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.

We introduce a class of logarithmic wave equation. We study the global existence of week solution for this class of equation. We deal with the initial boundary value problem of this class. Using the Galerkin method and the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Q-Ball Dynamic in particular.

We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assumed that the leading coefficients of viscosity and diffusion and the buoyancy force in the model equations depend on concentration. We develop mathematical apparatus of studying inhomogeneous boundary value problems under consideration. It is based on using of a weak solution of the boundary value problem and construction of liftings of the inhomogeneous boundary data. They remove the inhomogeneity of the data and reduce original problems to equivalent homogeneous boundary value problems. Based on this apparatus we will prove the theorem of the global existence of a weak solution to boundary value problem under study and establish important properties of the solution. In particular, we will prove the validity of the maximum principle for the substance’s concentration. We will also establish sufficient conditions for the problem data, ensuring the local uniqueness of weak solutions.

The Chebyshev collocation method (ChC) implemented as Chebfun is used in order to solve a class of second order one-dimensional singular and genuinely nonlinear boundary value problems. Efforts to solve these problems with conventional ChC have generally failed, and the outcomes obtained by finite differences or finite elements are seldom satisfactory. We try to fix this situation using the new Chebfun programming environment. However, for toughest problems we have to loosen the default Chebfun tolerance in Newton's solver as the ChC runs into trouble with ill-conditioning of the spectral differentiation matrices. Although in such cases the convergence is not quadratic the Newton updates decrease monotonically. This fact, along with the decreasing behaviour of Chebyshev coefficients of solutions, suggests that the outcomes are trustworthy, i.e., the collocation method has exponential (geometric) rate of convergence or at least an algebraic rate. We consider first a set of problems that have exact solutions or prime integrals and then another set of benchmark problems that do not possess these properties. Actually, for each test problem carried out we have determined how Chebfun solution converges, its length, the accuracy of the Newton method and especially how well the numerical results overlap with the analytical ones (existence and uniqueness).

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

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.

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.

Due to its economic benefits and the ability to reduce carbon emissions on a large scale, the CCUS-EOR project has been widely promoted and implemented globally. By using carbon dioxide flooding, oil water transition zone reservoirs that were once considered worthless may have new potential for development because of its rich geological reserves and high quality carbon sequestration conditions. Unlike water flooded layer, the oil in the TZ is unsaturated rather than residual oil after water flooding, which would lead to special oil-water seepage law of initial oil saturation. It is necessary to clarify special oil-water seepage law of oil-water transition zone to evaluate its production & storage potential. In this paper, we present a series of experiments to characterize the relationship between residual oil saturation and initial oil saturation. Cores in four different permeability and oil in four different viscosity are used to simulate different reservoir conditions, and that CO2 immiscible flooding experiments for each cores permeability and oil viscosity are performed with four different initial oil saturation. A total of 36 sets of CO2 flooding experiment data are used to draw the initial oil saturation & residual oil saturation chart. The results show that the residual oil saturation depends on the initial oil saturation rather than constant under certain conditions of core and oil. Under the condition of low permeability and high oil viscosity, the influence of initial oil saturation on residual oil saturation is relatively strong. The initial oil saturation & residual oil saturation chart can accurately calculate the residual oil saturation, initial water cut and final recovery based on the core permeability, oil viscosity and the initial oil saturation which is the first time to put forward this kind of chart and of the great significance to evaluate the recovery potential of the TZ.

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the complex parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic type functions in time and are bounded holomorphic in space. A set of logarithmic type solutions are shaped by means of Laplace transforms relatively to time and parameter and Fourier integrals in space. Furthermore, a formal logarithmic type solution is modeled which represents the common asymptotic expansion of Gevrey type of the genuine solutions with respect to the complex parameter on bounded sectors at the origin.

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.

We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step – generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

We examine a linear q-difference differential equation which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q-analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm log t and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q-difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q-Gevrey type growth.

