Sharif Digital Repository

We study phonon delocalization in disordered media in the presence of nonlinearity. By considering the Fermi-Pasta-Ulam β-model, we show that regardless of whether the initial state of the linear system is localized or not, the final state will be an extended mode after turning on the nonlinear term. We report on the results of an extensive dynamical simulation of a disordered nonlinear system, which show that, independent of the initial mode frequency, in the final state the energy spectrum is excited according to the Kolmogorov spectrum E(ω)∼ω-5/3. Finally, we show that disorder will not cause delocalization of intrinsic localized modes. © 2020 American Physical Society  

In this paper, the Extended Kalman filtering (EKF) approach has been used to infer gene regulatory networks using time-series gene expression data. Gene expression values are considered stochastic processes and the gene regulatory network, a dynamical nonlinear stochastic model. Using these values and a modified Kalman filtering approach, the model's parameters and consequently the interactions amongst genes are predicted. In this paper, each gene-gene interaction is modeled using a linear term, a nonlinear one, and a constant term. The linear and nonlinear term coefficients are included in the state vector together with the gene expressions' true values. Through the extended Kalman... 

There is a growing interest, both from the theoretical as well as experimental side, to test the validity of the quantum superposition principle, and of theories which explicitly violate it by adding nonlinear terms to the Schrödinger equation. We review the original argument elaborated by Gisin (1989 Helv. Phys. Acta 62 363), which shows that the non-superluminal-signaling condition implies that the dynamics of the density matrix must be linear. This places very strong constraints on the permissible modifications of the Schrödinger equation, since they have to give rise, at the statistical level, to a linear evolution for the density matrix. The derivation is done in a heuristic way here... 

In this work, we implement a relatively new analytical technique, the exp-function method, for solving nonlinear special form of generalized nonlinear (2 + 1) dimensional Broer-Kaup-Kupershmidt equation, which may contain high nonlinear terms. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations which applied in engineering mathematics. Some numerical examples are presented to illustrate the efficiency and reliability of exp method. It is predicted that exp-function method can be found widely applicable in engineering  

In this paper, a new approach is used to obtain the nonlinear mode for a flexible cantilever beam. The dependency of resonance of the beam on the exciting force amplitude is observed experimentally and theoretically. In this regard, the end response of a cantilever beam under the base excitation is measured for various force amplitudes. Then, by using the nonlinear normal modes, the reduced-order governing equation is obtained. The discrete model obtained according to identification of nonlinear terms can predict the frequency response of the beam and jump phenomenon properly. Comparison between experimental data and theoretical outputs show acceptable agreement. © 2020 Faculty of... 

Observability of bulk power transmission network by means of minimum number of phasor measurement units (PMUs), with the aid of the network topology, is a great challenge. This paper presents a novel equivalent integer linear programming method (EILPM) for the exhaustive search-based PMU placement. The state estimation implemented based on such a placement is completely linear, thereby eliminating drawbacks of the conventional SCADA-based state estimation. Additional constraints for observability preservation following single PMU or line outages can easily be implemented in the proposed EILPM. Furthermore, the limitation of communication channels is dealt with by translation of nonlinear... 

Carbon nanotubes (CNTs) are viewed as rolled graphene. Thus, an appropriate formulation describing the behavior of CNTs must contain the key information about both their initial configuration as graphene and final configuration as CNT.On this note, to date, somemodels, in particular based on the Cauchy- Born rule, for the description of CNTs behavior exist. A simplifying assumption in some of these models is that the length and perimeter of the CNT equal the corresponding dimensions of the unrolled initial configuration, thus neglecting the induced hoop and longitudinal strains. On the other hand, the present work offers a purely nonlinear continuum model suitable for the description of the... 

A new modeling and analysis of the nonlinearities caused by the capacitor mismatch errors in the pipeline analog-to-digital converters (ADCs) is presented. Error in each stage is modeled by an input-referred gain error and a nonlinear term. A method is proposed for calculation of the ADC integral nonlinearity (INL) from the total input referred error. Analytical expressions for estimation of the ADC INL in terms of standard deviation of random capacitor mismatch errors are derived. The proposed model is verified by system-level Monte Carlo simulations  

In the first part of this paper, the nonlinear coupled governing partial differential equations of vibrations by including the bending rotation of cross section, longitudinal and transverse displacements of an inclined pinned-pinned Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity are derived. To do this, the energy method (Hamilton's principle) based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations is used. These equations are solved using the Galerkin's approach via numerical integration methods to obtain dynamic... 

According to the fact that humans and animals show marvelous capacities in walking on irregular terrain, there is a strong need for adaptive algorithms in walking of biped robots to behave like them. Since the stance leg can easily rise from the ground, the problem of controlling the biped robots is difficult. In other words, the biped walkers have fewer actuators than the degrees of freedom. So they are underactuated mechanical systems. In this paper according to the humans and animals locomotion algorithms, the stability of an underactuated biped walker having point feet is investigated by central pattern generators. For tuning the parameters of the CPG, an effective energy based... 

In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various...