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At least 1,369 records · Page 76

Fermi–Löwdin orbital self-interaction correction of adsorption energies on transition metal ions

Density functional theory (DFT)-based descriptions of the adsorption of small molecules on transition metal ions are prone to self-interaction errors. Here, we show that such errors lead to a large over-estimation of adsorption energies of small molecules on Cu + , Zn + , Zn 2+ , and Mn + in local spin density approximation (LSDA) and Perdew, Burke, Ernzerhof (PBE) generalized gradient approximation calculations compared to reference values computed using the coupled-cluster with single, doubles, and perturbative triple excitations method. These errors are significantly reduced by removing self-interaction using the Perdew–Zunger self-interaction correction (PZ-SIC) in the Fermi–Löwdin Orbital (FLO) SIC framework. In the case of FLO-PBE, typical errors are reduced to less than 0.1 eV. Furthermore, analysis of the results using DFT energies evaluated on self-interaction-corrected densities [DFT(@FLO)] indicates that the density-driven contributions to the FLO-DFT adsorption energy corrections are roughly the same size in DFT = LSDA and PBE, but the total corrections due to removing self-interaction are larger in LSDA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Image-Guided Radiotherapy for Breast Cancer Patients: Surgical Clips as Surrogate for Breast Excision Cavity

Purpose: To determine the use of surgical clips as a surrogate for localization of the excision cavity and to quantify the stability of the clips' positions during the course of external beam radiotherapy for breast cancer patients, using cone beam computed tomography (CBCT) scans. Methods and Materials: Twenty-one breast cancer patients with surgical clips placed in the breast excision cavity were treated in a supine position with 28 daily fractions. CBCT scans were regularly acquired for a setup correction protocol. Retrospectively, the CBCT scans were registered to the planning CT scans, using gray-value registration of the excision cavity region and chamfer matching of the clips. Subsequently, residual setup errors (systematic [{Sigma}] and random [{sigma}]) of the excision cavity were estimated relative to the clips' registration. Finally, the stability of the clips' positions were quantified as the movement of each separate clip according to the center of gravity of the excision cavity. Results: When clips were used for online setup corrections, the residual errors of the excision cavity were {Sigma}{sub left-right} = 1.2, {sigma}{sub left-right} = 1.0; {Sigma}{sub cranial-caudal} = 1.3, {sigma}{sub cranial-caudal} = 1.2; and {Sigma}{sub anterior-posterior} = 0.7, {sigma}{sub anterior-posterior} = 0.9 mm. Furthermore, the average distance (over all patients) between the clips and centers of gravity of the excision cavities was 18.8 mm (on the planning CT) and was reduced to 17.4 mm (measured on the last CBCT scan). Conclusion: Clips move in the direction of the center of gravity of the excision cavity, on average, 1.4 mm. The clips are good surrogates for locating the excision cavity and providing small residual errors.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Software-controlled, highly automated intrafraction prostate motion correction with intrafraction stereographic targeting: System description and clinical results

Purpose: A new system for software-controlled, highly automated correction of intrafraction prostate motion,'' intrafraction stereographic targeting'' (iSGT), is described and evaluated. Methods: At our institute, daily prostate positioning is routinely performed at the start of treatment beam using stereographic targeting (SGT). iSGT was implemented by extension of the SGT software to facilitate fast and accurate intrafraction motion corrections with minimal user interaction. iSGT entails megavoltage (MV) image acquisitions with the first segment of selected IMRT beams, automatic registration of implanted markers, followed by remote couch repositioning to correct for intrafraction motion above a predefined threshold, prior to delivery of the remaining segments. For a group of 120 patients, iSGT with corrections for two nearly lateral beams was evaluated in terms of workload and impact on effective intrafraction displacements in the sagittal plane. Results: SDs of systematic ({Sigma}) and random ({sigma}) displacements relative to the planning CT measured directly after initial SGT setup correction were <0.5 and <0.8 mm, respectively. Without iSGT corrections, effective {Sigma} and {sigma} for the 11-min treatments would increase to {Sigma}{sub eff} < 1.1 mm and {sigma}{sub eff} < 1.2 mm. With the iSGT procedure with an action level of 4 mm, effective positioning errors were reduced to {Sigma}{sub eff} < 0.8 mm and {sigma}{sub eff} < 1.0 mm, with 23.1% of all fractions requiring a correction. Computer simulations demonstrated that with an action level of 2 mm, the errors would have been reduced to {Sigma}{sub eff} < 0.6 mm and {sigma}{sub eff} < 0.7 mm, requiring corrections in 82.4% of the fractions. Because iSGT is highly automated, the extra time added by iSGT is <30 s if a correction is required. Conclusions: Without increasing imaging dose, iSGT successfully reduces intrafraction prostate motion with minimal workload and increase in fraction time. An action level of 2 mm is recommended.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Investigating Tropical Versus Extratropical Influences on the Southern Hemisphere Tropical Edge in the Unified Model