Modeling fluid flow in three-dimensional (3D) Discrete Fracture Networks (DFNs) is of relevance in many engineering applications, such as hydraulic fracturing, oil/gas production, geothermal energy extraction, nuclear waste disposal and CO₂ sequestration. A new Boundary Element Method (BEM) technique with discontinuous quadratic elements and a parallel Domain Decomposition Method (DDM) is presented herein for the simulation of the steady-state fluid flow in 3D DFN systems with wellbores, consisting of planar fractures having arbitrary properties and wellbore trajectories. Numerical examples characterized by DFNs of increasing complexity are investigated to evaluate the accuracy and efficiency of the presented technique. The results show that accurate solutions can be obtained with less nodes than with mesh-based methods (e.g. Finite Element Method). In addition, the DDM algorithm used provides a quite fast convergence. The simulation results of the fluid flow around intersections among traces (linear intersections between fractures), intersections between traces and a fracture boundaries, and wellbore intersections is accurate. Source code is available at : https://github.com/BinWang0213/PyDFN3D.

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.

Meshfree particle method, which is always regarded as a pure Lagrangian approach, is easily represented complicated domain topologies, moving boundaries, and multiphase media. Solving acoustic problems with the mesfree particle method forms a branch of the acoustic wave modeling field, namely, particle-based computational acoustics (PCA). The aim of this paper is to improve the accuracy of using the PCA method to solve two-dimensional acoustic problems, and realize the particle representation with a hybrid meshfree and finite-difference time-domain (FDTD) method for acoustic boundary conditions at both the plane and curved surface. As a widely used Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) based on the support domain and the kernel function has developed rapidly in recent years. The traditional SPH method is easily implements parallel processing and has been applied in sound wave simulation. As a corrective method with higher accuracy than SPH, the acoustic propagation and scattering in the time domain is simulated with the corrective smoothed particle method (CSPM). Moreover, a hybrid meshfree-FDTD boundary treatment technique is utilized to represent different acoustic boundaries in the Lagrangian approach. In this boundary treatment technique, the parameter value of virtual particles is obtained with the FDTD method, which concerns truncation errors based on the Tayler series expansion. Soft, rigid, and Mur’s absorbing boundary conditions are developed to simulate sound waves in finite and infinite domain. Results of modeling acoustic propagation and scattering show that CSPM is accurate and convergence with exact solutions, and different acoustic boundaries are validated to be effective in the computation.

This paper studies an effective finite difference scheme for solving two-dimensional Heston stochastic volatility option pricing model problems. A dynamically balanced up-downwind strategy for approximating the cross-derivative is implemented and analyzed. Semi-discretized and spatially nonuniform platforms are utilized. The numerical method comprised is simple, straightforward with reliable first order overall approximations. The spectral norm is used throughout the investigation and numerical stability is proven. Simulation experiments are given to illustrate our results.

In this paper, the existence of two nontrivial stationary solutions for the nonlinear Gilpin Ayala two species competition model is given by using the mountain pass lemma, and the local stability criterion of the trivial solution is given by using Lyapunov function method. Based on the local stability criterion, we give some suggestions on how to avoid the population extinction. This is, when the population is on the verge of extinction, we should try our best to avoid the diffusion behavior and reduce the diffusion coefficient, otherwise the species are easy to go extinct. Numerical example shows the effectiveness of the proposed method.

In recent times, there has been a growing interest in the use of control charts as a feedback process monitoring technique. Particularly, CUSUM schemes have been proven to be efficient for monitoring processes where the magnitude of the sustained mean shifts is small or moderate. However, because of the constant control limits, the detection ability of CUSUM schemes becomes slow at the initial set-up of the process. The fast initial response FIR feature has often been used to enhance it at the process startup. Meanwhile, the dynamism of real-life problems has always encouraged a more sensitive CUSUM scheme capable of detecting process shifts more rapidly. In this paper, an improved CUSUM scheme for monitoring process mean is proposed. This scheme will be substantial for monitoring processes whose observations are obtained at a distant time interval for example hourly, daily or weekly and where the sustained shifts are assumed to be small or moderate. To demonstrate the practical applications of the proposed scheme, we present its real-life application using datasets from a bottling company and petroleum refinery laboratory.

