QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.

Spatiotemporal quasiperiodicity transition to chaos in the one-way coupled bistability lattice system

One-way coupled optical bnstability lattice (OCBL) system for open flow is investigated. By using numerical simulations spatiotemporal quasiperiodicity is found. A rough phase diagram indicating the main spatiotemporal dynamic behavior in weakly coupled lattice is given. The transitions between spatiotemporal quasiperiodicity and chaos are observed. This result is important for the understanding of turbulence.

Real eigenvalues determined by recursion of eigenstates

Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.

Mobility edges generated by the non-Hermitian flatband lattice

We study the cross-stitch flatband lattice subject to the quasiperiodic complex potential exp(ix). We firstly identify the exact expression of quadratic mobility edges through analytical calculation, then verify the theoretical predictions by numerically calculating the inverse participation ratio. Further more, we study the relationship between the real–complex spectrum transition and the localization–delocalization transition, and demonstrate that mobility edges in this non-Hermitian model not only separate localized from extended states but also indicate the coexistence of complex and real spectrum.

Infrared Transmission in Porous Silicon Multilayers

Porous silicon is a nanostructured material and exhibits efficient photo- and electro-luminescence in the visible range at room temperature, as well as a tunable refractive index determined by its porosity. Porous silicon samples can be obtained by etching a crystalline silicon wafer in a solution of hydrofluoric acid. In this work, we report the fabrication of porous silicon multilayers alternating layers with high and low porosities, which correspondingly produce low and high refractive indices. The free-standing multilayers were formed following three different sequences: periodic, Fibonacci and ThueMorse. These structures were verified by scanning electron microscopy and their infrared transmission spectra were measured by means of Fourier-transform infrared spectroscopy. On the other hand, we calculate the light transmittance of porous silicon multilayers by using the transfer matrix method for all directions of incidence and a wide range of wavelengths. The experimental measurements are compared with theoretical results and a good agreement is observed. In addition, an analysis of infrared absorption peaks due to the molecular vibrations at pore surfaces reveals the presence of hydrogen and oxygen atoms.

STRONGLY RESONANT BIFURCATIONS OF NONLINEARLY COUPLED VAN DER POL-DUFFING OSCILLATOR

In this paper, the strongly resonant bifurcations of a nonlinearly coupled Van der Pol-Duffing Oscillator by the classical multi-scale method are studied. It is shown that there exist Periodic motions of a single oscillator, frequency-locking andquasi-periodic motions of two oscillators when the parameters vary. Meanwhile,some numerical results are given to test the theoretical ones.

Invariable mobility edge in a quasiperiodic lattice

We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytically demonstrate that this critical energy is a constant independent of strength of potentials.Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal theory.All numerical results are in excellent agreement with the analytical results.Finally,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.

APPLICATION OF WAVELET TRANSFORM TO BIFURCATION AND CHAOS STUDY

The response of a nonlinear vibration system may be of three types, namely,periodic, quasiperiodic or chaotic. when foe parameters of foe system are changed. The periodic motions can be identified by Poincarb map, and harmonic wavelet transform(HAT) can distinguish quasiperiod from chaos, so the existing domains of differenttypes of motions of the system can be revealed in the parametric space with themethod of HWT joining with Poincare map.

Monte Carlo Simulation of the Potts Model on a Dodecagonal Quasiperiodic Structure

By means of a Monte Carlo simulation,we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern.The critical temperature and exponents are obtained from finite-size scaling analysis.It is shown that the Potts model on the quasiperiodic lattice belongs to the same universal class as those on periodic ones.

Spectral Structure and Gap-Labeling Properties for a New Class of One-Dimensional Quasilattices

A new class of 1D quasiperiodic lattices,for which the substitution rules are B→BA,and A→BAB,has been studied in several aspects.The high-dimensional projection method for obtaining the quasilattice is presented.A multifractral spectral behavior and gap fabeling properties have been found,which display the perfect quasiperiodicity of the studied model.

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.

The Problem of Quasiperiodic Photonic Structures Solved by Considering the Cut of 2D Periodic Structure

The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.

Studying of Deformation Processes by Two-Coordinate Laser Strainmeter

The results of experimental data processing of a two-coordinate laser strainmeter are discussed. The two-coordinate laser strainmeter consists of two laser strainmeters which measuring shoulders are oriented along the lines “North- South” and “West-East”. Measurement accuracy of the earth's crust microdisplacements of these devices makes 0 to1 nm. Working frequency range is from 0 to 1000 Hz. Processing experimental data the main attention is paid to high tides, natural oscillations of the Earth, natural oscillations of geoblocks, superficial sea waves. It is established that after separate earthquakes the natural oscillations of regional geoblocks are strongly excited. Besides, it is revealed that quasiperiodic fluctuations of crust in the range of periods from 1 to 12 min. are caused by atmospheric processes. Besides, it is revealed that quasiperiodic oscillations of the earth's crust in the range of periods from 1 to 12 minutes are caused by atmospheric processes.

