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.

Urban Heat Island and Boundary Layer Structures under Hot Weather Synoptic Conditions:A Case Study of Suzhou City,China

A strong urban heat island （UHI） appeared in a hot weather episode in Suzhou City during the period from 25 July to 1 August 2007. This paper analyzes the urban heat island characteristics of Suzhou City under this hot weather episode. Both meteorological station observations and MODIS satellite observations show a strong urban heat island in this area. The maximum UHI intensity in this hot weather episode is 2.2℃, which is much greater than the summer average of 1.0℃ in this year and the 37–year （from 1970 to 2006） average of 0.35℃. The Weather Research and Forecasting （WRF） model simulation results demonstrate that the rapid urbanization processes in this area will enhance the UHI in intensity, horizontal distribution, and vertical extension. The UHI spatial distribution expands as the urban size increases. The vertical extension of UHI in the afternoon increases about 50 m higher under the year 2006 urban land cover than that under the 1986 urban land cover. The conversion from rural land use to urban land type also strengthens the local lake-land breeze circulations in this area and modifies the vertical wind speed field.

THE MESHLESS VIRTUAL BOUNDARY METHOD AND ITS APPLICATIONS TO 2D ELASTICITY PROBLEMS

A novel numerical method for eliminating the singular integral and boundary effect is processed. In the proposed method, the virtual boundaries corresponding to the numbers of the true boundary arguments are chosen to be as simple as possible. An indirect radial basis function network （IRBFN） constructed by functions resulting from the indeterminate integral is used to construct the approaching virtual source functions distributed along the virtual boundaries. By using the linear superposition method, the governing equations presented in the boundaries integral equations （BIE） can be established while the fundamental solutions to the problems are introduced. The singular value decomposition （SVD） method is used to solve the governing equations since an optimal solution in the least squares sense to the system equations is available. In addition, no elements are required, and the boundary conditions can be imposed easily because of the Kronecker delta function properties of the approaching functions. Three classical 2D elasticity problems have been examined to verify the performance of the method proposed. The results show that this method has faster convergence and higher accuracy than the conventional boundary type numerical methods.

Simulation of the seismic response of sedimentary basins with constant-gradient velocity along arbitrary direction using boundary element method:SH case

We presented a boundary element method using the approximate analytical Green＇s function given by Sanchez-Sesma et al. Coordinate transform is introduced to extend the method to deal with the model with constant-gradient velocity along oblique direction. The method is validated by comparing the numerical results with other independent methods. This method provides a useful tool for analyzing local site effects. We computed seismic response for two series of models. The results in both frequency and time domains are analyzed and show complex amplification patterns. The fundamental mode of resonance is dependent not only on the velocity at the free surface but also on the velocity distribution of the whole basin. For the higher modes of vibration the heterogeneous basin also has its own characteristic.

A Laboratory Modeling of the Velocity Field in the Convective Boundary Layer with the Particle Image Velocimetry Technique

Based on the research of the convective boundary layer (CBL) temperature field in a convective tank, this paper studies the characteristics of the CBL velocity field in the convective tank. Aluminium powder (400 orders) is used as a tracer particle in the application of the particle image velocimetry (PIV) technique. The experiment demonstrates: the velocity distribution in the mixed layer clearly possesses the characteristics of CBL thermals; the velocity distribution in the top zone of the mixed layer shows entrainment layer characteristics; the vertical distribution of turbulent characteristic variables is reasonable, which is similar to field observations and other tank results; the error analysis demonstrates the validity of aluminium powder, which implies the reliability of the results.

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.

A Laboratory Study of the Turbulent Velocity Characteristics in the Convective Boundary Layer

Based on the measurement of the velocity field in the convective boundary layer （CBL） in a convection water tank with the particle image velocimetry （PIV） technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal＇s motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity wi^2/w＊^2. at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity （w＊）.

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.