Acute pancreatitis (AP) is a leading gastrointestinal disease that cause hospitalization. Initial management in the first 72 h after the diagnosis of AP is pivotal, which can influence the clinical outcomes of the disease. Initial management, including fluid resuscitation, pain control, nutritional support, antibiotic use, and endoscopic retrograde cholangiopancreatography (ERCP) in gallstone pancreatitis, plays a fundamental role in AP treatment. Recent updates for fluid resuscitation, including treatment goals, the type, rate, volume, and duration, have triggered a paradigm shift from aggressive hydration with normal saline to goal-directed and non-aggressive hydration with lactated Ringer’s solution. Evidence of the clinical benefit of early enteral feeding is becoming definitive. Routine use of prophylactic antibiotics is generally limited, and the procalcitonin based algorithm of antibiotic use has recently been investigated to distinguish between inflammation and infection in patients with AP. Although urgent ERCP (within 24 h) should be performed for patients with gallstone pancreatitis and cholangitis, urgent ERCP is not indicated in patients without cholangitis. Furthermore, convalescent treatment, including cholecystectomy in gallstone pancreatitis and alcohol intervention in alcoholic pancreatitis, is also important for improving the prognosis and prevent recurrence in patients with AP. This review focuses on recent updates on the initial and convalescent management strategies for AP.

This study explores the determinants of ICO success, where success is defined as the amount of capital a project was able to raise. ICOs are a tool for startups in the blockchain ecosystem to raise early capital with relative ease. The market for ICOs has grown at a rapid pace since its start in 2013. We analyze a unique dataset of 278 projects that finished their ICOs by August 2017 to assess determinants of funding success that we derive from the crowdfunding and venture capital literature. Our results show that ICOs exhibit similarities to classical crowdfunding and venture capital markets. Specifically, we identify resemblances in determinants of funding success regarding human capital characteristics, business model quality, project elaboration and social media activity.

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.

A robust methodology to simulate virtually the residual stresses pattern in welded steel plates is presented. The methodology is applied to the structural analysis of typical welded plates belonging to ship structures, and the effect of residual stresses on the elastoplastic behavior of plates loaded axially is analyzed in comparison to the residual stress free case, both for tension and compression and including initial imperfections. Residual stresses affect in different manner plates with different geometries; thus a parametric study is performed covering the usual range of variation of the most important plate parameters that control the strength of the plates, more precisely the slenderness and the aspect ratio. The results from finite elements analysis are compared with codes and most stablished formulations and recommendations of applicability in the prediction of load-shortening curves for hull’s bending strength evaluation, ultimate strength and ultimate strain of plate elements are made.

The present study aims at investigating the relationship between Initial Public Offerings (IPOs) variables mainly underpricing on one hand, and the brand value measures on the other. Our final data set is 104 international brand companies. We implement empirical approach using hierarchical OLS regression and descriptive statistics. We show that underpricing is positively related to brand value which emphasizes the marketing role of going public and underpricing in enhancing brand equity through the product market, which additionally confirms some information asymmetry models. We also find that on average brand companies had not been recognized as brands at the IPO time. Moreover, we show the positive role of private equity in enhancing brand value, additionally, the non-linear association between underpricing and brand value is not evident. Finally, we draw some policy implication and suggestions for future research.

Recent studies highlight the need to introduce objectives in Initial Teaching Education focused on the development of oral language competence (OLC). The main aim of the study is to examine activities to promote the development of OLC that are carried out in university classrooms and their evaluation, to analyze the relationship between students’ awareness of OLC work and class activities and to identify proposals to improve students’ OLC. Participants were 175 university teachers who teach on the bachelor’s degree in Initial Teacher Education (ITE) and the master’s degree in Secondary Education (MSE) at seven Catalan universities. The data collection instrument was an online questionnaire with 69 questions. The results indicate that 92.5% of participants work on OLC in their subjects, that 76.5% propose activities that are specifically linked to OLC and that 65.1% of participants evaluate OLC in their subject. A total of 39.4% of participants reported the need to increase discussions to generate processes of collaborative and interdisciplinary reflection between university teachers from different areas of knowledge, among others. We conclude that professional development processes need to be designed for ITE teachers to reflect on how they help students to develop OLC from a pragmatic perspective.

