This paper presents a steady-state and transient heat conduction analysis framework using the polygonal scaled boundary finite element method (PSBFEM) with polygon/quadtree meshes. The PSBFEM is implemented with commercial finite element code Abaqus by the User Element Subroutine (UEL) feature. The detailed implementation of the framework, defining the UEL element, and solving the stiffness/mass matrix by the eigenvalue decomposition are presented. Several benchmark problems from heat conduction are solved to validate the proposed implementation. Results show that the PSBFEM is reliable and accurate for solving heat conduction problems. Not only can the proposed implementation help engineering practitioners analyze the heat conduction problem using polygonal mesh in Abaqus, but it also provides a reference for developing the UEL to solve other problems using the scaled boundary finite element method.

A computational methodology for the hydrodynamic analysis of horizontal axis marine current turbines is presented. The approach is based on a boundary integral equation method for inviscid flows originally developed for marine propellers and adapted here to describe the flow features that characterize hydrokinetic turbines. To this purpose, semi-analytical trailing wake and viscous-flow correction models are introduced. A validation study is performed by comparing hydrodynamic performance predictions with two experimental test cases and with results from other numerical models in the literature. The capability of the proposed methodology to correctly describe turbine thrust and power over a wide range of operating conditions is discussed. Viscosity effects associated to blade flow separation and stall are taken into account and predicted thrust and power are comparable with results of blade element methods that are largely used in the design of marine current turbines. The accuracy of numerical predictions tend to reduce in cases where turbine blades operate in off-design conditions.

This study aimed to establish and verify the validity of an acoustic simulation method during sustained phonation of the Japanese vowels /i/ and /u/. The study participants were six healthy adults. First, vocal tract models were constructed based on computed tomography (CT) data, such as the range from the frontal sinus to the glottis, during sustained phonation of /i/ and /u/. Next, cylindrical shapes virtually extended by 12 cm were added to the vocal tract models to imitate the trachea between the tracheal bifurcation and lower part of the glottis. The Kirchhoff–Helmholtz integral equation was formulated as the wave equation for sound propagation, and the boundary element method was used for discretization. As a result, the relative discrimination thresholds of the vowel formant frequencies for /i/ and /u/ against actual voice were 1.1%–10.2% and 0.4%–9.3% for the first formant and 3.9%–7.5% and 5.0%–12.5% for second formant, respectively. In the vocal tract model with nasal coupling, a pole–zero pair was observed at around 500 Hz, and for both /i/ and /u/, a pole–zero pair was observed at around 1000 Hz regardless of the presence or absence of nasal coupling. These findings demonstrated that /i/ and /u/ could be simulated with high validity in a vocal tract model constructed from CT data obtained during sustained phonation using the boundary element method.

This paper introduces an innovative approach to numerically model Structure-Soil-Structure Interaction (SSSI) by integrating the Boundary Element Method (BEM) and the Finite Element Method (FEM) in a coupled manner. To assess the accuracy of the proposed method, a comparative study is undertaken, comparing its outcomes with those generated by the conventional FEM technique. Alongside accuracy, the computational efficiency aspect is crucial for the analysis of large-scale SSSI problems. Hence, the computational performance of the coupled BEM-FEM method undergoes a thorough examination and is compared with that of the standalone FEM method. The results from these comparisons illustrate the superior capabilities of the proposed method in comparison to the FEM method. The novel approach provides more reliable results compared to traditional FEM methods, serving as a valuable tool for engineers and researchers involved in structural analysis and design.

Permeability is a fundamental property of porous media, especially when studying resin transfer within a dense fibrous medium to manufacture composite materials. When the measurement of permeability tensor of composite reinforcements is difficult and time consuming, especially in thick, heterogeneous fibrous structures, a numerical approach based on the calculation of the tensor components on a 3D image of the material can be very advantageous. A new finite element based method proposed in this study allows solving very high-dimensional flow problems while limiting the biases associated with boundary conditions and the small size of the numerical samples addressed. The method is validated against academic test cases and against the results of a recent permeability benchmark exercise. The results emphasize that for heterogeneous and anisotropic microstructures, it is important to perform calculations on large samples using boundary conditions that do not suppress the transverse flows that occur when flow is forced out of the principal directions. Since these are not necessarily known in complex media, the permeability determination method must not introduce bias by generating non-physical flows.

This study investigates the solution of a boundary value problem using two numerical methods: the Rayleigh-Ritz method and the finite element method (FEM). The aim is to compare the performance of these methods and assess the reliability of FEM as a generalization of the Rayleigh-Ritz approach for more complex problems. The Rayleigh-Ritz method and the linear element formulation of the finite element method were employed to solve the boundary value problem. A detailed comparison of the results obtained from both methods was performed. Graphical illustrations were used to present the solutions, and potential sources of error were analyzed, including element and domain approximation errors, round-off errors, and the impact of using linear rather than quadratic elements in FEM. The solutions generated by both methods were found to be in close agreement, demonstrating that FEM is a viable alternative to the Rayleigh-Ritz method for solving boundary value problems. The minor discrepancies observed can be attributed to approximation errors and the choice of linear elements in the finite element analysis. This work highlights the applicability and effectiveness of both the Rayleigh-Ritz method and FEM in solving boundary value problems. It underscores the finite element method’s flexibility, especially in handling more complex boundary conditions and geometries, and contributes to the understanding of the factors influencing the accuracy of numerical methods in structural analysis.

Due to the numerous heat sources in electronic equipment, the periodic nature of stream-wise flow occurs in a cooling channel so often, necessitating the development of an effective technique to improve the heat-cooling convection in such a situation. This paper investigates thermal convection enhancement in a heated-block duct through the periodic boundary conditions using the element-by-element (EBE) treatment in a semi-implicit projection finite element method (FEM) through preconditioned conjugate gradient (PCG) solver. This paper used the time-mean Nusselt number ratio, friction factor, and thermal performance to study how installing rectangular cylinders in the channel works with periodic boundary conditions varying Reynolds numbers (100, 175, and 250). The outcomes show that the rectangular cylinders installed stream-wise above an upstream block promote thermal convection in the heated-block duct. However, increasing the number of rectangular cylinders can raise friction factor. As a result, the case for periodic boundary conditions with a rectangular cylinder above every two blocks has the best thermal performance.

The present study aims to develop an efficient numerical method for computing the diffraction and radiation of water waves with horizontal long cylindrical structures, such as floating breakwaters. A higher-order scheme is used to discretize geometry of the structure as well as the relevant physical quantities. As the kernel of this method, Wehausen’s free-surface Green function is calculated by a newly-developed Gauss-Kronrod adaptive quadrature algorithm after elimination of its Cauchy-type singularities. To improve computational efficiency, a Chebyshev approximation approach is applied to a fast calculation of the Green function that needs evaluation thousands of times. In addition, OpenMP parallel technique is used to the formation of influence coefficient matrix, which significantly reduces CPU time. Finally, computations are performed on wave exciting forces and hydrodynamic coefficients for the long cylindrical structures, either floating or submerged. Comparison with other numerical and analytical methods demonstrates good performance of the present method.

The magnetic polarization tensor has a promising capability of determining the geometry and material properties of metallic samples. In this paper, a novel computation method is proposed to estimate the magnetic polarization tensors for the metallic samples using the boundary element method. In this method, the metallic sample is placed in a uniformly distributed magnetic field. Based on assumptions that the excitation frequency and/or the conductivity of the sample is very high, the metallic sample is regarded as a perfect electrical conductor (PEC). Therefore, the scattered field at a certain distance can be simulated. By utilising the boundary element method, the magnetic polarization tensor can be derived from the simulated scattered field. The theoretical calculation is presented and simulations and experiments have been carried out to validate the proposed method. The results from the simulation are matched with the analytical solution for the case of sphere samples. Moreover, there is a good agreement between the simulation results and the experimental results for the copper cylindrical samples.

The paper describes the Field Boundary Element Method applied to the fracture analysis of a 2D rectangular plate made of Functionally Graded Material to calculate Mode I Stress Intensity Factor. The object of the Field Boundary Element Method is the transversely isotropic plane plate. Its material presents an exponential variation of the elasticity tensor depending on a scalar function of position, i.e., the elastic tensor results from multiplying a scalar function by a constant taken as a reference. Several examples using a parametric representation of the structural response show the suitability of the method that constitutes a sight of Stress Intensity Factor evaluation of Functionally Graded Materials plane plates even in the case of more complex geometries.

Nonlocal theories are gaining prominence because they can solve problems which lead to unphysical conclusions in standard models. This study presents a novel fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. This broad BEM solution combines two solutions: anisotropic fibrous polymer nanomaterials problem solution and nonlinear nonlocal thermoelasticity problem solution. The nonlinear nonlocal thermoelasticity problem solution divides the displacement field into complementary component and particular component. The overall displacement is generated using the boundary element technique, which is the solution to a Navier type problem, while the particular displacement is derived using local radial point. The New Modified Shift-Splitting (NMSS) approach, which reduces memory and processing time requirements, was used to solve linear systems created by BEM. Figures demonstrate the numerical findings, which show the effects of fractional and graded parameters on the thermal stresses of nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. The numerical results indicate the consistency and efficiency of the proposed methodology.

The main goal of this work is to develop a novel boundary element method (BEM) model for analyzing ultrasonic wave propaga-tion in three-temperature anisotropic viscoelastic porous media. Because of strong nonlinearity of ultrasonic wave propagation in three-temperature porous media problems, the analytical or numerical solutions to the problems under consideration are always challenging, necessitating the development of new computational techniques. As a result, we use a new BEM model to solve such problems. A time stepping procedure based on the linear multistep method is obtained after solving the discretized boundary in-tegral equation with the quadrature rule. The calculation of a double integral is required to obtain fundamental solutions, but this increases the total BEM computation time. Our proposed BEM technique is used to solve the current problem and improve the formulation efficiency. The numerical results are graphed to demonstrate the effects of viscosity and anisotropy on the nonlinear ultrasonic stress waves in three-temperature porous media. The validity, accuracy, and efficiency in the proposed methodology were demonstrated by comparing obtained results to the corresponding solution obtained from finite difference method (FDM).