Test particles and quasiperiodic oscillations around Kiselev black hole with cloud of strings

In the present study,we investigate the dynamics of test particles around a Schwarzschild black hole surrounded by quintessence and immersed in a scalar string cloud field.We start our study by defining the possible values of the quintessence and cloud of string parameters corresponding to the existence of the black hole horizon for fixed values of the parameters of the equation of state for dark energy.We also study the effects of the effective potential on the circular motion,energy,and angular momentum of the test particles together with the innermost stable circular orbits(ISCOs).We investigate the fundamental frequencies in the particle oscillations along stable circular orbits.We relate the stability of the orbits to the Lyapunov exponent,and the chaotic behavior is studied graphically.Finally,we apply the fundamental frequencies to describe quasiperiodic oscillations(QPOs)and find that,in the presence of both fields,low-frequency twin-peak QPOs are not observed.In addition,we obtain the constraint values for the string cloud parameter and mass of the black hole candidates located in the center of the microquasars GRO J1655-40 and GRS 1915+105 as well as the Milky Way galaxy.

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

Superperiodicity,chaos and coexisting orbits of ion-acoustic waves in a four-component nonextensive plasma

Superperiodicity,chaos and coexisting orbits of ion-acoustic waves(IAWs)are studied in a multi-component plasma consisting of fluid ions,q-nonextensive cold and hot electrons and Maxwellian hot positrons.The significant impacts of the system parameters on superperiodic and nonlinear periodic IAWs are presented.Considering an external periodic perturbation various types of quasiperiodic and chaotic features for IAWs are studied in different parametric ranges through time series’plots,phase spaces and Lyapunov exponents.It has been observed that there exist some coexisting orbits for IAWs.Coexisting orbits for IAWs in a classical electron-positron-ion plasma system are reported.

Quasiperiodic Motions for Asymmetric Oscillators

We prove the existence of quasiperiodic solutions and Lagrange stability for a class ofdifferential equations with jumping nonlinearity x+ax^+-bx^-+φ(x)=p(t), where a, b】0, p(t)∈C(R/2πZ) and φ: R→R is an unbounded function.

Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry

In this paper,we study the existence of quasi-periodic solutions and the bound-edness of solutions for a wide class nonlinear differential equations of second order.Using theKAM theorem of reversible systems and the theory of transformations,we obtain the existenceof quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.

Stability validation on the VLF waveform data of the China-Seismo-Electromagnetic Satellite

The China-Seismo-Electromagnetic Satellite(CSES),which was launched in February 2018,carries the search coil magnetometer(SCM)and the electric field detector(EFD)to realize the high-resolution electromagnetic field and wave detection in the upper ionosphere.Due to the complexity and variability of the ionospheric environment,the stability of such a high sampling rate and high-precision electromagnetic field detection systems is always an essential link in data processing and the scientific application of CSES.This work evaluates the stability of the very-low-frequency(VLF)band detection by validating the systemic sampling-time differences between SCM and EFD in the VLF burst-mode observations.The optimal waveform data preprocessing method is put forward according to the noise levels of the VLF burst-mode observation and the inherent design characteristics of EFD.The VLF waveform data of EFD is rebuilt by filling the data gaps among the sampling sub-periods,making it with a similar sample length to SCM.Then by precisely intercepting the maximum and minimum values of the burst-mode waveforms,the variation of the sampling-time difference between EFD and SCM is statistically evaluated.Results show that during the three years'operation,the sampling-time difference between EFD and SCM predominately keeps below 0.5 s,indicating good stability of EFD and SCM on orbit.Then we developed an automatic synchronization tool based on the similarity function and STA/LTA(short time average over long time average)characteristic function.This tool can effectively realize the precise synchronization between SCM and EFD in the VLF burst-mode observation.This work is helpful to upgrade the data quality of CSES and provides technical support for electromagnetic wave propagation studies.

Solutions of the Generalized Lennard-Jones System

在这份报纸，我们在 n ,$$\ddot x =\left 学习下列概括 Lennard-Jones 系统的解决方案结构({-\frac {\alpha }{{{{\left |x \right|}^{\alpha + 2 }}}}+\frac {\beta }{{{{\left |x \right|}^{\beta + 2 }}}}}\right )x$$ ，与 0 << 。就有零尖动量的周期的答案而言，我们证明相应问题堕落到 1-dimensional 并且无穷地拥有肯定正在震荡的许多周期的答案线答案或经常的答案。就有非零的答案而言尖动量，我们首先计算圆形的答案的莫尔斯索引，然后使用山通行证定理与非零显示出非圆形的答案的存在拓扑的度。我们进一步除系统 countably 事实上拥有的圆形的答案以外证明那有任意地大的拓扑的度的许多周期的答案，无穷地许多伪周期的答案，并且无穷地许多 asymptotic 答案。