In the polar region, the gravity vector and Earth's rotation vector tend to be in the same direction, leading to slower convergence speed and longer alignment time of the moving base alignment. When the alignment time is short, the alignment cannot converge, resulting in low azimuth accuracy. To address this issue, we propose a polar moving base alignment method based on backtracking scheme. Notably, this work first derives a polar coarse alignment method with the inertial frame based on the transverse Earth model. On this basis, we design a polar coarse alignment method based on backtracking scheme and optimize the data storage scheme. Then, an inverse navigation algorithm based on the transverse inertial navigation mechanical arrangement scheme was derived, and a polar fine alignment method based on backtracking scheme was designed. Semi-physical simulation experiments showed that the alignment algorithm based on backtracking scheme can converge in a short time with high alignment accuracy.

The measurements of the proton electromagnetic form factors in the time-like region using the initial state radiation technique are reviewed. Recent experimental studies have shown that initial state radiation processes at high luminosity electron-positron colliders can be effectively used to probe the electromagnetic structure of hadrons. The BABAR experiment at the B-factory PEP-II in Stanford and the BESIII experiment at the $\tau$-charm factory BEPC-II in Beijing have measured the time-like form factors of the proton using the initial state radiation process $e^{+}e^{-}\to pbar{p}\gamma$. The two kinematical regions where the photon is emitted from the initial state at small and large polar angles have been investigated. In the first case the photon is in the region not covered by the detector acceptance and is not detected. The Born cross section and the proton effective form factor have been measured over a wide and continuous range of the the momentum transfer squared $q^2$ from threshold up to ~42 (GeV/c)$^2$. The ratio of electric and magnetic form factors of the proton has been also determined. In this report, the theoretical aspect and the experimental studies of the initial state radiation process $e^{+}e^{-}\to p\bar{p}\gamma$ are described. The measurements of the Born cross section and the proton form factors obtained in these analyses near the threshold region and in the relatively large $q^2$ region are examined. The experimental results are compared to the predictions from theory and models. Their impact on our understanding of the nucleon structure is discussed.

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.

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.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

In this paper, we study the fractional pseudo-parabolic equations u_t + (−△)^s u + (−△)^s u_t = u log |u|. Firstly, we recall the relationship between the fractional Laplace operator (−△)^s and the fractional Sobolev space H^s and discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence of global weak solution: for the low initial energy J(u₀) < d, the solution is global in time with I(u₀) > 0 or ∥u₀∥X_0(Ω) = 0 and blows up +∞ with I(u₀) < 0; for the critical initial energy J(u₀) = d, the solution is global in time with I(u₀) ≥ 0 and blows up at +∞ with I(u₀) < 0. The decay estimate of the energy functional for the global solution is also given.

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.

In this study, the apparent variation range of acoustical parameters were investigated in a concert hall. The initial time delay gap (ITDG) was evaluated in terms of its just noticeable difference (JND) through two instruments, the cello and the trumpet. Even though the IDTG values were prolonged over the measurements and were not significantly varied, an ITDG range of 22 - 220 ms in increments of 91 steps was produced electro-acoustically in an anechoic chamber with a loudspeaker. The result of JNDc ((delta gap/gap) was rated 0.059 and 0.081 at 50% “different” judgement ranges for the cello and trumpet tracks, respectively. The effective duration of the autocorrection function (ACF) of the continuous brainwaves (CBWs) within the alpha (8-13 Hz) frequency range on the left hemisphere responding to 91-step ITDG increments revealed that the continuous ratio minimum Tauee e of CBW was approximately equal to 0.28 s on the trumpet. The continuous ratios of Tauee e_min ((Tauee e_min_rear - Tauee e_min_front)/ Tauee e_min_front) of CBWs were constantly at 0.4. Furthermore, a homologous period of resonance between the subjective JNDc and Tauee e values of the ACF of CBWs in the alpha range allowed us to conclude that the subjective JND of the ITDG in a room is related to the W_IACC value of the interaural cross-correlation function, which reflect the characteristics of source signal themselves and arouse the activities of brain on the right hemisphere (p < 0.01).

