Sharif Digital Repository

We consider the generalized Liénard systemfrac(d x, d t) = frac(1, a (x)) [h (y) - F (x)],frac(d y, d t) = - a (x) g (x), where a, F, g, and h are continuous functions on R and a (x) > 0, for x ∈ R. Under the assumptions that the origin is a unique equilibrium, we study the problem whether all trajectories of this system intersect the vertical isocline h (y) = F (x), which is very important in the global asymptotic stability of the origin, oscillation theory, and existence of periodic solutions. Under quite general assumptions we obtain sufficient and necessary conditions which are very sharp. Our results extend the results of Villari and Zanolin, and Hara and Sugie for this system with h... 

Periodic solutions and their existence are one of the most important subjects in dynamical systems. Fractional order systems like integer ones are no exception to this rule. Tavazoei and Haeri (2009) have shown that a time-invariant fractional order system does not have any periodic solution. In this article, this claim has been investigated and it is shown that although in any finite interval of time the solutions do not show any periodic behavior, when the steady state responses of fractional order systems are considered, periodic orbits can be detected  

Let S be a semigroup. The degree of S is the smallest natural number r such that for each x ∈ S, x(n(x)+r) = x(n(x)), where n(x) ∈ . If such a number r does not exist, we say that the degree of S is infinite. For a group G, this coincides with the exponent of G. We prove that for a periodic ring R, the degree of R equals exp(U(R)), where U(R) denotes the unit group of R. Then we determine all degrees for any rings. © 2008 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and Suzhou University  

Blazed gratings have so far been made tunable by mechanically changing the grating geometry, such as its periodicity. In this work, a low-profile planar blazed metasurface grating is demonstrated which is electronically tunable, with no moving or mechanically changing parts. The reflective metasurface is comprised of planar patch resonators with a cutting slot loaded with a surface mount varactor in each unit cell. Coupling of the incident wave to the resonant surface provides a high efficiency back reflection or blazing. We show that by changing the DC bias, we are able to control the blazing frequency and the reflection angle of the operation. This tuning has been confirmed by simulations... 

In this note, we show that under certain assumptions the matrix Riccati differential equation X′ = A(t)X + XB(t)X + C(t) with periodic coeffi cients admits at least one periodic solution. Also, we give an illustrative example in order to indicate the validity of the assumptions and the novelty of our result. © 2021, Tsing Hua University. All rights reserved  

The arithmetic mean of the first n Fibonacci numbers is not an integer for all n. However, for some values of n, it is. In this paper we consider the sequence of integers n for which the average of the first n Fibonacci numbers is an integer. We prove some interesting properties and present two related conjectures. © 2022, University of Waterloo. All rights reserved  

Recorded accelerograms in the regions near active faults may have specific characteristics that inclusion of their effects on the response of structures is necessary. Of particular importance are permanent displacement, i.e. fling-step, rupture directivity pulses and high-frequency content. Several researchers have focused on the effects of rupture directivity pulses on response of structures. They have shown that long-period structures are severely affected by these types of excitations. However, in near-fault regions, the question 'which building structures are long period?' has not been clearly and quantitatively answered. In this paper, responses of 10-, 20-, 30- and 40-story steel... 

In this paper, it is shown that the fractional-order derivatives of a periodic function with a specific period cannot be a periodic function with the same period. The fractional-order derivative considered here can be obtained based on each of the well-known definitions Grunwald-Letnikov definition, Riemann-Liouville definition and Caputo definition. This concluded point confirms the result of a recently published work proving the non-existence of periodic solutions in a class of fractional-order models. Also, based on this point it can be easily proved the absence of periodic responses in a wider class of fractional-order models. Finally, some examples are presented to show the... 