Traditional numerical techniques such as sliding mesh, dynamic grid mesh, and others, have many limitations in dealing with flow simulation with large-scale movement of solid boundaries; which is the case for complex-shaped hydraulic turbomachinery such as propellers, pumps and turbines. The immersed boundary (IB) method provides a new approach to solve the above limitations. Therefore, this study proposes an sharp-interface IB method based on the level-set function that is suitable for simulating the flow through turbomachinery with complex geometries. This method is applied to actual three-dimensional numerical simulations of high-Reynolds number propellers using an in-house computational fluid dynamics solver. The results show that the proposed method can provide comparatively accurate predictions of unsteady load coefficients within the propeller flow passage, and capture the correct propeller wake characteristics as well as the interaction between the propeller wake and free surface. This study aims at providing a theoretical basis and engineering reference for the application of the IB method in engineering numerical simulations.

In this paper, we propose an efficient numerical method to solve the diffusive logistic model with a free boundary which is often used to simulate the spreading of the new or invasive species. The boundary movement is tracked by the level-set method, where the Hamilton-Jacobi weighted essentially nonoscillatory (HJ-WENO) scheme is utilized to capture the boundary curve embedded by the Cartesian grids via the embedded boundary method. Then the radial basis function-finite difference (RBF-FD) method is adopted to the spatial discretization and the IMEX scheme is considered for time integration. A variety of numerical examples are carried out to demonstrate the evolution of diffusive logistic model in different initial boundaries.

This paper introduces a new adaptation of the enthalpic lattice Boltzmann method (LBM) tailored to simulate the intricate dynamics of conjugate heat transfer in non-homogeneous media, showcasing considerable potential for enhancing heat exchanger designs. This approach expands upon the conventional enthalpic LBM framework by seamlessly incorporating tailored source terms, enabling precise representation of local and transient variations in the medium’s thermophysical properties. The resulting LBM model comprehensively captures the energy conservation equation, with exceptions made only for flow compressibility and viscous dissipation, thereby significantly augmenting its versatility in analyzing heat exchanger configurations. Verification tests, comprising assessments of both transient and steady-state solutions, unequivocally validate the accuracy of the proposed model, further bolstering its reliability for analyzing heat exchange processes within intricate heat exchanger geometries. To demonstrate its efficacy, simulations of conjugate heat transfer processes involving fluid natural convection within structured cavities were performed, imposing both Dirichlet and Neumann boundary conditions to emulate scenarios encountered in practical heat exchanger operations. The findings yield compelling insights, particularly in the transient regime, revealing the beneficial impact of structured cavities on enhancing heat transfer processes. These insights inform potential design optimizations for heat exchangers. The results emphasize the potential of the modified enthalpic LBM approach to elucidate complex heat transfer phenomena in non-homogeneous media and structured geometries, offering valuable implications for heat exchanger engineering and optimization.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.

With permafrost degenerating caused by climate change, water accumulation increases in permafrost regions during last decades. Water accumulation will deteriorate existing status of engineering in cold regions. Water accumulation can make a thermal effect on permafrost under construction, even result in failure of the subgrade. Moreover, the thermal effect is related to water temperature. However, temperature variation of water accumulation is complex, and its influence factors include air temperature, environment, scope of water accumulation and so on. In order to make analysis of the damage mechanism of water accumulation on permafrost, it is necessary to explore the internal temperature change of water accumulation. This paper proposes a review about temperature calculation method of water accumulation in cold environment. The thermal calculation method between air and water boundary of water accumulation is summarized. Water temperature change of water accumulation with various type is analyzed. The thermal calculation considering phase transformation in water accumulation is discussed, and heat transfer from the bottom of water accumulation to the underlying soil is further studied. Finally, the key factors which are advantageous to make research about the thermal effect of water accumulation in permafrost is proposed to optimize calculation method.

Ship wave is of great interest for wave drag, coastal erosion and ship detection. In this paper, a highly-paralleled numerical scheme is proposed for simulating three-dimensional (3-D) nonlinear Kelvin ship waves effectively. First, a numerical model for nonlinear ship waves is established based on potential flow theory, boundary integral method and Jacobian-free Newton-Krylov (JFNK) method. In order to improve computational efficiency and reduce data storage of JFNK method, a banded preconditioner method is then developed by formulating the optimal bandwidth selection rule. After that, a Graphics Process Unit (GPU) based parallel computing framework is designed, and a GPU solver is developed by using Compute Unified Device Architecture (CUDA) language. Finally, numerical simulations of 3-D nonlinear ship waves under multiple scales are performed by using the GPU and CPU solvers. Simulation results show that the proposed GPU solver is more efficient than the CPU solver with the same accuracy. More than 66% GPU memory can be saved and the computational speed can be accelerated up to 20 times. Hence, the computation time for Kelvin ship waves simulation can be significantly reduced by applying the GPU parallel numerical scheme, which lays a solid foundation for practical ocean engineering.

With the growth of air traffic demand in busy airspace, there is an urgent need for airspace sectorization to increase air traffic throughput and ease the pressure on controllers. The purpose of this paper is to develop a method framework that can perform airspace sectorization automatically, reasonably, which can be used as an advisory tool for controllers as an automatic system, especially for eliminating irregular sector shapes generated by simulated annealing algorithm (SAA) based on region growth method. Two graph cutting method, dynamic Monte Carlo method by changing location of flexible vertices (MC-CLFV) and Monte Carlo method by radius changing (MC-RC) were developed to eliminating irregular sector shapes generated by SAA in post-processing. The experimental results show that the proposed method framework of AS can automatically and reasonably generate sector design schemes that meet the design criteria. Our methodology framework and software can provide assistant design and analysis tools for airspace planners to design airspace, improve the reliability and efficiency of airspace design, and reduce the burden of airspace planners. In addition, this lays the foundation for reconstructing airspace with more intelligent method.

This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context the numerical test is illustrated by two examples where we find meaningful numerical results.

The boundary layer height (BLH) distinguishes the interface between the lower and free atmosphere, which is a key variable in numerical simulation, aerosol, and environmental pollution studies. Thus, the goal of this work is to propose a novel method conjuncting with numerical regularization to analyze climate characteristics of the marine boundary layer height (MBLH) using 2007-2011 GPS-RO data from the COSMIC mission. While traditionally, the difference method has been used to achieve this aim, herein, we propose an innovative method, in which the bending angle profile gradient was calculated using the numerical regulation method where the regulation parameters are determined by the double-parameter model function method. Then, the MBLH was determined by employing the maximum gradient method to ascertain the height corresponding to the smallest gradient. The results show a correlation between currents and the MBLH—a relationship that has not been previously demonstrated. A low MBLH is associated with seasons and regions where cold ocean currents are prevailing; whereas a high MBLH is observed in the seasons and places where warm currents are prevailing. This correlation was validated by comparing the obtained results with different occultation data—i.e., atmprf and echprf—which also established that atmprf is more sensitive to convective cloud top capture. In seas with active convection, the armprf calculated bending angle is higher than that from echprf. Subsequently, the standard deviation was used to express the MBLH confidence level. The results show that the MBLH standard deviation is highest in low latitudes and lowest in the middle and high latitudes. Furthermore, we analyzed the interannual MBLH variation trend, which displayed a seasonal variation and spatial distribution corresponding with the current and subsolar point. Finally, we conducted a case study in the South China Sea, and identified a distinctive seasonal change and downward trend.

The development of computational acoustics allows simulation of sound generation and propagation in complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, smoothed particle hydrodynamics (SPH) method reduce the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve accuracy in solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. Main computational parameters are discussed, and different boundary conditions are validated to be effective for benchmark problems in computational acoustics.

In this paper, existence and stability results of non-local integro-differential equation with Hilfer derivative of order ω∈(1,2) have been investigated. In this derivative is applied in RLC circuit equation of various fractional order. To proposed problem the existence solutions are derived using Schaefer’s fixed point theorem and the Banach contraction principle is using for uniqueness results. To demonstrate the effectiveness and applicability of our theoretical conclusions and two-step Lagrange polynomial interpolation were used to solve four numerical results.

Cavitation bubbles are commonly existing in shipbuilding engineering, ocean engineering, mechanical engineering, chemical industry, and aerospace. Asymmetric deformation of bubble occurs near the boundary, and the non-spherical cavitation bubbles have strong destructive effects, inducing high amplitude loading at the nearby boundary. The purpose of this paper is to investigate the laser-induced of cavitation bubble, non-spherical collapse behavior near the boundary. In this study, experimental data such as bubble pulsation process and bubble surface velocity distribution were obtained by high-speed camera technique and full-field velocity calculation. The results show that the bubble appeared non-spherical collapse shapes, near different boundaries, with near-hemispherical, near-ellipsoidal, near-cone and near-pea shapes, and the bubble surface velocity distribution is not uniform. When bubble near the free surface or rigid boundary, the smaller the stand-off r is, the more obvious the repulsive effect of the free surface and the attractive effect of the rigid boundary are. As the stand-off r decreases, the larger the Bjerknes force and the bubble surface velocity difference, the more pronounced the non-spherical shape.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

The aim of this paper is the analysis of arbitrarily loaded isotropic rectangular Kirchhoff plates supported at all corner points, whereby the edges are arbitrarily supported (simply supported, clamped, or free). Analytical methods commonly used include the single trigonometric series of Lévy, the double trigonometric series of Navier, the power series expansions, etc. In this paper the deflection surface was approximated with the sum of a particular solution to the governing differential equation (GDE) and two single series. The terms of the single series were the product of an unknown function of an independent variable and a trigonometric function of the other independent variable, whereby the trigonometric functions were chosen to vanish at the corner points. On the one hand the terms of the series were required to satisfy the homogeneous GDE, leading to two uncoupled differential equations, one for each unknown function, and so the approximate solution satisfied exactly the GDE. On the other hand the boundary conditions were satisfied only at selected collocation points along the boundary, the number of collocation points in each direction corresponding to the number of terms of the associated series. Results for several plates supported at all corner points with arbitrary edge support conditions were presented and showed good agreement with the exact results, the accuracy increasing the more terms of series were considered. Cantilevered plates and plates having two adjacent edges free will be analyzed using this approach in future research.

