1D Experiments Research Articles

Identification of EMT-related alternative splicing event of TMC7 to promote invasion and migration of pancreatic cancer.

Epithelial-to-mesenchymal transition (EMT) is tightly associated with the invasion and metastasis of pancreatic cancer with rapid progression and poor prognosis. Notably, gene alternative splicing (AS) event plays a critical role in regulating the progression of pancreatic cancer. Therefore, this study aims to identify the EMT-related AS event in pancreatic cancer. The EMT-related gene sets, transcriptomes, and matched clinical data were obtained from the MSigDB, The Cancer Genome Atlas (TCGA), International Cancer Genome Consortium (ICGC), and Gene Expression Omnibus (GEO) databases. Key gene AS events associated with liver metastasis were identified by prognostic analysis, gene set variation analysis (GSVA), and correlation analysis in pancreatic cancer. The cell line and organoid model was constructed to evaluate these key gene AS events in regulating pancreatic cancer in vitro. Furthermore, we established an EMT-related gene set consisting of 13 genes by prognostic analysis, the role of which was validated in two other databases. Finally, the human pancreatic cancer tissue and organoid model was used to evaluate the correlation between the enrichment of this gene set and liver metastasis. Prognostic analysis and correlation analysis revealed that eight AS events were closely associated with the prognosis of pancreatic cancer. Furthermore, the expression of TMC7 and CHECK1 AS events was increased in the metastatic lesions of the human tissue and organoid model. Additionally, the knockdown of exon 17 of TMC7 significantly inhibited the proliferation, invasion, and migration of pancreatic cancer cells in 2D and 3D cell experiments. Finally, the expression of exon 17 of TMC17 exhibited a significant correlation with the poor prognosis in pancreatic ductal adenocarcinoma (PDAC). The AS events of TMC7 and CHECK1 were associated with liver metastasis in pancreatic cancer. Moreover, exon 17 of TMC7 could be a potential therapeutic target in pancreatic cancer.

1H NMR-based metabolic profile and chemometric analysis for the discrimination of Passiflora species genotypic variations

The species of the genus Passiflora (Passifloraceae family) have been used as food, cosmetic and traditional herbal. As a result, the Passiflora species are widely cultivated and has an economic, medicinal and ornamental importance. The popular designation as “passion fruit” and chemical profile of several Passiflora species remains unknown. The lack of chemical information contributes to the erroneous classification and adulteration. In recent years, special attention has been paid to the bioactivity and phytochemical profiles of several Passiflora species extracts. In this research, 1H NMR-based metabolic profiling coupled with chemometric tools was used to characterize and distinguish extracts obtained from different wild Passiflora species (P. alata, P. cincinnata, and P. setacea) and genetic varieties (P. alata var. BRS Pérola do Cerrado, P. cincinnata var. BRS Sertão Forte, and P. setacea var. BRS Pérola do Cerrado). Fourteen metabolites were identified by 1D and 2D NMR experiments, highlighting the presence of fatty acids, carbohydrates, saponins, alkaloids, and mainly C-glycosidic flavones. Principal components analysis (PCA) allowed discrimination of Passiflora extracts, which the quadranguloside, oleanolic acid-3-sophoroside, α-glucose, β-glucose, and vitexin-2-O”-rhamnoside were relevant in the differentiation of P. alata and P. alata var. BRS Pérola do Cerrado, while the flavones isovitexin and isovitexin-2-O”-xyloside were dominant in the grouping of P. setacea and P. setacea var. BRS Pérola do Cerrado, and finally P. cincinnata and P. cincinnata var. BRS Sertão Forte grouped by the influence of the fatty acids, sucrose, flavones (isoorientin and vitexin-2-O”-xyloside), and trigonelline. The varieties of P. setacea, and P. cincinnata are chemically equivalent to the original Passiflora species. However, the PCA analysis showed that the genetic variety of P. alata occupied a different position in the scores plot provoked mainly by the presence of oleanolic acid-3-sophoroside. The 1H NMR metabolic profile can be efficient for quality control evaluation, and can contribute to the investigation of new alternatives for official Passiflora herbal medicines.

Real-time monitoring of the sialic acid biosynthesis pathway by NMR.

