GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

Delineation of urban growth boundary based on FLUS model under the perspective of land use evaluation in hilly mountainous areas

With rapid economic development,the size of urban land in China is expanding dramatically.The Urban Growth Boundary(UGB)is an expandable spatial boundary for urban construction in a certain period in order to control the urban sprawl.Reasonable delineation of UGB can inhibit the disorderly spread of urban space and guide the normal development of the city.It is of practical significance for the construction of green urban space.The study utilizes GIS technology to establish a land construction suitability evaluation system for Nankang city,which is experiencing rapid urban expansion,and outlines the preliminary UGB under the future land use simulation(FLUS)model.At the same time,considering the coupled coordination of"Production-Living-Ecological Space",and based on the suitability evaluation,we revised the preliminary UGB by combining the advantages of the patch-generating land use simulation(PLUS)model and the convex hull model to delineate the final UGB.The results show that:1)the comprehensive score of the evaluation of the suitability of the construction of land from high to low shows the distribution of the center of the city to the surrounding circle type spread,the center of the city has the highest suitability score.The results of convex hull model show that the urban expansion type of Nankang is epitaxial.In the future,the urban expansion will mainly occur in the northern part of the city.The PLUS model predicts an increase of 3359.97 hm^(2)of construction land in Nankang by 2035,of which 2022.97 hm^(2)is urban construction land.2)The FLUS model has a prediction accuracy of 86.3%and delineates a preliminary UGB area of 9215.07 hm^(2).3)We used the results of the construction suitability evaluation,PLUS model simulation results,and convex hull model predictions to revise the originally delineated UGB.The final delineated UGB area is 8895.67 hm^(2)and it is capable of meeting the future development of the study area.The results of the delineation can promote sustainable urban development,and the delineation methodology can provide a reference basis for the preparation of territorial spatial planning.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Grain boundary engineering for enhancing intergranular damage resistance of ferritic/martensitic steel P92

Ferritic/martensitic(F/M)steel is widely used as a structural material in thermal and nuclear power plants.However,it is susceptible to intergranular damage,which is a critical issue,under service conditions.In this study,to improve the resistance to intergranular damage of F/M steel,a thermomechanical process(TMP)was employed to achieve a grain boundary engineering(GBE)microstructure in F/M steel P92.The TMP,including cold-rolling thickness reduction of 6%,9%,and 12%,followed by austenitization at 1323 K for 40 min and tempering at 1053 K for 45 min,was applied to the as-received(AR)P92 steel.The prior austenite grain(PAG)size,prior austenite grain boundary character distribution(GBCD),and connectivity of prior austenite grain boundaries(PAGBs)were investigated.Compared to the AR specimen,the PAG size did not change significantly.The fraction of coincident site lattice boundaries(CSLBs,3≤Σ≤29)and Σ3^(n) boundaries along PAGBs decreased with increasing reduction ratio because the recrystallization fraction increased with increasing reduction ratio.The PAGB connectivity of the 6%deformed specimen slightly deteriorated compared with that of the AR specimen.Moreover,potentiodynamic polarization studies revealed that the intergranular damage resistance of the studied steel could be improved by increasing the fraction of CSLBs along the PAGBs,indicating that the TMP,which involves low deformation,could enhance the intergranular damage resistance.

A High-Accuracy Curve Boundary Recognition Method Based on the Lattice Boltzmann Method and Immersed Moving Boundary Method

Applying numerical simulation technology to investigate fluid-solid interaction involving complex curved bound-aries is vital in aircraft design,ocean,and construction engineering.However,current methods such as Lattice Boltzmann(LBM)and the immersion boundary method based on solid ratio(IMB)have limitations in identifying custom curved boundaries.Meanwhile,IBM based on velocity correction(IBM-VC)suffers from inaccuracies and numerical instability.Therefore,this study introduces a high-accuracy curve boundary recognition method(IMB-CB),which identifies boundary nodes by moving the search box,and corrects the weighting function in LBM by calculating the solid ratio of the boundary nodes,achieving accurate recognition of custom curve boundaries.In addition,curve boundary image and dot methods are utilized to verify IMB-CB.The findings revealed that IMB-CB can accurately identify the boundary,showing an error of less than 1.8%with 500 lattices.Also,the flow in the custom curve boundary and aerodynamic characteristics of the NACA0012 airfoil are calculated and compared to IBM-VC.Results showed that IMB-CB yields lower lift and drag coefficient errors than IBM-VC,with a 1.45%drag coefficient error.In addition,the characteristic curve of IMB-CB is very stable,whereas that of IBM-VC is not.For the moving boundary problem,LBM-IMB-CB with discrete element method(DEM)is capable of accurately simulating the physical phenomena of multi-moving particle flow in complex curved pipelines.This research proposes a new curve boundary recognition method,which can significantly promote the stability and accuracy of fluid-solid interaction simulations and thus has huge applications in engineering.

Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems

In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.

Experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering boundary effect

The boundary condition is a crucial factor affecting the permeability variation due to suffusion.An experimental investigation on the permeability of gap-graded soil due to horizontal suffusion considering the boundary effect is conducted,where the hydraulic head difference(DH)varies,and the boundary includes non-loss and soil-loss conditions.Soil samples are filled into seven soil storerooms connected in turn.After evaluation,the variation in content of fine sand(ΔR_(f))and the hydraulic conductivity of soils in each storeroom(C_(i))are analyzed.In the non-loss test,the soil sample filling area is divided into runoff,transited,and accumulated areas according to the negative or positive ΔR_(f) values.ΔR_(f) increases from negative to positive along the seepage path,and Ci decreases from runoff area to transited area and then rebounds in accumulated area.In the soil-loss test,all soil sample filling areas belong to the runoff area,where the gentle-loss,strengthened-loss,and alleviated-loss parts are further divided.ΔR_(f) decreases from the gentle-loss part to the strengthened-loss part and then rebounds in the alleviated-loss part,and C_(i) increases and then decreases along the seepage path.The relationship between ΔR_(f) and Ci is different with the boundary condition.Ci exponentially decreases with ΔR_(f) in the non-loss test and increases with ΔR_(f) generally in the soil-loss test.

Development of D_α band symmetrical visible optical diagnostic for boundary reconstruction on EAST tokamak

To investigate the potential of utilizing visible spectral imaging for controlling the plasma boundary shape during stable operation of plasma in future tokamak, a D_α band symmetric visible light diagnostic system was designed and implemented on the Experimental Advanced Superconducting Tokamak(EAST). This system leverages two symmetric optics for joint plasma imaging. The optical system exhibits a spatial resolution less than 2 mm at the poloidal cross-section, distortion within the field of view below 10%, and relative illumination of 91%.The high-quality images obtained enable clear observation of both the plasma boundary position and the characteristics of components within the vacuum vessel. Following system calibration and coordinate transformation, the image coordinate boundary features are mapped to the tokamak coordinate system. Utilizing this system, the plasma boundary was reconstructed, and the resulting representation showed alignment with the EFIT(Equilibrium Fitting) results. This underscores the system's superior performance in boundary reconstruction applications and provides a diagnostic foundation for boundary shape control based on visible spectral imaging.

CONVEXITY OF THE FREE BOUNDARY FOR AN AXISYMMETRIC INCOMPRESSIBLE IMPINGING JET

This paper is devoted to the study of the shape of the free boundary for a threedimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.

Two Stages Segmentation Algorithm of Breast Tumor in DCE-MRI Based on Multi-Scale Feature and Boundary Attention Mechanism

Nuclearmagnetic resonance imaging of breasts often presents complex backgrounds.Breast tumors exhibit varying sizes,uneven intensity,and indistinct boundaries.These characteristics can lead to challenges such as low accuracy and incorrect segmentation during tumor segmentation.Thus,we propose a two-stage breast tumor segmentation method leveraging multi-scale features and boundary attention mechanisms.Initially,the breast region of interest is extracted to isolate the breast area from surrounding tissues and organs.Subsequently,we devise a fusion network incorporatingmulti-scale features and boundary attentionmechanisms for breast tumor segmentation.We incorporate multi-scale parallel dilated convolution modules into the network,enhancing its capability to segment tumors of various sizes through multi-scale convolution and novel fusion techniques.Additionally,attention and boundary detection modules are included to augment the network’s capacity to locate tumors by capturing nonlocal dependencies in both spatial and channel domains.Furthermore,a hybrid loss function with boundary weight is employed to address sample class imbalance issues and enhance the network’s boundary maintenance capability through additional loss.Themethod was evaluated using breast data from 207 patients at RuijinHospital,resulting in a 6.64%increase in Dice similarity coefficient compared to the benchmarkU-Net.Experimental results demonstrate the superiority of the method over other segmentation techniques,with fewer model parameters.

