A quasi-free position-dependent-mass jump and self-scattering correspondence

A quasi-free quantum particle endowed with Heaviside position dependent mass jump is observed to experience scattering effects manifested by its by-product introduction of the derivative of the Dirac's-delta point dipole interaction. Using proper parametric mappings, the reflection and transmission coefficients are obtained. A new ordering ambiguity parameters set, as the only feasibly admissible within the current methodical proposal, is suggested.Comment: 13 pages, no figure

Comment on "Position-dependent effective mass Dirac equations with PT- symmetric and non - PT- symmetric potentials" [J. Phys. A: Math. Gen. 39 (2006) 11877--11887]

Jia and Dutra (J. Phys. A: Math. Gen. 39 (2006) 11877) have considered the one-dimensional non-Hermitian complexified potentials with real spectra in the context of position-dependent mass in Dirac equation. In their second example, a smooth step shape mass distribution is considered and a non-Hermitian non - PT- symmetric Lorentz vector potential is obtained. They have mapped this problem into an exactly solvable Rosen-Morse Schrodinger model and claimed that the energy spectrum is real. The energy spectrum they have reported is pure imaginary or at best forms an empty set. Their claim on the reality of the energy spectrum is fragile, therefore.Comment: 3 pages, 1 figure. To appear in J. Phys.

3D discrete element modeling of concrete: study of the rolling resistance effects on the macroscopic constitutive behavior

The Discrete Element Method (DEM) is appropriate for modeling granular materials [14] but also cohesive materials as concrete when submitted to a severe loading such an impact leading to fractures or fragmentation in the continuum [1, 5, 6, 8]. Contrarily to granular materials, the macroscopic constitutive behavior of a cohesive material is not directly linked to contact interactions between the rigid Discrete Elements (DE) and interaction laws are then defined between DE surrounding each DE. Spherical DE are used because the contact detection is easy to implement and the computation time is reduced in comparison with the use of 3D DE with a more complex shape. The element size is variable and the assembly is disordered to prevent preferential cleavage planes. The purpose of this paper is to highlight the influence of DE rotations on the macroscopic non-linear quasi-static behavior of concrete. Classically, the interactions between DE are modeled by spring-like interactions based on displacements and rotation velocities of DE are only controlled by tangential forces perpendicular to the line linking the two sphere centroids. The disadvantage of this modeling with only spring-like interactions based on displacements is that excessive rolling occurs under shear, therefore the macroscopic behavior of concrete is too brittle. To overcome this problem a non linear Moment Transfer Law (MTL) is introduced to add a rolling resistance to elements. This solution has no influence on the calculation cost and allows a more accurate macroscopic representation of concrete behavior. The identification process of material parameters is given and simulations of tests performed on concrete samples are shown