Quantum Potential and Quantum Gravity

The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying classical system is the presence of an additional potential term being a functional of the real part of the wavefunction. In the present paper this approach is applied to the quantum theory of gravity based on Wheeler -- De Witt equation. We describe the derivation of the `quantum Einstein equation' and discuss the new features of their solutions.Comment: 12 pages LaTeX, to appear in From Field Theory to Quantum Groups. Birthday volume dedicated to Jerzy Lukierski, World Scientifi

The Congruence of Academic Motivation and Catholic Education

Student motivation is of central concern for all teachers, as students cannot learn if they are not engaged and attentive during class. This essay describes how Catholic schools are uniquely designed to promote positive motivational patterns in students based on their foundation in the mysteries of the Catholic faith. The Paschal Mystery relates to students pursuing mastery goals and persisting through challenges, the Trinitarian Mystery reflects the focus on community and belongingness, the Incarnation relates to striving for excellence, and the Eucharist reflects the need for purpose. When Catholic schools are rooted in these mysteries and the mission of the Church, students are primed for a positive motivational experience in school

The Bargmann representation for the quantum mechanics on a sphere

The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in: K. Kowalski and J. Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is discussed between the introduced formalism and the standard approach based on the Hilbert space of square integrable functions on a sphere S^2.Comment: LaTe

A Lagrangian approach to modeling heat flux driven close-contact melting

Close-contact melting refers to the process of a heat source melting its way into a phase-change material. Of special interest is the close-contact melting velocity, or more specifically the relative velocity between the heat source and the phase-change material. In this work, we present a novel numerical approach to simulate quasi-steady, heat flux driven close-contact melting. It extends existing approaches found in the literature, and, for the first time, allows to study the impact of a spatially varying heat flux distribution. We will start by deriving the governing equations in a Lagrangian reference frame fixed to the heat source. Exploiting the narrowness of the melt film enables us to reduce the momentum balance to the Reynolds equation, which is coupled to the energy balance via the velocity field. We particularize our derivation for two simple, yet technically relevant geometries, namely a 3d circular disc and a 2d planar heat source. An iterative solution procedure for the coupled system is described in detail and discussed on the basis of a convergence study. Furthermore, we present an extension to allow for rotational melting modes. Various test cases demonstrate the proficiency of our method. In particular, we will utilize the method to assess the efficiency of the close-contact melting process and to quantify the model error introduced if convective losses are neglected. Finally, we will draw conclusions and present an outlook to future work

On the definition of velocity in doubly special relativity theories

We discuss the definition of particle velocity in doubly relativity theories. The general formula relating velocity and four-momentum of particle is given.Comment: 7 page