In this paper, we study the semilinear pseudo-parabolic equations $\displaystyle u_{t} - \triangle_{\mathbb{B}}u - \triangle_{\mathbb{B}}u_{t} = \left|u\right|^{p-1}u$ on a manifold with conical singularity, where $\triangle _{\mathbb{B}}$ is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary $x_{1} = 0$. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we derive a threshold result of existence and nonexistence of global weak solution: for the low initial energy $J(u_{0})<d$, the solution is global in time with $I(u_{0}) >0$ or $\displaystyle\Vert \nabla_{\mathbb{B}}u_{0}\Vert_{L_{2}^{\frac{n}{2}}(\mathbb{B})} = 0$ and blows up in finite time with $I(u_{0}) < 0$; for the critical initial energy $J(u_{0}) = d$, the solution is global in time with $I(u_{0}) \geq0$ and blows up in finite time with $I(u_{0}) < 0$. The decay estimate of the energy functional for the global solution and the estimates of the lifespan of local solution are also given.

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.

The exceptional performance advantages of the fiber optic gyroscope (FOG) position it as a dominant player in middle and high-end inertial navigation systems. To prevent the loss of sensor precision caused by algorithm design and simplify the complex modeling strategy in traditional methods. We gradually demonstrate the significant role of Convolutional Neural Network (CNN) in the navigation system based on FOG, and utilize the particle swarm optimization algorithm (PSO) to expedite the convergence of the network. The experimental results demonstrate that the initial alignment method based on deep learning is more accurate than the traditional method. The attitude angle error is reduced by 81.25%, 92.54% and 36.53% respectively. The research provides support for the future application of deep learning in optical navigation systems.

A new utilization of entropy in the context of buckling is presented. The novel concept connecting strain energy and entropy for a pin-ended strut is derived. This concept rationalizes the ranking of buckling modes based on strain energy under the assumption of given entropy. By assigning identical entropy to all buckling modes, they can be ranked according to their deformation energy. Conversely, with identical strain energy assigned to all modes, ranking according to entropy is possible. Decreasing entropy was found to represent the scaling factors of buckling modes that coincide with the measurement of initial out-of-straightness imperfections in IPE160 beams. Applied to steel plane frames, scaled buckling modes can be used to model initial imperfections. It is demonstrated that the entropy (scale factor) for given energy roughly decreases with the inverse square of the mode index. For practical engineering, the study presents the possibility of using scaled buckling modes of steel plane frames to model initial geometric imperfections. Entropy proves to be a valuable complement to strain energy in structural mechanics.

This paper presents a comprehensive study based on multiphase seepage and wellbore multiphase flow theories. It establishes a gas intrusion rate calculation model that considers various factors including formation pore permeability, bottomhole pressure difference, drilling fluid rheology, and surface tension. Experiments were conducted to investigate the gas intrusion mechanism under shut-in conditions, and the experimental results were employed to validate the reliability of the proposed gas intrusion rate calculation method. Furthermore, the research explores the transportation rates of single bubbles and bubble clusters in drilling fluid under shut-in conditions. Meanwhile, empirical expressions were derived for the drag coefficient for single bubbles and bubble clusters in the wellbore. These expressions can be used to calculate gas transportation rates for various equivalent radii of single bubbles and bubble clusters. Additionally, a method was developed for calculating the rising velocity of bubble clusters in water based on experimental results. The study reveals that the average bubble size in the bubble cluster is significantly smaller than the size of the single bubble generated from the orifice. When the viscosity of the drilling fluid is low, the bubble cluster transportation velocity exhibits a positive correlation with the average bubble diameter. When the average bubble diameter exceeds 1 mm, the bubble velocity no longer varies with the change in the bubble cluster diameter. The initial bubble size of intrusive gas, the transportation speed of intrusive gas in the wellbore, the gas intrusion rate, and variations of the wellbore pressure after gas intrusion were analyzed. The research results provide theoretical support for wellbore pressure prediction and pressure control under shutdown conditions.

Lead-210 from natural atmospheric fallout is widely used in multidisciplinary studies to date recent sediments. Some of the ²¹⁰Pb-based dating models can produce historical records of sediment accumulation rates (SAR) and initial activity concentrations ( ). The former have been profusely used to track past changes in the sedimentary conditions. Both physical magnitudes are differently affected by model errors (those arising for the partial or null accomplishment of some model assumptions). This work is aimed at assessing the effects on SAR and of model errors in the CRS, CS, PLUM and TERESA dating models, due to random variability in ²¹⁰Pb fluxes, which is a usual sedimentary condition. Synthetic cores are used as virtual laboratories for this goal. Independently of the model choice, SARs are largely affected by model errors, resulting in some large and spurious deviations from the true values. This questions their general use for tracking past environmental changes. are less sensitive to model errors and their trends of change with time may reflect real changes in sedimentary conditions, as it is shown with some real cores from varved sediments.

