An affine generalized optimal scheme with improved free-surface expression using adaptive strategy for frequency-domain elastic wave equation

Effective frequency-domain numerical schemes were central for forward modeling and inversion of the elastic wave equation. The rotated optimal nine-point scheme was a highly used finite-difference numerical scheme. This scheme made a weighted average of the derivative terms of the elastic wave equations in the original and the rotated coordinate systems. In comparison with the classical nine-point scheme, it could simulate S-waves better and had higher accuracy at nearly the same computational cost. Nevertheless, this scheme limited the rotation angle to 45°; thus, the grid sampling intervals in the x- and z-directions needed to be equal. Otherwise, the grid points would not lie on the axes, which dramatically complicates the scheme. Affine coordinate systems did not constrain axes to be perpendicular to each other, providing enhanced flexibility. Based on the affine coordinate transformations, we developed a new affine generalized optimal nine-point scheme. At the free surface, we applied the improved free-surface expression with an adaptive parameter-modified strategy. The new optimal scheme had no restriction that the rotation angle must be 45°. Dispersion analysis found that our scheme could effectively reduce the required number of grid points per shear wavelength for equal and unequal sampling intervals compared to the classical nine-point scheme. Moreover, this reduction improved with the increase of Poisson’s ratio. Three numerical examples demonstrated that our scheme could provide more accurate results than the classical nine-point scheme in terms of the internal and the free-surface grid points.

An Analysis of the 8.85- and 4.42-Year Cycles in the Gulf of Maine

In the background of global warming and climate change, nuisance flooding is only caused by astronomical tides, which could be modulated by the nodal cycle. Therefore, much attention should be paid to the variation in the amplitude of the nodal cycle. In this paper, we utilize the enhanced harmonic analysis method and the independent point scheme to obtain the time-dependent amplitudes of the 8.85-year cycle of N2 tide and the 4.42-year cycle of 2N2 tide based on water level records of four tide gauges in the Gulf of Maine. Results indicate that the long-term trends of N2 and 2N2 tides vary spatially, which may be affected by the sea-level rise, coastal defenses, and other possible climate-related mechanisms. The comparison between Halifax and Eastport reveals that the topography greatly influences the amplitudes of those cycles. Moreover, a quasi 20-year oscillation is obvious in the 8.85-year cycle of N2 tide. This oscillation probably relates to a 20-year mode in the North Atlantic Ocean.

Differential Refractive Index Sensor Based on Coupled Plasmon Waveguide Resonance in the C-Band

We proposed a differential fiber-optic refractive index sensor based on coupled plasmon waveguide resonance (CPWR) in the C-band. The sensor head is a BK7 prism coated with ITO/Au/ITO/TiO2 film. CPWR is excited on the film by the S-polarized components of an incident light. The narrow absorption peak of CPWR makes it possible to realize dual-wavelength differential intensity (DI) interrogation by using only one incident point. To implement DI interrogation, we used a DWDM component to sample the lights with central wavelengths of 1529.55 and 1561.42 nm from the lights reflected back by the sensor head. The intensities of the dual-wavelength lights varied oppositely within the measurement range of refractive index, thus, a steep slope was produced as the refractive index of the sample increased. The experimental results show that the sensitivity is 32.15/RIUs within the measurement range from 1.3584 to 1.3689 and the resolution reaches 9.3 × 10−6 RIUs. Benefiting from the single incident point scheme, the proposed sensor would be easier to calibrate in bio-chemical sensing applications. Moreover, this sensing method is expected to be applied to retro-reflecting SPR sensors with tapered fiber tip to achieve better resolution than wavelength interrogation.

A 13-point sampling point scheme for 20-node brick elements

A new sampling point scheme with 13 evaluation points was introduced in this research study for 20-node brick elements. The new sampling points were located inside the brick element at the edges and the center point of the 20-node brick element. This integration scheme can be assumed to be an imitation of the Gaussian integration scheme. Standard benchmark problems were chosen from the different research works and compared with our proposed scheme. Finally, the proposed integration scheme achieves good results for 20-node brick elements on different performance parameters of finite element analysis.

A simple and high accurate finite volume scheme for diffusion equations

Most of numerical methods for diffusion equations, refer to vertex unknowns directly or indirectly, and their accuracy is ultimately determined by the approximation to vertex unknowns. Based on the “twin-fitting” method, a simple and high accurate treatment for the vertex unknowns is developed and is applied to the nine-point scheme for diffusion problem. Numerical experiments show that the resulting nine-point scheme is high accurate for diffusion problems with discontinuous diffusion coefficients on distorted meshes.