Sialic acids are part of the outermost component of the glycocalyx of all vertebrates; as such, they are fundamental markers in physiological and pathological processes. In this study, we introduce a real-time assay to monitor individual enzymatic steps of sialic acid biosynthesis, either with recombinant enzymes, in particular using UDP-N-acetylglucosamine 2-epimerase (GNE) or N-acetylmannosamine kinase (MNK), or in cytosolic rat liver extract. Using state-of-the-art NMR techniques, we are able to follow the characteristic signal of the N-acetyl methyl group, which displays different chemical shifts for the biosynthesis intermediates UDP-N-acetylglucosamine, N-acetylmannosamine (and its 6-phosphate) and N-acetylneuraminic acid (and its 9-phosphate). Pseudo 2- and 3-D NMR demonstrated that in rat liver cytosolic extract, the phosphorylation reaction of MNK is exclusive for N-acetylmannosamine generated by GNE. Thus, we speculate that phosphorylation of this sugar from other sources (e.g. external application to cells) or N-acetylmannosamine derivatives often applied in metabolic glycoengineering is not conducted by MNK but by a yet unknown sugar kinase. Competition experiments with the most prevalent neutral carbohydrates demonstrated that of these, only N-acetylglucosamine slowed N-acetylmannosamine phosphorylation kinetics, suggesting an N-acetylglucosamine-preferring kinase as the acting enzyme.

Design and Implementation of a Low Power Wireless Frequency-Division Multiplexed Magnetic 3D Localization Scheme With Sub-mm Precision for Capsule Endoscopy Applications

This letter presents a new magnetic localization scheme based on frequency-division multiplexing for capsule endoscopy applications. The approach significantly reduces the reference excitation coil sizes and decreases the required excitation current by three orders of magnitude compared to prior work, making it practical for wearable systems. Different spatial configurations of the reference coils are considered and simulated to provide design insight for maximizing localization accuracy. A fully integrated wireless receiver prototype is implemented in 180-nm bulk CMOS and packaged in an ingestible pill form factor. To the best of our knowledge, the new scheme achieves the best experimentally demonstrated tracking accuracy in both 2D and 3D localization experiments, achieving a sub-mm mean absolute position error and consuming only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$336~\mu \text{W}$ </tex-math></inline-formula> while running at 100% duty cycle.

Diffusive Regularization Inverse PINN Solutions to Discontinuous Problems

It is of great importance to numerically capture discontinuities for the numerical solutions to hyperbolic conservation laws equations. The PINN (physics-informed neural networks) was used to solve the forward problem of the hyperbolic conservation laws equations, with the diffusion term added, which is difficult to determine and needs to be obtained through high-cost trial calculation. To capture the discontinuous solutions and save calculation costs, the equation was regularized through addition of diffusive terms. Then the regularized equation was incorporated into the loss function, and the exact solutions or reference solutions to the conservation laws equations were used as the training set to learn the diffusion coefficients, and the solutions at different moments were predicted. Compared with that of the PINN method for solving forward problems, the resolution of discontinuous solutions was improved, and the trouble of massive trial calculation was avoided. Finally, the feasibility of the algorithm was verified by 1D and 2D numerical experiments. The numerical results show that, the new algorithm has better ability to capture discontinuities, produces no spurious oscillations and no screed phenomena. Additionally, the diffusive coefficients obtained with the new algorithm make a reference to construct the classic numerical scheme.

Double-resonance 17O NMR experiments reveal unique configurational information for surface organometallic complexes.

Obtaining three-dimensional (3D) configurational information of surface organometallic complexes is a persistent challenge due to the low spatial sensitivity of most spectroscopic methods. We show that employing 17O-enriched supports enables highly informative multidimensional NMR experiments, including radial and vertical distance measurements, that can be used to elucidate site geometry.

Tear metabolomics. An outstanding approach to the molecular diagnosis of glaucoma

AbstractPurpose: The open‐angle glaucoma (OAG) is the first cause of irreversible blindness worldwide, being the main risk factor the elevated intraocular pressure (IOP). The molecular mechanisms of OAG development and progression remains incomplete. Because of this, biomarkers for early diagnosis of OAG are not conclusive. We deal with understanding the metabolomics of OAG by using 1H‐ nuclear magnetic resonance (NMR) spectroscopy in tear samples for searching specific metabolites that improve early molecular diagnosis of OAG.Methods: 1H NMR monodimensional experiments were acquired from tears in 30 tear samples (OAG patients: n = 11 and healthy controls: n = 19). Additionally, 2D (TOCSY and 1H‐13C HSQC) experiments were acquired in a reduced set of samples to assign the resonances. Spectra underwent phase, baseline and chemical shift correction. The signals in the spectra were assigned, integrated and normalized to the total sum of integrals. Finally, data were analysed by multivariate statistics (PLS‐DA) to determine a model to discriminate between the controls and OAG tears. The whole data set was split into calibration (18 samples) to calculate the model and validation set (10 samples) to test the performance and the ability for disease discrimination.Results: The calculated PLS‐DA model showed a sensitivity of 100% and a specificity of 83.3% to discriminate OAG patient's tears versus control tears in the validation set. The set of metabolites participating is this discriminant model were obtained, mainly those involved in specific cellular and molecular pathways regarding the pathologic mechanisms of OAG.Conclusions: Data obtained by 1H‐NMR spectroscopy in tears confirms the validity of metabolomics as a non‐invasive approach to better OAG managing.