Abstract Since the late 1970s, observations have shown a widening of the tropical Hadley cell (HC) circulation. State‐of‐the‐art climate models reproduce the general trend along with a projected continuous expansion. Discrepancies in expansion rates of observation‐ and model‐based studies have been attributed to differences in applied methods, natural variability and model shortcomings. Furthermore, the driving influence of tropical or extratropical processes on these changes is not well understood. All of this highlights the dynamical mechanisms and the region of origin controlling the tropical width are still insufficiently understood. Here we examine the influence of systematic model biases of the atmosphere‐only Unified Model (UM) onto the simulation of the Southern Hemisphere (SH) tropical edge. We utilize nudged experiments with prescribed sea surface temperatures, where potential temperature and horizontal winds are relaxed back to ERA‐Interim reanalysis for a 20‐year period in selected regions. Correcting model biases in the tropics and extratropics separately allows us to dissect the dominant remote impacts of present model errors onto the SH tropical edge simulation. The experiments are applied to established tropical width metrics ranging from near‐surface to upper‐level metrics capturing the poleward flank of the HC. We find both regions work remotely to reduce errors in the UM fields and location of the tropical edge. Surprisingly, correcting the extratropical biases, south of 45°S, more consistently improves the tropical width across the metrics and seasons than nudging the tropics (10°N–10°S). These findings demonstrate the substantial role of extratropical influences in locating the SH tropical edge.

54 ENVIRONMENTAL SCIENCES↗

Validation of a pretreatment delivery quality assurance method for the CyberKnife Synchrony system

Purpose: To evaluate the geometric and dosimetric accuracies of the CyberKnife Synchrony respiratory tracking system (RTS) and to validate a method for pretreatment patient-specific delivery quality assurance (DQA). Methods: An EasyCube phantom was mounted on the ExacTrac gating phantom, which can move along the superior–inferior (SI) axis of a patient to simulate a moving target. The authors compared dynamic and static measurements. For each case, a Gafchromic EBT3 film was positioned between two slabs of the EasyCube, while a PinPoint ionization chamber was placed in the appropriate space. There were three steps to their evaluation: (1) the field size, the penumbra, and the symmetry of six secondary collimators were measured along the two main orthogonal axes. Dynamic measurements with deliberately simulated errors were also taken. (2) The delivered dose distributions (from step 1) were compared with the planned ones, using the gamma analysis method. The local gamma passing rates were evaluated using three acceptance criteria: 3% local dose difference (LDD)/3 mm, 2%LDD/2 mm, and 3%LDD/1 mm. (3) The DQA plans for six clinical patients were irradiated in different dynamic conditions, to give a total of 19 cases. The measured and planned dose distributions were evaluated with the same gamma-index criteria used in step 2 and the measured chamber doses were compared with the planned mean doses in the sensitive volume of the chamber. Results: (1) A very slight enlargement of the field size and of the penumbra was observed in the SI direction (on average <1 mm), in line with the overall average CyberKnife system error for tracking treatments. (2) Comparison between the planned and the correctly delivered dose distributions confirmed the dosimetric accuracy of the RTS for simple plans. The multicriteria gamma analysis was able to detect the simulated errors, proving the robustness of their method of analysis. (3) All of the DQA clinical plans passed the tests, both in static and dynamic conditions. No statistically significant differences were found between static and dynamic cases, confirming the high degree of accuracy of the Synchrony RTS. Conclusions: The presented methods and measurements verified the mechanical and dosimetric accuracy of the Synchrony RTS. Their method confirms the fact that the RTS, if used properly, is able to treat a moving target with great precision. By combining PinPoint ion chamber, EBT3 films, and gamma evaluation of dose distributions, their DQA method robustly validated the effectiveness of CyberKnife and Synchrony system.