We consider the homogenization of a Robin boundary value problem in a locally periodic perforated domain which is also time-dependent. We aim at justifying the homogenization limit, that we derive through asymptotic expansion technique. More exactly, we obtain the so-called corrector homogenization estimate that specifies the convergence rate. The major challenge is that the media is not cylindrical and changes over time. We also show the existence and uniqueness of solutions of the microscopic problem. © 2020 American Institute of Mathematical Sciences. All rights reserved  

In this paper, a modified transfer matrix method is applied for the analysis of electromagnetic slow wave propagation in Kronig-Penny photonic crystals. Analytic expressions for Bloch wavenumbers in terms of normalized frequency are derived and the asymptotic behaviour of electromagnetic slow wave propagation in these structures is investigated at different regimes. The tight binding method is also used for the analysis of electromagnetic slow wave propagation in Kronig-Penny photonic crystals and analytic expressions are given. It has been shown that forbidden wavenumbers rather than forbidden frequencies can be observed under specific circumstances  

A distributed, nonlinear dynamic vibration neutralizer is presented to improve vibration suppression characteristics of harmonically excited structures. The absorber subsection consists of a double-ended cantilever beam carrying intermediate lumped masses. The positions of the moving masses are adjustable along the beam in order to comply with the desired optimal performance. The absorber is assumed to be linearly elastic but with the inextensibility along the neutral axis of the beam. Due to the existence of parametric resonance, nonlinearities of the system begin to affect the motion and hence parametric instability occurs. The necessary and sufficient conditions for the existence of... 

In this paper we consider the nonlinear third-order quasi-linear differential equationx‴+k2x′=εfx,x′,x″and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one example to show the realizability of the conditions. The validity of the conditions for the parameter-free problemx‴+k2x′=fx,x′,x″also is considered. © 2001 Academic Press  

In this paper, parametric excitation for MEMS gyroscope proposed by Oropeza-Ramos, et al. [1-4] is examined and problems associated with this kind of excitation are shown. It is proved that origin has exponential stability for some sets of parameter values (including those considered in [1-4]). This stability is shown to be global for linearized system and local for the general nonlinear system. Hence, it is concluded that if there would be a periodic orbit, the system has difficulties reaching it. As a solution, a harmonic term to the parametric excitation is added and the new actuation is referred to as parametro-harmonic excitation. It is shown that there are some parameter values for... 

SFDTD was first introduced as modified Finite Difference Time Domain method by Aminian et al in [1]. They used this method to calculate the TE reflection coefficient for grounded slab and also for periodic array of metallic patches. Later Aminian et al used SFDTD for bandwidth determination of soft and hard ground planes [2] and for determination of permittivity of metamaterials [3]. Yunfei Mao et al also used SFDTD for Solving Oblique incident wave on other kind of patches array [4]  

The aim of this note is to highlight one of the basic differences between fractional order and integer order systems. It is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals. As a result, a limit cycle cannot be expected in the solution of these systems. Our investigation is based on Caputo's definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems. © 2009 Elsevier Ltd. All rights reserved  

The Goos-Haenchen shift of a totally reflected beam at the planar interface of two dielectric media, as if the incident beam is reflected from beneath the interface between the incident and transmitted media, has been geometrically associated with the penetration of the incident photons in the less-dense forbidden transmission region. This geometrical approach is here generalized to analytically calculate the Goos-Haenchen shift in one- and two-dimensional periodic structures. Several numerical examples are presented, and the obtained results are successfully tested against the well-known Artman's formula. The proposed approach is shown to be a fast, simple, and efficient method that can... 

In this study a new method of nonlinear dynamic analysis of structures is described. New one dimensional higher order elements have been used to more accurately model the behavior of the structure through computations on frame sections. In addition, more effects of periodic loading are accounted for in the element's powerful hysteretic loop model. © CIMNE, 2007  

Floquet dynamical quantum phase transitions (FDQPTs) are signified by recurrent nonanalytic behaviors of observables in time. In this work, we introduce a quench-free and generic approach to engineer and control FDQPTs for both pure and mixed Floquet states. By applying time-periodic modulations with two driving frequencies to a general class of spin chain model, we find multiple FDQPTs within each driving period. The model is investigated with equal, commensurate and incommensurate driving frequencies. The nonanalytic cusps of return probability form sublattice structures in time domain. Notably, the number and time locations of these cusps can be flexibly controlled by tuning the...