Application of the operator splitting to the Maxwell equations with the source term

Motivated by numerical solution of the time-dependent Maxwell equations, we consider splitting methods for a linear system of differential equations $w'(t)=Aw(t)+f(t),$ $A\in\mathbb{R}^{n\times n}$ split into two subproblems $w_1'(t)=A_1w_1(t)+f_1(t)$ and $w_2'(t)=A_2w_2(t)+f_2(t),$ $A=A_1+A_2,$ $f=f_1+f_2.$ First, expressions for the leading term of the local error are derived for the Strang-Marchuk and the symmetrically weighted sequential splitting methods. The analysis, done in assumption that the subproblems are solved exactly, confirms the expected second order global accuracy of both schemes. Second, several relevant numerical tests are performed for the Maxwell equations discretized in space either by finite differences or by finite elements. An interesting case is the splitting into the subproblems $w_1'=Aw_1$ and $w_2'=f$ (with the split-off source term $f$). For the central finite difference staggered discretization, we consider second order splitting schemes and compare them to the classical Yee scheme on a test problem with loss and source terms. For the vector Nédélec finite element discretizations, we test the Gautschi-Krylov time integration scheme. Applied in combination with the split-off source term, it leads to splitting schemes that are exact per split step. Thus, the time integration error of the schemes consists solely of the splitting error

Thermospheric heating at high latitudes as observed from intercosmos-Bulgaria-1300 and dynamics explorer-B

This paper reports the results of the first direct comparison of near simultaneous measurements obtained by the INTERCOSMOS-BULGARIA-1300 and the DYNAMICS EXPLORER-B satellites. The ICB-1300 is in a near circular orbit at a mean height of about 850 km. The DE-B satellite in an elliptical orbit is sometimes directly below the ICB-1300 satellite providing an opportunity to investigate the response of the thermosphere to particle fluxes from the magnetosphere. Energy fluxes in the range 0.2-15 keV are obtained from an energetic particle analyzer on board the ICB-1300 satellite. The thermospheric composition and density are obtained by a neutral gas mass spectrometer (NACS) on the DE-B satellite. During the period 20 August-20 November, 1981, observations show tht the times and locations of maxima in magnetospheric energy deposition coincide with regions of maximum thermospheric upwelling characterized by composition changes.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25883/1/0000446.pd

Measuring and modeling the effect of surface moisture on the spectral reflectance of coastal beach sand

Surface moisture is an important supply limiting factor for aeolian sand transport, which is the primary driver of coastal dune development. As such, it is critical to account for the control of surface moisture on available sand for dune building. Optical remote sensing has the potential to measure surface moisture at a high spatio-temporal resolution. It is based on the principle that wet sand appears darker than dry sand: it is less reflective. The goals of this study are (1) to measure and model reflectance under controlled laboratory conditions as function of wavelength () and surface moisture () over the optical domain of 350–2500 nm, and (2) to explore the implications of our laboratory findings for accurately mapping the distribution of surface moisture under natural conditions. A laboratory spectroscopy experiment was conducted to measure spectral reflectance (1 nm interval) under different surface moisture conditions using beach sand. A non-linear increase of reflectance upon drying was observed over the full range of wavelengths. Two models were developed and tested. The first model is grounded in optics and describes the proportional contribution of scattering and absorption of light by pore water in an unsaturated sand matrix. The second model is grounded in soil physics and links the hydraulic behaviour of pore water in an unsaturated sand matrix to its optical properties. The optical model performed well for volumetric moisture content 24% ( 0.97), but underestimated reflectance for between 24–30% ( 0.92), most notable around the 1940 nm water absorption peak. The soil-physical model performed very well ( 0.99) but is limited to 4% 24%. Results from a field experiment show that a short-wave infrared terrestrial laser scanner ( = 1550 nm) can accurately relate surface moisture to reflectance (standard error 2.6%), demonstrating its potential to derive spatially extensive surface moisture maps of a natural coastal beach

Application of operator splitting to the Maxwell equations including a source term

Motivated by numerical solution of the time-dependent Maxwell equations, we consider splitting methods for a linear system of differential equations $w'(t)=Aw(t)+f(t),$ $A\in\mathbb{R}^{n\times n}$ split into two subproblems $w_1'(t)=A_1w_1(t)+f_1(t)$ and $w_2'(t)=A_2w_2(t)+f_2(t),$ $A=A_1+A_2,$ $f=f_1+f_2.$ First, expressions for the leading term of the local error are derived for the Strang-Marchuk and the symmetrically weighted sequential splitting methods. The analysis, done in assumption that the subproblems are solved exactly, confirms the expected second order global accuracy of both schemes. Second, several relevant numerical tests are performed for the Maxwell equations discretized in space either by finite differences or by finite elements. An interesting case is the splitting into the subproblems $w_1'=Aw_1$ and $w_2'=f$ (with the split-off source term $f$). For the central finite difference staggered discretization, we consider second order splitting schemes and compare them to the classical Yee scheme on a test problem with loss and source terms. For the vector Nédélec finite element discretizations, we test the Gautschi-Krylov time integration scheme. Applied in combination with the split-off source term, it leads to splitting schemes that are exact per split step. Thus, the time integration error of the schemes consists solely of the splitting error

The role of MRI in staging and radiotherapy treatment planning in locally advanced nasopharyngeal carcinoma – case report

Nasopharyngeal carcinoma (NPC) is a rare disease. The “Golden imaging standard” for primary tumor and regional lymph nodes staging in NPC is MRI- magnetic resonance imaging. Radiotherapy is the main treatment modality in both early and locoregional advanced NPC. Radiotherapy alone is recommended only in T1N0M0 stage NPC, while in higher stages for best treatment results contributes radiotherapy with concomitant chemotherapy. The aim is to report a case of a patients with NPC presented to our department with clinical and MRI data for scull base and brain invasion. Tumor staging included PET/CT scan and MRI, which were used also for treatmentplanning. The patient was treated with definitive radiotherapy to 64 Gy, concomitantly with weekly Cisplatin. VMAT and IGRT treatment techniques were used. One year later a complete response is observed without late toxicity and grade 2 dry mouth. Using of MRI for initial staging and radiotherapy planning in NPC is very important due to precise findings of the tumor invasion and a correct definition of the treatment volume. MRI staging should be part of the initial staging and follow up algorithm in all patients with NPC