60 APPLIED LIFE SCIENCES↗

MEASURING HIGH-PRECISION ASTROMETRY WITH THE INFRARED ARRAY CAMERA ON THE SPITZER SPACE TELESCOPE

The Infrared Array Camera (IRAC) on the Spitzer Space Telescope currently offers the greatest potential for high-precision astrometry of faint mid-IR sources across arcminute-scale fields, which would be especially valuable for measuring parallaxes of cold brown dwarfs in the solar neighborhood and proper motions of obscured members of nearby star-forming regions. To more fully realize IRAC's astrometric capabilities, we have sought to minimize the largest sources of uncertainty in astrometry with its 3.6 and 4.5 μm bands. By comparing different routines that estimate stellar positions, we have found that Point Response Function (PRF) fitting with the Spitzer Science Center's Astronomical Point Source Extractor produces both the smallest systematic errors from varying intra-pixel sensitivity and the greatest precision in measurements of positions. In addition, self-calibration has been used to derive new 7th and 8th order distortion corrections for the 3.6 and 4.5 μm arrays of IRAC, respectively. These corrections are suitable for data throughout the mission of Spitzer when a time-dependent scale factor is applied to the corrections. To illustrate the astrometric accuracy that can be achieved by combining PRF fitting with our new distortion corrections, we have applied them to archival data for a nearby star-forming region, arriving at total astrometric errors of ∼20 and 70 mas at signal to noise ratios of 100 and 10, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

An AFM Dynamic Contact Model with Finite Thickness Correction to Study Micro-Rheology of Biological Cells

One of the major sources of error in Atomic Force Microscopy based Force Spectroscopic studies is bottom substrate effect, which comes due to assumption of infinite sample thickness. In the present work, anew experimentally validated mathematical correction for finite thickness of thesample is incorporated into a dynamic indentation model. This model is an extension of Sneddon’s static indentation contact model developed for conical tip indenters by incorporating the tip geometric effects, correction to hydrodynamic drag, viscoelastic nature of the sample and its finite thickness. The new model is applied to extract the viscoelastic properties of primary mesenchymal stem cells (MSC’s) extracted from human bone marrow and HCT-116 aggressive epithelial colorectal cancer cells. The micro-rheological studies indicated the presence of profound influence of infinite thickness assumption depending upon indentation depth and sample thickness at the point of indentation. The present model nullified this error and provided a better estimate of the rheological properties. The tests were conducted over a wide frequency bandwidth (0.5 to 126 Hz) and frequency dependent material properties were analyzed using power law structural damping model. It was found that MSC’s are stiffer and less viscous in nature compared to cancer cells.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Band-gap corrected density functional theory calculations for InAs/GaSb type II superlattices

We performed pseudopotential based density functional theory (DFT) calculations for GaSb/InAs type II superlattices (T2SLs), with bandgap errors from the local density approximation mitigated by applying an empirical method to correct the bulk bandgaps. Specifically, this work (1) compared the calculated bandgaps with experimental data and non-self-consistent atomistic methods; (2) calculated the T2SL band structures with varying structural parameters; (3) investigated the interfacial effects associated with the no-common-atom heterostructure; and (4) studied the strain effect due to lattice mismatch between the two components. This work demonstrates the feasibility of applying the DFT method to more exotic heterostructures and defect problems related to this material system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A REVISED EFFECTIVE TEMPERATURE SCALE FOR THE KEPLER INPUT CATALOG

