Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

A Discussion on the Establishment That a Fibre Metric on the Positive Definite Real Inner-Product of a Properly Embedded Smooth Submanifold Be Always Extended to a Riemannian Metric on the Positive Definite Real Inner-Product

Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|s i.e. a positive definite real inner-product on TpM for all p ∈ S, which depends smoothly on p ∈ S. The purpose of this article is to figure out that the fibre metric on TM|s can always be extended to a Riemannian metric on TM from a special perspective.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning

Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.

An Innovative Coupled Common-Node Discrete Element Method-Smoothed Particle Hydrodynamics Model Developed with LS-DYNA and Its Applications

In this study,a common-node DEM-SPH coupling model based on the shared node method is proposed,and a fluid–structure coupling method using the common-node discrete element method-smoothed particle hydrodynamics(DS-SPH)method is developed using LS-DYNA software.The DEM and SPH are established on the same node to create common-node DEM-SPH particles,allowing for fluid–structure interactions.Numerical simulations of various scenarios,including water entry of a rigid sphere,dam-break propagation over wet beds,impact on an ice plate floating on water and ice accumulation on offshore structures,are conducted.The interaction between DS particles and SPH fluid and the crack generation mechanism and expansion characteristics of the ice plate under the interaction of structure and fluid are also studied.The results are compared with available data to verify the proposed coupling method.Notably,the simulation results demonstrated that controlling the cutoff pressure of internal SPH particles could effectively control particle splashing during ice crushing failure.

A modified smoothed particle hydrodynamics method considering residual stress for simulating failure and its application in layered rock mass

Residual strength is an indispensable factor in evaluating rock fracture,yet the current Smoothed Particle Hydrodynamics(SPH)framework rarely considers its influence when simulating fracture.An improved cracking strategy considering residual stress in the base bond SPH method was proposed to simulate failures in layered rocks and slopes and verified by experimental results and other simulation methods(i.e.,the discrete element method).Modified Mohr–Coulomb failure criterion was applied to distinguish the mixed failure of tensile and shear.Bond fracture markψwas introduced to improve the kernel function after tensile damage,and the calculation of residual stress after the damage was derived after shear damage.Numerical simulations were carried out to evaluate its performance under different stress and scale conditions and to verify its effectiveness in realistically reproducing crack initiation and propagation and coalescence,even fracture and separation.The results indicate that the improved cracking strategy precisely captures the fracture and failure pattern in layered rocks and rock slopes.The residual stress of brittle tock is correctly captured by the improved SPH method.The improved SPH method that considers residual strength shows an approximately 13%improvement in accuracy for the safety factor of anti-dip layered slopes compared to the method that does not consider residual strength,as validated against analytical solutions.We infer that the improved SPH method is effective and shows promise for applications to continuous and discontinuous rock masses.

A Dual Domain Robust Reversible Watermarking Algorithm for Frame Grouping Videos Using Scene Smoothness

The proposed robust reversible watermarking algorithm addresses the compatibility challenges between robustness and reversibility in existing video watermarking techniques by leveraging scene smoothness for frame grouping videos.Grounded in the H.264 video coding standard,the algorithm first employs traditional robust watermark stitching technology to embed watermark information in the low-frequency coefficient domain of the U channel.Subsequently,it utilizes histogram migration techniques in the high-frequency coefficient domain of the U channel to embed auxiliary information,enabling successful watermark extraction and lossless recovery of the original video content.Experimental results demonstrate the algorithm’s strong imperceptibility,with each embedded frame in the experimental videos achieving a mean peak signal-to-noise ratio of 49.3830 dB and a mean structural similarity of 0.9996.Compared with the three comparison algorithms,the performance of the two experimental indexes is improved by 7.59%and 0.4%on average.At the same time,the proposed algorithm has strong robustness to both offline and online attacks:In the face of offline attacks,the average normalized correlation coefficient between the extracted watermark and the original watermark is 0.9989,and the average bit error rate is 0.0089.In the face of online attacks,the normalized correlation coefficient between the extracted watermark and the original watermark is 0.8840,and the mean bit error rate is 0.2269.Compared with the three comparison algorithms,the performance of the two experimental indexes is improved by 1.27%and 18.16%on average,highlighting the algorithm’s robustness.Furthermore,the algorithm exhibits low computational complexity,with the mean encoding and the mean decoding time differentials during experimental video processing being 3.934 and 2.273 s,respectively,underscoring its practical utility.

A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

Smoothed-Particle Hydrodynamics Simulation of Ship Motion and Tank Sloshing under the Effect of Regular Waves

Predicting the response of liquefied natural gas(LNG)contained in vessels subjected to external waves is extremely important to ensure the safety of the transportation process.In this study,the coupled behavior due to ship motion and liquid tank sloshing has been simulated by the Smoothed-Particle Hydrodynamics(SPH)method.Firstly,the sloshing flow in a rectangular tank was simulated and the related loads were analyzed to verify and validate the accuracy of the present SPH solver.Then,a three-dimensional simplified LNG carrier model,including two prismatic liquid tanks and a wave tank,was introduced.Different conditions were examined corresponding to different wave lengths,wave heights,wave heading angles,and tank loading rates.Finally,the effects of liquid tank loading rate on LNG ship motions and sloshing loading were analyzed,thereby showing that the SPH method can effectively provide useful indications for the design of liquid cargo ships.

