Cubic or 3-regular graphs are (simple) graphs where each vertex has degree 3. The class of cubic graphs is especially interesting for mathematical applications because for various important open problems in graph theory cubic graphs are the smallest or simplest possible potential counterexamples. In chemistry, cubic graphs serve as models for the Nobel Prize winning fullerenes [14] or, more gen...

selection of an appropriate model is important for quantifying response of germination rate to temperature and determination of cardinal temperatures. this study was done to evaluate different nonlinear regression models to describe response of germination rate to temperature in medicinal pumpkin, borago and black cumin. the regression models were dent-like, segmented, beta, curvilinear, quadra...

Silicon-hydrogen crystalline models are proposed to estimate theoretical hydrogen storage capacity in porous silicon media with nanostructure features like cubic nodules, columnar forests and thin wall honeycomb like networks. To simulate these nanostructure features and their hydrogen storage capacities, three basic crystalline types (cubic, column and plate) have been developed as building bl...

Recently, the first author and his coauthor proved a k-order homogeneous linear recursion for the genus polynomials of any H-linear family of graphs (called path-like graph families by Mohar). Cubic outerplanar graphs are tree-like graph families. In this paper, we derive a recursive formula for the total embedding distribution of any cubic outerplanar graph. We also obtain explicit formulas fo...

Cubic spiral is a curve whose direction is a cubic polynomial of arc length. It has been used as a path primitive for nonholonomic car-like mobile robot with restricted turning capability in free environment [1], [2]. In this paper, we investigate the use of cubic spiral segments for car-like mobile robots moving from a given start configuration to a given goal configuration in an environment c...

Using classical molecular dynamics with a more reliable reactive LCBOPII potential, we have performed a detailed study on the direct graphite-to-diamond phase transition. Our results reveal a new so-called "wave-like buckling and slipping" mechanism, which controls the transformation from hexagonal graphite to cubic diamond. Based on this mechanism, we have explained how polycrystalline cubic d...

We report detailed experimental studies on the rheology of cubic blue phases. We observe several flow regimes within each blue phase from rheomicroscopy and small angle light scattering experiments. Both the cubic blue phases exhibit solid-like response while the cholesteric phase shows gel-like behavior. The elastic modulus of BP-I is larger than that of BP-II. The shear induced yield transiti...

The cubic scalar field theory admits the bell-shaped solitary wave solutions which can be interpreted as massive Bose particles. We rule out the nonminimal p-brane action for such a solution as the point particle with curvature. When quantizing it as the theory with higher derivatives, it is shown that the corresponding quantum equation has SU(2) dynamical symmetry group realizing the exact spi...