Multi-soliton solutions of coupled Lakshmanan-Porsezian-Daniel equations with variable coefficients under nonzero boundary conditions

This paper aims to investigate the multi-soliton solutions of the coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions.These equations are utilized to model the phenomenon of nonlinear waves propagating simultaneously in non-uniform optical fibers.By analyzing the Lax pair and the Riemann–Hilbert problem,we aim to provide a comprehensive understanding of the dynamics and interactions of solitons of this system.Furthermore,we study the impacts of group velocity dispersion or the fourth-order dispersion on soliton behaviors.Through appropriate parameter selections,we observe various nonlinear phenomena,including the disappearance of solitons after interaction and their transformation into breather-like solitons,as well as the propagation of breathers with variable periodicity and interactions between solitons with variable periodicities.

A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies.However,the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis.This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions.The pressure-dependent length shrinkage coefficients,which quantify the length changes of the inner zone and propped fractures,are modified and incorporated into this multi-zone semi-analytical model.With simultaneous numerical iterations and numerical inversions in Laplace and real-time space,the transient solutions to pressure and rate behavior are determined in just a few seconds.The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods:fracture bilinear flow(FR1),dynamic PFs flow(FR2),inner-area linear flow(FR3),dynamic inner boundary flow(FR4),and outer-area dominated linear flow(FR5).The early hump during FR2 period and a positive upward shift during FR4period are captured on the log-log pressure transient curves,reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary.The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly.The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves.If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected,the flow rate will be overestimated in the later production period.

Mask Boundary R-CNN实例分割边界精度算法

边界模糊问题在实例分割中是一个经典的难题,即使是在以高精度著称的双阶段实例分割中,边界处的分割效果也不理想,这是因为实例分割网络大多使用分类置信度作为依据进行掩膜的选择,它忽略了分割的边界信息,针对这个问题,本文提出了Mask Boundary R-CNN的实例分割框架,它包含两个评分预测分支,融合了更多图像边界的特征,重新学习并预测了掩膜的边界评分,并将两分支结果进行融合,得到的综合评分更能代表掩膜的边界质量,通过优先选择边界质量更好的掩膜来提高边界处的分割性能.在没有其他任何附加功能的情况下,Mask Boundary R-CNN在COCO2017数据集上分割精度比Mask R-CNN提升了约1.6%,尤其是在使用最新评价掩膜边界质量的指标APboundary衡量时,其边界分割精度比Mask R-CNN提升了约2%.

Analytical solutions of turbulent boundary layer beneath forward-leaning waves

As a typical nonlinear wave,forward-leaning waves can be frequently encountered in the near-shore areas,which can impact coastal sediment transport significantly.Hence,it is of significance to describe the characteristics of the boundary layer beneath forward-leaning waves accurately,especially for the turbulent boundary layer.In this work,the linearized turbulent boundary layer model with a linear turbulent viscosity coefficient is applied,and the novel expression of the near-bed orbital velocity that has been worked out by the authors for forward-leaning waves of arbitrary forward-leaning degrees is further used to specify the free stream boundary condition of the bottom boundary layer.Then,a variable transformation is found so as to make the equation of the turbulent boundary layer model be solved analytically through a modified Bessel function.Consequently,an explicit analytical solution of the turbulent boundary layer beneath forward-leaning waves is derived by means of variable separation and variable transformation.The analytical solutions of the velocity profile and bottom shear stress of the turbulent boundary layer beneath forward-leaning waves are verified by comparing the present analytical results with typical experimental data available in the previous literature.

Thermodynamics-directed bulk/grain-boundary engineering for superior electrochemical durability of Ni-rich cathode

