THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

TIME ANALYTICITY FOR THE HEAT EQUATION ON GRADIENT SHRINKING RICCI SOLITONS

On a complete non-compact gradient shrinking Ricci soliton,we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable.This growth condition is sharp.As an application,we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with quadratic exponential growth on shrinkers.

Analyticity of Semigroups Generated by Singular Differential Matrix Operators

In this paper we prove the analyticity of the semigroups generated by some singular differential matrix operators of the form in the Banach space with suitable boundary conditions. To illustrate the work an example is discussed.

Analyticity of Semigroups generated by Degenerate Mixed Differential Operators

In this paper we are interested in studying the dissipativity of degenerate mixed differential operators involving an interface point. We show that, under particular interface conditions, such operators generate analytic semigroups on an appropriate Hilbert space . To illustrate the results an example is discussed.

On the Radius of Spatial Analyticity for the Inviscid Boussinesq Equations

In this paper,we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations.If the initial datum is real-analytic,the solution remains real-analytic on the existence interval.By an inductive method we can obtain a lower bound on the radius of spatial analyticity of the smooth solution.

State-of-the-art on the anchorage performance of rock bolts subjected to shear load

Rock bolts are extensively utilized in underground engineering as a means of offering support and stability to rock masses in tunnels,mines,and other underground structures.In environments of high ground stress,faults or weak zones can frequently arise in rock formations,presenting a significant challenge for engineering and potentially leading to underground engineering collapse.Rock bolts serve as a crucial structural element for the transmission of tensile stress and are capable of withstanding shear loads to prevent sliding of weak zones within rock mass.Therefore,a complete understanding of the behavior of rock bolts subjected to shear loads is essential.This paper presents a state-of-the-art review of the research progress of rock bolts subjected to shear load in three categories:experiment,numerical simulation,and analytical model.The review focuses on the research studies and developments in this area since the 1970s,providing a comprehensive overview of numerous factors that influence the anchorage performance of rock bolts.These factors include the diameter and angle of the rock bolt installation,rock strength,grouting material,bolt material,borehole diameter,rock bolt preload,normal stress,joint surface roughness and joint expansion angle.The paper reviews the improvement of mechanical parameter setting in numerical simulation of rock bolt shear.Furthermore,it delves into the optimization of the analytical model concerning rock bolt shear theory,approached from the perspectives of both Elastic foundation beam theory coupled with Elastoplasticity theory and Structural mechanic methods.The significance of this review lies in its ability to provide insights into the mechanical behavior of rock bolts.The paper also highlights the limitations of current research and guidelines for further research of rock bolts.

Analysis of the interaction between bolt-reinforced rock and surface support in tunnels based on convergence-confinement method

To investigate the interaction of the bolt-reinforced rock and the surface support,an analytical model of the convergence-confinement type is proposed,considering the sequential installation of the fully grouted rockbolts and the surface support.The rock mass is assumed to be elastic-brittle-plastic material,obeying the linear Mohr-Coulomb criterion or the non-linear Hoek-Brown criterion.According to the strain states of the tunnel wall at bolt and surface support installation and the relative magnitude between the bolt length and the plastic depth during the whole process,six cases are categorized upon solving the problem.Each case is divided into three stages due to the different effects of the active rockbolts and the passive surface support.The fictitious pressure is introduced to quantify the threedimensional(3D)effect of the tunnel face,and thus,the actual physical location along the tunnel axis of the analytical section can be considered.By using the bolt-rock strain compatibility and the rocksurface support displacement compatibility conditions,the solutions of longitudinal tunnel displacement and the reaction pressure of surface support along the tunnel axis are obtained.The proposed analytical solutions are validated by a series of 3D numerical simulations.Extensive parametric studies are conducted to examine the effect of the typical parameters of rockbolts and surface support on the tunnel displacement and the reaction pressure of the surface support under different rock conditions.The results show that the rockbolts are more effective in controlling the tunnel displacement than the surface support,which should be installed as soon as possible with a suitable length.For tunnels excavated in weak rocks or with restricted displacement control requirements,the surface support should also be installed or closed timely with a certain stiffness.The proposed method provides a convenient alternative approach for the optimization of rockbolts and surface support at the preliminary stage of tunnel design.