A Second‐Order Explicit Pressure Projection Method for Eulerian Fluid Simulation

AbstractIn this paper, we propose a novel second‐order explicit midpoint method to address the issue of energy loss and vorticity dissipation in Eulerian fluid simulation. The basic idea is to explicitly compute the pressure gradient at the middle time of each time step and apply it to the velocity field after advection. Theoretically, our solver can achieve higher accuracy than the first‐order solvers at similar computational cost. On the other hand, our method is twice and even faster than the implicit second‐order solvers at the cost of a small loss of accuracy. We have carried out a large number of 2D, 3D and numerical experiments to verify the effectiveness and availability of our algorithm.

Tailoring elastomeric meshes with desired 1D tensile behavior using an inverse design algorithm and material extrusion printing

Additive Manufacturing (AM) is a highly attractive technology in the production of medical devices due to its capability to tailor product functionalities in line with a person's complex body structure. AM can resolve the chronic discomfort of body-supporting devices felt by people, especially those that suffer from imprecise fits, inconvenience with adjustments required in these devices to fit the body, or limitation of body movements to normal operating ranges. To enhance the user experience of those who wear medical devices, elastomeric meshes with programmed “waves” can be additively produced to enable an adjustment of the tensile stiffness in small-strain and large-strain sections. In this study, we demonstrate a method by which to adjust the stiffness transition point from low small-strain stiffness to high large-strain stiffness of additively manufactured sinusoidal and semicircular elastic fibers and determine the key design factors for transition points. Mechanics model predicts the 1D tensile behavior and experiments with controlled mechanical testing verifies the model. We reveal the major design factors that can induce the difference in the stiffness akin to on-off before and after transition. In addition, we produce meshes by the superposition of different wavy fibers, leading to multi-transition tensile behavior and thus expanding the area where mechanical properties can be controlled. An inverse design strategy is developed to improve the utility of an elastomeric mesh which enables the facile customization of the mesh with desired properties. Finally, we demonstrate that users can implement desired functions - not only the size but also the degree of body restriction - through proper settings by producing locally tailored wearable mesh-aid devices. • We clarify the major design factors for tailoring the nonlinear tensile behavior of a material extruded wavy elastomeric fiber. • Wavy fibers can transit their tensile stiffness to 1,400 fold in maximum at transition points. • Overall 1D tensile behavior of a mesh is the superposition of composed wavy fibers. • Inverse design accompanied by additive manufacturing well duplicates the targeted non-linear tensile behavior.

Isolation, structure elucidation and in-vitro evaluation of new trisubstituted Tetrahydrofuran Lignans from Rabdosia lophanthoides var. gerardiana as anti-inflammatory agents

Four new trisubstituted tetrahydrofuran lignans, named (−)-sesaminone-rutinoside ( 1 ), (+)-episesaminone-rutinoside ( 2 ) and rabdosiacosides B ( 3 ) and C ( 4 ) were isolated from the air-dried whole herbs of Rabdosia lophanthoides var. gerardiana together with two known compounds, (+)− 1-hydroxypinoresinol-1-β- d -glucoside ( 5 ) and rosmarinic acid ( 6 ). The structures of these new lignans were elucidated by a combination of mass spectrometry, 1D and 2D NMR experiments including distortionless enhancement by polarization transfer, 1 H– 1 H correlation, heteronuclear single quantum coherence, heteronuclear multiple bond correlation, and nuclear Overhauser effect spectroscopies. Both the cell viability and their anti-inflammatory effects of the lignans were further studied. Among them, no significant cytotoxic activity was exhibited. Compound 4 dramatically suppressed LPS-induced nitric oxide release and reduced the release of the pro-inflammatory cytokines TNF-α and IL-6 in a dose-dependent manner. Overall, our findings indicate that compound 4 was noteworthy in reducing LPS-induced inflammatory responses in RAW264.7 macrophages. • Four new lignans were isolated and identified from Rabdosia lophanthoides. • All compounds exhibited no cytotoxic activity. • Rabdosiacoside C ( 4 ) suppressed LPS-induced NO release. • The release of pro-inflammatory cytokines was inhibited by rabdosiacoside C ( 4 ).

