Time to most recent common ancestor for stationary continuous state branching processes with immigration

Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables： the time to the most recent common ancestor （MRCA）, the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.     

Mesoscopic Numerical Study on Flow Boiling Heat Transfer Performance in Channels With Multiple Rectangular Heaters北大核心CSCD

The flow boiling phenomenon in a channel with multiple rectangular heaters under a constant wall temperature was numerically studied with the lattice Boltzmann method. The effects of spacings between heaters, heater lengths and heater surface wettabilities on the bubble morphology, the bubble area and the heat flux on the heater surface, were studied. The results show that, the bubble growth rate increases with the spacing between heaters. The larger the bubble area is, the earlier the nucleated bubbles will leave the heater surface. The corresponding boiling heat transfer performance increases by 12% with the spacing between heaters growing from 250 lattices to 1 000 lattices. On the other hand, the longer the heater length is, the earlier the bubble will nucleate and leave the heater surface, and the better the boiling heat transfer performance will be. The boiling heat transfer performance increases by 13% with the heater length rising from 16 lattices to 22 lattices. In addition, the bubble nucleates later on the hydrophilic surface than on the hydrophobic surface. Compared with the hydrophilic surface, the hydrophobic surface retains residual bubbles after the leaving of bubbles from the heater. The average heat flux and the bubble area of the hydrophilic surface are less than those of the hydrophobic surface. With the contact angle changing from 77° to 120°, the heat transfer performance increases by 26%. Finally, the orthogonal test results indicate that, the wettability of the heat exchanger surface has the greatest influence on the flow boiling heat transfer performance, while the heater length has the least influence. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Gamma-Dirichlet algebra and applications

The Gamma-Dirichlet algebra corresponds to the decomposition of the gamma process into the independent product of a gamma random variable and a Dirichlet process. This structure allows us to study the properties of the Dirichlet process through the gamma process and vice versa. In this article, we begin with a brief survey of several existing results concerning this structure. New results are then obtained for the large deviations of the jump sizes of the gamma process and the quasi-invariance of the two-parameter Poisson-Dirichlet distribution. We finish the paper with the derivation of the transition function of the Fleming-Viot process with parent independent mutation from the transition function of the measure-valued branching diffusion with immigration by exploring the Gamma-Dirichlet algebra embedded in these processes. This last result is motivated by an open R. C. Gritfiths. problem proposed by S. N. Ethier and     

Uzawa iteration method for stokes type variational inequality of the second kind

In this paper,the Uzawa iteration algorithm is applied to the Stokes problem with nonlinear slip boundary conditions whose variational formulation is the variational inequality of the second kind.Firstly, the multiplier in a convex set is introduced such that the variational inequality is equivalent to the variational identity.Moreover,the solution of the variational identity satisfies the saddle-point problem of the Lagrangian functional ?.Subsequently,the Uzawa algorithm is proposed to solve the solution of the saddle-point problem. We show the convergence of the algorithm and obtain the convergence rate.Finally,we give the numerical results to verify the feasibility of the Uzawa algorithm.     

Bregman iterative model using the G-norm

In this paper, we analyze the Bregman iterative model using the G-norm. Firstly, we show the convergence of the iterative model. Secondly, using the source condition and the symmetric Bregman distance, we consider the error estimations between the iterates and the exact image both in the case of clean and noisy data. The results show that the Bregman iterative model using the G-norm has the similar good properties as the Bregman iterative model using the L2-norm.     

Inverse Fluid-solid Interaction Scattering Problem Using Phased and Phaseless Far Field Data

We consider the inverse fluid-solid interaction scattering of incident plane wave from the knowledge of the phased and phaseless far field patterns.For the phased data,one direct sampling method for location and shape reconstruction is proposed.Only inner product is involved in the computation,which makes it very simple and fast to be implemented.With the help of the factorization of the far field operator,we give a lower bound of the proposed indicator functional for the sampling points inside the elastic body.While for the sampling points outside,we show that the indicator functional decays like the Bessel function as the points go away from the boundaries of the elastic body.We also show that the proposed indicator functional continuously dependents on the far field patterns,which further implies that the novel sampling method is extremely stable with respect to data error.For the phaseless data,to overcome the translation invariance,we consider the scattering of point sources simultaneously.By adding a reference sound-soft obstacle into the scattering system,we show some uniqueness results with phaseless far field data.Numerically,we introduce a phase retrieval algorithm to retrieve the phased data without the additional obstacle.The novel phase retrieval algorithm can also be combined with the sampling method for phased data.We also design two novel direct sampling methods using the phaseless data directly.Finally,some numerical simulations in two dimensions are conducted with noisy data,and the results further verify the effectiveness and robustness of the proposed numerical methods.     

