A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.

ALGORITHMS FOR TETRAHEDRAL NETWORK(TEN) GENERATION

The Tetrahedral Network(TEN) is a powerful 3-D vector structure in GIS, which has a lot of advantages such as simple structure, fast topological relation processing and rapid visualization. The difficulty of TEN application is automatic creating data structure. Although a raster algorithm has been introduced by some authors, the problems in accuracy, memory requirement, speed and integrity are still existent. In this paper, the raster algorithm is completed and a vector algorithm is presented after a 3-D data model and structure of TEN have been introducted. Finally, experiment, conclusion and future work are discussed.

Effects of tetrahedral framework nucleic acid/wogonin complexes on osteoarthritis

Osteoarthritis, a disorder characterized by articular cartilage deterioration, varying degrees of inflammation, and chondrocyte apoptosis, is the most common chronic joint disease. To slow or reverse its progression, inflammation should be inhibited, and chondrocyte proliferation should be promoted. Tetrahedral framework nucleic acids can be internalized by chondrocytes(even inflammatory chondrocytes) and can enhance their proliferation and migration. Wogonin, a naturally occurring flavonoid,suppresses oxidative stress and inhibits inflammation. In this study, tetrahedral framework nucleic acids were successfully selfassembled and used to load wogonin. We confirmed the effective formation of tetrahedral framework nucleic acid/wogonin complexes by dynamic light scattering, zeta potential analysis, transmission electron microscopy, and fluorescence spectrophotometry. Tetrahedral framework nucleic acids, wogonin, and especially tetrahedral framework nucleic acid/wogonin complexes effectively alleviated inflammation in vitro and in vivo and prevented cartilage destruction. In addition, these materials remarkably downregulated the expression of inflammatory mediators and matrix metalloproteinases, upregulated chondrogenic markers, and promoted tissue inhibitor of metalloproteinase 1 and B-cell lymphoma 2 expression. In vivo, after treatment with tetrahedral framework nucleic acid/wogonin complexes, the bone mineral density in regenerated tissues was much higher than that found in the untreated groups. Histologically, the complexes enhanced new tissue regeneration, significantly suppressed chondrocyte apoptosis, and promoted chondrogenic marker expression. They also inhibited cell apoptosis, increased chondrogenic marker expression, and suppressed the expression of inflammatory mediators in osteoarthritis. Therefore, we believe that tetrahedral framework nucleic acid/wogonin complexes can be used as an injectable form of therapy for osteoarthritis.

Tetrahedral Framework Nucleic Acid-Based Delivery of Resveratrol Alleviates Insulin Resistance:From Innate to Adaptive Immunity

Obesity-induced insulin resistance is the hallmark of metabolic syndrome,and chronic,low-grade tissue inflammation links obesity to insulin resistance through the activation of tissue-infiltrating immune cells.Current therapeutic approaches lack efficacy and immunomodulatory capacity.Thus,a new therapeutic approach is needed to prevent chronic inflammation and alleviate insulin resistance.Here,we synthesized a tetrahedral framework nucleic acid(tFNA)nanoparticle that carried resveratrol(RSV)to inhibit tissue inflammation and improve insulin sensitivity in obese mice.The prepared nanoparticles,namely tFNAs-RSV,possessed the characteristics of simple synthesis,stable properties,good water solubility,and superior biocompatibility.The tFNA-based delivery ameliorated the lability of RSV and enhanced its therapeutic efficacy.In high-fat diet(HFD)-fed mice,the administration of tFNAs-RSV ameliorated insulin resistance by alleviating inflammation status.tFNAs-RSV could reverse M1 phenotype macrophages in tissues to M2 phenotype macrophages.As for adaptive immunity,the prepared nanoparticles could repress the activation of Th1 and Th17 and promote Th2 and Treg,leading to the alleviation of insulin resistance.Furthermore,this study is the first to demonstrate that tFNAs,a nucleic acid material,possess immunomodulatory capacity.Collectively,our findings demonstrate that tFNAs-RSV alleviate insulin resistance and ameliorate inflammation in HFD mice,suggesting that nucleic acid materials or nucleic acid-based delivery systems may be a potential agent for the treatment of insulin resistance and obesity-related metabolic diseases.