A Kinematic Thermal Model for Descending Slabs with Velocity Boundary Layers:A Case Study for the Tonga Subducting Slab

For the purpose of investigating the influence of metastable olivine（MO） phase transformations on both deep seismicity and stagnation of slabs,we constructed a 2-dimensional finite element thermal model for a 120 Ma-old 50°dipping oceanic lithosphere descending at 10 cm/yr with velocity boundary layers,which would mitigate the interference of constant velocity field for the slab. The resulting temperatures show that most of intermediate and deep earthquakes occurring within the Tonga slab are occurring inside the 800℃and 1200℃isotherm,respectively.The elevation of olivine transformation near～410 km and respective persistence of metastable olivine and spinel within the transition zone and beneath 660 km would thus result in bimodal positive,zonal,negative density anomalies,respectively.These results together with the resulting pressure anomalies may reflect the stress pattern of the Tonga slab：（i） slab pull force exerts above a depth of～230 km;（ii） MO existence changes the buoyancy force within the transition zone and facilitates slab stagnation at a depth of 660 km;（iii） as the subducting materials accumulated over 660 km,deepest earthquakes occur due to MO transformation;（iv） a flattened‘slab’ may penetrate into the lower mantle due to the density increment of Sp transformation.

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.

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.

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.

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.

Enriched Constant Elements in the Boundary Element Method for Solving 2D Acoustic Problems at Higher Frequencies

The boundary element method(BEM)is a popular method for solving acoustic wave propagation problems,especially those in exterior domains,owing to its ease in handling radiation conditions at infinity.However,BEM models must meet the requirement of 6–10 elements per wavelength,using the conventional constant,linear,or quadratic elements.Therefore,a large storage size of memory and long solution time are often needed in solving higher-frequency problems.In this work,we propose two new types of enriched elements based on conventional constant boundary elements to improve the computational efficiency of the 2D acoustic BEM.The first one uses a plane wave expansion,which can be used to model scattering problems.The second one uses a special plane wave expansion,which can be used tomodel radiation problems.Five examples are investigated to showthe advantages of the enriched elements.Compared with the conventional constant elements,the new enriched elements can deliver results with the same accuracy and in less computational time.This improvement in the computational efficiency is more evident at higher frequencies(with the nondimensional wave numbers exceeding 100).The paper concludes with the potential of our proposed enriched elements and plans for their further improvement.

Riemann–Hilbert problem for the defocusing Lakshmanan–Porsezian–Daniel equation with fully asymmetric nonzero boundary conditions

The Riemann–Hilbert approach is demonstrated to investigate the defocusing Lakshmanan–Porsezian–Daniel equation under fully asymmetric nonzero boundary conditions.In contrast to the symmetry case,this paper focuses on the branch points related to the scattering problem rather than using the Riemann surfaces.For the direct problem,we analyze the Jost solution of lax pairs and some properties of scattering matrix,including two kinds of symmetries.The inverse problem at branch points can be presented,corresponding to the associated Riemann–Hilbert.Moreover,we investigate the time evolution problem and estimate the value of solving the solutions by Jost function.For the inverse problem,we construct it as a Riemann–Hilbert problem and formulate the reconstruction formula for the defocusing Lakshmanan–Porsezian–Daniel equation.The solutions of the Riemann–Hilbert problem can be constructed by estimating the solutions.Finally,we work out the solutions under fully asymmetric nonzero boundary conditions precisely via utilizing the Sokhotski–Plemelj formula and the square of the negative column transformation with the assistance of Riemann surfaces.These results are valuable for understanding physical phenomena and developing further applications of optical problems.

Atomistic study on the microscopic mechanism of grain boundary embrittlement induced by small dense helium bubbles in iron

The helium bubbles induced by 14 MeV neutron irradiation can cause intergranular fractures in reduced activation ferritic martensitic steel,which is a candidate structural material for fusion reactors.In order to elucidate the susceptibility of different grain boundaries(GBs)to helium-induced embrittlement,the tensile fracture processes of 10 types of GBs with and without helium bubbles in body-centered cubic(bcc)iron at the relevant service temperature of 600 K were investigated via molecular dynamics methods.The results indicate that in the absence of helium bubbles,the GBs studied here can be classified into two distinct categories:brittle GBs and ductile GBs.The atomic scale analysis shows that the plastic deformation of ductile GB at high temperatures originates from complex plastic deformation mechanisms,including the Bain/Burgers path phase transition and deformation twinning,in which the Bain path phase transition is the most dominant plastic deformation mechanism.However,the presence of helium bubbles severely inhibits the plastic deformation channels of the GBs,resulting in a significant decrease in elongation at fractures.For bubble-decorated GBs,the ultimate tensile strength increases with the increase in the misorientation angle.Interestingly,the coherent twin boundary∑3{112}was found to maintain relatively high fracture strength and maximum failure strain under the influence of helium bubbles.

THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY

We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.

Dynamics of fundamental and double-pole breathers and solitons for a nonlinear Schrodinger equation with sextic operator under non-zero boundary conditions

We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.