Effect of safety valve types on the gas venting behavior and thermal runaway hazard severity of large-format prismatic lithium iron phosphate batteries

The safety valve is an important component to ensure the safe operation of lithium-ion batteries(LIBs).However,the effect of safety valve type on the thermal runaway(TR)and gas venting behavior of LIBs,as well as the TR hazard severity of LIBs,are not known.In this paper,the TR and gas venting behavior of three 100 A h lithium iron phosphate(LFP)batteries with different safety valves are investigated under overheating.Compared to previous studies,the main contribution of this work is in studying and evaluating the effect of gas venting behavior and TR hazard severity of LFP batteries with three safety valve types.Two significant results are obtained:(Ⅰ)the safety valve type dominates over gas venting pressure of battery during safety venting,the maximum gas venting pressure of LFP batteries with a round safety valve is 3320 Pa,which is one order of magnitude higher than other batteries with oval or cavity safety valve;(Ⅱ)the LFP battery with oval safety valve has the lowest TR hazard as shown by the TR hazard assessment model based on gray-fuzzy analytic hierarchy process.This study reveals the effect of safety valve type on TR and gas venting,providing a clear direction for the safety valve design.

Shear behavior of single-joint bolted sandstone subjected to dryewet cycles:Experimental and analytical approaches

A series of direct shear tests under constant normal loading conditions were carried out on specimens of bolted sandstone single-joint treated with different numbers of dryewet cycles.The experimental results show that the peak shear strength and shear stiffness of bolted sandstone joints were significantly reduced after 12 dryewet cycles.The decrease in the shear strength of rough joints is more significant than that of flat joints.Due to the decrease in the strength of the surrounding rock,the deformation characteristics of the bolts are significantly affected by the number of dryewet cycles performed.With an increase in the number of dryewet cycles,the plastic hinge length of the bolt gradually increases,resulting in an increase in the corresponding shear displacement when the bolt breaks.Compared with the tensileeshear failure mode of the bolts in flat joints,the tensileebending failure mode arises for bolts in rough joints.A shear curve model describing the whole process of bolted rock joints is established based on the deterioration of rock mechanical parameters caused by dry‒wet cycles.The model proposed considers the change in the friction angle of the joint surface with the shear displacement,which is applied to the derivation of the model by introducing the dynamic evolutionary friction angle parameter.The reasonably good agreement between a predicted curve and the corresponding experimental curve indicates that this method can effectively predict the shear strength of a bolted rock joint involving rough joint under dryewet cycling conditions.

Applying an Improved Dung Beetle Optimizer Algorithm to Network Traffic Identification

Network traffic identification is critical for maintaining network security and further meeting various demands of network applications.However,network traffic data typically possesses high dimensionality and complexity,leading to practical problems in traffic identification data analytics.Since the original Dung Beetle Optimizer(DBO)algorithm,Grey Wolf Optimization(GWO)algorithm,Whale Optimization Algorithm(WOA),and Particle Swarm Optimization(PSO)algorithm have the shortcomings of slow convergence and easily fall into the local optimal solution,an Improved Dung Beetle Optimizer(IDBO)algorithm is proposed for network traffic identification.Firstly,the Sobol sequence is utilized to initialize the dung beetle population,laying the foundation for finding the global optimal solution.Next,an integration of levy flight and golden sine strategy is suggested to give dung beetles a greater probability of exploring unvisited areas,escaping from the local optimal solution,and converging more effectively towards a global optimal solution.Finally,an adaptive weight factor is utilized to enhance the search capabilities of the original DBO algorithm and accelerate convergence.With the improvements above,the proposed IDBO algorithm is then applied to traffic identification data analytics and feature selection,as so to find the optimal subset for K-Nearest Neighbor(KNN)classification.The simulation experiments use the CICIDS2017 dataset to verify the effectiveness of the proposed IDBO algorithm and compare it with the original DBO,GWO,WOA,and PSO algorithms.The experimental results show that,compared with other algorithms,the accuracy and recall are improved by 1.53%and 0.88%in binary classification,and the Distributed Denial of Service(DDoS)class identification is the most effective in multi-classification,with an improvement of 5.80%and 0.33%for accuracy and recall,respectively.Therefore,the proposed IDBO algorithm is effective in increasing the efficiency of traffic identification and solving the problem of the original DBO algorithm that converges slowly and falls into the local optimal solution when dealing with high-dimensional data analytics and feature selection for network traffic identification.