The exact similarity solutions (also called as special exact solutions) of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, no similarity solutions for two dimensional turbulent boundary layers have been reported in the literature. With the help of dimensional analysis and invariance principle, Prandtl mixing length $\ell=\kappa y$ for one dimensional turbulent boundary layer is extended to $\ell(x,y)=\kappa y (1-\frac{y}{\delta})\sqrt{\frac{\nu}{U\delta}} $ for the two dimensional turbulent boundary layers, furthermore, with a similarity transformation, we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation $f'''+ ff''+\beta(1-f'^2)+\kappa^2[\eta^2(1-\eta)^2f''|f''|]'=0$. As an application, similarity solutions of the two dimensional turbulent boundary layer on a flat plate at zero incidence have been studied in detail. To solve the ordinary differential equation numerically, a complete Maple code is provided.

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no similarity solutions (special exact solutions) have ever been found. In the light of Blasius' pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. By author's Maple code, we numerically solve the ordinary differential equation and produce some useful quantities.

This brief review introduces some general properties of lower atmospheric motions that may be exploited by birds, linking historical findings and current knowledge from both observational and modeling perspectives. The relative importance of turbulent mixing resulting from wind shear and that from buoyant thermals is emphasized as well as the determinants of the geometry of the resulting vertical motions.

The synchronization of complex networks is believed to be closely related to network topology. How to study synchronization of real network without clear topology and parameters? In this Letter, a synchronized stability boundary equation is derived that is system- and disturbance-independent and applicable to arbitrarily coupled grids. The results imply that spontaneous synchronization in a network may be network independent. These conclusions provide new research paths for network synchronization and analyze the synchronization stability of grids in a unified way.

This research has critically argued that a vigilant combination of flexibility and certainty in spatial planning can bring about the most optimum planning outcomes. Therefore, to reproachfully evaluate the core argument, this research has tried to empirically respond to the research question of which balance of government intervention and market freedom produces the optimal economic, social and spatial outcomes. This research question has been further translated into an associated central hypothesis i.e., a hybrid planning system with an optimal balance between discretionary and regulatory planning approach can bring about the desired economic, social, and spatial outcomes.

In this paper, a further mathematical analysis of some previous results of the author’s ongoing investigation regarding Prandtl’s equations is accomplished. In particular, the objective of the present work is the performance of an approximate explicit solution to Prandtl’s system of equations for a laminar, isothermal, incompressible and steady boundary layer flow of a Newtonian fluid, over an infinite horizontal flat plate.

Ventilation in cities is crucial for the well being of their inhabitants. Therefore, local governments require air ventilation assessments (AVAs) prior to the construction of new buildings. In a standard AVA, however, only neutral stratification is considered, although diabatic and particularly unstable conditions may be observed more frequently in nature. The results presented here indicate significant changes in ventilation within most of the area of Kowloon City, Hong Kong, included in the study. A new definition for calculating ventilation was introduced, and used to compare the influence of buildings on ventilation under conditions of neutral and unstable stratification. The overall ventilation increased due to enhanced vertical mixing. In the vicinity of exposed buildings, however, ventilation was weaker for unstable stratification than for neutral stratification. The influence on ventilation by building parameters, such as the plan area index, was altered when unstable stratification was considered. Consequently, differences in stratification were shown to have marked effects on ventilation estimates, which should be taken into consideration in future AVAs.

Pollution spillover is an important issue to improve the water environment of transboundary rivers, which has been aggravated by the decentralization of China's pollution control and promotion system.This paper analyzes the evolution of the pollution reduction mandates and the possible change of water environment in China which are tested with the water quality data of state key monitoring sections in 2004-2014 .In terms of research methods, this paper mainly uses Propensity Score Matching reference with group difference test and OLS. Empirical findings support the association between decentralization and pollution levels. The pollution levels of the monitoring points located at the boundary are significantly higher than that of interior counties. The pollution of tributary is more serious than trunk stream，which quickly reversed after the system changed. Water pollution levels rapidly changes when we compare the monitoring site in front of jurisdictional boundaries with that after the jurisdictional boundaries. We draw the following conclusions that local goverments may manipulate pollution within their jurisdictions and total pollutant control system will exacerbate border pollution, while water quality inspection can reduce marginal pollution.

Brittle fracture of iron and steel above twinning temperatures are caused by cementite grain boundary wall cracks. These were revealed by an Atomic Force Microscope. At temperatures below the Ductile-Brittle Transition, cracks must propagate longitudinally within the cementite walls until the stress is sufficient high for the cracks to propagate across ferrite grains. Calculations using these concepts correctly predict the stress and temperature at the Ductile-Brittle Transition required for fracture to occur. At temperatures above the Ductile-Brittle Transition for hypoeutectoid ferritic steels, dislocations must fracture these walls transversely for plastic deformation to continue. This is responsible for the upper yield point at the elastic limit in these steels followed by a large drop in stress to the lower yield point. Here the walls surround completely all of the grains. Where the walls are segmented such as in iron, dislocations can pass around the walls resulting in a gradual change from elastic to plastic deformation. The Cottrell atmosphere theory of yielding is not supported experimentally. It was the best available until later experiments including those using the Atomic Force Microscope were obtained. Methods are presented here giving yield strength versus temperature and also the parameters for the Hall-Petch and Griffith equations.

With the development of Internet, big data and artificial intelligence technology, personal information protection has become the focus of social attention. The legal boundary of data protection has become increasingly prominent, involving the collection, storage, use, transmission and disclosure of personal information. This paper aims to explore the legal boundary of data protection, analyze the legal basis, legal principles and legal provisions of personal information protection, and put forward corresponding legal suggestions, in order to provide reference for the improvement of China's data protection legal system.

Since the discovery of graphene, due to its excellent optical, thermal, mechanical and electrical properties, it has a broad application prospect in energy, materials, biomedicine, electromagnetism and other fields. A great quantity of researches on the physical mechanism of graphene has been applied to engineering in electromagnetism and optics. To study the properties of graphene, different kinds of numerical methods have been developed for simulating the electromagnetic field effects of graphene, and equivalent boundary conditions have been employed to replace graphene in the computational domain. In this work, the numerical methods with equivalent boundary conditions are reviewed, and some examples are provided to illustrate their applicability.

In a series of recent works the relevance of gravitational boundary degrees of freedom and their dynamics in gravity quantization and black hole information has been explored. In this work we further the progress by keenly focusing on the boundary degrees of freedom as the origin of black hole entropy. Wald's entropy formula is scrutinized, and the reason that the Wald's formula correctly captures the entropy of a black hole is examined. Afterwards, limitations of the Wald's method are discussed; a coherent view of entropy based on boundary dynamics is presented. The discrepancy observed in the literature between holographic and Wald's entropies is addressed. We generalize the entropy definition so as to handle a time-dependent black hole. Large gauge symmetry plays a pivotal role. Non-Dirichlet boundary conditions and gravitational analogues of Coleman-De Luccia bounce solutions are central in identifying the microstates and differentiating the origins of entropies associated with different classes of solutions. The result in the present work leads to a view that black hole entropy is entanglement entropy in a thermodynamic setup.

Considerable efforts have been devoted to modifying gravity, which aim to elucidate the possible existence or nature of dark matter and dark energy, achieve a better description of observation data, verify theoretical restrictions in the strong curvature regime and to formulate quantum gravity. In addition, despite the enormous success of the quantum field theory, the framework requires the so-called renormalization techniques and breaks down at high energies. Recently, the Planck Legacy 2018 release has confirmed the presence of an enhanced lensing amplitude in the cosmic microwave background power spectra, which prefers a positively curved early Universe with a confidence level greater than 99%. This study considers the implied positive curvature of the early Universe as the curvature of ‘the background or the 4D conformal bulk’ and distinguishes it from the localized curvature that is induced into the bulk by the presence of comparably smaller celestial objects that are regarded as ‘4D relativistic cloud-worlds’. To consider the interaction between the bulk and cloud-worlds, this paper presents interaction field equations in terms of the brane-world modified gravity counting for the bulk conformal curvature and the boundary terms, which could remove the singularities and satisfy a conformal invariance theory. Similarly, the quantum fields and clouds are regarded as ‘4D relativistic branes’ embedded in vacuum energy of a field strength reliant on the background curvature due to gravity. A visualization of the evolution of the 4D relativistic cloud-worlds over the conformal space-time of the 4D bulk is presented.

Phase transitions- both in the classical and in the quantum version- are the perfect playground for appreciating universality at work. Indeed, the fine details become unimportant and a classification in very few universality classes is possible. Very recently, a striking deviation from this picture has been discovered: some antiferromagnetic spin chains with competing interactions show a different set of phase transitions depending on the parity of number of spins in the chain. The aim of this article is to demonstrate that the same behavior also characterizes the most simple quantum spin chain: the Ising model in a transverse field. By means of an exact solution based on a Wigner-Jordan transformation, we show that a first order quantum phase transition appears at zero applied field in the odd spin case, while it is not present in the even case. A hint of a possible physical interpretation is given by the combination of two fact: at the point of the phase transition, the degeneracy of the ground state in the even and the odd case substantially differ, being respectively 2 and 2N, with N the number of spins; the spin of the most favorable kink states changes at that point.

