How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – ...

Effective mass (m*) is defined as: where x, y, z are the directions in the reciprocal Cartesian space (2π/A), En(k) is the dispersion relation for the n-th electronic band. The explicit form of the ...

Abstract: Based on the transmittance matrix (T-matrix) approach, an efficient and stable rigorous coupled-wave analysis (RCWA) method for ultrathin multilayer gratings without solving eigenvalues is ...

A bug was recently identified in the ModeMap.py script whereby normal-mode coordinates were scaled internally by 1/sqrt(N a), leading to U(Q) curves that were inconsistent with the harmonic mode ...

Numerov’s numerical method is developed in a didactic way by using Python in its Jupyter Notebook version 6.0.3 for three different quantum physical systems: the hydrogen atom, a molecule governed by ...

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. It started with a bet. In the late 1980s, at a ...

An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the ...

Soil-rock mixture is a complex multi-phase composite geotechnical material, and its strength is determined by the physical properties of constituent multi-phase materials and their coupling mechanical ...