The slow-motion approximation for the Gor'kov-Éliashberg equations

We want to describe the dynamics of magnetic vortices in type-II superconductors using the Gor’kov-Eliashberg equations. To solve this system is very difficult so we want to use an approximation, called Slow-Motion Approximation. This approximation is used quite a lot in physics and for our system of nonlinear partial differential equations we want to show, using rigorous mathematical arguments, that it is in fact an approximation to the exact solution. For the Abelian-Higgs model which shares the same time independent equations with the Gor’kov- Eliashberg system, such a mathematically rigorous proof was given by Stuart (1994). The mathematical discussion starts with an ansatz for the solution that involves the exact solution of the static problem and a small correction. It is well-known that the static solution is a 2N real-parameter family. Let us denote the parameters by q. In the Slow-Motion Approximation we assume that the parameters are time dependent. In our case we want to find the trajectory in the space of static solutions which is the closest, in some sense, to the exact solution. As in many approximation techniques we need a small parameter such that the approximation gets better and better the smaller the parameter becomes. The small parameter, denoted by e, is given by the Higgs self-coupling constant k2 = (1 + e ) /2. Guided by Stuart’s proof we assume that the time derivative of the parameters q is 0 (e). So the problem of proving the validity of the approximation is now turned into proving the existence and smallness of the corrections, which are the solutions of a parabolic linear partial differential equations system on M2. In order to prove this we try to imitate the techniques for finding solutions of the same class of equations in a bounded domain. We need also an iterative method that provide us with certain estimates in suitable Sobolev spaces. We get a system of equations for the parameters q(t) that is a Cauchy problem as soon as we fix initial conditions for q. Imposing initial conditions as well on the corrections of the static solution we simplify the equations for q and solve them. Substituting these q(tys into the static solution we obtain a good approximation for the exact solution of Gor’kov-Eliashberg equations

Massive choleperitoneum three months after mini-gastric bypass for morbid obesity: what every emergency surgeon should be prepared to face. A case report.

Background: Surgery for morbid obesity has spread worldwide, to the point that more than half a million people are operated on each year. As a result, significant numbers of people are living with a new anatomical condition. A mini-gastric bypass is a relatively new bariatric procedure that has gained popularity because of its simplicity and efficacy. Leak rate after this procedure is relatively low (on the order of 1.6%), but marginal ulcer of gastrojejunal anastomosis, if undetected, may lead to leak development. No cases of delayed massive choleperitoneum caused by an almost complete disruption of gastrojejunal anastomosis after mini-gastric bypass have yet been described. Case presentation: We describe here the case of a 51-year-old woman who presented at the emergency department three months after a mini-gastric bypass with acute abdomen caused by massive choleperitoneum due to an almost complete disruption of gastrojejunal anastomosis. The patient underwent an emergency conversion to a Roux-en-Y laparoscopic gastric bypass with associated re-gastrectomy. The postoperative period was characterized by fever due to an infected left pleural effusion, which required treatment with chest tube placement. The patient was discharged three weeks after the operation, in good condition. Six-month follow-up was regular. Conclusions: If suspected, the possibility of marginal ulcer should be investigated as soon as possible. When possible, every obese patient who has complications should be referred to a bariatric surgery department, but each emergency surgeon must be aware of these conditions to be able to treat them optimally

Deal2lkit: a Toolkit Library for High Performance Programming in deal.II

We propose a software design for the efficient and flexible handling of the building blocks used in high performance finite element simulations, through the pervasive use of parameters (parsed through parameter files). In the proposed design, all the building blocks of a high performance finite element program are built according to the command and composite design patterns.We present version 1.1.0 of the deal2lkit (deal.II ToolKit) library, which is a collection of modules and classes aimed at providing high level interfaces to several deal.II classes and functions, obeying the command and composite design patterns, and controlled via parameter files. Keywords: Object-orientation, Software design, Finite element methods, C+

Integration of prebend optimization in a holistic wind turbine design tool

This paper considers the problem of identifying the optimal combination of blade prebend, rotor cone angle and nacelle uptilt, within an integrated aero-structural design environment. Prebend is designed to reach maximum rotor area at rated conditions, while cone and uptilt are computed together with all other design variables to minimize the cost of energy. Constraints are added to the problem formulation in order to translate various design requirements. The proposed optimization approach is applied to a conceptual 10 MW offshore wind turbine, highlighting the benefits of an optimal combination of blade curvature, cone and uptilt angles

Free-Form Design of Rotor Blades

This work investigates an integrated free-form approach for the design of rotor blades, where airfoil shapes are treated as unknowns. This leads to the simultaneous optimization of the chord, twist and structural design variables, together with the airfoil shapes along the blade. As airfoils are automatically tailored to the evolution of the blade, this process results in a better exploration of the solution space and relieves the user from the burden of up-front choices, leading to better final designs. The proposed approach is demonstrated by sizing a 2 MW wind turbine blade

A Research Framework for the Multidisciplinary Design and Optimization of Wind Turbines

The design of very large wind turbines is a complex task which requires the development of dedicated tools and techniques. In this chapter, we present a system-level design procedure based on the combination of multi-body numerical models of the turbine and a multilevel optimization scheme. The overall design aims at the minimization of the cost of energy (COE) through the optimization of all the characteristics of the turbine, and the procedure automatically manages all the simulations required to compute relevant loads and displacements. This unique setup allows the designer to conduct trade-off studies in a highly realistic virtual environment and is an ideal test bench for advanced research studies in which it is important to assess the economic impact of specific design choices. Examples of such studies include the impact of stall-induced vibrations on fatigue, the development of active/passive control laws for large rotors, and the complete definition of 10–20 MW reference turbines

Thalamopeduncular Tumors in Pediatric Age: Advanced Preoperative Imaging to Define Safe Surgical Planning: A Multicentric Experience

Background: Thalamopeduncular tumors are challenging lesions arising at the junction between the thalamus and the cerebral peduncle. They represent 1-5% of pediatric brain tumors, are mainly pilocytic astrocytoma and occur within the first two decades of life. To date, the optimal treatment remains unclear. Methods: We retrospectively reviewed pediatric patients who underwent surgery for thalamopeduncular tumors in the Academic Pediatric Neurosurgery Unit of Padova and Verona from 2005 to 2022. We collected information on age, sex, symptoms, preoperative and postoperative neuroradiological studies, histological specimens, surgical approaches, and follow-up. Results: We identified eight patients with a mean age of 9 years. All lesions were pilocytic astrocytoma. The main symptoms were spastic hemiparesis, cranial nerve palsy, headache, and ataxia. The corticospinal tract was studied in all patients using diffusion-tensor imaging brain MRI and in two patients using navigated transcranial magnetic stimulation. The transsylvian approach was the most frequently used. A gross total resection was achieved in two patients, a subtotal resection in five and a partial resection in one. In three patients, a second treatment was performed due to the regrowth of the tumor, performing an additional surgery in two cases and a second-look surgery followed by adjuvant therapy in one. After the surgery, four patients maintained stability in their postoperative neurological exam, two patients improved, and two worsened but in one of them, an improvement during recovery occurred. At the last follow-up available, three patients were disease-free, four had a stable tumor residual, and only one patient died from the progression of the disease. Conclusions: Advanced preoperative tools allow one to define a safe surgical strategy. Due to the indolent behavior of thalamopeduncular tumors, surgery should be encouraged