Structure Elucidation of Antibiotics.

To date, there are hundreds of characterized natural products with antibacterial activity against pathogenic bacteria, and several have become bonafide antibiotic drugs. The development of antibacterial natural products into antibiotic drugs, both in the past and in the future, hinges upon an accurate description of the exact chemical structure of the compound. Bolstered by some form of mass spectrometry (MS), nuclear magnetic resonance (NMR) spectroscopy is the primary technique for elucidating the chemical structure of organic molecules including natural products. By combining various one-dimensional (1D) and two-dimensional (2D) experiments, the connectivity between atoms is established and a complete "picture" of the molecule is thereby revealed.

Kalihiacyloxyamides A-H, α-acyloxy amide substituted kalihinane diterpenes isolated from the sponge Acanthella cavernosa collected in the South China Sea

Eight unreported α-acyloxy amide substituted kalihinane diterpenes, named kalihiacyloxyamides A-H were isolated from the South China Sea sponge Acanthella cavernosa. The planar structures and absolute configurations were elucidated by detailed 1D and 2D NMR experiments along with HRESIMS analysis, single crystal X-ray diffraction and CD spectroscopic analysis. Two compounds showed significant cytotoxicity against K562 cell line with IC50 values of 6.4 and 6.3 μM, while two other compounds displayed moderate cytotoxicity against MDA-MB-231 with IC50 values of 7.3 and 7.9 μM.

Ensemble Kalman inversion for magnetic resonance elastography

Magnetic resonance elastography (MRE) is an MRI-based diagnostic method for measuring mechanical properties of biological tissues. MRE measurements are processed by an inversion algorithm to produce a map of the biomechanical properties. In this paper a new and powerful method (ensemble Kalman inversion with level sets (EKI)) of MRE inversion is proposed and tested. The method has critical advantages: material property variation at disease boundaries can be accurately identified, and uncertainty of the reconstructed material properties can be evaluated by consequence of the probabilistic nature of the method. EKI is tested in 2D and 3D experiments with synthetic MRE data of the human kidney. It is demonstrated that the proposed inversion method is accurate and fast.

A Functional in Vitro 3D Model of Human Hematopoietic Niches

Niches in the bone marrow (BM) regulate hematopoietic stem, progenitor and precursor cell fate and behaviour through cell-cell interactions and soluble factor secretion. Niche biology and niche-hematopoietic crosstalk are very complex processes not completely elucidated yet, due essentially to human material accessibility difficulties and limits of existing in vitro culture models. Here, we develop a 3D fully human bone marrow model recapitulating all hematopoietic and non-hematopoietic niche elements to aid further investigation of normal and pathological haematopoiesis and to move away from expensive, time-consuming and imperfect animal models. At first, we have developed a protocol to in vitro production and culture of all human main cellular non-hematopoietic components of bone marrow microenvironment. This comprehensive stroma is generated from human primary cells from femoral head, without any external cell lines contribution, and it reflects accurately the characteristics of the donor. In a 2-step culture process, mesenchymal stromal cells and endothelial cells are first selected and amplified simultaneously in an amplification medium, then they are cultured in the amplification medium as control or in a specific differentiation medium patented by the authors in conventional 2D culture plates or in 3D cultures: in spheroids, by self-organization in ultra-low-adherence plates or on a biomaterial (β-TriCalcium Phosphate), in the U-CUP perfused bioreactor. The resulting cellular stroma composition is analysed by quantifying the gene expression of markers of the osteoblastic (RUNX2, OSX, BSP), adipocytic (LPL, PPARγ, ADIPOQ) and endothelial (CD31) lineages . Moreover, specific markers of hematopoietic niche as ANG1, SCF, CXCL12, LEPR, VCAM, OPN are investigated by RT-qPCR. The spatial organization and the proportion of the different cellular stroma components are analysed by immunofluorescence (Osteoblastic cells: OSX marker, adipocytic cells: Bodipy probe, endothelial cells: CD31). The resulting tissues exhibited all compositional and structural features of human physiological BM: all stroma cells are presents and they express the main niche soluble factors. So, we explore if medullary stroma differentiated using our protocol is able to support the maintenance of HSPCs, to do this we performed coculture experiments in 2D with CD34+ cells sorted from umbilical cord blood. After 14 and 21 days of coculture, hematopoietic cells are recovered, counted and analysed by flow cytometry. Results show that our differentiated stroma is capable of maintaining, expanding and functionally regulated healthy human cord blood-derived HSPCs. An immature compartment (CD34+CD38-) is still present at day 21. Importantly, our primary in vitro niche model supports HSPCs with no cytokine addition. The same results are obtained with healthy human peripheral blood-derived HSPCs cocultured in 3D with the stroma organised in spheroids. Moreover, we demonstrated that our BM model is capable not only to maintain HSPC compartment but also to drive hematopoietic differentiation. In 2D coculture we detected mature blood cells and in 3D cultures, peripheral blood-derived HSPCs cocultured with spheroids are able to engage in erythroid lineage and recapitulate the early phases of erythropoiesis. These results demonstrate the fully complexity and huge versatility of our functional in vitro 3D model of human hematopoietic niches. Our exhaustive fully human hematopoietic niche model prepared from the primary cells of single donor, enables the design of advanced, tuneable in vitro BM proxies for the study of human physiological and pathological haematopoiesis and for screening molecules for predictive purposes in personalized medicine.