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.

Accelerating, exact, explicit and simple solutions of relativistic hydrodynamics allow for a simple and natural description of highly relativistic p+p collisions. These solutions yield a finite rapidity distribution, thus they lead to an advanced estimate of the initial energy density of high energy collisions. We show that such an advanced estimate yields an initial energy density in $\sqrt{s}=7$ and 8 TeV p+p collisions at LHC around or above the critical energy density from lattice QCD, and a corresponding initial temperature above the critical temperature from QCD and the Hagedorn temperature. This suggests that the collision energy of the LHC corresponds to a large enough initial energy density to create a non-hadronic perfect fluid even in pp collisions. %We also show, that several times the %critical energy density may have been reached in high multiplicity events, hinting at a non-hadronic medium created in %high multiplicity $\sqrt{s}=7$ and 8 TeV p+p collisions.

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

The issue of optimising the initial stand density (ISD) of tree plantations has high practical importance. The objective of this study was to nondestructively evaluate the influence of the initial stand density of Scots pine plantations located in the European part of the Russian Federation on wood basic density (BD), moisture content (MC), ultrasound velocity (UV), latewood content, and drilling resistance (DR). 45-year-old trees with stand densities of 500, 1000, 3000, 5000, and 10000 trees/ha were tested by a 5-cm-long core sample for gravimetric MCGM and BD, by PULSAR-2.2 for UV along the height (UVH) and through the tree trunk diameter (UVD), by the IML-RESI PD-400 tool for DR, and by GANN HT 85T for MC based on the electrical resistance method (MCERM). A significant influence of ISD was found on DBH, UVD, MCGM, and MCERM. ISD had no significant impact on BD, UVH, and DR. The wood BD ranged from 356 to 578 kg/m-3, with a mean value of 434±3.3 kg/m-3, and was restricted by the soil and environmental factors. DBH and 70% MCERM were good indicators of tree vitality. Linear correlations between DBH and MCERM (R2=0.67), DBH and MCGM (R2=0.74), DR and BD (R2=0.71), and the two-factor model MCGM=f(DBH, BD), (R2=0.76) were found.

The Korean Pathfinder Lunar Orbiter (KPLO)-MAGnetometer (KMAG) consists of three triaxial fluxgate sensors (MAG1, MAG2, and MAG3) to measure the magnetic field around the Moon. The three sensors are mounted in the order of MAG3, MAG2, and MAG1 inside a 1.2 m long boom away from the satellite body. Before it arrived on the Moon, we compared the magnetic field measurements taken by DSCOVR and KPLO in the solar wind to verify the measurement performance of the KMAG instrument. We found that there were artificial disturbances in the KMAG measurement data, such as step-like and spike-like disturbances, which were produced by the spacecraft body. To remove spacecraft-generated disturbances, we applied a multi-sensor method, employing the gradiometer technique and principal component analysis and using KMAG magnetic field data and confirmed the successful elimination of spacecraft-generated disturbances. This indicates that the multi-sensor method is able to clean the magnetic field data measured onboard the KPLO.

The fractional diffusion equations with integrals play a significant role in describing anomalous diffusion phenomena. We first construct an appropriate resolvent family, and use the convolution theorem of Laplace transform, the probability density function, Cauchy integral formula and Fubini theorem to study its related equicontinuity, strongly continuity, compactness, etc. Then, a reasonable mild solution is defined. Finally, by combining some fixed point theorems, we obtain some conclusions on the existence and uniqueness of mild solutions.

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.

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.

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.

