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One-dimensional monotone nonautonomous dynamical systems

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Science China mathematics 2024年第2期67卷 281-314页

作者： David Cheban Faculty of mathematics and Computer Science Laboratory of Fundamental and Applied MathematicsMoldova State UniversityChisinau 2009Moldova

This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.

关键词： one-dimensional dynamics pinched and minimal sets global attractors monotone nonautonomous cocycle almost periodic solutions scalar differential/difference equations

Exponentially Convergent Multiscale Finite Element Method

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Communications on applied mathematics and Computation 2024年第2期6卷 862-878页

作者： Yifan Chen Thomas Y.Hou Yixuan Wang applied and Computational mathematics CaltechPasadena 91106USA

We provide a concise review of the exponentially convergent multiscale finite element method(ExpMsFEM)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave *** ExpMsFEM is built on the non-overlapped domain decomposition in the classical MsFEM while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis *** most generalizations of the MsFEM in the literature,the ExpMsFEM does not rely on any partition of unity *** general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential ***,there are online and offline parts in the function representation provided by the *** online part depends on the right-hand side locally and can be computed in parallel *** offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.

关键词： Multiscale method Exponential convergence Helmholtz's equation Domain decomposition Nonlinear model reduction

A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow

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Advances in applied mathematics and Mechanics 2024年第1期16卷 181-207页

作者： Xiaolong Zhao Xijun Yu Zupeng Jia Shijun Zou Meilan Qiu School of mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China School of mathematics and Statistics Huizhou UniversityHuizhouGuangdong 516007China institute of applied Physics and Computational mathematics Beijing 100088China

In this paper,we present a new vertex-centered arbitrary LagrangianEulerian(ALE)finite volume scheme for two-dimensional compressible *** our scheme,the momentum equation is discretized on the vertex control volume,while the mass equation and the energy equation are discretized on the sub-cells which are included in the vertex control *** attain the average of the fluid velocity on the vertex control volume directly by solving the conservation *** we can obtain the fluid velocity at vertex with the reconstructed polynomial of the *** fluid velocity is chosen as the mesh velocity,which makes the mesh move in a Lagrangian *** WENO(Weighted Essentially Non-Oscillatory)reconstructions for the density(the total energy)and the velocity are used to make our scheme achieve the anticipated *** with the general vertexcentered schemes,our scheme with the new approach for the space discretization can simulate some multi-material flows which do not involve large *** addition,our scheme has good robustness,and some numerical examples are presented to demonstrate the anticipated accuracy and the good properties of our scheme.

关键词： Vertex-centered arbitrary Lagrangian-Eulerian sub-cells multi-material flows

Point defects in 2-D liquid crystals with a singular potential:Profiles and stability

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Science China mathematics 2024年第11期67卷 2515-2540页

作者： Zhiyuan Geng Wei Wang Basque Center for applied mathematics School of Mathematical Sciences Zhejiang University

We study radial symmetric point defects with degree k/2 in the 2-D disk or R2in the Q-tensor framework with a singular bulk energy,which is defined by Bingham ***,we obtain the existence of solutions for the profiles of radial symmetric point defects with degree k/2 in the 2-D disk or ***,we prove that the solution is stable for |k| = 1 and unstable for |k| > *** identities are derived and utilized throughout the proof of existence and stability/instability.

关键词： radial symmetric point defects singular bulk potential Bingham closure stability

Driver at 10 MJ and 1 shot/30 min for inertial confinement fusion at high gain:Efficient,compact,low-cost,low laser-plasma instabilities,beam color selectable from 2ω/3ω/4ω,applicable to multiple laser fusion schemes

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Matter and Radiation at Extremes 2024年第4期9卷 4-7页

作者：隋展蓝可 Shanghai institute of Laser Plasma China Academy of Engineering PhysicsShanghai 201800China instituteof applied Physics and Computational mathematics Beijing 100094China

The achievement of ignition at the National Ignition Facility(NIF)has prompted a global wave of further research on inertial fusion energy(IFE).However,IFE requires a target gain G of 30-100,and it is hard to achieve fusion at such high gain with the energy,configuration,and technical approach of the ***,we present a conceptual design for a next-generation laser driver that is applicable to multiple laser fusion schemes and provides 10 MJ,2-3 PW at 3ω(or 2ω,in which case the energy and power can be higher),and one shot per 30 min,with the aim of achieving G>*** is also efficient,compact,and low in cost,and it has low susceptibility to laser-plasma instabilities.

关键词： applicable compact instabilities

GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY

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Acta Mathematica Scientia 2024年第5期44卷 1735-1746页

作者： Gonglin YUAN Xiong ZHAO Jiajia YU School of mathematics and Information Science Center for Applied Mathematics of Guangxi(Guangxi University)Guangxi UniversityNanning530004China

A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization *** global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS *** some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection ***,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

关键词： cautious BFGS nonconvex problems Lipschitz continuity projection technique global convergence

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

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Acta Mathematica Scientia 2024年第2期44卷 532-550页

作者：马文贤杨四辈 School of mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for *** precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/***,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

关键词： elliptic operator Kato square root problem Muckenhoupt weight Riesz transform reverse Hölder inequality

Semi-hydro-equivalent design and performance extrapolation between 100 kJ-scale and NIF-scale indirect drive implosion

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Matter and Radiation at Extremes 2024年第1期9卷 25-34页

作者： Huasen Zhang Dongguo Kang Changshu Wu Liang Hao Hao Shen Shiyang Zou Shaoping Zhu Yongkun Ding Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 10088China institute of applied Physics and Computational mathematics Beijing 10088China

Extrapolation of implosion performance between different laser energy scales is investigated for indirect drive through a semi-hydroequivalent *** radiation transport is non-hydro-equivalent,the peak radiation temperature of the hohlraum and the ablation velocity of the capsule ablator are not scale-invariant when the sizes of the hohlraum and the capsule are scale-varied.A semi-hydro-equivalent design method that keeps the implosion velocity V_(i),adiabat α_(F),and P_(L)/R_(hc)^(2) (where P_(L) is the laser power and R_(hc) is the hohlraum and capsule scale length)scale-invariant,is proposed to create hydrodynamically similar *** semi-hydro-equivalent design and the scaled implosion performance are investigated for the 100 kJ Laser Facility(100 kJ-scale)and the National Ignition Facility(NIF-scale)with about 2 MJ laser *** is found that the one-dimensional implosion performance is approximately hydro-equivalent when V_(i) and α_(F) are kept the *** to the non-hydro-equivalent radiation transport,the yield-over-clean without α-particle heating(YOC_(noα))is slightly lower at 100 kJ-scale than at NIF-scale for the same scaled radiation asymmetry or the same initial perturbation of the hydrodynamic *** overall scaled two-dimensional implosion performance is slightly lower at 100 *** general Lawson criterion factor scales asχ_(noα) ^(2D)∼S^(1.06±0.04)(where S is the scale-variation factor)for the semi-hydro-equivalent implosion design with a moderate YOC_(noα).Our study indicates that χ_(noα)≈0.379 is the minimum requirement for the 100 kJ-scale implosion to demonstrate the ability to achieve marginal ignition at NIF-scale.

关键词： performance transport slightly

Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

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Chinese Physics B 2024年第7期33卷 303-309页

作者：刘勇波 College of mathematics Science Inner Mongolia Normal UniversityHohhot 010022China Inner Mongolia Center for applied mathematics Hohhot 010022China

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

关键词： electroosmotic flow(EOF) curved rectangular microchannels slip boundary conditions