Assessment of k–ε models using tetrahedral grids to describe the turbulent flow field of a PBT impeller and validation through the PIV technique

In turbulence modeling, the RNG and Realizable models have important improvements in the turbulent production and dissipation terms in comparison to the Standard. The selection of the appropriate turbulence model has an impact on the convergence and solution in STRs, and they are used in mixing, multiphase modeling or as starting solution of transient models as DES and LES. Although there are several studies with the pitched blade turbine(PBT) impeller, most of them used the Standard model as representative of all k–ε models, using structured hexahedral grids composed of low number of cells, and in some cases under axial symmetry assumptions.Accordingly, in this work the assessment of the Standard, RNG and Realizable models to describe the turbulent flow field of this impeller, using the Multiple Reference Frame(MRF) and Sliding Mesh(SM) approaches with tetrahedral domains in dense grids, is presented. This kind of cell elements is especially suitable to reproduce complex geometries. Flow velocities and turbulent parameters were verified experimentally by PIV and torque measurements. The three models were capable of predicting fairly the pumping number, the power number based on torque, and velocities. Although the RNG improved the predictions of the turbulent kinetic energy and dissipation rate, the Realizable model presented better performance for both approaches. All models failed in the prediction of the total dissipation rate, and a dependence of its value on the number of cells for the MRF was found.

Advances in regenerative medicine applications of tetrahedral framework nucleic acid-based nanomaterials: an expert consensus recommendation

With the emergence of DNA nanotechnology in the 1980s, self-assembled DNA nanostructures have attracted considerable attention worldwide due to their inherent biocompatibility, unsurpassed programmability, and versatile functions. Especially promising nanostructures are tetrahedral framework nucleic acids(t FNAs), first proposed by Turberfield with the use of a one-step annealing approach. Benefiting from their various merits, such as simple synthesis, high reproducibility, structural stability, cellular internalization, tissue permeability, and editable functionality, t FNAs have been widely applied in the biomedical field as threedimensional DNA nanomaterials. Surprisingly, t FNAs exhibit positive effects on cellular biological behaviors and tissue regeneration,which may be used to treat inflammatory and degenerative diseases. According to their intended application and carrying capacity,t FNAs could carry functional nucleic acids or therapeutic molecules through extended sequences, sticky-end hybridization,intercalation, and encapsulation based on the Watson and Crick principle. Additionally, dynamic t FNAs also have potential applications in controlled and targeted therapies. This review summarized the latest progress in pure/modified/dynamic t FNAs and demonstrated their regenerative medicine applications. These applications include promoting the regeneration of the bone,cartilage, nerve, skin, vasculature, or muscle and treating diseases such as bone defects, neurological disorders, joint-related inflammatory diseases, periodontitis, and immune diseases.

Effect of Substrate Bias on Microstructure and Properties of Tetrahedral Amorphous Carbon Films

The microstructure and properties of tetrahedral amorphous carbon (ta-C) films deposited by the filtered cathodic vacuum arc technology has been investigated by visible Raman spectroscopy, AFM and Nano-indentor. The Raman spectra have been fitted with a single skewed Lorentzian lineshape described by BWF function defining coupling coefficient, which characterizes the degree of asymmetry and is correlated with the sp3 content. When the substrate bias is -80 V, the sp3 content is the most and simultaneously the coupling coefficient is the least, following with the minimum root mean square surface roughness (Rq=0.23 nm) and the highest hardness (51.49 GPa), Young′s modulus (512.39 GPa), and critical scratching load (11.72 mN). As the substrate bias is increased or decreased, the sp3 content and other properties lower correspondingly.

