Solving hyperbolic-elliptic problems on singular mapped disk-like domains with the method of characteristics and spline finite elements

A common strategy in the numerical solution of partial differential equations is to define a uniform discretization of a tensor-product multi-dimensional logical domain, which is mapped to a physical domain through a given coordinate transformation. By extending this concept to a multi-patch setting, simple and efficient numerical algorithms can be employed on relatively complex geometries. The main drawback of such an approach is the inherent difficulty in dealing with singularities of the coordinate transformation. This work suggests a comprehensive numerical strategy for the common situation of disk-like domains with a singularity at a unique pole, where one edge of the rectangular logical domain collapses to one point of the physical domain (for example, a circle). We present robust numerical methods for the solution of Vlasov-like hyperbolic equations coupled to Poisson-like elliptic equations in such geometries. We describe a semi-Lagrangian advection solver that employs a novel set of coordinates, named pseudo-Cartesian coordinates, to integrate the characteristic equations in the whole domain, including the pole, and a finite element elliptic solver based on globally $C^1$ smooth splines (Toshniwal et al., 2017). The two solvers are tested both independently and on a coupled model, namely the 2D guiding-center model for magnetized plasmas, equivalent to a vorticity model for incompressible inviscid Euler fluids. The numerical methods presented show high-order convergence in the space discretization parameters, uniformly across the computational domain, without effects of order reduction due to the singularity. Dedicated tests show that the numerical techniques described can be applied straightforwardly also in the presence of point charges (equivalently, point-like vortices), within the context of particle-in-cell methods

Phenomenological subtypes of mania and their relationships with substance use disorders

Objective The aim of the present study was to determine the distinct clusters of subtypes among patients with bipolar disorder (BD) and the relationship between the clinical features of BD patients, particularly substance use disorders (SUDs) and the clusters. Method The present study initially assessed 96 inpatients who were hospitalized in the psychiatric clinic of BakIrköy Prof. Mazhar Osman Training and Research Hospital for Psychiatry and Neurology, for a BD manic episode. All patients were evaluated during the initial 3 days of their admission using the Young Mania Rating Scale (YMRS), the Montgomery-Asberg Depression Rating Scale (MADRS),the Scale for the Assessment of Positive Symptoms (SAPS), the Michigan Alcoholism Screening Test (MAST) and a sociodemographic questionnaire. The factor structures of the psychopathological scale items were determined with factor analyses and based on the factor loadings, cluster analyses were performed. The relationships among the clusters and the clinical variables were then evaluated. Results The factor analyses generated three factors: increased psychomotor activity, dysphoria, and psychosis. A hierarchical cluster analysis was applied to the three factor loadings, and revealed that factor 1 (increased psychomotor activity) was high in cluster 1 and that the effects of factors 2 (dysphoria) and 3 (psychosis) were high in cluster 2. Within cluster 1 (Psychomotor elevation), 39% of patients were diagnosed with an alcohol use disorder while 31.6% of patients in the cluster 2 (dysphoric-psychotic) were diagnosed with both alcohol and cannabis use disorders. Within cluster 2 (dysphoric-psychotic), 47.4% of patients had one suicide attempt and 21.1% of patients had two or more attempts during their lifetime. Conclusion There was a significant difference in the presence of SUDs between patients with psychomotor elevation and patients in dysphoric-psychotic cluster. This may be point out that pure manic patients with BD self-medicate using the sedative effects of alcohol and the causal relationship between cannabis and psychosis. Using a dimensional approach to study BD may enhance detection of the biological correlates of BD and improve the treatment and outcomes of the disorder. © 2014 Elsevier B.V

Simulasyon Ortammda lnsansiz Hava Araci ile Ray Takibi icin Goruntn Isleme Tabanh Bir Yontem Gelistirme

IEEE SMC Society;IEEE Turkey Section2021 Innovations in Intelligent Systems and Applications Conference, ASYU 2021 -- 6 October 2021 through 8 October 2021 -- -- Conference codeRail transport is considered one of the safest means of transport in the entire world. With the development of high- speed trains, great investments have been made in our country in the field of railway transportation in recent years. With the increasing railway line, the demand for railway transportation is increasing day by day. Millions of people who are dependent on this means of transportation every day frequently use the railways. A preventive system is needed to keep up with this intensity, prevent unexpected breakdowns and support railway infrastructure systems. For the railway infrastructure to provide healthy service, maintenance services must be carried out regularly. Traditional railway maintenance services require intensive labor and time. This manual maintenance service is carried out with various rail maintenance tools. As an alternative to traditional methods, an unmanned aerial vehicle-based maintenance system that autonomously monitors and takes images of railway tracks is proposed in this study. The proposed method detects the vanishing point with the front camera of the drone. Then the PID controller is used to maintain the vanishing point tracking. The proposed method was developed in the Gazebo environment. The general purpose ofthe study is to record the rail images with the camera of the unmanned aerial vehicle that autonomously follows the vanishing point. In this way, real-life umnanned aerial vehicle experiments will be completed in a shorter time. © 2021 IEEE