Discrete Adjoint Method for Variational Integration of Constrained ODEs and its application to Optimal Control of Geometrically Exact Beam Dynamics

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal solution. While the benefits of structure preserving or geometric methods have been known for decades, their exploration in the context of optimal control problems is a relatively recent field of research. In this work, the discrete adjoint method is derived for variational integrators yielding structure preserving approximations of the dynamics firstly in the ODE case and secondly for the case in which the dynamics is subject to holonomic constraints. The convergence rates are illustrated by numerical examples. Thirdly, the discrete adjoint method is applied to geometrically exact beam dynamics, represented by a holonomically constrained PDE.Comment: Funding: H2020 Marie-Sk\l{}odowska-Curie 86012

A new Lagrangian approach to control affine systems with a quadratic Lagrange term

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an affine control term and we allow linear coordinate changes in the configuration space. Classically, Pontryagin's maximum principle gives necessary optimality conditions for the optimal control problem. For smooth problems, alternatively, a variational approach based on an augmented objective can be followed. Here, we propose a new Lagrangian approach leading to equivalent necessary optimality conditions in the form of Euler-Lagrange equations. Thus, the differential geometric structure (similar to classical Lagrangian dynamics) can be exploited in the framework of optimal control problems. In particular, the formulation enables the symplectic discretisation of the optimal control problem via variational integrators in a straightforward way

Разработка алгоритма для выполнения операции обратного проецирования

High Power Pulsed Magnetron Sputtering (HPPMS) techniques jointly with the deposition of a graded Cr/CrN-nanointerlayer on cutting inserts can increase the film adhesion and consequently the tool life. These improvements depend on the roughness of the employed cemented carbide substrates. The investigations described in the present paper intend to explain the effect of Cr/CrN-interlayer thickness and substrate roughness on the coating adhesion and cutting performance. To attain various roughnesses, the applied cemented carbide inserts were superficially treated. These treatments were grinding at a medium roughness level, or grinding with subsequent polishing for enhancing the surface integrity and finally, in all cases, micro-blasting by fine Al2O3 grains. After Ar-ion etching, graded Cr/CrN adhesive layers with different thicknesses were deposited by HPPMS technology on the variously pretreated substrates. Subsequently, an approximately 3m thick (Ti,Al)N film was depos ited by HPPMS PVD on all used inserts. Rockwell C indentations and inclined impact tests were performed to assess qualitatively and quantitatively the films' adhesion. The cutting performance of the coated tools was investigated in milling of 42CrMo4 QT. FEM supported calculations of the developed stresses during the material removal process contributed in explaining the obtained tool wear results. In these calculations, the adhesion, dependent on the substrate roughness characteristics and on the adhesive interlayer thickness, was taken into account. The results revealed that the effectiveness of HPPMS adhesive graded Cr/CrN-nanointerlayer strongly depends on the substrate surface integrity and on the interlayer thickness. Thus, the film adhesion and consequently the cutting performance can be significantly improved if the interlayer thickness is adapted to the substrate roughness

Small primary adenocarcinoma in adenomyosis with nodal metastasis: a case report

<p>Abstract</p> <p>Background</p> <p>Malignant transformation of adenomyosis is a very rare event. Only about 30 cases of this occurrence have been documented till now.</p> <p>Case presentation</p> <p>The patient was a 57-year-old woman with a slightly enlarged uterus, who underwent total hysterectomy and unilateral adnexectomy. On gross inspection, the uterine wall displayed a single nodule measuring 5 cm and several small gelatinous lesions. Microscopic examination revealed a common leiomyoma and multiple adenomyotic foci. A few of these glands were transformed into a moderately differentiated adenocarcinoma. The endometrium was completely examined and tumor free. The carcinoma was, therefore, considered to be an endometrioid adenocarcinoma arising from adenomyosis. Four months later, an ultrasound scan revealed enlarged pelvic lymph nodes: a cytological diagnosis of metastatic adenocarcinoma was made.</p> <p>Immunohistochemical studies showed an enhanced positivity of the tumor site together with the neighbouring adenomyotic foci for estrogen receptors, aromatase, p53 and COX-2 expression when compared to the distant adenomyotic glands and the endometrium. We therefore postulate that the neoplastic transformation of adenomyosis implies an early carcinogenic event involving p53 and COX-2; further tumor growth is sustained by an autocrine-paracrine loop, based on a modulation of hormone receptors as well as aromatase and COX-2 local expression.</p> <p>Conclusion</p> <p>Adenocarcinoma in adenomyosis may be affected by local hormonal influence and, despite its small size, may metastasize.</p

Physical fitness, fatigue, and quality of life after liver transplantation

Fatigue is often experienced after liver transplantation. The aims of this cross-sectional study were to assess physical fitness (cardiorespiratory fitness, neuromuscular fitness, body composition) in liver transplant recipients and to explore whether physical fitness is related to severity of fatigue. In addition, we explored the relationship between physical fitness and health-related quality of life. Included were 18 patients 1–5 years after transplantation (aged 48.0 ± 11.8 years) with varying severity of fatigue. Peak oxygen uptake during cycle ergometry, 6-min walk distance, isokinetic muscle strength of the knee extensors, body mass index, waist circumference, skinfold thickness, severity of fatigue, and health-related quality of life were measured. Cardiorespiratory fitness in the liver transplant recipients was on average 16–34% lower than normative values (P ≤ 0.05). Furthermore, the prevalence of obesity seemed to be higher than in the general population (17 vs. 10%). We found no deficit in neuromuscular fitness. Cardiorespiratory fitness was the only fitness component that was related with severity of fatigue (rs = −0.61 to rs = -0.50, P ≤ 0.05). Particularly cardiorespiratory fitness was related with several aspects of health-related quality of life (rs = 0.48 to rs = 0.70, P ≤ 0.05). Results of our study imply that cardiorespiratory fitness and body composition are impaired in liver transplant recipients and that fitness is related with severity of fatigue (only cardiorespiratory fitness) and quality of life (particularly cardiorespiratory fitness) in this group. These findings have implications for the development of rehabilitation programs for liver transplant recipients