An explanation of aerodynamic lift still is under controversial discussion as can be seen, for example, in a recent published article in Scientific American [1]. In contrast to an approach via integral conservation laws we here review an approach via the classical Kutta-Condition and its relation to boundary layer theory. Thereby we summarize known results for viscous correction to the lift coefficient for thin aerodynamic profiles and try to remember the work on triple-deck or higher order Boundary Layer theory, its connection to interactive boundary layer theory, viscous/inviscid coupling as implemented to well-known engineering code Xfoil. Finally we compare its findings to simple 2D numerical solution of full Navier Stokes equations (CFD)models. As a conclusion, a clearer definition of terms like understanding and explanation applied to the phenomenon of aerodynamic lift will be given.

The paper describes problems with the current additive manufacturing chain before considering additive manufacturing as part of a modern manufacturing chain. Additive manufacturing can be used for near net-shape for finishing, for repair or for adding special features which cannot be made with traditional manufacturing. This paper describes how STEP-NC deals with these different scenarios in terms of accuracy, multi-material and variation of slice direction. The possibilities of multi-material objects also raises questions about the design of such objects and how these need to be handled by an advanced controller. The paper also describes non-planar slicing. Curved direction and cylindrical direction are shown to improve the accuracy of curved structure additive manufacturing. STEP-NC using boundary representation has better capability of depicting complex internal structures for additive processes. By using exact model of the final product represented by STEP-NC, the paper demonstrates improvements in data size reduction, slicing accuracy, and precise manipulation of internal structure.

In this paper, we introduce a simple yet powerful and working version of the molecular dynamics code using the Python 3.9 language. The code contents are published in the link given in the appendix 1. The structure and components of the program is given in detail using flowcharts and code snippets. The program consists of major features like velocity verlet integrator, thermostats, COM removal, input and output modules, virial, pressure, and other thermodynamic quantities estimation etc. The author believes that this program will be helpful to graduate students who perform research in molecular dynamics simulations who intend to write their own code instead of the sophisticated open source packages.

Knowledge about laminar-turbulent transition on operating multi-megawatt wind turbine blades needs sophisticated equipment like hot-films or microphone arrays. Contrarily thermographic pictures can easily be taken from the ground and temperature differences indicate different states of the boundary layer. The accuracy however, still is an open question, so that an aerodynamic glove known from experimental research on aero-planes was used to classify the boundary-layer state of a 2 megawatt wind turbine blade operating in the orthern part of Schleswig-Holstein, Germany. State-of-the-art equipment for measurering static surface pressure was used for monitoring the lift distribution. To distinguish laminar and turbulent parts of the boundary layer (suction side only) 48 microphones were applied together with ground-based thermographic cameras from two teams. Additionally, an optical camera mounted on the hub was used to survey vibrations. During start-up (from 0 to 9 rpm) extended, but irregularly shaped regions of a laminar boundary layer were observed which had the same extension measured both with microphones and Thermography. When an approximately constant rotor rotation (9 rpm corresponding to approximately 6 m/s wind-speed) was achieved, a flow transition was visible at the expected position of 40 % chord length on the rotor blade, which was fouled with dense turbulent wedges and an almost complete turbulent state on the glove was detected. In all observations, quantitative determination of the flow transition positions from thermography and microphones agree well within their accuracy.

The behavior of convective boundary conditions is studied to delineate their role in heat and mass relegation in the presence of radiation, chemical reaction, and hydromagnetic forces in three-dimensional Powell-Eyring nanofluids. Implications concerning non-Fourier’s heat flux and non-Fick’s mass flux with respect to temperature nanoparticle concentration were examined to discuss the graphical attributes of the principal parameters. An efficient optimal homotopy analysis method is used to solve the transformed partial differential equations. Tables and graphs are physically interpreted for significant parameters

Effects of oxygen content on microstructure and creep property of FGH96 superalloy were investigated. When oxygen content increased from 135ppm to 341ppm, prior particle boundary (PPB) rose from degree 2 to degree 3, and the size of γ′ phase on PPB enlarged from 1.07μm to 1.27μm, and MC carbide size grew from 77.4nm to 104.0nm. Meanwhile, the steady creep rate accelerated form 4.34×10-3 h-1 to 1.87×10-2 h-1, and the creep rupture life shortened from 176h to 94h, and the creep rupture mode transferred from intergranular and transgranular mixed fracture to along PPB fracture. During creep, the micro-twins formation and gliding will be restrained by ∑3 boundaries. FGH96 superalloy with higher oxygen content contains less ∑3 boundaries and its micro-twins cross slipped instead of single direction slip in lower oxygen content superalloy. Consequently, specimen with higher oxygen content creeped faster and raptured earlier.

Monge-Ampere equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge-Ampere equations with two parameters is investigated based on Guo-Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our main results.

The flow around thick airfoils at low Reynolds numbers and the possibility of using energy methods to control flowfield, increase lift and reduce drag are considered. For calculations, a series of propulsion airfoils is used, obtained by a combination of solving the inverse problem of aerodynamics and stochastic methods of global optimization. The calculations take into account the transition from the laminar flow regime to the turbulent one, which has a significant effect on the lift and airfoil drag. The applicability of various turbulence models for airfoil modelling at low Reynolds numbers is discussed. The results of numerical simulation make it possible to determine the dependence of the lift coefficient on the angle of attack and the optimal flow rate of air taken from the airfoil surface for each angle of attack. The results of numerical simulation are compared with the data of a physical experiment, and conclusions are drawn about the accuracy of various turbulence models.

As an important means of controlling the spread of cities, large-scale urban green belts have been widely used in the planning and construction of green space systems in various mega-size cities around the world. In previous studies, there has been more research on the overall isolation effect of green belts, while there has been less research on changes in their internal structure. There have been more perspectives on the land-use change (LUC) caused by urban expansion, and less systematic research on the dual driving factors of LUC. In this paper, we constructed a multi-dimensional index system to measure the "contraction-expansion" mechanism of land use in the overlapping vegetation areas of large green belts under the dual influence of urban expansion and urban greening, from the perspectives of quantity, space, and connectivity during different construction periods. Taking the boundary of two green belts in Beijing as an example, we hope to provide scientific support for the construction and ecological protection of Beijing's green belts.

Nonparametric density estimation for nonnegative data is considered in a situation where a random sample is not directly available but the data are instead observed from the length-biased sampling. Due to the boundary bias problem of the location-scale kernel, the approach in this paper is an application of asymmetric kernel. Two nonparametric density estimators are proposed. The mean integrated squared error, strong consistency, and asymptotic normality of the estimators are investigated. Some simulations illustrate the finite sample performance of the estimators.

We study the existence of positive solutions for a system of Hadamard fractional differential equations on an infinite interval with nonnegative nonlinearities, subject to coupled nonlocal boundary conditions which contain Hadamard fractional derivatives and Riemann-Stieltjes integrals. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem.

This paper proposes a data-driven approach to the calculation of ship overtaking boundary conditions in narrow channels based on ship overtaking characteristics by the Automatic Identification System (AIS) data. First, we collect the ship tracking process data in a narrow channel by processing the original AIS data, followed by a normality test and correlation analysis, and finally, the boundary conditions are obtained using a weighted K-means clustering algorithm. to identify the relevant data. We applied the proposed approach to estimate the overtaking boundary conditions of ships in the straight channel section of Shanghai South Passage. The method yields boundary conditions that significantly reduce collision risk when a ship engages in pursuit behavior in narrow waterways, providing a scientific basis for the overtaking of Marine Autonomous Surface Ships (MASS) in autonomous navigation within such environments, further promoting the automation level of USVs and autonomous vessels.

The perception in pair trading is to recognize two stocks that move together, and their prices will converge to a mean value in future. However, finding the mean-reverted point at which the value of the pair will converge, and optimal boundaries of the trade is not easy. As uncertainty and model misspecifications may lead to losses. To cater for the problems, this study employs the novel entropic approach that utilizes entropy as penalty function for the misspecification of the model. The use of entropy as a measure of risk in pair trading is a nascent idea and this study utilizes daily data for 64 companies listed on PSX for the years 2017, 2018, and 2019, respectively to compute the returns based on the entropic approach. These companies cover the major sectors including Cement, Chemical, Automobile Assembler, Food and Personal Care Products, Oil and Gas Marketing Companies, Oil and Gas Exploration Companies Ltd, Power Generation and Distribution, Refinery and Pharmaceuticals. The returns to these stocks are then evaluated and compared with the Buy and Hold strategy. The results show positive and significant returns from pair trading using an entropic approach.

A century-old scientific conundrum is solved in this paper. The Prandtl mixing length modelled plane boundary turbulent flow is described by: $\frac{du^+}{d{y^+} }+\kappa^2{y^+} ^2\left( \frac{du^+}{d{y^+} }\right)^2=1$, together with boundary condition $ {y^+} =0:\, u^+=0$. Only an approximate solution to this nonlinear ordinary differential equation (ODE) has been sought so far, however, the exact solution to this ODE has not been obtained. By introducing a transformation, $2\kappa y^+=\sinh \xi$, I successfully find the exact solution of the ODE as follows: $u^+=\frac{1}{\kappa}\ln(2\kappa {y^+} +\sqrt{1+4\kappa^2{y^+} ^2})-\frac{2{y^+} }{1+\sqrt{1+4\kappa^2{y^+} ^2}}$.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

Interface between matrix/coating or coating/coating in fact represents a very complicate thin interfacial layer. So interface model is necessary to avoid the difficulty on considering such a complicate thin layer in analysis. Classic interface model and cohesive model have been widely used in stress analysis of coating materials, though they cannot represent the effect of very thin interfacial layer accurately. A complete interface model has been deduced from the equivalent constitutive of interfacial layer in this paper. It is found that both classic interface model and cohesive model sometimes cannot give correct analysis results, while the complete interface model can always give a correct result. Moreover, the stress parallel to interface within the interfacial layer can also be analyzed by the new model. Besides, this model can also be used to describe the equivalent properties of interfacial layer, thereby, can provide a quantitative characterizing method for interfacial layer itself.