Isometric Immersions of Lightlike Warped Product Manifolds

In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.

Influence of Angiotensin II on α1-Adrenergic Receptors Function in Rat Aorta and Expression in Vascular Smooth Muscle Cells

Angiotensin II (Ang II) is the main mediator of the Renin-Angiotensin-System acting on AT1 and other AT receptors. It is regarded as a pleiotropic agent that induces many actions, including functioning as a growth factor, and as a contractile hormone, among others. The aim of this work was to examine the impact of Ang II on the expression and function of α1-adrenergic receptors (α1-ARs) in cultured rat aorta, and aorta-derived smooth muscle cells. Isolated Wistar rat aorta was incubated for 24 h in DMEM at 37˚C, then subjected to isometric tension and to the action of added norepinephrine, in concentration-response curves. Ang II was added (1 × 10−5 M), and in some experiments, 5-Methylurapidil (α1A-AR antagonist), AH11110A (α1B-AR antagonist), or BMY-7378 (α1D-AR antagonist), were used to identify the α1-AR involved in the response. Desensitization of the contractile response to norepinephrine was observed due to incubation time, and by the Ang II action. α1D-AR was protected from desensitization by BMY-7378;while RS-100329 and prazosin partially mitigated desensitization. In another set of experiments, isolated aorta-derived smooth muscle cells were exposed to Ang II and α1-ARs proteins were evaluated. α1D-AR increased at 30 and 60 min post Ang II exposure, the α1A-AR diminished from 1 to 4 h, while α1B-AR remained unchanged over 24 h of Ang II exposure. Ang II induced an increase of α1D-AR at short times, and BMY-7378 protected α1D-AR from desensitization.

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.

SMOOTHNESS OF INERTIAL MANIFOLD UNDER TIME DISCRETIZATION

In this paper we discuss the smoothness of inertial manifolds under time discretization. By the fibre contract principle, see Section 4, we obtain a sufficient condition for C-k(k greater than or equal to 1) inertial manifolds. In view of the numerical computation for dissipative nonlinear evolution equations, it is more important to consider the discretized case than continuous case([3]).

SMOOTH AND PATH CONNECTED BANACH SUBMANIFOLD Σ_r OF B(E,F) AND A DIMENSION FORMULA IN B(R^n,R^m)

Given two Banach spaces E, F, let B（E, F） be the set of all bounded linear operators from E into F, ∑r the set of all operators of finite rank r in B（E, F）, and ∑r^# the number of path connected components of ∑r. It is known that ∑r is a smooth Banach submanifold in B（E,F） with given expression of its tangent space at each A ∈ ∑r. In this paper, the equality ∑r^# = 1 is proved. Consequently, the following theorem is obtained： for any nonnegative integer r,∑r is a smooth and path connected Banach submanifold in B（E, F） with the tangent space TA∑r = {B E B（E,F） ： BN（A） belong to R（A）} at each A ∈ ∑r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of ∑r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = R^n and F = R^m, then ∑r is a smooth and path connected submanifold of B（R^n,R^m） and its dimension is dim ∑r = （m ＋ n）r- r^2 for each r, 0≤r 〈 min{n,m}.

MicroRNA-146a Promotes Embryonic Stem Cell Differentiation towards Vascular Smooth Muscle Cells through Regulation of Kruppel-like Factor 4

Objective Vascular smooth muscle cell(VSMC)differentiation from stem cells is one source of the increasing number of VSMCs that are involved in vascular remodeling-related diseases such as hypertension,atherosclerosis,and restenosis.MicroRNA-146a(miR-146a)has been proven to be involved in cell proliferation,migration,and tumor metabolism.However,little is known about the functional role of miR-146a in VSMC differentiation from embryonic stem cells(ESCs).This study aimed to determine the role of miR-146a in VSMC differentiation from ESCs.Methods Mouse ESCs were differentiated into VSMCs,and the cell extracts were analyzed by Western blotting and RT-qPCR.In addition,luciferase reporter assays using ESCs transfected with miR-146a/mimic and plasmids were performed.Finally,C57BL/6J female mice were injected with mimic or miR-146a-overexpressing ESCs,and immunohistochemistry,Western blotting,and RT-qPCR assays were carried out on tissue samples from these mice.Results miR-146a was significantly upregulated during VSMC differentiation,accompanied with the VSMC-specific marker genes smooth muscle-alpha-actin(SMαA),smooth muscle 22(SM22),smooth muscle myosin heavy chain(SMMHC),and h1-calponin.Furthermore,overexpression of miR-146a enhanced the differentiation process in vitro and in vivo.Concurrently,the expression of Kruppel-like factor 4(KLF4),predicted as one of the top targets of miR-146a,was sharply decreased in miR-146a-overexpressing ESCs.Importantly,inhibiting KLF4 expression enhanced the VSMC-specific gene expression induced by miR-146a overexpression in differentiating ESCs.In addition,miR-146a upregulated the mRNA expression levels and transcriptional activity of VSMC differentiation-related transcription factors,including serum response factor(SRF)and myocyte enhancer factor 2c(MEF-2c).Conclusion Our data support that miR-146a promotes ESC-VSMC differentiation through regulating KLF4 and modulating the transcription factor activity of VSMCs.