We present a catalog of revised effective temperatures for stars observed in long-cadence mode in the Kepler Input Catalog (KIC). We use Sloan Digital Sky Survey (SDSS) griz filters tied to the fundamental temperature scale. Polynomials for griz color-temperature relations are presented, along with correction terms for surface gravity effects, metallicity, and statistical corrections for binary companions or blending. We compare our temperature scale to the published infrared flux method (IRFM) scale for V{sub T}JK{sub s} in both open clusters and the Kepler fields. We find good agreement overall, with some deviations between (J - K{sub s} )-based temperatures from the IRFM and both SDSS filter and other diagnostic IRFM color-temperature relationships above 6000 K. For field dwarfs, we find a mean shift toward hotter temperatures relative to the KIC, of order 215 K, in the regime where the IRFM scale is well defined (4000 K to 6500 K). This change is of comparable magnitude in both color systems and in spectroscopy for stars with T{sub eff} below 6000 K. Systematic differences between temperature estimators appear for hotter stars, and we define corrections to put the SDSS temperatures on the IRFM scale for them. When the theoretical dependence on gravity is accounted for, we find a similar temperature scale offset between the fundamental and KIC scales for giants. We demonstrate that statistical corrections to color-based temperatures from binaries are significant. Typical errors, mostly from uncertainties in extinction, are of order 100 K. Implications for other applications of the KIC are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

Stochastic characterization of phase detection algorithms in phase-shifting interferometry

Phase-shifting interferometry (PSI) is the preferred non-contact method for profiling sub-nanometer surfaces. Based on monochromatic light interference, the method computes the surface profile from a set of interferograms collected at separate stepping positions. Errors in the estimated profile are introduced when these positions are not located correctly. In order to cope with this problem, various algorithms that minimize the effects of certain types of stepping errors (linear, sinusoidal, etc.) have been developed. Despite the relatively large number of algorithms suggested in the literature, there is no unified way of characterizing their performance when additional unaccounted random errors are present. Here, we suggest a procedure for quantifying the expected behavior of each algorithm in the presence of independent and identically distributed (i.i.d.) random stepping errors, which can occur in addition to the systematic errors for which the algorithm has been designed. As a result, the usefulness of this method derives from the fact that it can guide the selection of the best algorithm for specific measurement situations.

42 ENGINEERING↗

Spin-crossover complexes: Self-interaction correction vs density correction

Complexes containing a transition metal atom with a 3d 4 –3d 7 electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi–Löwdin self-interaction correction. Considering that Hartree–Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree–Fock method and the Perdew–Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. Here, we find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

TOWARD A NEW KIND OF ASTEROSEISMIC GRID FITTING

Recent developments in instrumentation (e.g., in particular the Kepler and CoRoT satellites) provide a new opportunity to improve the models of stellar pulsations. Surface layers, rotation, and magnetic fields imprint erratic frequency shifts, trends, and other non-random behavior in the frequency spectra. As our observational uncertainties become smaller, these are increasingly important and difficult to deal with using standard fitting techniques. To improve the models, new ways to compare their predictions with observations need to be conceived. In this paper, we present a completely probabilistic (Bayesian) approach to asteroseismic model fitting. It allows for varying degrees of prior mode identification, corrections for the discrete nature of the grid, and most importantly implements a treatment of systematic errors, such as the 'surface effects'. It removes the need to apply semi-empirical corrections to the observations prior to fitting them to the models and results in a consistent set of probabilities with which the model physics can be probed and compared. As an example, we show a detailed asteroseismic analysis of the Sun. We find a most probable solar age, including a 35 {+-} 5 million year pre-main-sequence phase, of 4.591 billion years, and initial element mass fractions of X{sub 0} = 0.72, Y{sub 0} = 0.264, Z{sub 0} = 0.016, consistent with recent asteroseismic and non-asteroseismic studies.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-F-T-410: Investigation of Treatment Planning Accuracy with the Presence of Magnetic Injection Port (breast Tissue Expander)