Delaying the onset of laminar-turbulent transition is an attractive method in reducing skin friction drag, especially on streamlined bodies where Tollmien-Schlichting instabilities are the dominating mechanism for transition. Miniature vortex generators (MVGs) offer an effective approach to attenuate these instabilities by generating counter-rotating vortex pairs. They are placed in pairs within an array and resemble small winglet-type elements. The conventional methodology involves adjusting MVG parameters and conducting computationally expensive DNS and/or downstream stability analyses to assess their effectiveness. However, analyzing the vortex parameters of MVG-generated vortices can potentially guide a more targeted approach in modifying MVG parameters and identifying critical factors for transition delay. Therefore, this study investigates changes in three primary MVG parameters, namely inner distance, periodicity and height, and utilizes computational fluid dynamics (CFD) analysis to create a dataset that examines the characteristics of the generated counter-rotating vortex pairs and their potential in drag reduction. The objective is to establish correlations among these parameters and their influence on delaying transition.

Utilizing deep learning for semantic segmentation of cropland from remote sensing imagery has become a crucial technique in land surveys. Cropland illustrates diverse morphologies and degrees of fragmentation on the Earth’s surface, underscoring the importance of accurately perceiving the complex boundaries of cropland which are crucial for effective segmentation. This paper introduces a UNet-like boundary-aware compensation model BAFormer. Cropland boundaries typically exhibit rapid transformations in pixel values and texture features, often appearing as high-frequency features in remote-sensing images. To enhance the recognition of these high-frequency features as represented by cropland boundaries, the proposed BAFormer integrates a Feature Adaptive Mixer (FAM) and develops a Deep Wide Large Kernel Multi-Layer Perceptron (DWLK-MLP) to enrich the global and local cropland boundaries features separately. Specifically, FAM adaptively mixes high-frequency and low-frequency features through the advantages of convolution and self-attention; DWLK-MLP expands the convolutional receptive field by deeply decomposing large kernel convolutions. The efficacy of BAFormer has been evaluated on the Vaihingen, Potsdam, and LoveDA public datasets, as well as the Mapcup dataset. It has demonstrated advanced performance, achieving mIoU scores of 84.5%, 87.3%, 53.5%, and 83.1% on these datasets respectively. Notably, BAFormer-T, the lightweight iteration of the model, surpasses other lightweight models on the Vaihingen dataset with scores of 91.3% F1 and 84.1% mIoU. The source code is available at https://github.com/WangYouM1999/BAFormer.

Friction, one of the oldest technologies harnessed by humanity, has thus far eluded a theoretical model capable of predicting kinetic friction forces across a broad range of sliding velocities. This study employs the first principle of thermodynamics to delve into sliding friction. For the first time, a general expression for the friction force has been derived, revealing that the damping of sliding friction is inversely proportional to the relative sliding velocity between the two interfaces in motion, contrary to the assumption in traditional models that it is directly proportional to the relative velocity. To simplify the general result, the concept of a friction boundary layer is introduced. An approximate expression is found to reveal the mechanism for reducing friction, which involves increasing the sliding velocity while decreasing the vibration velocity of the object perpendicular to the sliding interface.

The amount of heat transfer in gas turbine blades depends on cooling techniques and various flow phenomena. The effect of eddies, passing shock waves and free flow turbulence has been noticed by many researchers since the beginning. The focus of the upcoming work is on the numerical investigation of the effects of turbulence intensity and Reynolds number on the amount of heat transfer from the blade surface with internal cooling. The SST model has been used to solve this problem, which has been compared with the experimental work to ensure the correctness of the numerical simulation. In this regard, by changing the free flow turbulence intensity with values of 1, 5, 7, and 10% and at three Reynolds numbers of 150,000, 350,000, and 750,000, the changes in heat transfer coefficients have been investigated. The results show that with the increase of the turbulence intensity at different Reynolds numbers, due to the positive effect of the flow turbulence on the suppression of separation and promotion of the boundary layer transition, the blade surface heat transferincreases and this increase is more evident at higher Reynolds numbers.

In this study, we investigate the existence of positive solutions within a system of Riemann-Liouville fractional differential equations that incorporate the (r1,r2,r3)-Laplacian operator while being subject to three-point boundary conditions. These equations incorporate various fractional derivatives and are influenced by parameters represented as (ψ1,ψ2,ψ3). Our approach involves employing techniques such as cone expansion and compression of the functional type, in conjunction with the Leggett-Williams fixed point theorem, to establish the existence of positive solutions. To emphasize the practical significance of our findings in the realm of fractional differential equations, we provide two illustrative examples.

The influence of small-scale processes at the ocean-atmosphere boundary layer such as spray and foam on the surface waves prediction is studied. Estimates of the effect of including the exact number of specific fragmentation "parachute" type in the spray on the resulting drag coefficient is shown. For the estimates, the numerical simulations within WAVEWATCH III wave model are performed. The parameterizations of wind input were tested within WAVEWATCH III wave model: default ST4 and ST6 parameterizations and the ST1 and ST6 parameterizations used together with the implemented drag coefficient parameterization. The proposed parameterization takes into account the presence of foam and spay. The obtained results are compared with the NDBC buoys data. The importance of small-scale processes for waves at hurricane winds prediction and the prospects for their inclusion in modern numerical wave models is shown.

In this paper, the authors consider the influence of the type of power supply and the internal parameters of the DC-DC converter on the stability of the system at constant power load. The stability of the system under consideration is important in the design and development of the power supply system for an autonomous consumer. Such a typical system can be a DC microgrid. In the work, when analyzing the stability of the system, the power source is not considered an ideal voltage source, but the active-inductive nature of the voltage source is taken into account, which is equivalent to using a synchronous machine with permanent magnets. The Rauss-Hurwitz algebraic criterion was used as a criterion for analyzing the stability of the system. This will make it possible to build and analyze the areas and boundaries of the system's stability. As a result, the areas and boundaries of the stability of the system were presented. The general trend towards the behavior of the zone of instability of the system was given. At the same time, dependences describing the boundaries of instability are presented, which are combinations of parameters of the DC-DC converter, beyond which the system becomes unstable. The presented definitions of the instability limits can be used as a corrective device of the control system to ensure the stability of the system in the upper limits of the power consumption.

The gauge field equation for fluid mechanics established in Part 1 is developed into a first-order scattering theory in the simplified case of a two-dimensional incompressible flow over a flat plate. This is used to present a model for the origin of Tollmien-Schlichting (TS) waves based on scattering between fluid particles. As a result, analytical formulae for the maximum amplification factor and the transition point from laminar to turbulent flow in the boundary layer are obtained. The mathematical transformations from the stationary field equations in Part 1 to a scattering theory with time evolution along the flow axis using Wick rotation are elaborated in detail.

Forests across the world stand at the crossroad with climate and land use changes shaping their future. Despite the demonstration of political will and global efforts, forest loss, fragmentation and land degradation continue unabated. No clear evidence exists that these initiatives are working. Why are policies designed to halt deforestation and increase restoration of forest landscapes failing? A key reason for this apparent ineffectiveness lies in the failure to recognize the agency of the stakeholders involved and the adaptive capacities of the systems we seek to steer. Landscapes do not happen. We make them. They are the result of the sum of individual actions and decisions made by all stakeholders, and the interactions between these and biophysical processes. Likewise, forest transitions are not ecological, but social and behavioral. They are a product of the way humans manage ecosystems. Decision-makers need to integrate better representations of people’s agency in their mental models. We suggest possible solution pathways to overcome this key current barrier. These involve eliciting mental models behind policy decision, changing perspectives to better understand divergent points of view and refining strategies through explicit theories of change. Games designed to represent the constraints and opportunities that exist in the landscapes can help decision makers in these task.

Structural vibration induced by dynamic load or natural vibration is a nonnegligible factor in failure analysis. Based on vibrating boundary condition, impact resistance of shape memory alloy reinforced composites is investigated. In this investigation, modified Hashin’s failure criterion, Brinson’s model and visco-hyperelastic model are implemented into the numerical model to charactering the mechanical behavior of glass fiber/epoxy resin laminates, SMAs and interphase, respectively. First, fixed boundary condition is maintained in simulation to verify the accuracy of material parameters and procedures by comparing with experimental data. Then, a series of vibrating boundaries with different frequencies and amplitudes are applied during the simulation process to reveals the effect on impact resistances. The statistics of absorbed energy and contact force indicate that impact resistance of the composite under high frequency and large amplitude is lower than that under low frequency and small amplitude, and summarized by a mathematical expression.

For advancing manufacturing, arising AM, with an inverse philosophical approach compared to conventional procedures, has benefits that include intricate fabrication, reduced material waste, flexible design, and more. Regardless of its potential, AM must overcome several challenges due to multi-physical processes with miscellaneous physical stimuli in diverse materials systems and situations, such as anisotropic microstructure and mechanical properties, a restricted choice of materials, defects, and high cost. Unlike conventional experimental work that requires extensive trial and error resources and FEM, which generally consumes substantial computational power, the analytical approach based on physics is an exceptional choice. Understanding the relationship between the microstructure and material properties of the fabricated parts is a crucial focus in AM research. Texture is a vital factor in almost every modern industry. This study first proposed a physics-based model to foreshadow the multi-phase crystallographic orientation distribution in Ti-6Al-4V LPBF while considering the part boundary conditions due to the importance of part geometry in real industry. The thermal distribution obtained from this function operates as the information for the single-phase crystallographic texture model. In this model, we forerun and validate the orientations of single-phase materials utilizing three Euler Angles with the principles of CET and thermodynamics, as well as the intensity of the texture by approximating them with published results. Then, we transform the single-phase texture into a dual-phase texture in Bunge calculation, illustrating visualized by pole figures of both BCC and HCP phases. This texture evolution model provides a new paradigm for future researchers to model the texture or microstructure evolution semi-analytically and save many computational resources in a real-world perspective. Others have not yet done this work about simulating the multi-phase texture in an analytical approach, so this work bridges the gap in this field. Furthermore, this paper establishes the foundation for future research on materials properties affected by microstructure or texture in academic and industrial environments. The precision and dependability of the results obtained through this method make it a valuable tool for ongoing research and advancement.