IMPACT OF AMMONIUM PYROLIDINE DITHIOCARBAMATE ON BIOMECHANICAL CHARACTERISTICS OF FEMORAL BONE IN RATS UNDER THE CONDITIONS OF COMBINED EXCESSIVE INTAKE OF FLUORIDE AND SODIUM NITRATE

This article describes the effect of ammonium pyrrolidine dithiocarbamate, an inhibitor of NF-κB activation, on the biomechanical characteristics of femoral bones in rats under the conditions of combined excess intake of fluoride and sodium nitrate. The series of experiments were performed on 30 white Wistar rats weighing 190-240 g, divided into 3 groups: 1st group included intact animals, 2nd group included animals exposed to the combined administration of sodium fluoride (10 mg/kg body weight) and sodium nitrate (500 mg / kg body weight) for 30 days; the 3rd group included rats, who starting from the 15th day of intoxication were injected with an inhibitor of NF-κB activation, ammonium pyrrolidine dithiocarbamate is a dose of 76 mg / kg 3 times a week. The investigation of the biomechanical properties of the femur was performed according to a 2-point scheme (linear rupture test) and a 3-point scheme (bending test) using a rupture machine RMU-0.05-1 with an assessment of rupture load (strength) and bone elongation (elasticity); we also applied a 4-point scheme (bending test) using the deformation test setup MRC-1 with following calculation of the Young's modulus, tensile strength, relative residual deformation to failure and relative elongation to failure. The administration of ammonium pyrrolidine dithiocarbamate under the conditions of the experiment significantly increased the tensile load at linear rupture and bending by 35.3 and 23.5%, respectively, compared with the results in the 2nd group. The relative elongation of the femoral bones in the test for linear rupture and flexion was more pronounced than the values ​​of the 2nd group by 7.9 and 18.6%. When testing for bending according to the 4-point scheme using the deformation setup MRK-1, we revealed a probable increase in the Young's modulus of elasticity by 19.8% compared to the results in the 2nd group. However, the indicators of the limit of elasticity and strength, the relative elongation of the extreme fibers before fracture did not change significantly. This enables us to conclude that ammonium pyrrolidine dithiocarbamate, the inhibitor of the NF-κB transcription factor, used under the conditions of combined administration of fluoride and sodium nitrate can serve an effective osteoprotective agent, which increases the strength and elasticity of the femoral bones.

Combinatorial study of stable categories of graded Cohen–Macaulay modules over skew quadric hypersurfaces

In this paper, we present a new connection between representation theory of noncommutative hypersurfaces and combinatorics. Let S be a graded ($$\pm 1$$ ± 1 )-skew polynomial algebra in n variables of degree 1 and $$f =x_1^2 + \cdots +x_n^2 \in S$$ f = x 1 2 + ⋯ + x n 2 ∈ S . We prove that the stable category $$\mathsf {\underline{CM}}^{\mathbb Z}(S/(f))$$ CM ̲ Z ( S / ( f ) ) of graded maximal Cohen–Macaulay module over S/(f) can be completely computed using the four graphical operations. As a consequence, $$\mathsf {\underline{CM}}^{\mathbb Z}(S/(f))$$ CM ̲ Z ( S / ( f ) ) is equivalent to the derived category $$\mathsf {D}^{\mathsf {b}}({\mathsf {mod}}\,k^{2^r})$$ D b ( mod k 2 r ) , and this r is obtained as the nullity of a certain matrix over $${\mathbb F}_2$$ F 2 . Using the properties of Stanley–Reisner ideals, we also show that the number of irreducible components of the point scheme of S that are isomorphic to $${\mathbb P}^1$$ P 1 is less than or equal to $$\left( {\begin{array}{c}r+1\\ 2\end{array}}\right) $$ r + 1 2 .

Discrete curvature and torsion from cross-ratios

Motivated by a Möbius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular Möbius invariant point-insertion-rule, comparable to the classical four-point-scheme, we construct circles along discrete curves. Asymptotic analysis shows that these circles defined on a sampled curve converge to the smooth curvature circles as the sampling density increases. We express our discrete torsion for space curves, which is not a Möbius invariant notion, using the cross-ratio and show its asymptotic behavior in analogy to the curvature.