Acoustic wave propagation with new spatial implicit and temporal high-order staggered-grid finite-difference schemes

The implicit staggered-grid (SG) finite-difference (FD) method can obtain significant improvement in spatial accuracy for performing numerical simulations of wave equations. Normally, the second-order central grid FD formulas are used to approximate the temporal derivatives, and a relatively fine time step has to be used to reduce the temporal dispersion. To obtain high accuracy both in space and time, we propose a new spatial implicit and temporal high-order SG FD stencil in the time–space domain by incorporating some additional grid points to the conventional implicit FD one. Instead of attaining the implicit FD coefficients by approximating spatial derivatives only, we calculate the coefficients by approximating the temporal and spatial derivatives simultaneously through matching the dispersion formula of the seismic wave equation and compute the FD coefficients of our new stencil by two schemes. The first one is adopting a variable substitution-based Taylor-series expansion (TE) to derive the FD coefficients, which can attain (2M + 2)th-order spatial accuracy and (2N)th-order temporal accuracy. Note that the dispersion formula of our new stencil is non-linear with respect to the axial and off-axial FD coefficients, it is complicated to obtain the optimal spatial and temporal FD coefficients simultaneously. To tackle the issue, we further develop a linear optimisation strategy by minimising the L2-norm errors of the dispersion formula to further improve the accuracy. Dispersion analysis, stability analysis and modelling examples demonstrate the accuracy, stability and efficiency advantages of our two new schemes.

Mid-IR Optical Property of Dy:CaF2-SrF2 Crystal Fabricated by Multicrucible Temperature Gradient Technology

Dy3+-doped CaF2-SrF2 crystals with various Dy3+ dopant concentrations were synthesized by multicrucible temperature gradient technology (MC-TGT). Dy:CaF2-SrF2 crystals were fluorite structured and crystallized in cubic Fm3¯m space group, as characterized by X-ray diffraction. The crystallographic site concentration was calculated from the measured density by Archimedes’ hydrostatic weighing principle. The optical transmission reached over 90% with a sample thickness of 1.0 mm. The Sellmeier dispersion formula was obtained following the measured refractive index in a mid-IR range of 1.7–11 μm. Absorption coefficients of 6.06 cm−1 and 12.71 cm−1 were obtained at 804 nm and 1094 nm in 15% Dy:CaF2-SrF2 crystal. The fluorescence spectra of 15 at.% Dy:CaF2-SrF2 showed the strongest wavelength peak at 2919 nm with a full width at half maximum (FWHM) of 267 nm under an excitation wavelength of 808 nm. The fluorescence lifetimes were illustrated for different Dy3+ dopant levels of 5%, 10% and 15%. The results indicate that the Dy:CaF2-SrF2 crystal is a promising candidate for compact mid-IR lasers.

Dissolution profile of Curcumin from solid dispersion prepared at a high drug load of Curcumin using Poloxamer 407 as the carrier

Introduction: Curcumin, a BCS II drug, suffers from poor bioavailability. Increasing curcumin dissolution is a way to increase its bioavailability. Solid dispersion formulation can be used to improve curcumin dissolution. However, the successful curcumin solid dispersion is limited to a relatively low drug load (< 20%). Objective: This study aimed to investigate the dissolution behaviour of curcumin at a higher drug load (27.9%, 42.3%, and 56.6%) using a surfactant carrier of poloxamer 407. Methods: The solvent evaporation method was employed to prepare high drug load solid dispersion of curcumin. A physical mixture of the corresponding solid dispersion formulation was prepared as a control. Drug load, dissolution behaviour in 180 minutes, and dissolution efficiency (DE180) were determined. Results: The results showed that incorporating curcumin into a poloxamer 407 solid dispersion significantly improves the dissolution rate of curcumin. In the solid dispersion formula, the dissolution behaviour of curcumin was found to be carrier-dependent.

