Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schrodinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the(2+1)-dimensional coupled nonlinear Schrodinger equations with propagation distance dependent diffraction,nonlinearity and gain(loss)using the developing Hirota bilinear method,and analyze the dynamical behaviors of these nondegenerate solitons.The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers,varying diffraction and nonlinearity parameters.In addition,when all the variable coefficients are chosen to be constant,the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons.Finally,it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

A Coupled Variable Coefficient Modified KdV Equation Arising from a Two-Layer Fluid System

A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityreductions of the coupled VCmKdV equation are obtained and their corresponding group explanations are discussed.Some exact solutions of the coupled equations are also presented.

EXPLICIT SOLUTIONS TO THE COUPLED KdV EQUATIONS WITH VARIABLE COEFFICIENTS

By means of sn-function expansion method and cn-function expansion method, several kinds of explicit solutions to the coupled KdV equations with variable coefficients are obtained, which include three sets of periodic wave-like solutions. These solutions degenerate to solitary wave-like solutions at a certain limit. Some new solutions are presented.

Evaluation and Improvement of a SVD-Based Empirical Atmospheric Model

An empirical atmospheric model(EAM) based on the singular value decomposition(SVD) method is evaluated using the composite El Ni(?)o/Southern Oscillation(ENSO) patterns of sea surface temperature (SST) and wind anomalies as the target scenario.Two versions of the SVD-based EAM were presented for comparisons.The first version estimates the wind anomalies in response to SST variations based on modes that were calculated from a pair of global wind and SST fields(i.e.,conventional EAM or CEAM).The second version utilizes the same model design but is based on modes that were calculated in a region-wise manner by separating the tropical domain from the remaining extratropical regions(i.e.,region-wise EAM or REAM). Our study shows that,while CEAM has shown successful model performance over some tropical areas, such as the equatorial eastern Pacific(EEP),the western North Pacific(WNP),and the tropical Indian Ocean(TIO),its performance over the North Pacific(NP) seems poor.When REAM is used to estimate the wind anomalies instead of CEAM,a marked improvement over NP readily emerges.Analyses of coupled modes indicate that such an improvement can be attributed to a much stronger coupled variability captured by the first region-wise SVD mode at higher latitudes compared with that captured by the conventional one. The newly proposed way of constructing the EAM(i.e.,REAM) can be very useful in the coupled studies because it gives the model a wider application beyond the commonly accepted tropical domain.

Variable Coupling Strength of Silicene on Ag(lll)

We perform a scanning tunneling microscopy and spectroscopy study on the electronic structures of √3×√3- silicene on Ag（111）. It is found that the coupling strength of √3×√3-silicene with the Ag-（111） substrate is variable in different regions, giving rise to notable effects in experiments. This evidence of decoupling or variable interaction of silicene with the substrate is helpful to in-depth understanding of the structure and clectronic properties of silieene.

Stochastic fluctuations of permittivity coupling regulate seizure dynamics in partial epilepsy

Partial epilepsy is characterized by recurrent seizures that arise from a localized pathological brain region. During the onset of partial epilepsy, the seizure evolution commonly exhibits typical timescale separation phenomenon. This timescale separation behavior can be mimicked by a paradigmatic model termed as Epileptor, which consists of coupled fast-slow neural populations via a permittivity variable. By incorporating permittivity noise into the Epileptor model, we show here that stochastic fluctuations of permittivity coupling participate in the modulation of seizure dynamics in partial epilepsy. In particular, introducing a certain level of permittivity noise can make the model produce more comparable seizure-like events that capture the temporal variability in realistic partial seizures. Furthermore, we observe that with the help of permittivity noise our stochastic Epileptor model can trigger the seizure dynamics even when it operates in the theoretical nonepileptogenic regime. These findings establish a deep mechanistic understanding on how stochastic fluctuations of permittivity coupling shape the seizure dynamics in partial epilepsy,and provide insightful biological implications.

Coupling concepts for simulation:A systematic and comprehensive view and advantages with declarative models

A brief review of the importance of simulation-based engineering and science(including social sciences)is followed by a historic perspective of model-based simulation.Section 2 is on declarative modeling of component systems as well as its advantages for self-documentation and for computer-aided checks and coupling.As an example for declarative modeling,General System Theory(GEST)implementor is given.In Sec.3,basic concepts for coupling of component models,and rules for computer-assisted coupling specification are explained.Section 4 is devoted to possible computerized checks in couplings of declarative models such as:(1)automatic unit checking to avoid meaning-less input/output matching at the time of coupling specification,(2)automatic threshold checking to provide warnings and/or to avoid disasters,and(3)automatic unit conversion for convenience of using library models.Section 5 is about several layers of nested couplings for modeling systems of systems.In Sec.6,two types of variable couplings are discussed:(1)couplings with variable connections(to allow input/output relations of models to depend on time or state conditions)and(2)coupling with variable component models(to allow component(or coupled)models to be switched based on time or state conditions).Section 7 is on the use of multimodels as component models in couplings.Section 8 is on types of inputs and their use in couplings as well as on exter-nal inputs to simulation studies.In Sec.9,conclusions and future work for complex systems are outlined.Especially,the values of simulation systems engineering as well as understanding and avoidance of misunderstanding in cognitive and emotive simulations are stressed.Appendix A is a list of almost 50 types of couplings and Appendix B lists over 50 terms related with couplings in modeling and simulation.To show the richness of“input”concept which is important in specification of input/output relations of component models,Appendix C lists almost 150 types of inputs.Information shared in this article may be useful in developing advanced modeling and simulation software,tools and environments.

Feedback analysis and design of inductive power links driven by Class-E amplifiers with variable coupling coefficients

The efficiency of inductive power links driven by Class-E amplifiers may deteriorate due to variation in the coupling coefficient when the relative position of the radio frequency (RF) coils changes.To solve this problem,a new design methodology of power links is presented in this paper.The aim of the new design is to use the feedback signal,which is a phase difference between the driving signal and the output current of the Class-E amplifier,to adjust the duty cycle and angular frequency of the driving signal to maintain the optimum state of the inductive power link,and to adjust the supply voltage to keep the output power constant when the coupling coefficient of the RF coils changes.The parameter adjustments with respect to the coupling coefficient and the feedback signal are derived from the design equation of the inductive power link.To validate the feedback control rules,a prototype of the inductive power link was constructed,and its performance validated with the coupling coefficient set at 0.2 and a duty cycle of 0.5.The experimental results showed that,by adjusting the duty cycle,the angular frequency,and the supply voltage,the power link can be kept in optimal operation with a constant output power when the coupling coefficient changes from 0.2 to 0.1 to 0.25.