The Inverse Scattering Method and Systems of Equations qxy = F(q,qy)

Consider equations of the form where q is in general a complex vector and the function F depends nontrivially both on q and on q_y. We show that a family S of such equations can be investigated by the inverse scattering method. If an equation (*) belongs to S, the function F depends linearly on q and algebraically on q_y. We show that the family S contains a subfamily in which each equation can be obtained from the two dimensional Toda lattice equations by a Bäcklund transformation.     

Noninvasive Temperature Measurement in Dental Materials Using Nd3+, Yb3+ Doped Nanoparticles Emitting in the Near Infrared Region

In this work, the application of near infrared (NIR)-emitting NaYbF₄:1%Tm³⁺@NaLuF₄:30%Nd³⁺ core–shell nanoparticles is reported for noninvasive probing and monitoring the temperature during photopolymerization of dental materials. When excited at 808 nm, the synthesized nanoparticles emit NIR photoluminescence (PL) with two distinctive peaks at 865 and 980 nm which correspond to radiative transitions from the doped Nd³⁺ and Yb³⁺ ions, respectively. Luminescence intensity ratio between these two bands is found to vary with temperature due to temperature-dependent electronic excitation energy transfer between Nd³⁺ and Yb³⁺ ions at the core/shell interface. This finding allows luminescence ratiometric evaluation of the in situ temperature during photopolymerization of resin cement (doped with nanoparticles) in a veneer placement procedure. In addition, the NIR emission also enables PL imaging of the distribution of the adhesive under the veneer. The results highlight that rare-earth ions–doped nanoparticles with both excitation and emission in the NIR spectral range are advantageous for both PL-based nanothermometry and imaging due to the reduced attenuation of NIR light by dental ceramics.     

Multifunctional Sulfur-Hyperdoped Silicon Nanoparticles with Engineered Mid-Infrared Sulfur-Impurity and Free-Carrier Absorption

Si nanoparticles (NPs), which are innovative promising light-harvesting components of thin-film solar cells and key-enabling biocompatible theranostic elements of infrared-laser and radiofrequency hyperthermia-based therapies of cancer cells in tumors and metastases, are significantly advanced in their near/mid-infrared band-to-band and free-carrier absorption via donor sulfur-hyperdoping during high-throughput facile femtosecond-laser ablative production in liquid carbon disulfide. High-resolution transmission electron microscopy and Raman microscopy reveal their mixed nanocrystalline/amorphous structure, enabling the extraordinary sulfur content of a few atomic percents and very minor surface oxidation/carbonization characterized by energy-dispersive X-ray spectroscopy and X-ray photoelectron spectroscopy. A 200-nm thick layer of the nanoparticles exhibits near−mid-infrared absorbance, comparable to that of the initial 380-micron thick n-doped Si wafer (phosphor-dopant concentration ≈10¹⁵ cm⁻³), with the corresponding extinction coefficient for the hyperdoped NPs being 4–7 orders higher over the broadband spectral range of 1–25 micrometers. Such ultimate, but potentially tunable mid-IR structured, multi-band absorption of various sulfur-impurity clusters and smooth free-carrier absorption are break through advances in mid-infrared (mid-IR) laser and radiofrequency (RF) hyperthermia-based therapies, as envisioned in the RF-heating tests, and in fabrication of higher-efficiency thin-film and bulk photovoltaic devices with ultra-broad (UV−mid-IR) spectral response.     

On transmittance and localization of the electromagnetic wave in two-dimensional graphene-based photonic crystals

Two-dimensional graphene-based photonic crystal (GPC) formed by a periodic array of the homogeneous dielectric cylinders etched in the alternating graphene and dielectric layers and its inverse counterpart are considered. The transmittance of the photonic crystal is obtained. The waveguide due to the localization of the electromagnetic wave on the lattice defect that breaks the translational symmetry of the GPC of two different topologies is studied. The different topologies of GPC are characterized by different photonic band structures with different widths of photonic band gaps (PBG) and provide different frequencies for the localized electromagnetic wave due to the defect. The frequencies of the localized mode for both type of the GPC, located inside the lowest PBG, are in the range of THz or tens of THz depending on the topology of the GPC. It is shown that the photonic band gap always can be tuned by changing the chemical potential of graphene to provide formation of the localized photonic mode due to the defect. The technological advantages of the GPC, as well as the opportunity to tune the PBG and the frequency of the localized electromagnetic wave in the terahertz region of spectrum for the GPC are discussed.     

Ultrasonic wave propagation across a thin nonlinear anisotropic layer between two half-spaces

Boundary conditions and perturbation theory are combined to create a set of equations which, when solved, yield the reflected and transmitted wave forms in the case of a thin layer of material that is perfectly bonded between two isotropic half-spaces. The set of perturbed boundary conditions is created by first using the fully bonded boundary conditions at each of the two interfaces between the thin layer and the half-spaces. Then, by restricting the layer's thickness to be much smaller than an acoustic wavelength, perturbation theory can be used on these two sets of boundary equations, producing a set of equations which effectively treat the thin layer as a single interface via a perturbation term. With this set of equations, the full range of incident and polar angles can be considered, with results general enough to use with a layer that is anisotropic, nonlinear, or both anisotropic and nonlinear. Finally the validity of these equations is discussed, comparing the computer simulation results of this theory to results from standard methods, and looking at cases where the results (or various properties of the results) are known or can be predicted.     

Structure factor of a hard-core fluid with short-range Yukawa attraction: analytical FMSA theory against Monte Carlo simulations

ABSTRACT

Analytical solution of the first-order Ornstein–Zernike equation known as the first-order mean spherical approximation (FMSA) theory due to Tang and Lu [J. Chem. Phys. 99, 9828 (1993)] is used to write down a closed equation for the static structure factor of the hard-sphere fluid with a short-range Yukawa attraction. Calculations are performed for a Yukawa decay exponent that corresponds to a range of attraction that does not exceed the first coordination shell of Lennard-Jones-like simple fluids. By comparison with Monte Carlo simulation data it is shown that the analytical FMSA equation for the static structure factor is of the same or even of superior accuracy as that within the seminumerical mean spherical approximation theory.     

Which stresses affect the glide of screw dislocations in bcc metals?

By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2?111? screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation but, instead, on their combination that causes an equibiaxial tension-compression (and thus shear) in the plane perpendicular to the dislocation line. The Peierls stress of 1/2?111? screw dislocations then depends only on the orientation of the plane in which the shear stress parallel to the Burgers vector is applied and on the magnitude and orientation of the shear stress perpendicular to the slip direction.