This paper presents an interpretable support vector machine (SVM) and its application to rehabilitation assessment. We introduce the concept of nearest boundary point to standardize the one-class SVM decision function and determine the shortest path for data from abnormal cases to become those from normal cases. This analytical approach is computationally simple and provides a unique solution. The nearest boundary point of abnormal data can also be used to analyze the cause of abnormal classification and indicate countermeasures for normalization. These properties render the proposed interpretable SVM valuable for medical assessment applications and other problems that require careful consideration of classification results for treatment. Simulation and application results demonstrate the feasibility and effectiveness of the proposed method.

Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the truncation error and add correction terms. Numerical studies on test functions show that the proposed method reduces errors significantly near boundaries compared to quasi-interpolation without corrections, for both equally spaced and Chebyshev points. The convergence and accuracy with the boundary corrections are generally better with Chebyshev points compared to equally spaced points. The proposed method provides an efficient way to perform quasi-interpolation on compact intervals while controlling the boundary errors.

Rational delineation of urban–rural boundaries is a foundational prerequisite for holistic urban and rural development planning and rational resource allocation. However, the results of division of urban–rural boundaries extracted using a single data source are non-comprehensive. To address this problem, the present study proposes a method for using multiple sources such as population data, nighttime light data, land use, and points of interest (POI) data to extract urban–rural boundaries. Considering Guizhou Province for a case study, we here present a two-step method for identifying urban–rural boundaries. First, the random forest model was combined with the dasymetric mapping method to obtain the population spatialization data with a 30-m resolution in the studied province. Second, using the breaking point method, we extracted the urban–rural boundary for Guizhou Province in 2020 based on the spatialized population. This method fully integrated the benefits of various data and judiciously extracted the boundaries of the main urban areas and small- and medium-sized towns of each city in the study province at the same spatial scale. The stratified random sampling method revealed that the average overall accuracy was 88.05%. The method proposed has certain universality and application value and allows identifying the urban–rural boundaries more accurately and practically.

Metachrony is defined as coordinated asynchronous movement throughout multiple appendages, such as the cilia of cells and swimmerets of crustaceans. We investigate the process of metachronal propulsion, notably used by species of crustaceans and microscopic cells to move through fluid. A rigid crustacean model with paddles moving in symmetric strokes was created to simulate metachronal movement. Coupled with the surrounding fluid domain, we employ the immersed boundary method to analyze fluid-structure interactions. To explore the effect of nonlinear morphology on the efficiency of metachronal propulsion, we generate and simulate a range of crustacean body shapes, from upward curves to downwards curves. We found that the highest propulsion velocity is achieved when the crustacean model morphology follows a downwards curve, specifically a parabola of leading coefficient k=−0.4. This curved morphology results in 4.5% higher velocity compared to the linear model. As k deviates from −0.4, the propulsion velocity decreases with increasing magnitude, forming a concave downward trend. The impact of body shape on propulsion velocity is shown by how the optimal velocity with k=−0.4 is 71.5% larger than the velocity at k=1. Overall, this study suggests that morphology has a significant impact on metachronal propulsion.

The studies of laminar unsteady boundary layer flows is crucial for understanding laminar-turbulence transition and origins of turbulence. However, the task of finding its solutions poses a significant challenge. In this paper, we propose a novel approach by introducing a similar transformation to convert the 2D unsteady laminar boundary layer equations into a single partial differential equation. By applying this transformation, we are able to obtain the "exact" similarity solutions for the 2D unsteady laminar boundary layer equations, specifically for the case of flat plate boundary flow. Notably, this is the first time that such an exact solution has been obtained. Application of this exact solution is being used to solve Stokes' first problem in 2D boundary layer. Perspectives on the transition fron Rayleigh solution to Blasius solution is provided.

Oxide additive-free α- ⇀ β-Si3N4 phase transformation of a high-purity commercial α-Si3N4 powder was investigated at 1600 to 1900 ℃ under nitrogen pressure of 980 kPa. The XRD analysis revealed that the α- ⇀ β-Si3N4 phase transformation proceeded mainly at 1900 ℃, and was completed by the extensive 1900 ℃-heat treatment for 20 h. This phase transformation temperature was 33 ℃ lower than the theoretical α-Si3N4 dissociation temperature and confirmed as completely different from that often discussed for the liquid phase sintering of α-Si3N4 powder by direct comparison with the phase transformation behavior of a reference powder, α-Si3N4 powder doped with 1 mol% Y2O3. The unique α- ⇀ β-Si3N4 phase transformation was further studied by a set of characterization techniques including elemental analysis, HAADF-STEM and STEM-EDS analyses. The results strongly suggested that the oxide additive-free α- ⇀ β-Si3N4 phase transformation was governed by the for-mation of metastable solid solution between α-Si3N4 and impurity oxygen of approximately 0.6 wt%, which promoted the dissociation below the theoretical α-Si3N4 dissociation temperature to afford thermodynamically favorable β-Si3N4. Along with the β-Si3N4 formation, the impurity oxygen was concentrated at the Si3N4 crystal grain boundaries and subsequently released from the sample via the grain boundary diffusion.

This research work deals with the formulation of numerical scheme with algorithm to compute singularly perturbed partial differential equations(SP-PDEs) involving a significant negative shift. The problem involves small parameter which causes a rapidly changing boundary layers in the vicinity of a body, and the negative shift term causes interior layer. Such appearance of an abruptly varying layers causes difficulties to find the exact solution and it is not adequate to employ classical numerical methods. The technique presented in this research work simplifies these challenges and yields accurate numerical solution.The stability and convergence analyses of the methods are examined and proven. To test the developed technique, numerical experiments are carried out and confirmed with theoretical analysis.

Barrier coverage is a fundamental application in wireless sensor networks, which is widely used to protect a region through intruder detection for smart city. In this paper, we study a new branch of barrier coverage, named warning barrier coverage (WBC). Different from the classic barrier coverage, WBC has the inverse protect direction, which protects unexpected visitors by warning them away from the region enclosed by sensor barriers. The WBC holds a promising prospect in many danger keep out applications for smart city. For example, a WBC can enclose the debris area in the sea and alarm any approaching ships in order to avoid their damaging propellers. One special feature of WBC is that the target region is usually dangerous and its boundary is previously unknown. Hence, the scattered mobile nodes need to detect the boundary and form the barrier coverage themselves. It is challenging to form these distributed sensor nodes into a barrier because a node can sense only the local information and there is no global information of the unknown region or other nodes. To this end, we propose a novel solution AutoBar for mobile sensor nodes to automatically form a WBC for smart city. To pursue the high coverage quality, we theoretically derive the optimal distribution pattern of sensor nodes using convex theory. Based on the analysis, we design a fully distributed algorithm that enables nodes to collaboratively move towards the optimal distribution pattern. In addition, AutoBar is able to reorganize the barrier even any node is broken. To validate the feasibility of AutoBar, we develop the prototype of the specialized mobile node, which consists of two kinds of sensors: one for boundary detection and another for visitor detection. Based on the prototype, we conduct extensive real trace driven simulations in various smart city scenarios. Performance results demonstrate that AutoBar outperforms the existing barrier coverage strategies in terms of coverage quality, formation duration, and communication overhead.

In this paper, by using the variational method, a sufficient condition for the unique existence of the stationary solution of the reaction-diffusion ecosystem is obtained, which directly leads to the global asymptotic stability of the unique equilibrium point. Moreover, delayed feedback ecosystem with reaction-diffusion item is considered, and utilizing impulse control results in the globally exponential stability criterion of the delayed ecosystem. It is worth mentioning that the Neumann zero-boundary value that the infected and the susceptible people or animals should be controlled in the epidemic prevention area and not allowed to cross the border, which is a good simulation of the actual situation of epidemic prevention. And numerical examples illuminate the effectiveness of impulse control, which has a certain enlightening effect on the actual epidemic prevention work . That is, in the face of the epidemic situation, taking a certain frequency of positive and effective epidemic prevention measures is conducive to the stability and control of the epidemic situation. Particularly, the newly-obtained theorems quantifies this feasible step. Besides, utilizing Laplacian semigroup derives the $p$th moment stability criterion for the impulsive ecosystem.

The famous Toms effect (1948) consists of a substantial increase of the critical Reynolds number when a small amount of soluble polymer is introduced into water. The most noticeable influence of polymer additives is manifested in the boundary layer near solid surfaces. The goal of the present paper is a group analysis of the boundary layer equations in two mathematical models of the flow of aqueous polymer solutions: the second grade fluid (Rivlin and Ericksen, 1955) and the model derived by Pavlovskii (1971). The equations of the unsteady two-dimensional boundary layer in the Pavlovskii and Rivlin-Ericksen models are analyzed for the first time here. These equations have no definite type so that finding their exact solutions is very important in order to understand the mathematical nature of the above mentioned models. The problem of group classification with respect to the arbitrary function of the longitudinal coordinate and time present in the equations, which sets the pressure gradient of the external flow, arises. All functions for which an extension of the admitted Lie group occurs are found. The task includes the ratio of two characteristic length scales. One of them is the Prandtl scale, and another is defined as the square root of the normalized coefficient of relaxation viscosity (Frolovskaya and Pukhnachev, 2018) and does not depend on the characteristics of the motion. The paper contains a number of exact solutions in the Pavlovskii model including a solution describing the flow near a critical point. Among the solutions of the new model of the boundary layer, a special place is taken by the solution of the stationary problem of flow around a rectilinear plate. Within the framework of the Prandtl theory of the boundary layer, such a solution was constructed by Blasius (1908). As is well-known, this solution has a non-removable defect: the transverse velocity near the edge of the plate increases without bound. The introduction of a relaxation term into the model makes it possible to eliminate this singularity.