Stochastic modelling of geometrically imperfect steel frame structures requires inputs of statistical values of the imperfection parameters, in some cases also with suitably selected mutual correlations between these input parameters. The paper presents a verification study of two stochastic methods to directly model the initial global geometrical imperfections of the steel frame structures. The stochastic input values of geometrical imperfections are derived from the tolerance criteria of the corresponding European Standard. Two advanced stochastic methods have been developed, referred as #RSS (random story sway) and #RSP (random story position). These methods are verified using random sampling simulations. This study provides useful provisions for the advanced numerical analyses of multi-story steel frames of various geometries. The proposed methods are verified for equidistant story heights and for structures of up to 24 stories, hence might be used for the most types of the standard steel frame structures.

The 20–60-μm axon initial segment (AIS) is proximally located at the interface between the axon and cell body. AIS has characteristic molecular and structural properties regulated by the crucial protein, ankyrin-G. The AIS contains a high density of Na+ channels relative to the cell body, which allows low thresholds for initiation of action potential (AP). Molecular and physiological studies have shown that the AIS is also a key domain for the control of neuronal excitability by homeostatic mechanisms. The AIS has high plasticity in normal developmental processes and pathological activities such as injury, neurodegeneration, and neurodevelopmental disorders (NDDs). In the first half of this review, we provide an overview of the molecular, structural, and ion-channel characteristics of AIS, AIS regulation through axo-axonic synapses, and axo-glial interactions. In the second half, to understand the relationship between NDDs and AIS, we discuss the activity-dependent plasticity of AIS, the human mutation of AIS regulatory genes, and the pathophysiological role of the abnormal AIS in the NDD model animals and patients. We propose that AIS may provide a potentially valuable structural biomarker in response to abnormal network activity in vivo as well as a new treatment concept at the neural circuit level.

Current proposals on the temporal sequence in the processing of emotional visual stimuli are partially incompatible with growing empirical data. In the majority of them, the initial evaluation structures (IES) postulated to be in charge of the earliest detection of emotional stimuli (i.e., salient for the individual), are high order structures (i.e., those receiving visual inputs after several synapses). Thus, their latency of response cannot account for the first visual cortex response to emotional stimuli (peaking 80 ms in humans). Additionally, these proposed structures lack the necessary infrastructure to locally analyze the visual features of the stimulus (shape, color, motion, etc.) that define a stimulus as emotional. In particular, the amygdala is defended as the cornerstone IES also in humans, and cortical areas such as the ventral prefrontal cortex or the insula have been proposed as well to intervene in this initial evaluation process. The present review describes several first-order brain structures (i.e., receiving visual inputs after one synapsis), and second order structures (two synapses) that may complement the former, that accomplish with both prerequisites: presenting response latencies compatible with the observed activity at the visual cortex and possessing the necessary architecture to rudimentarily analyze in situ relevant features of the visual stimulation. The visual thalamus, and particularly the lateral geniculate nucleus (LGN), a first-order thalamic nucleus that actively processes visual information, is a good candidate to be the core IES, with the complementary action of the thalamic reticular nucleus (TRN). This LGN-TRN tandem could be supported, also in an ascending, initial evaluation phase, by the pulvinar, a second order thalamic structure, and first-order extra-thalamic nuclei (superior colliculus and certain nuclei of pretectum and the accessory optic system). In sum, the visual thalamus, scarcely studied in relation to emotional processing, is a serious candidate to be the missing link in early emotional evaluation and, in any case, is worth exploring in future research.

Liquefaction risk assessment is critical for the safety and economics of structures. As the soil strata of Ramsar area in north Iran is mostly composed of poorly graded clean sand and the ground water table is found at shallow depths, it is highly susceptible to liquefaction. In this study, a series of isotropic and anisotropic consolidated undrained triaxial tests are performed on reconstituted specimens of Ramsar sand to identify the liquefaction potential of the area. The specimens are consolidated isotropically to simulate the level ground condition, and anisotropically to simulate the soil condition on a slope and/ or under a structure. The various states of soil behavior are studied by preparing specimens at different initial relative densities and applying different levels of effective stress. The critical state soil mechanics approach for identifying the liquefaction susceptibility is adopted and the observed phenomena are further explained in relation to the micro-mechanical behavior. As only four among the 27 conducted tests did not exhibit liquefactive behavior, Ramsar sand can be qualified as strongly susceptible to liquefaction. Furthermore, it is observed that the pore pressure ratio is a good indication of the liquefaction susceptibility

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

The class of A-stable symmetric one-step Hermite-Obrechkoff (HO) methods introduced in [1] for dealing with Initial Value Problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order schemes are conjugate symplectic which is a benefit when the methods have to be applied to Hamiltonian problems. Furthermore a new efficient approach for the computation of the spline extension is introduced, adopting the same strategy developed in [2] for the BS linear multistep methods. The performances of the schemes are tested in particular on some Hamiltonian benchmarks and compared with those of the Gauss Runge-Kutta schemes and Euler-Maclaurin formulas of the same order.

