Multiple Soliton Asymptotics in a Spin-1 Bose–Einstein Condensate

Spinor Bose–Einstein condensates(BECs)are formed when atoms in the multi-component BECs possess single hyperfine spin states but retain internal spin degrees of freedom.This study concentrates on a(1+1)-dimensional three-couple Gross–Pitaevskii system to depict the macroscopic spinor BEC waves within the meanfield approximation.Regarding the distribution of the atoms corresponding to the three vertical spin projections,a known binary Darboux transformation is utilized to derive the𝑁matter-wave soliton solutions and triple-pole matter-wave soliton solutions on the zero background,where𝑁is a positive integer.For those multiple matterwave solitons,the asymptotic analysis is performed to obtain the algebraic expressions of the soliton components in the𝑁matter-wave solitons and triple-pole matter-wave solitons.The asymptotic results indicate that the matter-wave solitons in the spinor BECs possess the property of maintaining their energy content and coherence during the propagation and interactions.Particularly,in the𝑁matter-wave solitons,each soliton component contributes to the phase shifts of the other soliton components;and in the triple-pole matter-wave solitons,stable attractive forces exist between the different matter-wave soliton components.Those multiple matter-wave solitons are graphically illustrated through three-dimensional plots,density plot and contour plot,which are consistent with the asymptotic analysis results.The present analysis may provide the explanations for the complex natural mechanisms of the matter waves in the spinor BECs,and may have potential applications in designs of atom lasers,atom interferometry and coherent atom transport.

Exact Tail Asymptotics for a Queueing System with a Retrial Orbit and Batch Service

This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.

Asymptotic Behaviors of Hankelians, Whose Entries Involve Regularly- or Rapidly-Varying Functions, as the Variable Tends to +∞. Part I

The rich literature concerning “asymptotic behavior of Hankel determinants” concerns the behavior, as the order n tends to ∞, of Hankel determinants whose entries are numbers, e.g., with a combinatorial interest or arising as values of special classes of functions. Such determinants are numbers depending on n, playing roles in number theory, combinatorics, random matrices and the like;and mathematicians in the involved fields have been interested in their asymptotic behaviors as n goes to ∞, as previously mentioned, with no single exception to the author’s knowledge. The study carried on in the present paper treats an altogether different situation as suggested by the specification in the title “as the variable tends to +∞”. We deal with those types of Hankel determinants (purposely called Hankelians) which are special cases of Wronskians and, continuing our work on the asymptotics of Wronskians, we study the asymptotic behaviors of n-order Hankelians, whose entries involve either regularly- or rapidly-varying functions, when the variable tends to +∞. As in the study of Wronskians, the treatment of this case also needs the whole apparatus of the theory of higher-order types of asymptotic variation, but the most demanding results are not automatic corollaries of the general theory. In fact, in the study of generic Wronskians (study motivated by applications to asymptotic expansions), the entries were required to belong to one of the classes of “higher-order regular or rapid variation”;on the contrary, in the case of Hankelians, we are confronted with functions whose logarithms are either “regularly- or rapidly-varying functions”, roughly classifiable as “ultrarapidly-varying functions”, and the study requires both special devices and a number of preliminary lemmas about products and linear combinations of functions in the mentioned classes.

Reinforcement learning based adaptive control for uncertain mechanical systems with asymptotic tracking

This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation.The considered system can depict the behavior of a large class of engineering systems,such as vehicular systems,robot manipulators and satellites.All these systems are often characterized by highly nonlinear characteristics,heavy modeling uncertainties and unknown perturbations,therefore,accurate-model-based nonlinear control approaches become unavailable.Motivated by the challenge,a reinforcement learning(RL)adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics.The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error(RISE)control approach.Different from a classical RISE control law,a tanh(·)function is utilized instead of a sign(·)function to acquire a more smooth control signal.The developed controller requires very little prior knowledge of the dynamic model,is robust to unknown dynamics and exogenous disturbances,and can achieve asymptotic output tracking.Eventually,co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom(3-DOF)manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach.

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization

This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.

THE LOGARITHMIC SOBOLEV INEQUALITY FOR A SUBMANIFOLD IN MANIFOLDS WITH ASYMPTOTICALLY NONNEGATIVE SECTIONAL CURVATURE

In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.

THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS

In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

Enhanced Differentiable Architecture Search Based on Asymptotic Regularization

In differentiable search architecture search methods,a more efficient search space design can significantly improve the performance of the searched architecture,thus requiring people to carefully define the search space with different complexity according to various operations.Meanwhile rationalizing the search strategies to explore the well-defined search space will further improve the speed and efficiency of architecture search.With this in mind,we propose a faster and more efficient differentiable architecture search method,AllegroNAS.Firstly,we introduce a more efficient search space enriched by the introduction of two redefined convolution modules.Secondly,we utilize a more efficient architectural parameter regularization method,mitigating the overfitting problem during the search process and reducing the error brought about by gradient approximation.Meanwhile,we introduce a natural exponential cosine annealing method to make the learning rate of the neural network training process more suitable for the search procedure.Moreover,group convolution and data augmentation are employed to reduce the computational cost.Finally,through extensive experiments on several public datasets,we demonstrate that our method can more swiftly search for better-performing neural network architectures in a more efficient search space,thus validating the effectiveness of our approach.

