New line generation algorithm is proposed for generating lines over 3D body-centered cubic lattice, a kind of optimal lattice in 3D space. The main contribution in this paper is employing the 3D Bresenham algorithm, a popular algorithm for generating 3D lines on a cubic lattice, to produce the BCC lattice occupied by 3D lines, with the help of the adjunct parallelepiped space, having the same c...

Solid metallic hip implants have much higher stiffness than the femur bone, causing stress-shielding and subsequent implant loosening. The development of low-stiff using porous structures has been reported in literature. Ti6Al4V alloy is a commonly used biomaterial for implants. In this work, Body-Center-Cubic (BCC), Cubic, Spherical four different porosities (82%, 76%, 70%, 67%) were investiga...

The grain boundaries of three Laves phase-related body-center-cubic (bcc) solid-solution, metal hydride (MH) alloys with different phase abundances were closely examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and more importantly, electron backscatter diffraction (EBSD) techniques. By using EBSD, we were able to identify the alignment of the crystallograp...

We introduce the theoretical criterion for achieving three-dimensional self-collimation of light in a photonic crystal. Based on this criterion, we numerically demonstrate a body-center-cubic structure that supports wide-angle self-collimation and is directly compatible with the recently developed holographic fabrication technique. We further show that both bends and beam splitters can be intro...

From the Dirac sea concept, we infer that a body center cubic quark lattice exists in the vacuum. Adapting the electron Dirac equation, we get a special quark Dirac equation. Using its low-energy approximation, we deduced the rest masses of the quarks: m(u)=930 Mev, m(d)=930 Mev, m(s)=1110 Mev, m(c)=2270 Mev and m(b)=5530 Mev. We predict new excited quarks dS(1390), uC(6490) and db(9950).

It is often computationally advantageous to model space as a discrete set of points forming lattice grid. This technique particularly useful for difficult problems such quantum many-body systems. For reasons simplicity and familiarity, nearly all calculations have been performed on simple cubic lattices. Since the removal artifacts an important concern, it would be perform using more than one g...

Here, using self-consistent ab initio lattice dynamical calculations that go beyond the quasiharmonic approximation, we show that the high-pressure high-temperature bcc-Fe phase is dynamically stable. In this treatment the temperature-dependent phonon spectra are derived by exciting all the lattice vibrations, in which the phonon-phonon interactions are considered. The high-pressure and high-te...

Mechanical behavior of additively manufactured lattice materials has been mainly investigated under uniaxial compression, while their performance and multiaxial tension are yet to be understood. To address this gap, a generic elastoplastic homogenization scheme with continuum damage model is developed, three different materials, namely cubic, modified face-center cubic body-center analyzed unia...

Using the solution of the center-focus problem from [4], we present the investigation of isochronicity and critical period bifurcations of two families of cubic 3-dim systems of ODEs. Both cubic systems have a center manifold filled with closed trajectories. The presented study is performed using computer algebra systems Mathematica and Singular.