Preconditioning for Allen-Cahn variational inequalities with non-local constraints

The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach

Achieving Results Through Community School Partnerships

Outlines the importance of and strategies for building and maintaining successful partnerships for community schools that integrate academics, youth development, family support, health and social services, and community development. Makes recommendations

The Impact Of Parental Involvement On Academic Achievement In Children

Academic achievement in children is affected by many factors including family income, family structure, class size, parental education, and parental expectations. Recent research on academic achievement has evaluated the relationship between parental involvement in children’s education and academic achievement. Using data from the National Education Longitudinal Study of 1988, this study investigates the socioeconomic and parental factors that affect academic achievement in children. The question of endogeneity between parental involvement and academic achievement is also explored. The statistical analysis performed utilized OLS regression and instrumental variable techniques. OLS regression techniques demonstrate a negative relationship between parental involvement and academic achievement while instrumental variable techniques demonstrate a strong positive relationship. The results of this study provide evidence of the importance of parental involvement in children’s academic achievement and may serve as an impetus for further research into the effect of specific parental factors on academic achievement in children

The Physiology of Social-Emotional Learning: Integrating Biomarkers of Self-Regulation into the Assessment and Implementation of Programs

In the last two decades, formalized social-emotional learning (SEL) programs in schools have proliferated in response to a staggering increase in mental, social, and emotional challenges for youth. SEL programs differ in their theoretical foundations, though there are commonalities among them. Self-regulation (SR) surfaces as an important pillar. Researchers have relied mostly on self-reporting and teacher questionnaires to measure the effectiveness of these programs to improve SR and other aspects of youth well-being, without explicitly considering the physiological effects of these interventions on the biomarkers of youth. By addressing this gap, program researchers, developers, and educators can reach their stated objectives more effectively, thereby better nurturing SR and other social-emotional competencies. This paper explores a new model and rationale for incorporating physiological metrics (biomarkers), such as vagal tone (VT), into current SEL program impact-assessments and recommends incorporating mind-body practices such as exercise, breathing, mindfulness, and yoga into SEL interventions. This model hypothesizes that the integration of physiological measures and the practices that affect these markers will lead to an increase in SR via a bidirectionally-causative upward spiral. Recommendations for school-based interventions to affect VT are discussed, along with considerations for implementation

Allen-Cahn and Cahn-Hilliard variational inequalities solved with Optimization Techniques

Parabolic variational inequalities of Allen-Cahn and Cahn- Hilliard type are solved using methods involving constrained optimization. Time discrete variants are formulated with the help of Lagrange multipliers for local and non-local equality and inequality constraints. Fully discrete problems resulting from finite element discretizations in space are solved with the help of a primal-dual active set approach. We show several numerical computations also involving systems of parabolic variational inequalities

High-Tc ramp-type Josephson junctions on MgO substrates for Terahertz applications

The authors successfully fabricated high-Tc ramp-type junctions with PrBa2Cu3-xGaxO7-δ (PBCGO: x=0.1, 0.4) barriers on MgO substrates. The junctions showed resistively shunted Josephson junction (RSJ)-like I-V curves with thermally and voltage activated conductivity. The IcRn products for these junctions scaled very well with the Ga-doping. Maximum response of the junctions for 100-GHz millimeter-wave irradiation could be observed up to 12 mV corresponding to 6 THz. Using far infrared laser radiation, we confirmed a terahertz (THz) response of these junctions. These results show promise for THz-wave applications of ramp-type Josephson junctions