Filtering Strategies for Deformation-Rate Distributed Acoustic Sensing.

Deformation-rate distributed acoustic sensing (DAS), made available by the unique designs of certain interrogator units, acquires seismic data that are theoretically equivalent to the along-fiber particle velocity motion recorded by geophones for scenarios involving elastic ground-fiber coupling. While near-elastic coupling can be achieved in cemented downhole installations, it is less obvious how to do so in lower-cost horizontal deployments. This investigation addresses this challenge by installing and freezing fiber in shallow backfilled trenches (to 0.1 m depth) to achieve improved coupling. This acquisition allows for a reinterpretation of processed deformation-rate DAS waveforms as a "filtered particle velocity" rather than the conventional strain-rate quantity. We present 1D and 2D filtering experiments that suggest 2D velocity-dip filtering can recover improved DAS data panels that exhibit clear surface and refracted arrivals. Data acquired on DAS fibers deployed in backfilled, frozen trenches were more repeatable over a day of acquisition compared to those acquired on a surface-deployed DAS fiber, which exhibited more significant amplitude variations and lower signal-to-noise ratios. These observations suggest that deploying fiber in backfilled, frozen trenches can help limit the impact of environmental factors that would adversely affect interpretations of time-lapse DAS observations.

4-Methyl-7-((2-((5-methyl-1,3,4-thiadiazol-2-yl)thio)ethyl)thio)-coumarin

The novel compound 4-methyl-7-((2-((5-methyl-1,3,4-thiadiazol-2-yl)thio)ethyl)thio)-coumarin is obtained in good yield via a two-step protocol; that is, initial synthesis of the reagent 2-((2-chloroethyl)thio)-5-methyl-1,3,4-thiadiazole followed by alkylation of 7-mercapto-4-methylcoumarin. The product’s structure is assigned by 1D and 2D NMR experiments and is confirmed by single-crystal XRD.

Estimations of secondary electron emission coefficients of Si, SiO2, and polyimide electrodes in dual-frequency capacitively coupled discharge

In a dual-frequency capacitively coupled Ar plasma, the secondary electron emission (SEE) coefficients were estimated using a 2D fluid model and experiments. The electron density was measured in the plasma chamber with the upper and lower electrodes of Si. The electron density was calculated by changing the SEE coefficient. The SEE coefficient of the Si electrode was estimated to be 0.06 so that the electron density of the 2D fluid model was close to that of the experimental result. Next, the electron density was measured in the chamber of the lower electrode covered with SiO2 and polyimide, and the SEE coefficients were estimated by comparing experiments and the 2D fluid model. The SEE coefficients of the SiO2 and the polyimide were estimated to be 0.24 and 0.22, respectively. Moreover, The SEE coefficients of SiO2 were almost the same in the range between 300 and 500 W of the lower electrode power.

