Interaction of pulses in the nonlinear Schrödinger model

A study was conducted on the interaction of two pulses in the nonlinear Schrodinger (NLS) model. The presence of different scenarios of the behavior depending on the initial parameters of the pulses, such as the pulse areas, the relative phase shift, the spatial and frequency separations were shown. It was observed that a pure real initial condition of the NLS equation can result in additional moving solitons.

On Nonlinear Dynamics and Control of A Particular Portal Frame Foundation Model, Excited by a Non-Ideal Motor

The nonlinear dynamic response and a nonlinear control method of a particular portal frame foundation for an unbalanced rotating machine with limited power (non-ideal motor) are examined. Numerical simulations are performed for a set of control parameters (depending on the voltage of the motor) related to the static and dynamic characteristics of the motor. The interaction of the structure with the excitation source may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. A mathematical model having two degrees of freedom simplifies the non-ideal system. The study of controlling steady-state vibrations of the non-ideal system is based on the saturation phenomenon due to internal resonance.

Nonlinear dynamic model and simulation of morphing wing profile actuated by shape memory alloys

Morphing aircraft have the ability to actively adapt and change their shape to achieve different missions efficiently. The development of morphing structures is deeply related with the ability to model precisely different designs in order to evaluate its characteristics. This paper addresses the dynamic modeling of a sectioned wing profile (morphing airfoil) connected by rotational joints (hinges). In this proposal, a pair of shape memory alloy (SMA) wires are connected to subsequent sections providing torque by reducing its length (changing airfoil camber). The dynamic model of the structure is presented for one pair of sections considering the system with one degree of freedom. The motion equations are solved using numerical techniques due the nonlinearities of the model. The numerical results are compared with experimental data and a discussion of how good this approach captures the physical phenomena associated with this problem. © The Society for Experimental Mechanics, Inc. 2012.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

An analog model for quantum lightcone fluctuations in nonlinear optics

We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable. © 2012 Elsevier Inc.

On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

Suppression of vibrations in a nonlinear half-car model using a magneto-rheological damper

The present work investigates the nonlinear response of a half-car model. The disturbances of the road are assumed to be sinusoidal. After constructing the bifurcation diagram, we use the 0-1 test to identify chaotic motions. The main objective of this study is to eliminate chaotic behavior of the chassis and reduce its vibrations. To accomplish this, a semi-active vehicle suspension control system, using magneto-rheological dampers, is proposed. The proposed semi-active control strategy consists of two nonlinear control laws: a feedforward control, and a feedback control. They are obtained by considering the SDRE (State Dependent Riccati Equation) control, where the control parameter is the voltage applied to the coils of the magneto-rheological dampers. Numerical results show that the proposed control method is effective in significantly reducing of the chassis vibration, increasing, therefore, passenger comfort.

Nonlinear three-dimensional noise filter with low-dose CT angiography: effect on the detection of small high-contrast objects in a phantom model

To study the effect of a nonlinear noise filter on the detection of simulated endoleaks in a phantom with 80- and 100-kVp multidetector computed tomographic (CT) angiography.

A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro

Purpose Femoral fracture is a common medical problem in osteoporotic individuals. Bone mineral density (BMD) is the gold standard measure to evaluate fracture risk in vivo. Quantitative computed tomography (QCT)-based homogenized voxel finite element (hvFE) models have been proved to be more accurate predictors of femoral strength than BMD by adding geometrical and material properties. The aim of this study was to evaluate the ability of hvFE models in predicting femoral stiffness, strength and failure location for a large number of pairs of human femora tested in two different loading scenarios. Methods Thirty-six pairs of femora were scanned with QCT and total proximal BMD and BMC were evaluated. For each pair, one femur was positioned in one-legged stance configuration (STANCE) and the other in a sideways configuration (SIDE). Nonlinear hvFE models were generated from QCT images by reproducing the same loading configurations imposed in the experiments. For experiments and models, the structural properties (stiffness and ultimate load), the failure location and the motion of the femoral head were computed and compared. Results In both configurations, hvFE models predicted both stiffness (R2=0.82 for STANCE and R2=0.74 for SIDE) and femoral ultimate load (R2=0.80 for STANCE and R2=0.85 for SIDE) better than BMD and BMC. Moreover, the models predicted qualitatively well the failure location (66% of cases) and the motion of the femoral head. Conclusions The subject specific QCT-based nonlinear hvFE model cannot only predict femoral apparent mechanical properties better than densitometric measures, but can additionally provide useful qualitative information about failure location.

Loop formulation of the supersymmetric nonlinear O(N) sigma model

We derive the fermion loop formulation for the supersymmetric nonlinear O(N) sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For N ≥ 3 this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For N = 2 we determine the critical point and present boson and fermion masses in the critical regime.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Numerical methods in Nonlinear Analysis of shell structures

The design of shell and spatial structures represents an important challenge even with the use of the modern computer technology.If we concentrate in the concrete shell structures many problems must be faced,such as the conceptual and structural disposition, optimal shape design, analysis, construction methods, details etc. and all these problems are interconnected among them. As an example the shape optimization requires the use of several disciplines like structural analysis, sensitivity analysis, optimization strategies and geometrical design concepts. Similar comments can be applied to other space structures such as steel trusses with single or double shape and tension structures. In relation to the analysis the Finite Element Method appears to be the most extended and versatile technique used in the practice. In the application of this method several issues arise. First the derivation of the pertinent shell theory or alternatively the degenerated 3-D solid approach should be chosen. According to the previous election the suitable FE model has to be adopted i.e. the displacement,stress or mixed formulated element. The good behavior of the shell structures under dead loads that are carried out towards the supports by mainly compressive stresses is impaired by the high imperfection sensitivity usually exhibited by these structures. This last effect is important particularly if large deformation and material nonlinearities of the shell may interact unfavorably, as can be the case for thin reinforced shells. In this respect the study of the stability of the shell represents a compulsory step in the analysis. Therefore there are currently very active fields of research such as the different descriptions of consistent nonlinear shell models given by Simo, Fox and Rifai, Mantzenmiller and Buchter and Ramm among others, the consistent formulation of efficient tangent stiffness as the one presented by Ortiz and Schweizerhof and Wringgers, with application to concrete shells exhibiting creep behavior given by Scordelis and coworkers; and finally the development of numerical techniques needed to trace the nonlinear response of the structure. The objective of this paper is concentrated in the last research aspect i.e. in the presentation of a state-of-the-art on the existing solution techniques for nonlinear analysis of structures. In this presentation the following excellent reviews on this subject will be mainly used.