Section 3 contains the general derivation of the linear tensor equation for one component that is equivalent to the Dirac equation. Formulations of the linear tensor equation in terms of antisymmetric second-rank tensors and 3D vectors are provided, respectively, in Sects. 4 and 5. The supplement...
crystallizationThe one-dimensional classical wave equation is derived using a simple, rigorous mathematical approach based on a general feature of one-dimensional linear waves.doi:10.1088/0143-0807/28/4/N01LieouCharles K CEuropean Journal of Physics...
polar-optical phonons. For these phonons, the local dipoles parametrized by the Born effective charges drive the LO-TO splitting of bulk materials; this splitting actually breaks down in two-dimensional materials. Here, we develop the theory for one-dimensional (1D) systems—nanowires, nanotubes, ...
To eliminate this error, one can generalize the approach of Fokinet al.21by assuming that the reflection coefficient depends on the incident wave propagation direction. This is achieved by measuring the reflection and transmission coefficients,RandT, respectively, of a finite length one-dimensional eff...
In this report, we theoretically formulate an electric mechanism to interfere electron orbits, by focusing on a one-dimensional (1D) spin-orbit-coupled nanowire QD. Owing to the existence of SOC and a pulsed electric field, different spin-orbit states are shown to interfere with each other, ...
The UNSATCHEM software Package for Simulating the One-Dimensional Variably Saturated Water Flow, Heat Transport, Carbon Dioxide Production and Transport, and Multicomponent Solute Transport with Major Ion Equilibrium and Kinetic Chemistry Version 2 .O Research Report No. 141 November, 1996 U. S. ...
microscopic space-time satisfies the one dimensional classical wave equation. Next, let us consider Hypothesis Ⅱ. This is the Euler -Lagrangian equation in the microscopic space-time. The L is defined by the macroscopic space-time as follows, ...
Let us turn our attention to the two dimensional case,for which equation (2) can be generalized to a double summation over a tensor.The dominant contribution to the longitudinal eigenmode is the following sum: ω2D(k)∝ = ∞,r=1 sin[kr]22 ...
Effective-one-body (EOB) theory was originally proposed based on the post-Newtonian (PN) approximation and plays an important role in the analysis of gravitational wave signals. Recently, the post-Minkowskian (PM) approximation has been applied to the EOB theory. The energy map and the effectiv...
Su Boundary Value Problems (2021) 2021:92 https://doi.org/10.1186/s13661-021-01570-1 RESEARCH Open Access On global classical solutions to one-dimensional compressible Navier–Stokes/Allen–Cahn system with density-dependent viscosity and vacuum Menglong Su1* *Correspondence: mlsulynu@163.com 1...