitly show how network depth and data quantity jointly improve the agreement between the learned and the true model. This work shows how to leverage the power of machine learning to transparently extract microscopic models from data

Clomiphene, Metformin, or Both for Infertility in the Polycystic Ovary Syndrome

Background The polycystic ovary syndrome is a common cause of infertility. Clomiphene and insulin sensitizers are used alone and in combination to induce ovulation, but it is unknown whether one approach is superior. Methods We randomly assigned 626 infertile women with the polycystic ovary syndrome to receive clomiphene citrate plus placebo, extended-release metformin plus placebo, or a combination of metformin and clomiphene for up to 6 months. Medication was discontinued when pregnancy was confirmed, and subjects were followed until delivery. Results The live-birth rate was 22.5% (47 of 209 subjects) in the clomiphene group, 7.2% (15 of 208) in the metformin group, and 26.8% (56 of 209) in the combinationtherapy group (P\u3c0.001 for metformin vs. both clomiphene and combination therapy; P=0.31 for clomiphene vs. combination therapy). Among pregnancies, the rate of multiple pregnancy was 6.0% in the clomiphene group, 0% in the metformin group, and 3.1% in the combination-therapy group. The rates of first-trimester pregnancy loss did not differ significantly among the groups. However, the conception rate among subjects who ovulated was significantly lower in the metformin group (21.7%) than in either the clomiphene group (39.5%, P=0.002) or the combinationtherapy group (46.0%, P\u3c0.001). With the exception of pregnancy complications, adverse-event rates were similar in all groups, though gastrointestinal side effects were more frequent, and vasomotor and ovulatory symptoms less frequent, in the metformin group than in the clomiphene group. Conclusions Clomiphene is superior to metformin in achieving live birth in infertile women with the polycystic ovary syndrome, although multiple birth is a complication. (ClinicalTrials.gov number, NCT00068861.