Accuracy assessment methods are necessary for functional data used in simulation-based design optimization to ensure model and optimal solution validity. Although many error metrics exist and perform well for one-dimensional (1D) applications, the suitability of such metrics for higher dimensional functional data, such as two-dimensional (2D) performance maps, have been largely unexplored. This...

We investigate a two-species Fermi gas in which one species is confined in a two-dimensional plane (2D) or one-dimensional line (1D) while the other is free in the three-dimensional space (3D). We discuss the realization of such a system with the interspecies interaction tuned to resonance. When the mass ratio is in the range 0.0351<m_(2D)/m_(3D)<6.35 for the 2D-3D mixture or 0.006 46<m_(1D)/m_...

Sound propagation in the sonic crystal (SC) along the symmetry direction is modeled by sound propagation through a variable cross-sectional area waveguide. A one-dimensional (1D) model based on the Webster horn equation is used to obtain sound attenuation through the SC. This model is compared with two-dimensional (2D) finite element simulation and experiment. The 1D model prediction of frequen...

Behaviors of liquids in two-dimensional (2D), lyophobic nanoenvironment were investigated experimentally by using a surface-modified, graphene-based nanoslit composite (GBNC). Different from previous reports on one-dimensional (1D) nanofludic behaviors, the infiltration pressure of 2D nanofluid is not dependent on the infiltration volume, leading to a flat infiltration plateau in the sorption i...

Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a fivefold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three band gaps. These solitons are mobile, and they collide elastically. Man...

Two-dimensional (2D) materials are among the most promising candidates for next-generation electronics due to their atomic thinness, allowing for flexible transparent electronics and ultimate length scaling. Thus far, atomically thin p-n junctions, metal-semiconductor contacts, and metal-insulator barriers have been demonstrated. Although 2D materials achieve the thinnest possible devices, prec...

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) possess interesting one-dimensional (1D) properties at its edges and inversion domain boundaries, where properties markedly different from the 2D basal plane, such as 1D metallicity and charge density waves, can be observed. Although 2D TMDCs crystals are widely grown by chemical vapor deposition (CVD), the fabrication of 1D TMDCs ri...

– The speed of traveling fronts for a two-dimensional model of a delayed reactiondispersal process is derived analytically and from simulations of molecular dynamics. We show that the one-dimensional (1D) and two-dimensional (2D) versions of a given kernel do not yield always the same speed. It is also shown that the speeds of time-delayed fronts may be higher than those predicted by the corres...

We consider the problem of image recognition via two-dimensional random projection and nearest constrained subspace. First, image features are extracted by a two-dimensional random projection. The two-dimensional random projection for feature extraction is an extension of the 1D compressive sampling technique to 2D and is computationally more efficient than its 1D counterpart and 2D reconstruct...

We consider dimension reduction for the three dimensional (3D) Schödinger equation with the Coulomb interaction and an anisotropic confining potential to lower dimensional models in the limit of infinitely strong confinement in two or one space dimensions and obtain formally the surface adiabatic model (SAM) or surface density model (SDM) in two dimensions (2D) and the line adiabatic model (LAM...