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nonlinearity and periodic solution of a standard-beam balance oscillation system

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Chinese Physics B 2012年第6期21卷 339-343页

作者：李世松兰江韩冰谭红李正坤 Department of Electrical Engineering Tsinghua University National Institute of Metrology(NIM)

We present the motion equation of the standard-beam balance oscillation system, whose beam and suspensions, compared with the compound pendulum, are connected flexibly and vertically. The nonlinearity and the periodic solution of the equation are discussed by the phase-plane analysis. We find that this kind of oscillation can be equivalent to a standard-beam compound pendulum without suspensions; however, the equivalent mass centre of the standard beam is extended. The derived periodic solution shows that the oscillation period is tightly related to the initial pivot energy and several systemic parameters： beam length, masses of the beam, and suspensions, and the beam mass centre. A numerical example is calculated.

关键词： balance oscillation nonlinearity limit cycle phase plane

On the Differential Uniformity and nonlinearity of a Class of Permutation Quadrinomials Over F_(2 2 m)

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Communications in Mathematical Research 2022年第2期38卷 223-245页

作者： Mengyu Hu Nian Li Xiangyong Zeng Hubei Key Laboratory of Applied Mathematics Faculty of Mathematics and StatisticsHubei UniversityWuhanChina

Permutation polynomials with low differential uniformity and high nonlinearity are preferred in cryptographic systems. In 2018, Tu, Zeng and Helleseth constructed a new class of permutation quadrinomials over the finite field F_(2 2m) for an odd integer m. In this paper, we aim to investigate the differential uniformity and nonlinearity of this class of permutation polynomials so as to find 4-uniform permutation polynomials with high nonlinearity.

关键词： Differential uniformity finite field nonlinearity permutation polynomial

nonlinearity Modulating Intensities and Spatial Structures of Central Pacific and Eastern Pacific El Nio Events

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Advances in Atmospheric Sciences 2017年第6期34卷 737-756页

作者： Wansuo DUAN Chaoming HUANG Hui XU State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG) Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China University of Chinese Academy of Sciences Beijing 100049 China

This paper compares data from linearized and nonlinear Zebiak-Cane model, as constrained by observed sea surface temperature anomaly （SSTA）, in simulating central Pacific （CP） and eastern Pacific （EP） E1 Nino. The difference between the temperature advections （determined by subtracting those of the linearized model from those of the nonlinear model）, referred to here as the nonlinearly induced temperature advection change （NTA）, is analyzed. The results demonstrate that the NTA records warming in the central equatorial Pacific during CP E1 Nino and makes fewer contributions to the structural distinctions of the CP E1 Nino, whereas it records warming in the eastern equatorial Pacific during EP E1 Nino, and thus significantly promotes EP E1 Nino during E1 Nino-type selection. The NTA for CP and EP E1 Nino varies in its amplitude, and is smaller in CP E1 Nino than it is in EP E1 Nino. These results demonstrate that CP E1 Nino are weakly modulated by small intensities of NTA, and may be controlled by weak nonlinearity; whereas, EP E1 Nino are significantly enhanced by large amplitudes of NTA, and are therefore likely to be modulated by relatively strong nonlinearity. These data could explain why CP E1 Nino are weaker than EP E1 Nino. Because the NTA for CP and EP E1 Nino differs in spatial structures and intensities, as well as their roles within different E1 Nino modes, the diversity of E1 Nino may be closely related to changes in the nonlinear characteristics of the tropical Pacific.

关键词： E1 Nifio diversity nonlinearity intensity spatial structures nonlinear temperature advection

Nontrivial coupling of light into a defect:the interplay of nonlinearity and topology

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Light(Science & Applications) 2020年第1期9卷 646-655页

作者： Shiqi Xia Dario Jukic Nan Wang Daria Smirnova Lev Smirnov Liqin Tang Daohong Song Alexander Szameit Daniel Leykam Jingjun Xu Zhigang Chen Hrvoje Buljan The MOE Key Laboratory of Weak-Light Nonlinear Photonics TEDA Applied Physics Institute and School of PhysicsNankai UniversityTianjin 300457China Faculty of Civil Engineering University of ZagrebA.Kacica Miosica 2610000 ZagrebCroatia Nonlinear Physics Centre Research School of PhysicsAustralian National UniversityCanberraACT 2601Australia Institute of Applied Physics Russian Academy of ScienceNizhny Novgorod 603950Russia Collaborative Innovation Center of Extreme Optics Shanxi UniversityTaiyuan 030006 ShanxiPR China Institut für Physik Universitat RostockAlbert-Einstein-Strasse 2318059 RostockGermany Center for Theoretical Physics of Complex Systems Institute for Basic Science(IBS)Daejeon 34126Republic of Korea Basic Science Program Korea University of Science and TechnologyDaejeon 34113Republic of Korea Department of Physics and Astronomy San Francisco State UniversitySan FranciscoCA 94132USA Department of Physics Faculty of ScienceUniversity of ZagrebBijenička c.3210000 ZagrebCroatia