Introducing high-valence Ta element is an essential strategy for addressing the structu ral deterioration of the Ni-rich LiNi_(1-x-y)Co_(x)Mn_(y)O_(2)(NCM)cathode,but the enlarged Li/Ni cation mixing leads to the inferior rate capability originating from the hindered Li~+migration.Note that the non-magnetic Ti~(4+)ion can suppress Li/Ni disorder by removing the magnetic frustration in the transition metal layer.However,it is still challenging to directionally design expected Ta/Ti dual-modification,resulting from the complexity of the elemental distribution and the uncertainty of in-situ formed coating compounds by introducing foreign elements.Herein,a LiTaO_3 grain boundary(GB)coating and bulk Ti-doping have been successfully achieved in LiNi_(0.834)Co_(0.11)Mn_(0.056)O_(2) cathode by thermodynamic guidance,in which the structural formation energy and interfacial binding energy are employed to predict the elemental diffusion discrepancy and thermodynamically stable coating compounds.Thanks to the coupling effect of strengthened structural/interfacial stability and improved Li~+diffusion kinetics by simultaneous bulk/GB engineering,the Ta/Ti-NCM cathode exhibits outstanding capacity retention,reaching 91.1%after 400 cycles at 1 C.This elaborate work contributes valuable insights into rational dual-modification engineering from a thermodynamic perspective for maximizing the electrochemical performances of NCM cathodes.

Influence of the boundary effect on the mechanical response test of pavement cushion under the wetting effect of silt

Through a self-developed model test system,the mechanical properties of silt and the deformation characteristics of airport runways were investigated during the period of subgrade wetting.Based on the test results,the reliability of the numerical simulation results was verified.Numerical models with different sizes were established.Under the same cushion parameter and loading width ranges,the effects of the cushion parameters and loading conditions on the mechanical responses of the cushion before and after subgrade wetting were analyzed.The results show that the internal friction angles of silt with different wetting degrees are approximately 34°.The cohesion is from 8 to 44 kPa,and the elastic modulus is from 15 to 34 MPa.Before and after subgrade wetting,the variation rates of the cushion horizontal tensile stresses with the same cushion parameters and loading width ranges are different under the influence of boundary effects.After subgrade wetting,the difference in the variation rates of the cushion horizontal tensile stresses under the same cushion parameter range decreases compared with that before subgrade wetting;however,this difference increases under the same loading width range.Before and after subgrade wetting,the influence of the boundary effect on the mechanical response evaluation of the cushion is not beneficial for optimizing the pavement design parameters.When the cushion thickness is more than 0.25 m,the influence of the boundary effect can be disregarded.

The Boundary Element Method for Ordinary State-Based Peridynamics

The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.

Towards designing high mechanical performance low-alloyed wrought magnesium alloys via grain boundary segregation strategy:A review

Low-alloyed magnesium(Mg)alloys have emerged as one of the most promising candidates for lightweight materials.However,their further application potential has been hampered by limitations such as low strength,poor plasticity at room temperature,and unsatisfactory formability.To address these challenges,grain refinement and grain structure control have been identified as crucial factors to achieving high performance in low-alloyed Mg alloys.An effective way for regulating grain structure is through grain boundary(GB)segregation.This review presents a comprehensive summary of the distribution criteria of segregated atoms and the effects of solute segregation on grain size and growth in Mg alloys.The analysis encompasses both single element segregation and multi-element co-segregation behavior,considering coherent interfaces and incoherent interfaces.Furthermore,we introduce the high mechanical performance low-alloyed wrought Mg alloys that utilize GB segregation and analyze the potential impact mechanisms through which GB segregation influences materials properties.Drawing upon these studies,we propose strategies for the design of high mechanical performance Mg alloys with desirable properties,including high strength,excellent ductility,and good formability,achieved through the implementation of GB segregation.The findings of this review contribute to advancing the understanding of grain boundary engineering in Mg alloys and provide valuable insights for future alloy design and optimization.

Quantification of grain boundary effects on the geometrically necessary dislocation density evolution and strain hardening of polycrystalline Mg-4Al using in situ tensile testing in scanning electron microscope and HR-EBSD

In situ tensile testing in a scanning electron microscope(SEM)in conjunction with high-resolution electron backscatter diffraction(HR-EBSD)under load was used to characterize the evolution of geometrically necessary dislocation(GND)densities at individual grain boundaries as a function of applied strain in a polycrystalline Mg-4Al alloy.The increase in GND density was investigated at plastic strains of 0%,0.6%,2.2%,3.3% from the area including 76 grains and correlated with(i)geometric compatibility between slip systems across grain boundaries,and(ii)plastic incompatibility.We develop expressions for the grain boundary GND density evolution as a function of plastic strain and plastic incompatibility,from which uniaxial tensile stress-strain response of polycrystalline Mg-4Al are computed and compared with experimental measurement.The findings in this study contribute to understanding the mechanisms governing the strain hardening response of single-phase polycrystalline alloys and more reliable prediction of mechanical behaviors in diverse microstructures.