Optical Properties of Tetrahedral Amorphous Carbon Films and Their Potential for Lab-on-a-Chip

In this study, tetrahedral amorphous carbon (ta-C) films with thicknesses between several 100 nm and several micrometers have been deposited onto polished tungsten carbide and steel substrates by pulsed laser deposition (PLD) using an excimer laser (248 nm wavelength). We investigate the optical properties (e.g. the refractive index (n) and extinction coefficient (k) in the visible and near-infrared wavelength range) of these layers in dependence of the used laser ablation fluence on the target. It is shown that n of ~2000 nm thick ta-C films can be tuned, depending on the sp3-content, between n = 2.5 and 2.8 at a wavelength of 632 nm. Besides of this k reduces with the sp3-content and is as low as 0.03 at sp3-contents of more than 75%. We proof that this gives the opportunity to prepare coating with tailored optical properties. Furthermore, it is shown that the ta-C films have low background fluorescence in the wavelengths range of 380 - 750 nm, which make this thin films attractive for certain optical, medical and biotechnological applications. We present for the first time that one possible application is the use in Lab-on-a-Chip-systems (LOC). Within these systems, the ultrasensitive detection of fluorescence markers and dyes is a challenge. In order to increase the signal-to-noise-ratio, a setup was developed, that used the specific optical properties of ta-C films produced by PLD. We used the ta-C film as an integrated reflector that combined low background fluorescence, a low reflectivity at the excitation wavelength and the high reflectivity at the emission wavelength. We prove that this setup improves the detection of fluorescence photons.

SYNTHESES OF TETRAHEDRAL METAL CLUSTER COMPOUNDS

The carbyne compound [Br(CO)_2(Py)_2Mo(≡CC_6H_5)] (Py=pyridine) (1a) reacts with Co_2 (CO)_8, Fe_2(CO)_9 and Mn_2 (CO)_(10) to give tetrahedral tri-metal cluster compounds Co_2Mo(μ_3-CC_6H_5)Br(CO)_8(Py)_2 (2), Fe_2Mo(μ_3-CC_6H_5) Br(CO)_9(Py)_2 (3) and Mn_2Mo(μ_3-CC_6H_5)Br(CO)_(10) (Py)_2 (4) respectively. Tri-metal cluster compound Co_2Mo(μ_3-CC_6H_5)Br(CO)_8-(bipy) (bipy=α,α'dipyridyl) (5) is prepared in a similar reaction sequence from [Br(CO)_2(bipy)Mo(≡CC_6H_5)] (1b) and Co_2(CO)_8. IR, ~1H and ^(13)C NMR spectral data of these compounds are reported and discussed. The crystal structure of compound (5) has been determined by X-ray diffraction.

Application of High Performance Liquid Chromatography to Separation of Novel Chiral Tetrahedral Heterometal Clusters

A series of novel chiral tetrahedral heterometal clusters have firstly been separated on cellulose tris-(3,5-dimethylphenylcarbamate) stationary phase by high performance liquid chrom-atography, using hexane as the mobile phase with various alcohols as modifiers.

ENHANCING ADHESION OF TETRAHEDRAL AMORPHOUS CARBON FILMS

Objective The high energy ion bombardment technique is applied to enhancing the adhesion of the tetrahedral amorphous carbon (TAC) films deposited by the filtered cathode vacuum arc (FCVA). Methods The abrasion method, scratch method, heating and shaking method as well as boiling salt solution method is used to test the adhesion of the TAC films on various material substrates. Results The test results show that the adhesion is increased as the ion bombardment energy increases. However, if the bombardment energy were over the corresponding optimum value, the adhesion would be enhanced very slowly for the harder material substrates and drops quickly, for the softer ones. Conclusion The optimum values of the ion bombardment energy are larger for the harder materials than that for the softer ones.