The flourishing of topological photonics in the last decade was achieved mainly due to developments in linear topological photonic structures.However,when nonlinearity is introduced,many intriguing questions arise.For example,are there universal fingerprints of the underlying topology when modes are coupled by nonlinearity,and what can happen to topological invariants during nonlinear propagation?To explore these questions,we experimentally demonstrate nonlinearity-induced coupling of light into topologically protected edge states using a photonic platform and develop a general theoretical framework for interpreting the mode-coupling dynamics in nonlinear topological systems.Performed on laser-written photonic Su-Schrieffer-Heeger lattices,our experiments show the nonlinear coupling of light into a nontrivial edge or interface defect channel that is otherwise not permissible due to topological protection.Our theory explains all the observations well.Furthermore,we introduce the concepts of inherited and emergent nonlinear topological phenomena as well as a protocol capable of revealing the interplay of nonlinearity and topology.These concepts are applicable to other nonlinear topological systems,both in higher dimensions and beyond our photonic platform.

关键词： nonlinearity topological coupling

nonlinearity and Finite-Time Instability in a T21L3 Quasigeostrophic Model

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Acta meteorologica Sinica 2011年第4期25卷 419-429页

作者：姜智娜王东海 State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences

In this paper, a nonlinear optimization method is used to explore the finite-time instability of the atmospheric circulation with a three-level quasigeostrophic model under the framework of the conditional nonlinear optimal perturbation （CNOP）. As a natural generalization of linear singular vector （SV）, CNOP is defined as an initial perturbation that makes the cost function the maximum at a prescribed forecast time under certain physical constraint conditions. Special attentions are paid to the different structures and energy evolutions of the optimal perturbations. The results show that the most instable region of the global atmospheric circulation lies in the midlatitude Eurasian continent. More specially, SV and CNOP in the total energy norm with an optimization time of 2 days both present localness： they are mainly located in the midlatitude Asian continent and its east coast. With extension of the optimization time, SVs are more upstream and less localized in the zonal direction, and CNOPs differ essentially from SVs with broader zonal and meridional coverages; as a result, CNOPs acquire larger kinetic and available potential energy amplifications than SVs in the nonlinear model at the corresponding optimization time. For the climatological wintertime flow, it is seen that the baroclinic terms remain small over the entire time evolution, and the energy production comes essentially from the eddy kinetic energy, which is induced by the horizontal shear of the basic flow. In addition, the effects of SVs and CNOPs on the Eurasian atmospheric circulation are explored. The results show that the weather systems over the Eurasian continent in the perturbed fields by CNOPs are stronger than those by SVs at the optimization time. This reveals that the CNOP method is better in evaluating the instability of the atmospheric circulation while the SV method underestimates the possibility of extreme weather events.

关键词： nonlinearity finite-time instability barotropic baroclinic

Chirped Bright and Kink Solitons in Nonlinear Optical Fibers with Weak Nonlocality and Cubic-Quantic-Septic nonlinearity

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Chinese Physics Letters 2022年第4期39卷 12-16页

作者：周勤钟毓 Houria Triki 孙运周徐四六刘文军 Anjan Biswas Research Center of Nonlinear Science School of Mathematical and Physical SciencesWuhan Textile UniversityWuhan 430200China Radiation Physics Laboratory Department of PhysicsFaculty of SciencesBadji Mokhtar UniversityP.O.Box 1223000 AnnabaAlgeria School of Electronic and Information Engineering Hubei University of Science and TechnologyXianning 437100China State Key Laboratory of Information Photonics and Optical Communications School of ScienceBeijing University of Posts and TelecommunicationsBeijing 100876China Beijing University of Posts and Telecommunications Research Institute Shenzhen 518057China Department of Physics Chemistry and MathematicsAlabama A&M UniversityNormalAL 35762-4900USA Mathematical Modeling and Applied Computation(MMAC)Research Group Department of MathematicsKing Abdulaziz UniversityJeddah 21589Saudi Arabia

This work focuses on chirped solitons in a higher-order nonlinear Schrodinger equation,including cubic-quinticseptic nonlinearity,weak nonlocal nonlinearity,self-frequency shift,and self-steepening effect.For the first time,analytical bright and kink solitons,as well as their corresponding chirping,are obtained.The influence of septic nonlinearity and weak nonlocality on the dynamical behaviors of those nonlinearly chirped solitons is thoroughly addressed.The findings of the study give an experimental basis for nonlinear-managed solitons in optical fibers.