The three-axes Doppler sodar Latan-3 operated on an oceanographic stationary platform in the coastal zone of the Black Sea in June 2015. The platform is located 450 meters offshore from the southern coast of the Crimea Peninsula in the region of Katsiveli (44.39°N, 33.99°E). The water depth at the site is about 30 meters. The atmospheric boundary layer (ABL) typical for the mediterranean seas was observed when the wind is from the sea. The physical processes typical for the coastal mountain terrain was observed when the wind was from the shore. Complex measurements of the ABL parameters were performed using a sodar. Auxiliary measurements of the ABL parameters were performed using a temperature profiler and an ultrasonic thermometer-anemometer. Observations were made mostly during a fair weather with a pronounced diurnal course of meteorological parameters. Sodar data analysis revealed a strong wave activity in the ABL. Internal gravity waves with amplitudes of up to one hundred meters were regularly observed in a layered turbulence structure under stable conditions. Various forms of Kelvin-Helmholtz billows were observed at the interface between the sea breeze and the return flow aloft and in the low level jets.

In this article, we establish the existence of and then compare smallest eigenvalues for nabla fractional boundary value problems involving a fractional difference boundary condition, using the theory of u0-positive operators with respect to a cone in a Banach space.

Bioconvective flows have attracted attention in recent years due to actual and potential applications. In this paper, we consider a steady and laminar convective MHD flow of a nanofluid with heat, mass and microorganism transfer with a heat source/sink present. In addition, we assume there exists a first order chemical reaction. The governing partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) using the scaling group transformation and the associated boundary value problem is then solved. The influences of selected governing parameters on the dimensionless velocity, temperature, nanoparticle concentration, density of motile microorganisms, skin friction, heat transfer, mass transfer, and motile microorganism density rates are computed and discussed

We performed for the first time to our knowledge fully ab initio molecular dynamics simulations of additive tribochemistry in boundary lubrication conditions. We consider an organophosphourus additive that has been experimentally shown to reduce friction in steel-on-steel sliding contacts thanks to the tribologically-induced formation of an iron phosphide tribofilm. The simulations allow us to observe in real time the molecular dissociation at the sliding iron interface under pressure and to understand the mechanism of iron phosphide formation. We discuss the role played by the mechanical stress by comparing the activation times for molecular dissociation observed in the tribological simulations at different applied loads with that expected on the basis of the dissociation barrier.

Non-uniform grain boundary sliding can induce strain and rotation incompatibilities at perfectly planar interfaces. Explicit analytic expressions of stress and lattice rotation jumps are thus derived at a planar interface in the general framework of heterogeneous anisotropic thermo-elasticity with plasticity and grain boundary sliding. Both elastic fields are directly dependent on in-plane gradients of grain boundary sliding. It is also shown that grain boundary sliding is a mechanism that may relax incompatibility stresses of elastic, plastic and thermal origin although the latter are not resolved on the grain boundary plane. This relaxation may be a driving force for grain boundary sliding in addition to the traditionally considered local shears on the grain boundary plane. Moreover, the obtained analytic expressions are checked by different kinds of bicrystal shearing finite element simulations allowing grain boundary sliding and where a pinned line in the interface plane aims at representing the effect of a triple junction. A very good agreement is found between the analytic solutions and the finite element results. The performed simulations particularly emphasize the role of grain boundary sliding as a possible strong stress generator around the grain boundary close to the triple line because of the presence of pronounced gradients of sliding.

Large values and gradients of stresses and deformations, triggering concentrations of stresses and deformations, arise in the corner areas of a structure. The action of forced deformations, leading to the finite rupture of the contact between the elements of a structure, also triggers the concentration of stresses, while the rupture reaches an irregular point, a line on the area boundary. The theoretical analysis of the stress-strain state (SSS) of areas with angular cutouts in the boundary under the action of discontinuous forced deformations is reduced to the study of singular solutions to the homogeneous problem of the elasticity theory that has power-related features. The calculation of stress concentration coefficients in the domain of a singular solution to the elastic problem makes no sense. It is experimentally proven that the zone, that is close to the vertex of the angular cutout in the area boundary, has substantial deformations, rotations, and it corresponds to rising values of the first and second derivatives of displacements along the radius in cases of sufficiently small radii in the neighbourhood of the irregular point of the boundary. For such areas, it is necessary to consider the plane problem of the elasticity theory, taking into account the geometric nonlinearity under the action of forced deformations. This will allow analyzing the effect of relations between orders of values of deformations, rotations, and forced deformations on the form of the equation of equilibrium. The purpose of this work is to analyze the effect of relations of deformation orders, rotations, forced deformations on the form of the equilibrium equation in the polar coordinate system for a V-shaped area under the action of forced temperature-induced deformations with regard for the geometrical non-linearity and physical linearity.

The task of weakly supervised point cloud semantic segmentation has received widespread attention and also has been widely used in autonomous driving, robotics, and modern industries. Due to the high dimensionality and large volume of point cloud data, many technical difficulties appeal to weakly supervised semantic processing, especially segmentation. However, weakly-supervised schemes usually provide only partial labelling information of the underlying point cloud data and thus need to effectively extract local features, geometric information, and contextual relationships only using these limited labelled data for supervised learning. To improve weakly-supervised semantic segmentation, we propose a novel segmentation network through the boundary-based feature aggregation based on a K-NN algorithm with down-sampling operation, and also introduce the smoothness loss and Siamese loss for effective segmentation. The experiments on public datasets demonstrate that our presented segmentation method exceeds most of the existing fully supervised and weakly-supervised methods in terms of mIoU. Specifically, our network has high segmentation accuracy on the labels of objects with similar geometrical structures, such as ceiling, wall, floor, chair and table, reaching 91.2%, 98.8%, 83.3%, 75.3% and 80.2%, respectively. Extensive experiments also illustrate its robustness, effectiveness, and generalization of the proposed weakly supervised segmentation network.

Two-dimensional heat diffusion problem with heat source which is quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are used as a boundary conditions. Since the problem is not linear, Picard’s successive approximation theorem is used. Under certain conditions of natural regularity and consistency imposed on the input data, establish the existence, uniqueness and constant dependence of the solution on the data using the generalized Fourier method. As a numerical solution, implicit finite difference scheme is used. The results ob-tained from analytical and the numerical solutions are so close to each other.

Haemodynamic simulations are increasingly used to study vascular diseases like Intracranial Aneurysms (IA) and to further develope treatment options. However, due to limited data, some aspects must rely on heuristics, especially at the simulation’s distal ends. In literature, Murray’s Law is often used to model the outflow split based on vessel cross-section area, but this poses challenges for the communicating arteries in the Circle of Willis (CoW). In this study, we contribute by assessing the impact of Murray’s Law in patient-specific geometries featuring IA at the posterior communication. We simulate different domain extensions, representing common modelling choices. We establish Full CoW simulations as a baseline to evaluate the effect of these modelling assumptions on haemodynamic indicators, focusing on IA growth and rupture-related factors like Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI). Our findings reveal qualitative alterations in haemodynamics when not modeling posterior communication. Comparisons between computing the anterior circulation and computing the whole Circle of Willis reveal quantitative changes in WSS may reach up to 80%, highlighting the significance of modelling choices in assessing IA risks and treatment strategies.

In this paper we overview all analytical engineering solutions for corrosion problems in pressure vessels delivered over the past 60 years. We briefly detail strengths and weaknesses of existing approaches, thus demonstrating the need for novel uniform corrosion analysis methods for both current and new applications. To complement the review, we also present a new analytical model allowing to estimate the lifetime of pressured elastic vessels with mechanically assisted corrosion. Both internal/external pressure and internal/external corrosion are captured and dissolution driven corrosion is also considered. The readily implemented method improves existing analytical approaches and is shown to be effective for thin and thick shells, as well as various loading and corrosion intensity and geometrical conditions.

In the laboratory practice, several standards for testing the bending stiffness of corrugated board are used. There are often cases of tests where the results depend on the way the sample is placed on the supports. The problem arises when the board is five-ply (with two corrugated layers with different corrugation heights) or when the board has asymmetrically selected papers on the flat layers. In this article, we focus our attention on the problem related to boundary conditions, with particular attention to the local effects of the support of the sample. Since the cardboard layers, both flat and corrugated, have a small thickness, a slight deformation of the papers can always be observed at the point of contact between the sample and the support, which affects the readings of the measured stiffness. The paper presents theoretical and numerical analyzes showing how much the method of supporting the sample affects the measured bending stiffness of various samples. Numerical observations were also compared with the results of analyzes presented by other scientists as well as with experimental results.