An h-Adaptivity DG Method on Locally Curved Tetrahedral Mesh for Solving Compressible Flows

For the numerical simulation of compressible flows,normally different mesh sizes are expected in different regions.For example,smaller mesh sizes are required to improve the local numerical resolution in the regions where the physical variables vary violently(for example,near the shock waves or in the boundary layers)and larger elements are expected for the regions where the solution is smooth.h-adaptive mesh has been widely used for complex flows.However,there are two difficulties when employing h-adaptivity for high-order discontinuous Galerkin(DG)methods.First,locally curved elements are required to precisely match the solid boundary,which significantly increases the difficulty to conduct the"refining"and"coarsening"operations since the curved information has to be maintained.Second,h-adaptivity could break the partition balancing,which would significantly affect the efficiency of parallel computing.In this paper,a robust and automatic h-adaptive method is developed for high-order DG methods on locally curved tetrahedral mesh,for which the curved geometries are maintained during the h-adaptivity.Furthermore,the reallocating and rebalancing of the computational loads on parallel clusters are conducted to maintain the parallel efficiency.Numerical results indicate that the introduced h-adaptive method is able to generate more reasonable mesh according to the structure of flow-fields.

Quality Improvement Algorithm for Tetrahedral Mesh Based on Optimal Delaunay Triangulation

The concept of optimal Delaunay triangulation (ODT) and the corresponding error-based quality metric are first introduced. Then one kind of mesh smoothing algorithm for tetrahedral mesh based on the concept of ODT is examined. With regard to its problem of possible producing illegal elements, this paper proposes a modified smoothing scheme with a constrained optimization model for tetrahedral mesh quality improvement. The constrained optimization model is converted to an unconstrained one and then solved by integrating chaos search and BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm efficiently. Quality improvement for tetrahedral mesh is finally achieved by alternately applying the presented smoothing scheme and re-triangulation. Some testing examples are given to demonstrate the effectiveness of the proposed approach.

Open Volumetric Mesh-An Efficient Data Structure for Tetrahedral and Hexahedral Meshes

This work introduces a scalable and efficient topological structure for tetrahedral and hexahedral meshes. The design of the data structure aims at maximal flexibility and high performance. It provides a high scalability by using hierarchical representa-tions of topological elements. The proposed data structure is array-based, and it is a compact representation of the half-edge data structure for volume elements and half-face data structure for volumetric meshes. This guarantees constant access time to the neighbors of the topological elements. In addition, an open-source implementation named Open Volumetric Mesh （OVM） of the pro-posed data structure is written in C＋＋ using generic programming concepts.

Un-thorough Delaunay Approach for Tetrahedral Mesh Generation

An integrated tetrahedrization algorithm in 3D domain which combines the Delaunay tetrahedral method with un-Delaunay tetrahedral method is described. The algorithm was developed by constructing Delaunay Tetrahedrons from a scattered point set, recovering boundaries using Delaunay and un-Delaunay method, inserting additional nodes in unsuitable tetrahedrons, optimizing tetrahedrons and smoothing the tetrahedral mesh with the 2D-3D Laplacian method. The algorithm has been applied to the injection molding CAE preprocessing.

Tetrahedral framework nucleic acids promote the proliferation and differentiation potential of diabetic bone marrow mesenchymal stem cell

Diabetes mellitus considerably affects bone marrow mesenchymal stem cells(BMSCs),for example,by inhibiting their proliferation and differentiation potential,which enhances the difficulty in endogenous bone regeneration.Hence,effective strategies for enhancing the functions of BMSCs in diabetes have farreaching consequences for bone healing and regeneration in diabetes patients.Tetrahedral framework nucleic acids(tFNAs)are nucleic acid nanomaterials that can autonomously enter cells and regulate their behaviors.In this study,we evaluated the effects of tFNAs on BMSCs from diabetic rats.We found that tFNAs could promote the proliferation,migration,and osteogenic differentiation of BMSCs from rats with type 2 diabetes mellitus,and inhibited cell senescence and apoptosis.Furthermore,tFNAs effectively scavenged the accumulated reactive oxygen species and activated the suppressed protein kinase B(Akt)signaling pathway.Overall,we show that tFNAs can recover the proliferation and osteogenic potential of diabetic BMSCs by alleviating oxidative stress and activating Akt signaling.The study provides a strategy for endogenous bone regeneration in diabetes and also paves the way for exploiting DNA-based nanomaterials in regenerative medicine.