Analyticity of thermoelastic plates with dynamical boundary conditions

We consider a thermoelastic plate with dynamical boundary conditions. Using the contradictionargument of Pazy's well-known analyticity criterion and P.D.E. estimates, we prove that the corresponding C0semigroup is analytic, hence exponentially stable.

Comprehensive Evaluation of Flower Border Application Value of New and Superior Plants in Hefei Area

An analytic hierarchy process(AHP)was employed to assess the applicability of 18 new and superior varieties of flowers in Hefei City flower border applications.A total of 12 indicators were selected from three distinct aspects of adaptability,ornamental characteristics and use traits,in order to establish a comprehensive evaluation model.The results demonstrate that grade I(J≥2.685)exhibits excellent application value,encompassing six species of plants,such asHydrangeamacrophylla‘Endless Summer’;grade II(2.684≤J≤2.420)is also of notable application value,encompassing five species of plants,such asCallistemonrigidus;grade III(2.419≤J≤2.615)is of average application value,including five species of plants,such asCrocosmiacrocosmiflora;grade IV(J≤2.16)is of relatively poor application value.The evaluation results may be utilized as a theoretical reference for the promotion of new and superior varieties in the flower border of Hefei.

The analyticity of solutions to a class of degenerate elliptic equations

In the present paper,the analyticity of solutions to a class of degenerate elliptic equations is obtained.A kind of weighted norms are introduced and under such norms some degenerate elliptic operators are of weak coerciveness.

Hamiltonian system for the inhomogeneous plane elasticity of dodecagonal quasicrystal plates and its analytical solutions

A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.

Orientation and Decision-Making for Soccer Based on Sports Analytics and AI:A Systematic Review

Due to ever-growing soccer data collection approaches and progressing artificial intelligence(AI) methods, soccer analysis, evaluation, and decision-making have received increasing interest from not only the professional sports analytics realm but also the academic AI research community. AI brings gamechanging approaches for soccer analytics where soccer has been a typical benchmark for AI research. The combination has been an emerging topic. In this paper, soccer match analytics are taken as a complete observation-orientation-decision-action(OODA) loop.In addition, as in AI frameworks such as that for reinforcement learning, interacting with a virtual environment enables an evolving model. Therefore, both soccer analytics in the real world and virtual domains are discussed. With the intersection of the OODA loop and the real-virtual domains, available soccer data, including event and tracking data, and diverse orientation and decisionmaking models for both real-world and virtual soccer matches are comprehensively reviewed. Finally, some promising directions in this interdisciplinary area are pointed out. It is claimed that paradigms for both professional sports analytics and AI research could be combined. Moreover, it is quite promising to bridge the gap between the real and virtual domains for soccer match analysis and decision-making.

Analytical Method for the Wave Diffraction of Asymmetrically Arranged Breakwaters

The layout forms of several breakwater structures can be generalized as asymmetrical arrangements in actual engineering.However,the problem of wave diffraction around asymmetrically arranged breakwaters has not been adequately investigated.In this study,we propose an analytical method of wave diffraction for regular waves passing through asymmetrically arranged breakwaters,and we use the Nyström method to obtain the analytical solution numerically.We compared the results of this method with those of previous analytical solutions and with numerical results to demonstrate the validity of our approach.We also provided diffraction coefficient diagrams of breakwaters with different layout forms.Moreover,we described the analytical expression for the problem of diffraction through long-wave incident breakwaters and presented an analysis of the relationship between the diffraction coefficients and the widths of breakwater gates.The analytical method presented in this study contributes to the limited literature on the theory of wave diffraction through asymmetrically arranged breakwaters.

An approximate analytical model for unconventional reservoir considering variable matrix blocks and simultaneous matrix depletion

In regard to unconventional oil reservoirs,the transient dual-porosity and triple-porosity models have been adopted to describe the fluid flow in the complex fracture network.It has been proven to cause inaccurate production evaluations because of the absence of matrix-macrofracture communication.In addition,most of the existing models are solved analytically based on Laplace transform and numerical inversion.Hence,an approximate analytical solution is derived directly in real-time space considering variable matrix blocks and simultaneous matrix depletion.To simplify the derivation,the simultaneous matrix depletion is divided into two parts:one part feeding the macrofractures and the other part feeding the microfractures.Then,a series of partial differential equations(PDEs)describing the transient flow and boundary conditions are constructed and solved analytically by integration.Finally,a relationship between oil rate and production time in real-time space is obtained.The new model is verified against classical analytical models.When the microfracture system and matrix-macrofracture communication is neglected,the result of the new model agrees with those obtained with the dual-porosity and triple-porosity model,respectively.Certainly,the new model also has an excellent agreement with the numerical model.The model is then applied to two actual tight oil wells completed in western Canada sedimentary basin.After identifying the flow regime,the solution suitably matches the field production data,and the model parameters are determined.Through these output parameters,we can accurately forecast the production and even estimate the petrophysical properties.