Mechanochemical technology is developing rapidly, judging by the scientific information in both basic and applied studies. However, many issues and points of view remain to be discussed. This review presents some new key issues for the optimization of mechanochemical processes in theoretical and practical aspects. Emphasis is placed on powder technology aspects, which are not always discussed compared to functional or microscopic viewpoints. The transfer of chemical species across the interparticle interface between organic and inorganic species during the mechanosynthesis of nanocomposite oxides offers many new possibilities, which are discussed here in detail. Since all material transport is preceded by charge transfer, its driving force has been searched for using terminology beyond the well-established electrochemical ones. The role of organic compounds during the whole process is emphasized, regardless of their survival in the final product. The similarity with the pharmaceutical phenomena is pointed out, although its mentality is very different from that of the synthesis of nanocomposites. Not only for the rational amorphization of the active pharmaceutical ingredient, but also for the stabilization of molecular dispersion states with the participation of excipients are discussed. The effects of liquids, either added or formed by mechanochemical auto-liquefaction, are presented with reference to the comparison between wet and dry grinding. Finally, mechanisms of apparent stabilization of mechanically activated states of products are elucidated to investigate the practical applicability of mechanochemically synthesized products

Laminate structures composed of stiff plates and thin soft interlayers are widely used in aerospace, automotive and civil engineering encouraging the development of reliable non-destructive strategies for their condition assessment. In the paper, elastodynamic behaviour of such laminate structures is investigated with emphasis on its application in ultrasonic based NDT and SHM for the identification of interlayer mechanical and interfacial contact properties. A particular attention is given to the practically important frequency range, in which the wavelength considerably exceeds the thickness of the film. Three layer model with spring-type boundary conditions employed for imperfect contact simulation is used for numerical investigation. Novel effective boundary conditions are derived via asymptotic expansion technique and used for analysis of the peculiar properties of elastic guided waves in considered laminates. It is revealed that the thin and soft film influences the behaviour of the laminate mainly via the effective stiffnesses being a combination of the elastic moduli of the film, its thickness and interface stiffnesses. To evaluate each of these parameters separately (or to figure out that the available experimental data are insufficient), a step-wise procedure employing the effective boundary conditions is proposed and tested versus the laser Doppler vibrometry data for Lamb waves in Aluminium/Polymer film/Alumunium structure. The possibility of using film-related thickness resonance frequencies to estimate the film properties and contact quality is also demonstrated. Additionally, the rich family of edge waves is also investigated, and the splitting of fundamental edge waves into pairs is revealed.

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

This work investigates centered polygonal lacunary functions restricted from the unit disk onto symmetry angle space which is defined by the symmetry angles of a given centered polygonal lacunary function. This restriction allows for one to consider only the p-sequences of the centered polygonal lacunary functions which are bounded, but not convergent, at the natural boundary. The periodicity of the $p$-sequences naturally gives rise to a convergent subsequence, which can be used as a grounds for decomposition of the restricted centered polygonal lacunary functions. A mapping of the unit disk to the sphere allows for the study of the line integrals of restricted centered polygonal that includes analytic progress towards closed form representations. Obvious closures of the domain obtained from the spherical map lead to four distinct topological spaces of the "broom topology'' type.

An improved anti-noise morphology vision navigation algorithm is proposed for intelligent tractor tillage in a complex agricultural field environment. At first the two key steps, Guided Filtering and improved anti-noise morphology navigation line extraction were addressed in detail. Then the experiments were carried out in order to verify the effectiveness and advancement of the presented algorithm. Finally, the optimal template and it’s application condition were studied for improving the image processing speed. The comparison experiment results show that the YCbCr color space has minimum time consumption of 0.094 s in comparison with HSV, HIS and 2R-G-B color spaces. The Guided Filtering method can effectively distinguish the boundary between the new and old soil than other competing vanilla methods such as Tarel, Multi-scale Retinex, Wavelet-based Retinex and Homomorphic Filtering inspite of having the fastest processing speed of 0.113 s. The extracted soil boundary line of the improved anti-noise morphology algorithm has best precision and speed compared with other operators such as Sobel, Roberts, Prewitt and Log. After comparing different size of image template, the optimal template with the size of 140×260 pixels can meet high precision vision navigation while the course deviation angle is not more than 7.5°. The maximum tractor speed of the optimal template and global template are 51.41 km/h and 27.47 km/h respectively which can meet real-time vision navigation requirement of the smart tractor tillage operation in the field. The experimental vision navigation results demonstrated the feasibility of the autonomous vision navigation for tractor tillage operation in the field using the new and old soil boundary line extracted by the proposed improved anti-noise morphology algorithm which has broad application prospect.

An improved anti-noise morphology vision navigation algorithm is proposed for intelligent tractor tillage in a complex agricultural field environment. Firstly, the two key steps, Guided Filtering and improved anti-noise morphology navigation line extraction, were addressed in detail. Then the experiments were carried out in order to verify the effectiveness and advancement of the presented algorithm. Finally, the optimal template and its application condition were studied for improving the image processing speed. The comparison experiment results show that the YCbCr color space has minimum time consumption, 0.094 s, compared with HSV, HIS and 2R-G-B color spaces. The Guided Filtering method can enhance the new & old soil boundary effectively than any other methods such as Tarel, Multi-scale Retinex, Wavelet-based Retinex and Homomorphic Filtering, meanwhile, has the fastest processing speed of 0.113 s. The extracted soil boundary line of the improved anti-noise morphology algorithm has best precision and speed compared with other operators such as Sobel, Roberts, Prewitt and Log. After comparing different size of image template, the optimal template with the size of 140×260 pixels can meet high precision vision navigation while the course deviation angle is not more than 7.5°. The maximum tractor speed of the optimal template and global template are 51.41 km/h and 27.47 km/h respectively which can meet real-time vision navigation requirement of the smart tractor tillage operation in the field. The experimental vision navigation results demonstrated the feasibility of the autonomous vision navigation for tractor tillage operation in the field using the new & old soil boundary line extracted by the proposed improved anti-noise morphology algorithm which has broad application prospect.

Abstract: Characterization the 3-D structure of clouds is needed for a more complete understanding of the Earth's radiative and latent heat fluxes. Here we develop and explore a “ray casting” algorithm applied to the Multi-angle Imaging SpectroRadiometer (MISR) on board the Terra satellite, to reconstruct 3-D cloud volumes for observed clouds. The ray casting algorithm is first applied to geometrically simple synthetic clouds to show that, under the assumption of perfect, clear-conservative cloud masks, the reconstruction method yields overestimation whose magnitude depends on the cloud geometry and the resolution of the reconstruction grid relative to the image pixel resolution. The method is then applied to two select MISR scenes, fully accounting for MISR’s viewing geometry for reconstructions over the Earth’s ellipsoidal surface. The MISR Radiometric Camera-by-camera Cloud Masks at 1.1 km resolution and custom cloud masks at 275 m resolution independently derived from MISR RGB channels are used as input cloud masks. A wind correction method, termed “cloud spreading”, is devised and applied to the cloud masks to offset potential cloud movements over short time intervals (around 7 minutes at maximum) between the cameras. The MISR cloud top height product is used as a constraint to reduce the overestimation at the cloud top. The reconstruction results show that their uncertainty is significant when the wind correction is applied, and that they have more refined structures when the input cloud mask has a higher resolution. Recommendations for improving the presented cloud volume reconstructions as well as for future passive remote sensing satellite missions are discussed.

A synthetic jet actuator (SJA) is a fluidic device often consisting of a vibrating diaphragm that alters the volume of a cavity to produce a synthesized jet through an orifice. The cyclic ingestion and expulsion of the working fluid leads to a zero-net mass-flux and the transfer of linear momentum to the working fluid over an actuation cycle, leaving a train of vortex structures propagating away from the orifice. SJAs are a promising technology for flow control applications due to their unique features, such as no external fluid supply or ducting requirements, short response time, low weight, and compactness. Hence, they have been the focus of many research studies over the past few decades. Despite these advantages, implementing an effective control scheme using SJAs is quite challenging due to the large parameter space involving several geometrical and operational variables. This article aims to explain the working mechanism of SJAs and provide a comprehensive review of the effects of SJA design parameters in quiescent conditions and crossflow.

Traditional 3D reconstruction models have consistently encountered a challenge: attaining high recall of object edges while preserving precision. In this paper, we introduce a post-processing method Multi-Head Attention Refiner (MA-R) aimed at tackling this challenge by integrating a multi-head attention mechanism within the U-Net style refiner module. The 3D reconstruction model applying this method demonstrates excellence in parsing intricate image details, resulting in significant enhancement of boundary predictions and increased recall rates. In our experiments, our method significantly enhances the reconstruction performance of Pix2Vox++ when multiple images are utilized as input. Specifically, it achieves an enhanced Intersection Over Union score of approximately 1.1% compared to the original Pix2Vox++ model when 16-view images are employed.

The challenging terrain and deep ravines characteristic of mountainous regions often result in slower path planning and suboptimal flight paths for Unmanned Aerial Vehicles (UAVs) when traditional meta-heuristic optimization algorithms are employed. This study investigates the application of an Improved Enhanced Snake Optimizer (IESO) for three-dimensional path planning in a simulated rugged mountainous terrain. The initialization process in the enhanced snake optimizer is refined by integrating the Chebyshev chaotic map. Additionally, a non-monotonic factor is introduced to modulate the "temperature," and a boundary condition is incorporated into the dynamic opposition learning mechanism. These modifications collectively reduce the likelihood of population convergence to local optima during optimization. The feasibility of IESO is validated through time complexity and global convergence analyses. Comparative simulation experiments benchmarked IESO against five state-of-the-art optimization algorithms across test functions and path-planning simulated scenarios. The experimental results indicate that the enhanced algorithm achieves superior optimization precision, faster convergence speeds, and improved quality in the planned trajectories by 30%.

Data obtained by Direct Numerical Simulations (DNS) of pressure-driven turbulent channel flow are studied in the range 180 ≤ Reτ≤ 10,000. Reynolds number effects on the Mean Velocity Profile (MVP) and second order statistics are analyzed with a view of finding logarithmic behavior in the overlap region or even further from the wall, well in the boundary layer’s outer region. Values of Kármán constant for the MVPs and the Townsend-Perry constants for the streamwise and spanwise fluctuation variances are determined for the Reynolds numbers considered. A data-driven model of the MVP, proposed and validated for zero pressure gradient flow over a flat plate, is employed for pressure-driven channel flow by appropriately adjusting Coles’ strength of the wake function parameter, Π. There is excellent agreement between the analytic model predictions of MVP and the DNS-computed MVP as well as of the Reynolds shear stress profile. The skin friction coefficient Cf is calculated analytically. The agreement between the analytical model predictions and the DNS-based computed discrete values of Cf is excellent.