Purpose: Mastectomy patients with breast reconstruction usually have a magnetic injection port inside the breast during radiation treatments. The magnet has a very high CT number and produces severe streaking artifact across the entire breast in CT images. Our routine strategy is to replace the artifact volumes with uniform water, and it is necessary to validate that the planned dose, with such an artifact correction, is sufficiently accurate. Methods: A phantom was made with a gelatine-filled container sitting on a Matrixx detector, and the magnetic port was inserted into gelatine with specific depths and orientations. The phantom was scanned on a CT simulator and imported into Eclipse for treatment planning. The dose distribution at the Matrixx detector plane was calculated for raw CT images and artifact-corrected images. The treatment beams were then delivered to the phantom and the dose distributions were acquired by the Matrixx detector. Gamma index was calculated to compare the planned dose and the measurement. Results: Three field sizes (10×10, 15×15 and 20×20) and two depths (50mm and 20mm) were investigated. With the 2%/2mm or 3%/3mm criteria, several points (6–10) failed in the plan for raw CT images, and the number of failure was reduced close to zero for the corrected CT images. An assignment of 10,000 HU to the magnet further reduced the dose error directly under the magnet. Conclusion: It is validated that our routine strategy of artifact correction can effectively reduce the number of failures in the detector plane. It is also recommended to set the magnet with a CT number of 10,000HU, which could potentially improve the dose calculation at the points right behind the magnet.

60 APPLIED LIFE SCIENCES↗

SU-F-J-211: Scatter Correction for Clinical Cone-Beam CT System Using An Optimized Stationary Beam Blocker with a Single Scan

Purpose: X-ray scatter photons result in significant image quality degradation of cone-beam CT (CBCT). Measurement based algorithms using beam blocker directly acquire the scatter samples and achieve significant improvement on the quality of CBCT image. Within existing algorithms, single-scan and stationary beam blocker proposed previously is promising due to its simplicity and practicability. Although demonstrated effectively on tabletop system, the blocker fails to estimate the scatter distribution on clinical CBCT system mainly due to the gantry wobble. In addition, the uniform distributed blocker strips in our previous design results in primary data loss in the CBCT system and leads to the image artifacts due to data insufficiency. Methods: We investigate the motion behavior of the beam blocker in each projection and design an optimized non-uniform blocker strip distribution which accounts for the data insufficiency issue. An accurate scatter estimation is then achieved from the wobble modeling. Blocker wobble curve is estimated using threshold-based segmentation algorithms in each projection. In the blocker design optimization, the quality of final image is quantified using the number of the primary data loss voxels and the mesh adaptive direct search algorithm is applied to minimize the objective function. Scatter-corrected CT images are obtained using the optimized blocker. Results: The proposed method is evaluated using Catphan@504 phantom and a head patient. On the Catphan©504, our approach reduces the average CT number error from 115 Hounsfield unit (HU) to 11 HU in the selected regions of interest, and improves the image contrast by a factor of 1.45 in the high-contrast regions. On the head patient, the CT number error is reduced from 97 HU to 6 HU in the soft tissue region and image spatial non-uniformity is decreased from 27% to 5% after correction. Conclusion: The proposed optimized blocker design is practical and attractive for CBCT guided radiation therapy. This work is supported by grants from Guangdong Innovative Research Team Program of China (Grant No. 2011S013), National 863 Programs of China (Grant Nos. 2012AA02A604 and 2015AA043203), the National High-tech R&D Program for Young Scientists by the Ministry of Science and Technology of China (Grant No. 2015AA020917)

60 APPLIED LIFE SCIENCES↗

SU-F-T-245: The Investigation of Failure Mode and Effects Analysis and PDCA for the Radiotherapy Risk Reduction

Purpose: To optimize the clinical processes of radiotherapy and to reduce the radiotherapy risks by implementing the powerful risk management tools of failure mode and effects analysis(FMEA) and PDCA(plan-do-check-act). Methods: A multidiciplinary QA(Quality Assurance) team from our department consisting of oncologists, physicists, dosimetrists, therapists and administrator was established and an entire workflow QA process management using FMEA and PDCA tools was implemented for the whole treatment process. After the primary process tree was created, the failure modes and Risk priority numbers(RPNs) were determined by each member, and then the RPNs were averaged after team discussion. Results: 3 of 9 failure modes with RPN above 100 in the practice were identified in the first PDCA cycle, which were further analyzed to investigate the RPNs: including of patient registration error, prescription error and treating wrong patient. New process controls reduced the occurrence, or detectability scores from the top 3 failure modes. Two important corrective actions reduced the highest RPNs from 300 to 50, and the error rate of radiotherapy decreased remarkably. Conclusion: FMEA and PDCA are helpful in identifying potential problems in the radiotherapy process, which was proven to improve the safety, quality and efficiency of radiation therapy in our department. The implementation of the FMEA approach may improve the understanding of the overall process of radiotherapy while may identify potential flaws in the whole process. Further more, repeating the PDCA cycle can bring us closer to the goal: higher safety and accuracy radiotherapy.

