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Skyrmion-(non)crystal structure stabilized by dipolar interaction

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Rare Metals 2022年第9期41卷 3160-3169页

作者： Ming-xiu Sui Yong Hu Department of Physics College of SciencesNortheastern UniversityShenyang110819China State Key Laboratory of Rolling and Automation Northeastern UniversityShenyang110819China

We report a numerical study on the role of longrange dipolar interaction played on the creation and stabilization of skyrmion-(non)crystal structure in chiral ferromagnetic thin films without any anisotropies,based on a Monte-Carlo simulation *** the increase of external magnetic field,the microscopic spin configuration is transformed from a spin-spiral stripe or labyrinth structure,depending on the strength of dipolar interaction,into a skyrmion-(non)crystal structure,and then into a skyrmiongas structure,and finally into a ferromagnetic ***,with the increase of dipolar interaction,the skyrmion-crystal structure evolves from a triangular arrangement into a square arrangement with the change of skyrmion shape from circle to *** larger dipolar interactions,the skyrmion-crystal structure loses the regular arrangements and the skyrmions,remaining topological,exhibit different shapes and sizes and squeeze with each other,whose distributions are analogous to a non-crystal ***,different skyrmion-(non)crystal structures are stabilized in different ranges of dipolar interactions,which further promotes the applications of skyrmions as non-volatile information carriers.

关键词： Chiral ferromagnetic thin film Skyrmion(non)crystal structure Interfacial Dzyaloshinskii-Moriya interaction Dipolar interaction Monte-Carlo simulation

On the Convergence of Products _sh_1h_n in the Adams Spectral Sequence

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Acta Mathematica Sinica,English Series 2007年第6期23卷 1025-1032页

作者： xiu Gui LIU School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 P.R. China

Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by （b0hn-h1bn-1）∈ ExtA^3,（p^n＋p）q（Zp,Zp） in the Adams spectral sequence. At the same time, he proved that i.（hlhn） ∈ExtA^2,（p^n＋P）q（H^＊M, Zp） is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π（p^n＋p）q-2M. In this paper, with Lin＇s results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq ＋ sp^2q ＋ spq ＋（s - 2）q ＋ s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s＋2,＊-term of the Adams spectral sequence, where p ≥ 7, q = 2（p - 1）, n ≥ 4 and 3 ≤ s 〈 p.

关键词： stable homotopy groups of spheres Adams spectral sequence May spectral sequence

Global Existence of Periodic Solutions in a Physiological Model with Delay

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 1043-1048页

作者： xiu-ling LI College of Applied Mathematics Jilin University of Finance and Economics

A physiological model with delay is considered. The time delay being regarded as a parameter, a group of conditions that guarantee the model have multiple periodic solutions is obtained by the global Hopf bifurcation theorem for FDE and Bendixson＇s criterion for high-dimensional ODE. The results are illustrated by some numerical simulations.

关键词： time delay physiological model periodic solutions

Asymptotic Behavior of Solutions of a Free Boundary Problem Modeling Multi-layer Tumor Growth in Presence of Inhibitor

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Acta Mathematica Sinica,English Series 2011年第8期27卷 1621-1636页

作者： xiu Mei HOU Wuhan Bioengineering Institute Wuhan 430415 P. R. China Department of Mathematics Sun Yat-Sen University Guangzhou 510275 P. R. China

In this paper we study well-posedness and asymptotic behavior of solution of a free boundary problem modeling the growth of multi-layer tumors under the action of an external inhibitor. We first prove that this problem is locally well-posed i[n little H61der spaces. Next we investigate asymptotic behavior of the solution. By computing the spectrum of the linearized problem and using the linearized stability theorem, we give the rigorous analysis of stability and instability of all stationary fiat solutions under the non-fiat perturbations. The method used in proving these results is first to reduce the free boundary problem to a differential equation in a Banach space, and next use the abstract well-posedness and geometric theory for parabolic differential equations in Banach spaces to make the analysis.