Smoother manifold for graph meta-learning

Meta-learning provides a framework for the possibility of mimicking artificial intelligence.How-ever,data distribution of the training set fails to be consistent with the one of the testing set as the limited domain differences among them.These factors often result in poor generalization in existing meta-learning models.In this work,a novel smoother manifold for graph meta-learning(SGML)is proposed,which derives the similarity parameters of node features from the relationship between nodes and edges in the graph structure,and then utilizes the similarity parameters to yield smoother manifold through embedded propagation module.Smoother manifold can naturally filter out noise from the most important components when generalizing the local mapping relationship to the global.Besides suiting for generalizing on unseen low data issues,the framework is capable to easily perform transductive inference.Experimental results on MiniImageNet and TieredImageNet consistently show that applying SGML to supervised and semi-supervised classification can improve the performance in reducing the noise of domain shift representation.

Inhibitory Effect of PPARδAgonist GW501516 on Proliferation of Hypoxia-induced Pulmonary Arterial Smooth Muscle Cells by Regulating the mTOR Pathway

Objective This study aimed to investigate the effects of the peroxisome proliferator-activated receptorδ(PPARδ)agonist GW501516 on the proliferation of pulmonary artery smooth muscle cells(PASMCs)induced by hypoxia,in order to search for new drugs for the treatment and prevention of pulmonary vascular remodeling.Methods PASMCs were incubated with different concentrations of GW501516(10,30,100 nmol/L)under the hypoxic condition.The proliferation was determined by a CCK-8 assay.The cell cycle progression was analyzed by flow cytometry.The expression of PPARδ,S phase kinase-associated protein 2(Skp2),and cell cycle-dependent kinase inhibitor p27 was detected by Western blotting.Then PASMCs were treated with 100 nmol/L GW501516,100 nmol/L mammalian target of rapamycin(mTOR)inhibitor rapamycin and/or 2µmol/L mTOR activator MHY1485 to explore the molecular mechanisms by which GW501516 reduces the proliferation of PASMCs.Results The presented data demonstrated that hypoxia reduced the expression of PPARδin an oxygen concentration-and time-dependent manner,and GW501516 decreased the proliferation of PASMCs induced by hypoxia by blocking the progression through the G0/G1 to S phase of the cell cycle.In accordance with these findings,GW501516 downregulated Skp2 and upregulated p27 in hypoxia-exposed PASMCs.Further experiments showed that rapamycin had similar effects as GW501516 in inhibiting cell proliferation,arresting the cell cycle,regulating the expression of Skp2 and p27,and inactivating mTOR in hypoxia-exposed PASMCs.Moreover,MHY1485 reversed all the beneficial effects of GW501516 on hypoxia-stimulated PASMCs.Conclusion GW501516 inhibited the proliferation of PASMCs induced by hypoxia through blocking the mTOR/Skp2/p27 signaling pathway.

Secret Sharing Scheme Based on the Differential Manifold

In this paper, the concepts of topological space and differential manifold are introduced, and it is proved that the surface determined by function F (x2, x2, …, xt) of class Cr in Euelidean Rt is a differential manifold. Using the intersection of the tangent plane and the hypernormal of the differential manifold to construct the shared master key of participants, an intuitive, secure and complete (t,n)-threshold secret sharing scheme is designed. The paper is proved to be safe, and the probability of successful attack of attackers is only 1/pt-1. When the prime number p is sufficiently large, the probability is almost 0. The results show that this scheme has the characteristics of single-parameter representation of the master key in the geometric method, and is more practical and easy to implement than the Blakley threshold secret sharing scheme.

SOME CONVERGENCE PROBLEMS REGARDING THE FRACTIONAL SCHRODINGER PROPAGATOR ON NONCOMPACT MANIFOLDS

Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x)a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds.

An efficient non-iterative smoothed particle hydrodynamics fluid simulation method with variable smoothing length

In classical smoothed particle hydrodynamics(SPH)fluid simulation approaches,the smoothing length of Lagrangian particles is typically constant.One major disadvantage is the lack of adaptiveness,which may compromise accuracy in fluid regions such as splashes and surfaces.Attempts to address this problem used variable smoothing lengths.Yet the existing methods are computationally complex and non-efficient,because the smoothing length is typically calculated using iterative optimization.Here,we propose an efficient non-iterative SPH fluid simulation method with variable smoothing length(VSLSPH).VSLSPH correlates the smoothing length to the density change,and adaptively adjusts the smoothing length of particles with high accuracy and low computational cost,enabling large time steps.Our experimental results demonstrate the advantages of the VSLSPH approach in terms of its simulation accuracy and efficiency.