Tensile properties of phase interfaces in Mg Li alloy: A first principles study

Employing density functional theory, we study the tensile and fracture processes of the phase interfaces in Mg–Li binary alloy. The simulation presents the strain–stress relationships, the ideal tensile strengths, and the fracture processes of three phase interfaces. The results show that the α/α and α/β interfaces have larger tensile strength than that of β/β interface. The fractures of both α/α and β/β interfaces are ductile fractures, while the α/β fractures abruptly._Further analyses show that the fracture of the α/β occurs at the interface.

From E=mc^(2) to E=mc^(2)/22—A Short Account of the Most Famous Equation in Physics and Its Hidden Quantum Entanglement Origin

Einstein’s energy mass formula is shown to consist of two basically quantum components E(O) = mc2/22 and E(D) = mc2(21/22). We give various arguments and derivations to expose the quantum entanglement physics residing inside a deceptively simple expression E = mc2. The true surprising aspect of the present work is however the realization that all the involved “physics” in deriving the new quantum dissection of Einstein’s famous formula of special relativity is actually a pure mathematical necessity anchored in the phenomena of volume concentration of convex manifold in high dimensional quasi Banach spaces. Only an endophysical experiment encompassing the entire universe such as COBE, WMAP, Planck and supernova analysis could have discovered dark energy and our present dissection of Einstein’s marvelous formula.

Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation

We propose finite-volume schemes for the Cahn-Hilliard equation which unconditionally and discretely preserve the boundedness of the phase field and the dissipation of the free energy.Our numerical framework is applicable to a variety of free-energy potentials,including Ginzburg-Landau and Flory-Huggins,to general wetting boundary conditions,and to degenerate mobilities.Its central thrust is the upwind methodology,which we combine with a semi-implicit formulation for the freeenergy terms based on the classical convex-splitting approach.The extension of the schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature,which allows to efficiently solve higher-dimensional problems with a simple parallelisation.The numerical schemes are validated and tested through a variety of examples,in different dimensions,and with various contact angles between droplets and substrates.