Large-aperture Telescope Tracking Control Based on Time-synchronization Strategy

A time-synchronization strategy for packetized transmission of target position about a large-aperture telescope observation control system has been proposed in this study.Compared with the existing telescope tracking strategy,the target position packing and sending strategy based on the time synchronization method proposed in this paper has the advantages of high stability and reliability.First,the telescope tracking observation control method was elaborated in this paper,including the motion pattern during telescope tracking.Then,the strategy for packetizes transmission of target positions based on time-synchronization is established and lists the detailed steps.Finally,the performance of the tracking strategy is verified using the 2.5 m telescope for the simulated uniform speed star and the blind-tracking fixed star HIP 31216,respectively.The test results show that the accuracy root mean square of the tracking strategy proposed in this paper is less than 0".02 at 30 minutes,and the performance is much better than the design requirement of 0".3.The most important advantage of this tracking strategy is that the telescope can guarantee normal tracking for a certain period of time even if the hardware or software of the host computer is abnormal.

A Quick Calculation Method for Radiation Pattern of Submillimeter Telescope with Deformation and Displacement

Radiation pattern captures the electromagnetic performance of reflector antennas,which is significantly affected by the deformation of the primary reflector due to gravity and the displacement of the secondary reflector.During the design process of large reflector antennas,a substantial amount of time is often dedicated to iteratively adjusting structural parameters and validating electromagnetic performance.To improve the efficiency of the design process,we first propose an approximate calculation method of optical path difference(OPD)for the deformation of the primary reflector under gravity and the displacement of the secondary reflector.Then an OPD fitting function based on the modified Zernike polynomials is proposed to capture the phase difference of radiation over the aperture plane,based on which the radiation pattern will be obtained quickly by the aperture field integration method.Numerical experiments demonstrate the effectiveness of the proposed quick calculation method for analyzing the radiation pattern of a 10.4 m submillimeter telescope antenna at its highest operating frequency of 856 GHz.In comparison with the numerical simulation method based on GRASP(which is an antenna electromagnetic analysis tool combining physical optics(PO)and physical theory of diffraction(PTD)),the quick calculation method reduces the time for radiation pattern analysis from more than one hour to less than two minutes.Furthermore,the quick calculation method exhibits excellent accuracy for the figure of merit(FOM)of the radiation pattern.Therefore,the proposed quick calculation method can obtain the radiation pattern with high speed and accuracy.Compared to the time-consuming numerical simulation method(PO and PTD),it can be employed for quick analysis of the radiation pattern for the lateral displacement of the secondary reflector and the deformation of the primary reflector under gravity in the design process of a reflector antenna.

Consolidation of high replacement ratio stone column-reinforced ground:Analytical solutions incorporating clogging effect

The utilization of stone columns has emerged as a popular ground improvement strategy,whereas the drainage performance can be adversely hampered by clogging effect.Despite the ample progress of calculation methods for the consolidation of stone column-improved ground,theoretical investigations into the clogging effect have not been thoroughly explored.Furthermore,it is imperative to involve the column consolidation deformation to mitigate computational error on the consolidation of composite ground with high replacement ratios.In this context,an analytical model accounting for the initial clogging and coupled time and depth-dependent clogging of stone columns is established.Then,the resulting governing equations and analytical solutions are obtained under a new flow continuity relationship to incorporate column consolidation deformation.The accuracy and reliability of the proposed model are illustrated by degradation analysis and case studies with good agreements.Subsequently,the computed results of the current study are juxtaposed against the existing models,and an in-depth assessment of the impacts of several crucial parameters on the consolidation behavior is conducted.The results reveal that ignoring column consolidation deformation leads to an overestimate of the consolidation rate,with maximum error reaching up to 16%as the replacement ratio increases.Furthermore,the initial clogging also has a significant influence on the consolidation performance.Additionally,the increment of depth and time-clogging factors a and b will induce a noticeable retardation of the consolidation process,particularly in the later stage.