Optimal control for cooperative systems involving fractional Laplace operators

In this work, the elliptic $2\times 2$ 2 × 2 cooperative systems involving fractional Laplace operators are studied. Due to the nonlocality of the fractional Laplace operator, we reformulate the problem into a local problem by an extension problem. Then, the existence and uniqueness of the weak solution for these systems are proved. Hence, the existence and optimality conditions are deduced.

“You sleep with the devil; you wake up in hell!”: On the new EU-Turkey Deal

Right from the start in 2016, the United Nations High Commissioner for Refugees (UNHCR) and Amnesty International challenged the legitimacy of the so-called refugee deal between Turkey and the EU. Toward the end of 2020, the EU concluded another agreement with Turkey as part of the €6 billion in funding covered by the refugee deal, in spite of Turkey’s deteriorating human rights record. Against a backdrop of Turkey’s weaponizing of refugees against Europe and Europe’s treatment of the refugee issue as a local problem, the European border and coast guard organization Frontex has been practicing illegal pushbacks. It is clear that once you toy with the devil, you cannot escape hell.

The New Right: Conservative student political repertoires and intragroup conflict

This qualitative single-site case study explores how students identifying as conservative position themselves within the discursive field of their campus, how they understand their rhetorical and discursive development in relation to their more liberal peers, and what increasing political polarization means for college campuses. I find that the differences within the conservative student group studied are stronger and more concerning than how they describe differing from their liberal peers, particularly as the conservative student group I analyzed radicalized and became overtly racist and nationalistic. This is worrisome, as my participants noted this was not “a local problem” and mentioned that this was happening at a state and national level. This reality was evidenced by the recent insurrection at the Capitol.

Distributed moving horizon state estimation for sensor networks with low computation capabilities

This paper focuses on distributed state estimation for sensor network observing a discrete-time linear system. The provided solution is based on a Distributed Moving Horizon Estimation (DMHE) algorithm considering a pre-estimating Luenberger observer in the formulation of the local problem solved by each sensor. This leads to reduce the computation load, while preserving the accuracy of the estimation. Moreover, observability properties of local sensors are used for tuning the weights related to consensus information fusion built on a rank-based condition, in order to improve the convergence of the estimation error. Results obtained by Monte Carlo simulations are provided to compare the performance with existing approaches, in terms of accuracy of the estimations and computation time.

Nonlocal problem with the integral condition for a loaded heate equation

В работе рассмотрена нелокальная задача с интегральным условием для нагруженного уравнения теплопроводности, где нагруженное слагаемое представляет собой производную второго порядка от неизвестной функции в начале координат. Доказано существование и единственность регулярного решения. С помощью функции Грина и тепловых потенциалов доказанао существование регулярного решения исследуемой задачи. Доказательство основано на редукции поставленной задачи к интегральному уравнению Вольтерра второго рода со слабой особенностью. Из разрешимости полученных интегральных уравнений Вольтерра следует существование единственного решения поставленной задачи. In this paper, we consider a non-local problem with the integral condition for the loaded heat equation, where the loaded term is a derivative of the second order from an unknown function at the origin. The existence and uniqueness of a regular solution is proven. Using the Green’s functions and thermal potentials, the existence of a regular solution to this problem is proved. The proof is based on the reduction of the formulated problem to the second kind Volterra integral equation with a weak singularity. The solvability of the obtained Volterra integral equations implies the existence of a unique solution to the problem.

Influence of discontinuities on fatigue strength using the example of additively manufactured specimens made of AlSi10Mg

Fatigue strength is largely affected by the influence of discontinuities: geometric notches like holes and corners in components, surface notches (roughness), pores and inclusions in the material. Therefore fatigue of structures and materials is a local problem and fatigue strength calculations are best carried out using local approaches such as local stress concept, local strain concept or fracture mechanical concepts. In this investigation, the influence of discontinuities on low cycle and high cycle fatigue strength of materials was examined on the example of additively produced material specimens made of aluminium AlSi10Mg by using a fracture mechanics parameter. Results of fatigue tests on hourglass-specimens made from four different series of 3-D printed specimens are presented. The examination of the fracture surfaces revealed that damage always started from pores located near the surface of the specimens. The fractography gave information about geometry, size and position of the crack-causing pores. The influence of such pores on the fatigue strength of the printed aluminium was investigated by using a modification of Murakami’s √area parameter. The common scatter band of the four test series could thus be reduced significantly.

A Conforming A-FEM for Modeling Arbitrary Crack Propagation and Branching in Solids

In this paper, an improved conforming AFEM (C-AFEM) for efficient modeling of arbitrary crack propagation and branching is proposed and validated. An explicit formulation for branching cracks has been derived within the C-AFEM framework. The conjugate gradient method is integrated into the C-AFEM formulation to solve the local problem that consists of all elements traversed by single or multiple cracks. Multiple numerical evidences show that this new approach can substantially improve the modeling efficiency. The solution accuracy and numerical robustness are also significantly improved.