THE AVERAGE ABUNDANCE FUNCTION WITH MUTATION OF THE MULTI-PLAYER SNOWDRIFT EVOLUTIONARY GAME MODEL

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation.The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of the results of numerical simulation on the basis of the intuitive expression of the average abundance function.In addition,the biological background of this research lies in research on the effects of mutation,which is regarded as a biological concept and a disturbance to game behavior on the average abundance function.The mutation will make the evolutionary result get closer to the neutral drift state.It can be deduced that this affection is not only related to mutation,but also related to selection intensity and the gap between payoff and aspiration level.The main research findings contain four aspects.First,we have deduced the concrete expression of the expected payoff function.The asymptotic property and change trend of the expected payoff function has been basically obtained.In addition,the intuitive expression of the average abundance function with mutation has been obtained by taking the detailed balance condition as the point of penetration.It can be deduced that the effect of mutation is to make the average abundance function get close to 1/2.In addition,this affection is related to selection intensity and the gap.Secondly,the first-order Taylor expansion of the average abundance function has been deduced for when selection intensity is sufficiently small.The expression of the average abundance function with mutation can be simplified from a composite function to a linear function because of this Taylor expansion.This finding will play a significant role when analyzing the results of the numerical simulation.Thirdly,we have obtained the approximate expressions of the average abundance function corresponding to small and large selection intensity.The significance of the above approximate analysis lies in that we have grasped the basic characteristics of the effect of mutation.The effect is slight and can be neglected when mutation is very small.In addition,the effect begins to increase when mutation rises,and this effect will become more remarkable with the increase of selection intensity.Fourthly,we have explored the influences of parameters on the average abundance function with mutation through numerical simulation.In addition,the corresponding results have been explained on the basis of the expected payoff function.It can be deduced that the influences of parameters on the average abundance function with mutation will be slim when selection intensity is small.Moreover,the corresponding explanation is related to the first-order Taylor expansion.Furthermore,the influences will become notable when selection intensity is large.     

ON CONTRACTION AND SEMI-CONTRACTION FACTORS OF GSOR METHOD FOR AUGMENTED LINEAR SYSTEMS

The generalized successive overrelaxation （GSOR） method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102（2005）, pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.     

ON THE FINITE ELEMENT APPROXIMATION OF SYSTEMS OF REACTION-DIFFUSION EQUATIONS BY p/hp METHODS

We consider the approximation of systems of reaction-diffusion equations, with the finite element method. The highest derivative in each equation is multiplied by a parameter ε∈ （0, 1], and as ε → 0 the solution of the system will contain boundary layers. We extend the analysis of the corresponding scalar problem from [Melenk, IMA J. Numer. Anal. 17（1997）, pp. 577-601], to construct a finite element scheme which includes elements of size O（εp） near the boundary, where p is the degree of the approximating polynomials. We show that, under the assumption of analytic input data, the method yields exponential rates of convergence, independently of ε, when the error is measured in the energy norm associated with the problem. Numerical computations supporting the theory are also presented, which also show that the method yields robust exponential convergence rates when the error in the maximum norm is used.     

An analysis of single-index model with monotonic link function

The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h（.）. Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

OPTIMAL PORTFOLIO ON TRACKING THE EXPECTED WEALTH PROCESS WITH LIQUIDITY CONSTRAINTS

In this article, the authors consider the optimal portfolio on tracking the expected wealth process with liquidity constraints. The constrained optimal portfolio is first formulated as minimizing the cumulate variance between the wealth process and the expected wealth process. Then, the dynamic programming methodology is applied to reduce the whole problem to solving the Hamilton-Jacobi-Bellman equation coupled with the liquidity constraint, and the method of Lagrange multiplier is applied to handle the constraint. Finally, a numerical method is proposed to solve the constrained HJB equation and the constrained optimal strategy. Especially, the explicit solution to this optimal problem is derived when there is no liquidity constraint.     