Phytochemical constituents from Elsholtzia ciliata (Thunb.) Hyl. and their nitric oxide production inhibitory activities

A new megastigmane glycoside, (3S,4R,7E)-megastigma-5,7-diene-9-one-3,4-diol 3-O-β-D-apiofuranosyl-(1→2)-β-D-glucopyranoside (1) and a new cyanogenic glycosyl derivative, (S)-2-(6′-O-R-rosmarinoyl-β-D-glucopyranosyloxy)-phenylacetonitrile (2) were isolated from the methanol extract of the Elsholtzia ciliata together with twelve known compounds, 1-O-β-D-glucopyranosyl-2-hydroxy-4-allylbenzene (3), citrusin C (4), 1,2-di-O-β-D-glucopyranosyl-4-allylbenzene (5), manglieside B (6), 4-allyl-2-hydroxyphenyl 1-O-β-D-apiofuranosyl-(1→6)-β-D-glucopyranoside (7), (-)-isolariciresinol 3α-β-D-glucopyranoside (8), 7R,8R-threo-4,7,9-trihydroxy-3,3′-dimethoxy-8-O-4′-neolignan-9′-O-β-D-glucopyranoside (9), 7R,8R-threo-4,7,9,9′-tetrahydroxy-3-methoxy-8-O-4′-neolignan-9′-O-β-D-glucopyranoside (10), cedrusin-4-O-β-D-glucopyranoside (11), icariside E3 (12), everlastoside L (13) and rosmarinic acid (14). Their chemical structures were elucidated on the basic of extensive 1D and 2D-NMR experiments, as well as their mass spectroscopic data. The absolute configurations of the compounds 1 and 2 were successfully indicated by both theoretical and calculated CD spectra. Compounds 3–7, 9 and 10 potential inhibited NO production in LPS-activated RAW264.7 cells with IC50 values of 6.71, 8.97, 12.38, 14.27, 16.13, 13.54, 16.27 µM, respectively, compared to that of the positive control of N G-monomethyl-L-arginine acetate (L-NMMA), IC50 = 32.51 µM.

Joint K-space and Image-space Parallel Imaging (KIPI) for accelerated chemical exchange saturation transfer acquisition.

To develop an auto-calibrated technique by joint K-space and Image-space Parallel Imaging (KIPI) for accelerated CEST acquisition. The KIPI method selects a calibration frame with a low acceleration factor (AF) and auto-calibration signals (ACS) acquired, from which the coil sensitivity profiles and artifact correction maps are calculated after restoring the k-space by GRAPPA. Then the other frames with high AF and without ACS can be reconstructed by SENSE and artifact suppression. The signal leakage due to the T2 -decay filtering in k-space compromises the SENSE reconstruction, which can be corrected by the artifact suppression algorithm of KIPI. The 2D and 3D imaging experiments were done on the phantom, healthy volunteer, and brain tumor patient with a 3T scanner. The proposed KIPI method was evaluated by retrospectively undersampled data with variable AFs and compared against existing parallel imaging methods (SENSE/auto, GRAPPA, and ESPIRiT). KIPI enabled CEST frames with random AFs to achieve similar image quality, eliminated the strong aliasing artifacts, and generated significantly smaller errors than the other methods (p < 0.01). The KIPI method permitted an AF up to 12-fold in both phase-encoding and slice-encoding directions for 3D CEST source images, achieving an overall 8.2-fold speedup in scan time. KIPI is a novel auto-calibrated parallel imaging method that enables variable AFs for different CEST frames, achieves a significant reduction in scan time, and does not compromise the accuracy of CEST maps.

Meshfree methods for nonlinear equilibrium radiation diffusion equation

The radiation diffusion problem is usually applied to astrophysics and inertial confinement fusion. It seems that the traditional numerical methods such as finite difference method and finite element method is not efficiency to solve the problem because of its nonlinearity and complex computational domain. In this paper, some fast meshfree methods based on radial basis function are proposed to solve the equilibrium radiation diffusion equation. Because the modeling problem has two nonlinear terms, so we use the successive permutation iteration and linearization methods to approximate the nonlinear terms. Firstly, diffusion terms of the one-dimensional (1D) and two-dimensional (2D) equilibrium radiation diffusion equations are linearized by constructing a successive permutation iteration method for fully-implicit discretization. Then, three kinds of different linearization methods (factorization iteration, Picard–Newton iteration and Richtmyer iteration) are proposed and used to linearization of other nonlinear terms. Finally, the linearized equation is solved numerically by Kansa’s method with compactly supported radial basis function. The reliability, accuracy and effectiveness of new methods are verified by 1D and 2D numerical experiments. The advantages of presented method are apparent. They require neither domain nor boundary discretization, and no domain integration is required. New methods are easy for implementation and coding. They not only avoid the complexity of generation mesh, but also solve the equilibrium radiation diffusion equation with high accuracy.