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.

In this paper a new approximate procedure is developed for calculating the inclination angle of the end points of statically determinate beams. The method is based on the topology comparison of simple (hinge-roller combination) supported beam and a resemblant cantilever beam. Assuming that the support reactions of the beam are active forces, the virtual displacements at the points of the reaction forces are calculated. Based on these values the inclination angle is calculated. Several examples are considered and the suggested in this paper, while the procedure is applied for various types of structures and loadings. The results, obtained by the suggested numerical procedure, are compared with analytical ones, and they are in good agreement.

We argue that the problem of time is not a crucial issue inherent in the quantum picture of the universe evolution. On the minisuperspace model example with the massless scalar field, we demonstrate four approaches to the description of quantum evolution, which give similar results explicitly. The relevance of these approaches to building a quantum theory of gravity is discussed.

Initial water content significantly affects the efficiency of soil stabilization. In this study, the effects of initial water content on the compressibility, strength, microstructure and composition of a lean clay soil stabilized by compound calcium-based stabilizer were investigated by static compaction test, unconfined compression test, optical microscope observations, environment scanning electron microscopy, energy dispersive X-ray spectroscopy and X-ray diffraction spectroscopy. The results indicate that as the initial water content increases in the range studied, both the compaction energy and the maximum compaction force decrease linearly and there are less soil aggregates or agglomerations, and smaller proportion of large pores in the compacted mixture structure. In addition, for specimens cured with or without external water supply and under different compaction degrees, the variation law of the unconfined compressive strength with initial water content is different and the highest strength value is obtained at various initial water contents. With the increase of initial water content, the percentage of oxygen element tends to increase in the reaction products of the calcium-based stabilizer, whereas the crystalline mineral of the soil did not change obviously.

In this study, a mixed rule of degree of precision nine has been developed and implemented in the field of electrical sciences to obtain the instantaneous current in the RLC- circuit for particular value .The linearity has been performed with the Volterra’s integral equation of second kind with particular kernel . Then the definite integral has been evaluated through the mixed quadrature to obtain the numerical result which is very effective. A polynomial has been used to evaluate Volterra’s integral equation in the place of unknown functions. The accuracy of the proposed method has been tested taking different electromotive force in the circuit and absolute error has been estimated.

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

This paper aims at computing feasible control strategies and the corresponding feasible state trajectories to drive an autonomous rear-axle bicycle robot from a given initial state to a final state such that the total running cost is minimized. Pontryagin’s Minimum Principle is applied and derives the optimality conditions from which the feasible control functions, expressed as functions of state and costate variables, are substituted into the combined state-costate system to obtain a new free-control state-costate nonlinear system of ordinary differential equations. A computer program was written in Scilab to solve the combined state-costate system and obtain the feasible state functions, the feasible costate functions and the feasible control functions. Associated Computational Simulations were provided to show the effectiveness and the reliability of the approach.

A discharge mixing zone (DMZ) is a defined geographical area or volume of water in the receiving environment of a discharge where initial dilution of the effluent occurs and where exceedance of water quality criteria may be permitted. DMZs are essential to inform determination of discharge consent conditions and an important element of risk management frameworks to reduce any effects of the discharges on the environment and human health. In this review, we describe the principles and technical application of DMZs. We present an overview of the physical processes that govern the dispersion and dilution of wastewater discharges and the fate of contaminants in coastal environments and define key criteria for determining the size of DMZs. We summarize DMZ requirements in international legislation and guidance and exemplify their application to different types of discharges by means of case studies. The selected case studies illustrate different modelling tools for defining DMZs and different monitoring approaches to assess their effectiveness in achieving ecological and human health objectives.

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.

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.