An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic

We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and Xin.These methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional case.These kinetic models depend on a small parameter that can be seen as a"Knudsen"number.The method is asymptotic preserving in this Knudsen number.Also,the computational costs of the method are of the same order of a fully explicit scheme.This work is the extension of Abgrall et al.(2022)[3]to multidimensional systems.We have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.

Asymptotic Dynamics of a Single-species Model with Resource-dependent Dispersal in One Dimension

In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.

不良级配粉细砂路基碾压数值模拟

我国滨海地区存在大量粉细砂,其级配较差,为减少客土使用,可将其用做路基填料。依托海南某旅游公路粉细砂填筑路基项目,建立不良级配粉细砂路基压实过程的PFC2D模型,研究压实作用力、静动碾压和压实遍数的压实效果,建立压实度K和孔隙率n关系。结果发现,不同压实力作用下粉细砂孔隙率沿深度变化不明显,动碾相对于静碾压实效果更好且作用深度更深,随碾压遍数增加,粉细砂孔隙率减小,路基压实度增大,但碾压超过一定遍数后,对压实效果提升不明显。数值模拟与现场试验结果较为一致。

调和分数Ornstein-Uhlenbeck金融模型的参数估计

为了描述金融资产价格过程的长相依性和自相似性,首先构建由调和分数布朗运动驱动的分数Ornstein-Uhlenbeck(O-U)模型.由于调和分数布朗运动是分数布朗运动的推广,故所构建的模型具有更广泛的应用.然后基于离散观测样本,利用最小二乘方法,得到模型漂移参数的估计量,并证明了估计量的相合性和渐近分布.最后,通过模拟展示了所得估计量的有限样本性质,模拟结果显示估计量的值拟合参数真值的效果较好.

广西某高速公路沥青路面车辙病害影响因素分析

对实体依托工程的现场调研、室内试验和建立模型进行分析,从重载交通、路面结构、抗压强度、压实度等因素分析了对广西高速公路沥青路面车辙病害的影响,提出加强对重载、超载的管制,进行针对性路面结构设计,提高沥青路面施工质量稳定性的对策建议。

一类具有脉冲干预措施的COVID-19模型的稳定性分析

建立了一类对易感人群实施脉冲干预措施的COVID-19模型,得出了模型的基本再生数R_(0)和无病周期解。当R_(0)<1时,根据脉冲微分不等式和Lyapunov函数分析了无病周期解的全局稳定性,并数值模拟了这一结论。最后,探讨了脉冲预防策略在COVID-19传染病预防中的效果。

Asymptotic Stability in the Large of Zero Solution of Second Order Nonlinear Differential Equation

There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.

The Asymptotic Stability for a Class of Nonlinear Large Sceale System

This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.

The asymptotic field of mode Ⅰ quasi-static crack growth on the interface between a rigid and a pressure-sensitive material

A mechanical model of the quasi-static interface of a mode I crack between a rigid and a pressure-sensitive viscoelastic material was established to investigate the mechanical characteristic of ship-building engineering hi-materials. In the stable growth stage, stress and strain have the same singularity, ie （σ, ε） ∝ r^-1/（n-1）. The variable-separable asymptotic solutions of stress and strain at the crack tip were obtained by adopting Airy＇s stress function and the numerical results of stress and strain in the crack-tip field were obtained by the shooting method. The results showed that the near-tip fields are mainly governed by the power-hardening exponent n and the Poisson ratio v of the pressure-sensitive material. The fracture criterion of mode I quasi-static crack growth in pressure-sensitive materials, according to the asymptotic analyses of the crack-tip field, can be viewed from the perspective of strain.

空位缺陷硅烯纳米带结构与自旋极化电子性质的密度泛函紧束缚研究

随着纳米电子器件和自旋电子学的不断发展,对小尺寸的纳米硅材料物理和化学性质的研究是研发新型微电子材料器件的基础.硅烯纳米带在实验制备和理论研究中均备受关注.本研究利用基于自洽电荷的密度泛函理论紧束缚方法,研究了不同宽度的硅烯纳米带的结构、稳定性和自旋极化电子性质.研究发现,稳定的完美和带有空位缺陷的硅烯纳米带表现为带有曲翘褶皱的蜂窝结构.纳米带边缘的曲翘度大于中心位置.空位缺陷更容易出现在纳米带边缘.纳米带的宽度可实现完美的硅烯纳米带的半导体性质和金属性之间的转换.硅烯纳米带中出现空位缺陷可有效调控纳米带自旋电子性质从半导体向金属性转变、半导体向半金属性转变,及金属性向为半导体或者半金属性质的转变.这种自旋电子性质的调控手段使得该种纳米材料在纳米电子自旋器件上有着潜在的应用价值.

Asymptotic Behavior and Nonexistence of Positive Solutions of Delay Difference Equations *L

Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.