关键词： Free boundary problem multi-layer tumor inhibitor well-posedness asymptotic behavior

Matrix Integrable Fourth-Order Nonlinear Schr?dinger Equations and Their Exact Soliton Solutions

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Chinese Physics Letters 2022年第10期39卷 1-6页

作者： Wen-xiu Ma Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700USA School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz-Kaup-Newell-Segur matrix eigenvalue *** on properties of eigenvalue and adjoint eigenvalue problems,we solve the corresponding reflectionless Riemann-Hilbert problems,where eigenvalues could equal adjoint eigenvalues,and formulate their soliton solutions via those reflectionless Riemann-Hilbert *** solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.

关键词： eigenvalue integrable adjoint

Interaction solutions to Hirota-Satsuma-Ito equation in (2+1)-dimensions

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Frontiers of Mathematics in China 2019年第3期14卷 619-629页

作者： Wen-xiu MA Department of Mathematics Zhejiang Normal University Jinhua 321004 China Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia Department of Mathematics and Statistics University of South Florida Tampa FL 33620 USA College of Mathematics and Physics Shanghai University of Electric Power Shanghai 200090 China College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao 266590 China Department of Mathematical Sciences North-West University Mafikeng Campus Mmabatho 2735 South Africa

Abundant exact interaction solutions, including lump-soliton, lump-kink, and lump-periodic solutions, are computed for the Hirota-Satsuma-Ito equation in (2+1)-dimensions, through conducting symbolic computations with Maple. The basic starting point is a Hirota bilinear form of the Hirota-Satsuma-Ito equation. A few three-dimensional plots and contour plots of three special presented solutions are made to shed light on the characteristic of interaction solutions.

关键词： Symbolic computation lump solution interaction solution

A combined Liouville integrable hierarchy associated with a fourth-order matrix spectral problem

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Communications in Theoretical Physics 2024年第7期76卷 1-8页

作者： Wen-xiu Ma Department of Mathematics Zhejiang Normal UniversityJinhua 321004China Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South Florida TampaFL 33620-5700United States of America Material Science Innovation and Modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusMmabatho 2735South Africa

This paper aims to propose a fourth-order matrix spectral problem involving four potentials and generate an associated Liouville integrable hierarchy via the zero curvature formulation.A bi-Hamiltonian formulation is furnished by applying the trace identity and a recursion operator is explicitly worked out,which exhibits the Liouville integrability of each model in the resulting *** specific examples,consisting of novel generalized combined nonlinear Schrodinger equations and modified Korteweg-de Vries equations,are given.

关键词： integrable hierarchy Hamiltonian structure zero curvature equation Lax pair matrix spectral problem

Linear superposition of Wronskian rational solutions to the KdV equation

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Communications in Theoretical Physics 2021年第6期73卷 1-5页

作者： Wen-xiu Ma Department of Mathematics Zhejiang Normal UniversityJinhua 321004ZhejiangChina Department of Mathematics King Abdulaziz UniversityJeddah 21589Saudi Arabia Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700United States of America School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

A linear superposition is studied for Wronskian rational solutions to the Kd V equation,which include rogue wave *** is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear Kd V *** is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.

关键词： soliton equation Wronskian solution rational solution rogue wave the KdV equation

A Nontrivial Product of Filtration s+5 in the Stable Homotopy of Spheres

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Acta Mathematica Sinica,English Series 2007年第3期23卷 385-392页

作者： xiu Gui LIU Department of Mathematics and LPMC Nankai University Tianjin 300071 P. R. China

In this paper, some groups Ext A^s.t （Zp, Zp） with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s＋5 in the stable homotopy groups of spheres πpnq＋（s＋3）pq＋（s＋1）q-5S which is represented （up to a nonzero scalar） by β＋2bohh∈ExtA^s＋5,P^nq＋（n＋3）pq＋（n＋1）q＋s（Zp, Zp） in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2（p - 1）.

关键词： Stable homotopy of spheres Adams spectral sequence Toda Smith spectrum May spectral sequence