A tetrahedral framework nucleic acid based multifunctional nanocapsule for tumor prophylactic mRNA vaccination

Synthetic antigen-encoding mRNA plays an increasingly significant role in tumor vaccine technology owing to its antigen-specific immune-activation. However, its immune efficacy is challenged by inferior delivery efficiency and demand for suitable adjuvants. Here, we develop a novel mRNA nanovaccine based on a multifunctional nanocapsule, which is a dual-adjuvant formulation composed of cytosine-phosphateguanine motifs loaded tetrahedral framework nucleic acid(CpG-tFNA) and an immunopeptide murine β-defensin 2(mDF2β). This m RNA nanovaccine successfully achieves intracellular delivery, antigen expression and presentation of dendritic cells, and proliferation of antigen-specific T cells. In a tumor prophylactic vaccination model, it exerts an excellent inhibitory effect on lymphoma occurrence through cellular immunity. This mRNA nanovaccine has promising prophylactic applications in tumors and many other diseases.

Pressure-stabilized hexagonal perovskite-related isolated tetrahedral anion silicate La_(6)Sr_(3)Si_(6)O_(24)

The discovery of new perovskite compounds under high pressure mainly focuses on the ABO_(3)compositions and the compositions highly deviated from ABO_(3)are less explored.Here we demonstrate that the La_(6)Sr_(3)Si_(6)O_(24)silicate composition can be stabilized as a hexagonal perovskite-related structure with isolated tetrahedra anions under high pressure of 6 GPa.The compound adopts 9-layer shifted hexagonal perovskite-like structure with both B-cation and oxygen deficiencies and contains pseudo-cubic(c)(La/Sr)O_(2)layers and hexagonal(h)(La/Sr)O_(3)layers stacked according to(c hh)_(3)sequence.This structure features both B-cation vacancy ordering between the two consecutive hexagonal layers and oxygen vacancy ordering in c-(La/Sr)O_(2)layers,resulting in isolated tetrahedral Si O_(4)anions and ionic conduction behavior.This work demonstrates the practicability of accessing new perovskite-related functional materials from the compositions highly deviated from ABO_(3)under high pressure.

Biological regulation on synovial fibroblast and the treatment of rheumatoid arthritis by nobiletin-loaded tetrahedral framework nucleic acids cargo tank

The hyperplasia and destruction of synovial tissue have an important impact on the development of rheumatoid arthritis(RA), the abnormal proliferation and migration of synovial fibroblast in synovial tissue is similar to tumor cells. Targeting anomalous synovial fibroblast and designing a high bioavailability nano drug delivery system can reduce the dosage for the treatment of rheumatoid arthritis and it is of great significance to reduce toxic and side effects and improve curative effect. In this experiment, the nobiletin-loaded tetrahedral framework nucleic acids cargo tank was established, carrying antiinflammatory small molecule monomer drug nobiletin with minimal bioavailability. Both in vitro cell experiments and in vivo animal studies proved the nano cargo tank enhance the role of nobiletin in reducing the invasiveness of pathological synovial fibroblast and promote their apoptosis, effectively alleviate the disease development of rheumatoid arthritis.

Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

We construct and analyze a family of quadratic finite volume method(FVM)schemes over tetrahedral meshes.In order to prove the stability and the error estimate,we propose the minimum V-angle condition on tetrahedral meshes,and the surface and volume orthogonal conditions on dual meshes.Through the technique of element analysis,the local stability is equivalent to a positive definiteness of a 9 × 9 element matrix,which is difficult to analyze directly or even numerically.With the help of the surface orthogonal condition and the congruent transformation,this element matrix is reduced into a block diagonal matrix,and then we carry out the stability result under the minimum V-angle condition.It is worth mentioning that the minimum V-angle condition of the tetrahedral case is very different from a simple extension of the minimum angle condition for triangular meshes,while it is also convenient to use in practice.Based on the stability,we prove the optimal H^(1) and L^(2) error estimates,respectively,where the orthogonal conditions play an important role in ensuring the optimal L^(2) convergence rate.Numerical experiments are presented to illustrate our theoretical results.