A semi-Lagrangian scheme for the game pp-Laplacian via pp-averaging

We present and analyze an approximation scheme for the two-dimensional game $p$-Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian scheme which exploits the idea of $p$-averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game $p$-Laplacian. We also present a numerical implementation of the scheme for different values of $p$; the numerical tests show that the scheme is accurate.Comment: 34 pages, 3 figures. To appear on Applied Numerical Mathematic

DSM-5 non-suicidal self-injury disorder in a community sample: comparing NSSI engagement, recency and severity among emerging adults

Up to one in five emerging adults engage in non-suicidal self-injury (NSSI). Providing a better understanding of factors that differentiate between who engages in lifetime NSSI and who is more likely to engage in recent and clinically severe NSSI can provide meaningful information for prevention and intervention of NSSI. The present study (n = 669) considered NSSI lifetime engagement (no prior history of NSSI vs. lifetime NSSI), recency [past NSSI (>12 months ago) vs. recent (≤12-month) NSSI], and clinical severity among those with recent NSSI (subthreshold vs. DSM-5 NSSI disorder). The prevalence of NSSI disorder was 8.4% in emerging adults aged 18 to 26 years old. Higher anxiety levels were related to NSSI engagement, but only depressive symptoms and NSSI versatility were consistently associated with more recent NSSI and NSSI disorder. A stepped-care approach may be required in addressing NSSI among emerging adults

Supra-oscillatory critical temperature dependence of Nb-Ho bilayers

We investigate the critical temperature Tc of a thin s-wave superconductor (Nb) proximity coupled to a helical rare earth ferromagnet (Ho). As a function of the Ho layer thickness, we observe multiple oscillations of Tc superimposed on a slow decay, that we attribute to the influence of the Ho on the Nb proximity effect. Because of Ho inhomogeneous magnetization, singlet and triplet pair correlations are present in the bilayers. We take both into consideration when solving the self consistent Bogoliubov-de Gennes equations, and we observe a reasonable agreement. We also observe non-trivial transitions into the superconducting state, the zero resistance state being attained after two successive transitions which appear to be associated with the magnetic structure of Ho.Comment: Main article: 5 pages, 4 figures; Supplementary materials: 4 pages, 5 figure

Studies of resistance switching effects in metal/YBa2Cu3O7-x interface junctions

Current-voltage characteristics of planar junctions formed by an epitaxial c-axis oriented YBa2Cu3O7-x thin film micro-bridge and Ag counter-electrode were measured in the temperature range from 4.2 K to 300 K. A hysteretic behavior related to switching of the junction resistance from a high-resistive to a low-resistive state and vice-versa was observed and analyzed in terms of the maximal current bias and temperature dependence. The same effects were observed on a sub-micrometer scale YBa2Cu3O7-x thin film - PtIr point contact junctions using Scanning Tunneling Microscope. These phenomena are discussed within a diffusion model, describing an oxygen vacancy drift in YBa2Cu3O7-x films in the nano-scale vicinity of the junction interface under applied electrical fields.Comment: To be published in Applied Surface Science