Obtaining the relativistic formula for the refraction of light and the practice of its application

The aim of this scientific study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to the widest range of transparent substances. This study was based on the hypothesis of the dependence of the speed of propagation of photons inside matter on the density of electron clouds of atoms of matter. In the course of research on the basis of Einstein's relativistic formula, this dispersion formula was obtained. The new physical formula was used to calculate 26 refractive indices of light in 5 transparent substances in three states of aggregation. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which amounted to T10 -7h10 -5 in the calculated wavelength ranges of more than 100 nm. The successful application of the relativistic formula to processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

Obtaining the relativistic formula for the refraction of light and the practice of its application

The aim of this scientific study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to the widest range of transparent substances. This study was based on the hypothesis of the dependence of the speed of propagation of photons inside matter on the density of electron clouds of atoms of matter. In the course of research on the basis of Einstein's relativistic formula, this dispersion formula was obtained. The new physical formula was used to calculate 26 refractive indices of light in 5 transparent substances in three states of aggregation. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which amounted to T10 -7h10 -5 in the calculated wavelength ranges of more than 100 nm. The successful application of the relativistic formula to processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

New dispersion formula and results of its application

The aim of the study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to a wide range of transparent substances. In the process of research on the basis of Einstein's relativistic formula, such a dispersion formula was obtained. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which was ±10 -7 − 10 -5 in the calculated wavelength ranges of more than 100 nm.The new dispersion formula is obtained on the basis of the mathematical dependence of the speed of propagation of photons in a transparent substance on the energy density of electron clouds of atoms of the substance. Energy is a universal category, therefore, it is possible to apply the basic version of the new formula (where instead of the wavelength there is the energy density of electron clouds) when conducting research in all areas of light generation, manipulation and detection.And, finally, the very fact of applying the adapted relativistic Einstein's formula to physical processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

«New dispersion formula and results of its application»

The aim of the study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to a wide range of transparent substances. In the process of research on the basis of Einstein's relativistic formula, such a dispersion formula was obtained. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which was ±10 -7-10 -5 in the calculated wavelength ranges of more than 100 nm. The new dispersion formula is obtained on the basis of the mathematical dependence of the speed of propagation of photons in a transparent substance on the energy density of electron clouds of atoms of the substance. Energy is a universal category, therefore, it is possible to apply the basic version of the new formula (where instead of the wavelength there is the energy density of electron clouds) when conducting research in all areas of light generation, manipulation and detection. And, finally, the very fact of applying the adapted relativistic Einstein's formula to physical processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.

Dispersion formulas in QFTs, CFTs and holography

We study momentum space dispersion formulas in general QFTs and their applications for CFT correlation functions. We show, using two independent methods, that QFT dispersion formulas can be written in terms of causal commutators. The first derivation uses analyticity properties of retarded correlators in momentum space. The second derivation uses the largest time equation and the defining properties of the time-ordered product. At four points we show that the momentum space QFT dispersion formula depends on the same causal double-commutators as the CFT dispersion formula. At n-points, the QFT dispersion formula depends on a sum of nested advanced commutators. For CFT four-point functions, we show that the momentum space dispersion formula is equivalent to the CFT dispersion formula, up to possible semi-local terms. We also show that the Polyakov-Regge expansions associated to the momentum space and CFT dispersion formulas are related by a Fourier transform. In the process, we prove that the momentum space conformal blocks of the causal double-commutator are equal to cut Witten diagrams. Finally, by combining the momentum space dispersion formulas with the AdS Cutkosky rules, we find a complete, bulk unitarity method for AdS/CFT correlators in momentum space.

Bulk Structure of the Crust and Upper Mantle beneath Alaska from an Approximate Rayleigh-Wave Dispersion Formula

We introduce a method for estimating crustal thickness and bulk crustal and upper-mantle shear-wave velocities directly from high-quality measurements of fundamental-mode Rayleigh-wave dispersion in the period range from 10 to 40 s. The method is based on an approximate Rayleigh-wave dispersion formula and provides fast results with minimal model parameterization. We apply the method to Rayleigh-wave phase maps in Alaska to reveal first-order structure in a region that had not been systematically and densely instrumented prior to the Transportable Array (TA). To demonstrate the consistency of the results, we also apply the same method to existing Rayleigh-wave phase maps derived from TA data in the conterminous United States, where crustal and upper mantle structures are better known. We contrast features observed in maps of crustal thickness and bulk shear-wave velocity between the Cascadia and Alaska-Aleutian subduction zones to highlight differences in the two regions. Our results show that, contrary to conventional wisdom, first-order information on the location of major depth discontinuities (e.g., the Moho) can be extracted in a fast, straightforward manner from measurements of Rayleigh-wave dispersion alone.