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.

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.

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.

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.

Nonlinear Study on the Mechanical Performance of Built-Up Cold-Formed Steel Concrete-Filled Columns under Compression

Given their numerous functional and architectural benefits,such as improved bearing capacity and increased resistance to elastic instability modes,cold-formed steel(CFS)built-up sections have become increasingly developed and used in recent years,particularly in the construction industry.This paper presents an analytical and numerical study of assembled CFS two single channel-shaped columns with different slenderness and configurations(backto-back,face-to-face,and box).These columns were joined by double-row rivets for the back-to-back and box configurations,whereas they were welded together for the face-to-face design.The built-up columns were filled with ordinary concrete of good strength.Finite element models were applied,using ABAQUS software,to assess mechanical performance and study the influence of assembly techniques on the behavior of cold-formed columns under axial compression.Analytical approaches based on Eurocode 3 and Eurocode 4 recommendations for un-filled and concrete-filled columns respectively were followed for the numerical analysis,and concrete confinement effects were also considered per American Concrete Institute(ACI)standards for face-to-face and box configurations.The obtained results indicated a good correlation between the numerical results and the proposed analytical methodology which did not exceed 8%.The failure modes showed that the columns failed due to instabilities such as local and global buckling.

The suitability assessment on site selection for bottom seeding scallop culture based on analytic hierarchy process

Scallop culture is an important way of bottom-seeding marine ranching,which is of great significance to improve the current situation of fishery resources.However,there are some problems in site-selection evaluation of marine ranching,such as imperfect criteria system,complex structure,untargeted criteria quantification,etc.In addition,no site-selection evaluation method of bottom-seeding culture areas for scallops is available.Therefore,we established a hierarchy structure model according to the analytic hierarchy process(AHP)theory,in which social,physical,chemical,and biological environments are used as main criteria,and marine functional zonation,water depth,current,water temperature,salinity,substrate type,water quality,sediment quality,red tide,phytoplankton,and zooplankton are used as sub-criteria,on which a multi-parameter evaluation system is set up.Meanwhile,the dualism method,assignment method,and membership function method were used to quantify sub-criteria,and a quantitative evaluation for the entire criteria was added,including the evaluation and analysis of two types of unsuitable environmental situations.By overall consideration in scallop yield,quality,and marine ranching construction objectives,the weight of the main criteria could be determined.Five grades in the suitability corresponding to the evaluation result were divided,and the Python language was used to create an evaluation system for efficient calculation and intuitive presentation of the evaluation outcome.Eight marine cases were simulated based on existing survey data,and the results prove that the method is feasible for evaluating and analyzing the site selection of bottom-seeding culture areas for scallops under various environmental situations.The proposed evaluation method can be promoted for the site selection of bottom-seeding marine ranching.This study provided theoretical and methodological references for the site selection evaluation of other types of marine ranching.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked sheet.With the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is illustrated.The resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity transformations.The transformed differential equations are solved analytically.Impacts of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted graphically.The skin friction and Nusselt number were also evaluated.In addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching one.Further,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O nanofluid.Furthermore,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.

A New Scheme of the ARA Transform for Solving Fractional-Order Waves-Like Equations Involving Variable Coefficients

The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations(PDEs)with variable coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The process of finding approximations for dynamical fractional-order PDEs is challenging,but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.

Application of the finite analytic numerical method to a flowdependent variational data assimilation

An anisotropic diffusion filter can be used to model a flow-dependent background error covariance matrix,which can be achieved by solving the advection-diffusion equation.Because of the directionality of the advection term,the discrete method needs to be chosen very carefully.The finite analytic method is an alternative scheme to solve the advection-diffusion equation.As a combination of analytical and numerical methods,it not only has high calculation accuracy but also holds the characteristic of the auto upwind.To demonstrate its ability,the one-dimensional steady and unsteady advection-diffusion equation numerical examples are respectively solved by the finite analytic method.The more widely used upwind difference method is used as a control approach.The result indicates that the finite analytic method has higher accuracy than the upwind difference method.For the two-dimensional case,the finite analytic method still has a better performance.In the three-dimensional variational assimilation experiment,the finite analytic method can effectively improve analysis field accuracy,and its effect is significantly better than the upwind difference and the central difference method.Moreover,it is still a more effective solution method in the strong flow region where the advective-diffusion filter performs most prominently.

Atmospheric transmission algorithm for pulsed X-rays from high-altitude nuclear detonations based on scattering correction

In high-altitude nuclear detonations,the proportion of pulsed X-ray energy can exceed 70%,making it a specific monitoring signal for such events.These pulsed X-rays can be captured using a satellite-borne X-ray detector following atmospheric transmission.To quantitatively analyze the effects of different satellite detection altitudes,burst heights,and transmission angles on the physical processes of X-ray transport and energy fluence,we developed an atmospheric transmission algorithm for pulsed X-rays from high-altitude nuclear detonations based on scattering correction.The proposed method is an improvement over the traditional analytical method that only computes direct-transmission X-rays.The traditional analytical method exhibits a maximum relative error of 67.79% compared with the Monte Carlo method.Our improved method reduces this error to within 10% under the same conditions,even reaching 1% in certain scenarios.Moreover,its computation time is 48,000 times faster than that of the Monte Carlo method.These results have important theoretical significance and engineering application value for designing satellite-borne nuclear detonation pulsed X-ray detectors,inverting nuclear detonation source terms,and assessing ionospheric effects.

Analytical solutions to the precession relaxation of magnetization with uniaxial anisotropy

Based on the Landau-Lifshitz-Gilbert(LLG)equation,the precession relaxation of magnetization is studied when the external field H is parallel to the uniaxial anisotropic field H_(k).The evolution of three-component magnetization is solved analytically under the condition of H=nH_(k)(n=3,1 and 0).It is found that with an increase of H or a decrease of the initial polar angle of magnetization,the relaxation time decreases and the angular frequency of magnetization increases.For comparison,the analytical solution for H_(k)=0 is also given.When the magnetization becomes stable,the angular frequency is proportional to the total effective field acting on the magnetization.The analytical solutions are not only conducive to the understanding of the precession relaxation of magnetization,but also can be used as a standard model to test the numerical calculation of LLG equation.