...) is based on the Gross–Pitaevskii (GP) equation for the MF wave function ψ(x, y, z, t), which includes the OL (optical-lattice) potential, with depth 2U₀, and cubic nonlinearity. In the scaled form, the GP equation takes the form (7.1) i ψ...

... in Photorefractive (PhR) Media The technique The experimental technique that makes it possible to create various types of stable 2D solitons in media combining saturable nonlinearity and an effective lattice potential was proposed by Efremidis et al. (2003) . A laser beam creating the soliton was shone...

... potential of a single ion in a crystal ( Gilman, 2003 ; and Courtney, 2005 ). Note that the derivation of A_M approximates the ions in the crystal by point charges. The Madelung constant depends on the geometry of the crystal (lattice parameters, anioncation distances, volume...

...) with periodic dilation of a lattice wave (elongation and conduction). This change in the bandgap is attributed to the variation of electrostatic potential induced by the corresponding change in the periodicity within the crystal. Bardeen and Shockley (1950) extended the theories of Pekar (1946) and James...

... are not necessary since the strain inherently changes the ion–ion and ion–electron interaction potential due to changes in the ionic distances. Thus, whether it is a chemical or lattice strain, the strain-dependent properties are controlled by the underlying crystal potential. The reader should keep this in mind...

... energy because they can release part of the absorbed energy to the lattice before being placed Existence of the energy cut off as a fact in favor of a corpuscular interpretation of light Heisenberg Principle and uncertainty meaning Meaning of “something is a wave” The intensity of photons...

... Bardeen , J. and Shockley , W. , “ Deformation potentials and mobilities in non-polar crystals ,” Phys. Rev.   80 , 72 – 80 ( 1950 ). 10.1103/PhysRev.80.72 Bernardini , F. , Fiorentini , V. , and Vanderbilt , D. , “ Spontaneous polarization and piezoelectric constants of III...

... lattice strain and electronic structure changes leading to the conductance modulation in semiconductors is of long-standing interest in materials science and has potential applications in piezoresistive strain gauges, pressure sensors, and cantilever force sensors. Studies have shown that the electronic...

... hindrances of realizing BFO as a potential candidate for room temperature multiferroic is the difficulty in synthesizing BFO in single phase ( Wang et al., 2003 ; and Lou et al., 2007 ). However, the advancement of various fabrication techniques led to the fabrication of various complex...

... which is the change of the magnetization of a magnetic material when subjected to mechanical deformation ( Joule, 1847 ; Culity, 1972 ; and Buschow, 1980 ). Magnetostriction basically results from the coupling between the magnetic interactions on the state of strain of the lattice. During...

... of lead-free Ba_0.85Ca_0.15Zr_0.1Ti_0.9O₃ (BCZT) and CoFe₂O₄ (CFO) at the nanoscale with various grain orientations and simultaneously retaining an atomically sharp epitaxy-like interface. Since, both BCZT and CFO have a lattice...

... of the absorbed energy to the lattice before being placed Existence of the energy cut off as a fact in favor of a corpuscular interpretation of light Heisenberg Principle and uncertainty meaning Meaning of “something is a wave” The intensity of photons emitted in random directions decreases as 1...

...). More specifically, the elastic relaxation takes place at the peaks and the troughs get more stressed. Thus, once started, the process is self-propagating. If in addition, new material is added, the chemical potential differences are such that the atoms attach at the peaks leading to the enhancement...

... and B.   Schmidt ( IOS Press , Amsterdam , 2016 ), pp. 87 – 90 . Knegjens , R. , “ Simulation of a wind tunnel using lattice cellular automata ” ( 2008 ), see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.533.1785andrep=rep1andtype=pdf . Kohn , A. S. , Child Dev...

... and h_ijk, whereas d i j k † and h i j k † are the tensors defining the converse piezoelectric effect ( Völker, 2011 ). From the thermodynamic potential, we can also derive the isothermal elastic compliance at constant electric field S i j k l E i , θ...

... , J. , Scuseria , G. E. , and Ernzerhof , M. , “ Hybrid functionals based on a screened Coulomb potential ,” J. Chem. Phys.   118 , 8207 – 8215 ( 2003 ). 10.1063/1.1564060 Hohenberg , P. and Kohn , W. , “ Thermal properties of the inhomogeneous electron gas ,” Phys. Rev...

.... Speck and E. Farzana (AIP Publishing, Melville, New York, 2023), pp. 12-1–12-26. Ultra-wide bandgap semiconductors have the potential for extreme radiation tolerance due to their inherently high bond energies along with their high figures of merit for power and RF electronics. Among these materials...