关键词： effect nonlinearity solitons

Optical force-induced nonlinearity and self-guiding of light in human red blood cell suspensions

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Light(Science & Applications) 2019年第1期8卷 927-935页

作者： Rekha Gautam Yinxiao Xiang Josh Lamstein Yi Liang Anna Bezryadina Guo Liang Tobias Hansson Benjamin Wetzel Daryl Preece Adam White Matthew Silverman Susan Kazarian Jingjun Xu Roberto Morandotti Zhigang Chen Department of Physics and Astronomy San Francisco State UniversitySan FranciscoCA 94132USA Department of Biomedical Engineering Vanderbilt UniversityNashvilleTN 37240USA MOE Key Lab of Weak-Light Nonlinear Photonics TEDA Applied Physics Institute and School of PhysicsNankai UniversityTianjin 300457China Guangxi Key Lab for Relativistic Astrophysics Guangxi Colleges and Universities Key Lab of Novel Energy Materials and Related TechnologySchool of Physical Science and TechnologyGuangxi UniversityNanningGuangxi 530004China Department of Physics and Astronomy California State University NorthridgeNorthridgeCA 91330USA Institut National de la Recherche Scientifique Universite du QuebecVarennesQC J3X 1S2Canada Department of Physics Chemistry and BiologyLinkoping UniversityLinkoping SE-58183Sweden School of Mathematical and Physical Sciences University of SussexSussex HouseFalmerBrighton BN19RHUK Department of Biomedical Engineering University of California IrvineIrvineCAUSA Clinical Laboratory Science Program San Francisco State UniversitySan FranciscoCA 94132USA Institute of Fundamental and Frontier Sciences University of Electronic Science and Tech.of ChinaChengdu 610054China ITMO University Saint Petersburg 197101Russia

Osmotic conditions play an important role in the cell properties of human red blood cells(RBCs),which are crucial for the pathological analysis of some blood diseases such as malaria.Over the past decades,numerous efforts have mainly focused on the study of the RBC biomechanical properties that arise from the unique deformability of erythrocytes.Here,we demonstrate nonlinear optical effects from human RBCs suspended in different osmotic solutions.Specifically,we observe self-trapping and scattering-resistant nonlinear propagation of a laser beam through RBC suspensions under all three osmotic conditions,where the strength of the optical nonlinearity increases with osmotic pressure on the cells.This tunable nonlinearity is attributed to optical forces,particularly the forward-scattering and gradient forces.Interestingly,in aged blood samples(with lysed cells),a notably different nonlinear behavior is observed due to the presence of free hemoglobin.We use a theoretical model with an optical force-mediated nonlocal nonlinearity to explain the experimental observations.Our work on light self-guiding through scattering biosoft-matter may introduce new photonic tools for noninvasive biomedical imaging and medical diagnosis.

关键词： nonlinearity suspensions nonlinear

On nonlinearity of S-Boxes and Their Related Binary Codes

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Chinese Journal of Electronics 2016年第1期25卷 167-173页

作者： LIU Jian CHEN Lusheng School of Mathematical Sciences Nankai University

The nonlinearity of S-boxes and their related supercodes of the first order Reed-Muller code are discussed. Based on the properties of multi-output bent functions and almost bent functions, we determine the maximum size of linear supercodes of the first order ReedMuller code which have optimal or suboptimal minimum distance, and we also give the weight distributions of these supercodes which achieve the best possible size. Furthermore, an upper bound on the minimum distance of a class of binary linear codes is presented, which yields a new upper bound on the nonlinearity of S-boxes. The new bound on nonlinearity improves a bound given by Carlet et al. in 2007.

关键词： S-boxes nonlinearity Bent functions Almost bent functions Reed-Muller codes

Effective Bose-Hubbard interaction with enhanced nonlinearity in an array of coupled cavities

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Chinese Physics B 2011年第7期20卷 198-204页

作者：周玲刘忠菊闫伟斌穆青霞 School of Physics and Optoelectronics Engineering Dalian University of Technology

An array of coupled cavities, each of which contains an N four-level atom, is investigated. When cavity fields dispersively interact with the atoms, an effective Bose-Hubbard model can be achieved. By numerically comparing the full Hamiltonian with the effective one, we find that within the parameters region, the effective Hamiltonian can completely account for the Mort-insulator as well as the phase transition from the similar Mort-insulator to superfluid. Through jointly adjusting the classical Rabi frequency and the detuning, the nonlinearity can be improved.

关键词： nonlinearity Bose-Hubbard model quantum phase transition