The analysis of the interior scattering from open cavities with small modifications is an important task in designing a stealthy jet engine. Previous research has shown the magnetic field integral equation with the Kirchhoff approximation can be used to calculate the cavity interior scattering. However, it must repeat the expensive method of moments (MoM) solution even when the cavity is modified only slightly. In this Letter, the efficient method based on the partitionedinverse formula and the Sherman-Morrison-Woodbury formula is employed to address this problem. It can avoid the repeated MoM direct solution. We only need to solve the lower-upper (LU) decomposition of the impedance matrix of the original cavity, and can efficiently derive the solution of the modified cavities via matrix identities without loss of accuracy. Numerical results are given to demonstrate the performance of the proposed approach.

In arid area, the liquid water and water vapour states in soil profiles and fluxes at the upper and bottom interfaces are extremely complex due to heterogeneity of soil textures and the driving forces of heat and matrix potential. In this study, we used Hydrus-1D to simultaneously simulate liquid water, water vapour, and heat transport based on the observed datasets of atmosphere, soil and groundwater at three soil profiles in an arid area of northwest China. Based on the comparison of the observed and simulated results at the three soil profiles, we show that there are diurnal vapour entry and outlet fluxes at the dry surface layer of 30 cm in the summer season. The vapour entry and re-evaporation account for about 14% of annual precipitation for the heterogeneity soil profile with a mean groundwater depth of 210 cm. Because of limited soil moisture in this arid area, vapour induced re-evaporation occurs shortly in the early daytime. Moreover, the extent of vapour entry, condensation and reevaporation are strongly dependent on soil properties and water table depth. The deeper water table produces the drier soil surface, allowing more vapour entry, condensation and re-evaporation. Whereas the finer grained soil layers benefit the vapour fixation to produce zero fluxes that substantially inhibit the upward liquid water and vapour fluxes, and thereby reduces soil actual evaporation (AE). The reduced AE correspondingly decreases the capillary effect on phreatic evaporation, given that AE decreases slowly with decline of water table and the large extinct depth of phreatic evaporation for the finer grained soil profiles. The estimated extinct depths are 180 and 200 cm for the soil profiles consisting of silt loam and loamy sand, respectively, much larger than 100 cm of the typical sandy soil profile. Additionally, as water table is comparably higher and lower than the extinct depth, the models neglecting the vapourheat function could, respectively, overestimate and underestimate soil evaporation.

In arid area, the liquid water and water vapor states in soil profiles and fluxes at the upper and bottom interfaces are extremely complex due to heterogeneity of soil textures and the driving forces of heat and matrix potential. In this study, we used Hydrus-1D to simultaneously simulate liquid water, water vapor, and heat transports based on the observed data of atmosphere, soil and groundwater at three soil profiles in an arid area of northwest China. Comparison and contrast of the observed and simulated results at the three soil profiles show that there are diurnal vapor entry and outlet fluxes at the dry surface layer (DSL) of 30 cm in the summer season. The vapor entry and re-evaporation account for about 14% of annual precipitation for the heterogeneity soil profile with a mean groundwater depth of 210 cm. Because of limited soil moisture in this arid area, vapor induced re-evaporation occurs shortly in the early daytime. Moreover, the extent of vapor entry, condensation and re-evaporation strong depends on soil properties and water table depths. The lower water table produces the drier soil surface, allowing more vapor entry, condensation and re-evaporation. Whereas the finer grained soil layers benefits the vapor fixation to produce zero fluxes that substantially inhibit the upward liquid water and vapor fluxes, and thereby reduces soil evaporation. The reduced soil evaporation correspondingly decreases the capillary effect on phreatic evaporation, proven by that soil evaporation decreases slowly with decline of water table and the large extinct depth of phreatic evaporation for the finer grained soil profiles. The estimated extinct depth is 180 cm and 200 cm for the soil profiles consisting of silt loam and loamy sand, respectively, much larger than 100 cm of the sandy soil profile. Additionally, as water table is higher and lower than the extinct depth, the models neglecting the vapor - heat function could respectively overestimate and underestimate soil evaporation.

The magnetic field integral equation based method of moments (MoM) with the Kirchhoff approximation can predict the interior scattering from cavities with impedance boundary condition (IBC) walls. However, if the IBC wall is a small part of the whole wall and is modified multiple times, the conventional MoM may be time-consuming due to the repeated and expensive lower-upper (LU) decompositions of impedance matrices. In this Letter, the Sherman-Morrison-Woodbury (SMW) formula is used to mitigate the problem. The authors only require to perform the LU decomposition of the cavity without IBC walls, and to efficiently obtain the solutions of the cavity with different IBC walls by reusing the LU decomposition and the SMW formula.