60 APPLIED LIFE SCIENCES↗

Improving the Estimation of the Atmospheric Water Vapor Pressure Using Interpretable Long Short-Term Memory Networks: Dataset, Python code, and trained models

Atmospheric water vapor pressure is an essential meteorological control on land surface and hydrologic processes. It is not as frequently observed as other meteorologic conditions, but often inferred through the August–Roche–Magnus formula by simply assuming dew point and daily minimum temperatures are equivalent or by empirically correlating the two temperatures using an aridity correction. The performance of both methods varies considerably across different regions and during different time periods; obtaining consistently accurate estimates across space and time remains a great challenge. We applied an interpretable Long Short-Term Memory (iLSTM) network conditioned on static, location specific attributes to estimate daily vapor pressure for 83 FLUXNET sites in the United States and Canada. This data package includes all raw data of the 83 FLUXNET sites, input data for model training/validation/test, trained models and results, and python codes for the manuscript "Improving the Estimation of the Atmospheric Water Vapor Pressure Using an Interpretable Long Short-term Memory Network". Specifically, it consists of five parts. - First, "1_Daymet_data_83sites.zip" includes raw data downloaded from Daymet for the 83 sites used in the paper according to their longitude and latitude, in which vapor pressure is used. It also includes a pre-processed CSV data file combining all data from the 83 sites which is specifically used for the paper. - Second, "2_Fluxnet2015_data_83sites.zip" includes raw half hourly data of the 83 sites downloaded from FLUXNET2015 data portal, pre-processed daily data of the 83 sites, a CSV file including combined pre-processed daily data of the 83 sites, and a CSV file including the information (site ID, site name, latitude, longitude, data available period) of the 83 sites. - Third, "3_MODIS_LAI_data_83sites_raw.zip" includes raw leaf area index (LAI) data downloaded from the AppEEARs data portal. - Fourth, "4_Scripts.zip" includes all scripts related to model training and post-processing of a trained model, and a jupyter notebook showing an example for model post-processing. Two typo errors in files titled "run2get_args.py" and "postprocess.py" were corrected on March 27, 2024 to avoid confusions. - Finally, "Trained_models_and_results.zip" includes three folders and three files with suffix ".npy", and each folder corresponds to one file with suffix ".npy" with the same title. Each of the three folders include all trained models associated with one iLSTM model configuration (35 models for each configuration, details are described in the paper). Each file with suffix ".npy" includes the post-processed results of the corresponding 35 models under one iLSTM model configuration.

54 ENVIRONMENTAL SCIENCES↗

Author Correction: Building a global alliance of biofoundries

The original version of this Comment contained errors in the legend of Figure 2, in which the locations of the fifteenth and sixteenth GBA members were incorrectly given as '(15) Australian Genome Foundry, Macquarie University; (16) Australian Foundry for Advanced Biomanufacturing, University of Queensland'. The correct version replaces this with '(15) Australian Foundry for Advanced Biomanufacturing (AusFAB), University of Queensland and (16) Australian Genome Foundry, Macquarie University'. This has been corrected in both the PDF and HTML versions of the Comment.

59 BASIC BIOLOGICAL SCIENCES↗

Mass-preserving time second-order explicit–implicit domain decomposition schemes for solving parabolic equations with variable coefficients

In this paper, the new mass-preserving time second-order explicit–implicit domain decomposition (DD) schemes for solving parabolic equations with various coefficients are proposed. In the schemes, first, the interface values on the interfaces of sub-domains are explicitly calculated, in which two kinds of explicit difference schemes are used. Second, the interior values in sub-domains are determined by the implicit schemes. Third, the interface values are recalculated explicitly to preserve mass. The important feature is that the developed schemes are more than first order in time step and the correction operators at the third step ensure the schemes’ mass conservative. The stability and convergence are analyzed for the two schemes. The optimal error estimates are obtained in the H{sup 1} semi-norm under a stability condition. Numerical experiments confirm the theoretical results.

97 MATHEMATICS AND COMPUTING↗