WAVE COMPUTATION ON THE HYPERBOLIC DOUBLE DOUGHNUT

We compute the waves propagating on the compact surface of constant negative curvature and genus 2 that is a toy model in quantum chaos theory and cosmic topology. We adopt a variational approach using finite elements. We have to implement the action of the fuchsian group by suitable boundary conditions of periodic type. Despite the ergodicity of the dynamics that is quantum weak mixing, the computation is very accurate. A spectral analysis of the transient waves allows to compute the spectrum and the eigenfunctions of the Laplace-Beltrami operator. We test the exponential decay due to a localized dumping satisfying the assumption of geometric control.     

CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works .     

Numerical Simulation of Transient Non-Isothermal Viscoelastic Couette Flows Based on the SPH Method北大核心CSCD

Based on the smoothed particle hydrodynamics (SPH) method, the transient non-isothermal viscoelastic flows were numerically simulated. First, the viscoelastic Couette flow based on the Oldroyd-B model under isothermal condition was simulated. Then, the simulation was extended to the non-isothermal case, in which the Reynolds exponential model was adopted to evaluate the dependence of the viscosity and the relaxation time on the temperature. The accuracy and effectiveness of the SPH method for simulating transient non-isothermal viscoelastic flows were verified through comparison with the finite volume method and evaluation of numerical convergence. The different flow characteristics of the non-isothermal flow compared with those of the isothermal flow were discussed. The effects of the temperature dependence coefficient and the Péclet number on the flow physics were analyzed. The numerical results demonstrate that, the SPH method can accurately and effectively simulate transient non-isothermal viscoelastic flow problems. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

OPTIMAL LOGISTICS FOR MULTIPLE JEEPS

We consider variations of the classical jeep problems： the optimal logistics for a caravan of jeeps which travel together in the desert. The main purpose is to arrange the travels for the one-way trip and the round trip of a caravan of jeeps so that the chief jeep visits the farthest destination. Based on the dynamic program principle, the maximum distances for the caravan when only part of the jeeps should return and when all drivers should return are obtained. Some related results such as the efficiency of the abandoned jeeps, and the advantages of more jeeps in the caravan are also presented.     

The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cut-off.This equation is partially elliptic in the velocity direction and degenerates in the spatial variable.We consider the nonlinear Cauchy problem for the fluctuation around the Maxwellian distribution and prove that any solution with mild regularity will become smooth in the Gevrey class at positive time with the Gevrey index depending on the angular singularity.Our proof relies on the symbolic calculus for the collision operator and the global subelliptic estimate for the Cauchy problem of the linearized Boltzmann operator.     

Robust Estimation in Partial Linear Mixed Model for Longitudinal Data

In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.     

The Elements in Crystal Bases Corresponding to Exceptional Modules

According to the Ringel-Green theorem, the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group. Furthermore, its Drinfeld double can be identified with the whole quantum group, in which the BGP- reflection functors coincide with Lusztig＇s symmetries. It is first asserted that the elements corresponding to exceptional modules lie in the integral generic composition algebra, hence in the integral form of the quantum group. Then it is proved that these elements lie in the crystal basis up to a sign. Eventually, it is shown that the sign can be removed by the geometric method. The results hold for any type of Cartan datum.     

Responses of SDOF Structures With SPIS-Ⅱ Dampers Under Random Seismic Excitation北大核心CSCD

A closed-form solution of responses of SDOF structures with SPIS-Ⅱ dampers under seismic excitation modeled with the Clough-Pezien spectrum was proposed, and the shock absorption performance and influential factors of this system were studied based on the proposed method. Firstly, the motion equation for the SPIS-Ⅱ damper was established, and the unified expressions of frequency domain solutions of structural responses, such as the structural displacement and the inerter force, were obtained. Secondly, based on the rational expression decomposition and the residue theorem, the quadratic orthogonal equations of the frequency response eigenvalue function and the Clough-Pezien spectrum were obtained respectively, and in turn the quadratic orthogonal equation of the structural response power spectrum was deduced. Thirdly, the concise closed-form solutions of the 0~2nd-order spectral moments of the structural responses were acquired. The proposed method and the virtual excitation method were used to analyze a case respectively, which verifies the correctness of the proposed method. Finally, the proposed method was used to analyze the effects of the inerter parameters on the seismic performances of the structure. The research shows that, the proposed method gives closed-form solutions better than those given by the virtual excitation method in terms of computation efficiency and accuracy. The damping performance will improve with the increase of µm and µξ for a constant µω and the damping performance will reach the optimum for µω=1. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.