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The objective of this study is to investigate the post-buckling of sandwich beams possessing functionally graded material (FGM) faces and functionally graded porous (FGP) cores in thermal environment. Thus, the critical buckling temperature and the deformation of such sandwich beams are determined and discussed in detail for three main types of temperature distributions which are uniform, linear and nonlinear temperature rises. An improved third-order shear deformable theory based on more rigorous kinematics of displacements is employed with von Kármán nonlinearity for constructing the energy equations of the problem. A Jacobi–Ritz method cooperating with the direct iteration procedure and Newton–Raphson technique is utilized to carry out the solutions of the sandwich beams associated with several parameters of material composition, porous coefficient, geometrical ratio and others. Based on the results, it can be disclosed that the beams can withstand the deformation due to thermal loadings if they have more pores inside the core. The resistance to deformation brought on by thermal loadings is significantly improved by increasing the sandwich thickness ratio.

In nuclear physics, the relativistic mean-field theory describes the nucleus as a system of Dirac nucleons which interact via meson fields. In a static case and without nonlinear self-coupling of the σ meson, the relativistic mean-field equations become a system of Dirac equations where the potential is given by the meson and photon fields. The aim of this work is to prove the existence of solutions of these equations. We consider a minimization problem with constraints that involve negative spectral projectors and we apply the concentration-compactness lemma to find a minimizer of this problem. We show that this minimizer is a solution of the relativistic mean-field equations considered.

Electroencephalogram (EEG) signals, which record the electrical activity in the brain, are useful for assessing the mental state of a person. Since these signals are nonlinear and non-stationary in nature, it is very difficult to decipher the useful information from them using conventional statistical and frequency domain methods. Hence, the application of nonlinear time series analysis to EEG signals could be useful to study the dynamical nature and variability of the brain signals. In this paper, we propose a Computer Aided Diagnostic (CAD) technique for the automated identification of normal and alcoholic EEG signals using nonlinear features. We first extract nonlinear features such as Approximate Entropy (ApEn), Largest Lyapunov Exponent (LLE), Sample Entropy (SampEn), and four other Higher Order Spectra (HOS) features, and then use them to train Support Vector Machine (SVM) classifier of varying kernel functions: 1st, 2nd, and 3rd order polynomials and a Radial basis function (RBF) kernel. Our results indicate that these nonlinear measures are good discriminators of normal and alcoholic EEG signals. The SVM classifier with a polynomial kernel of order 1 could distinguish the two classes with an accuracy of 91.7%, sensitivity of 90% and specificity of 93.3%. As a pre-analysis step, the EEG signals were tested for nonlinearity using surrogate data analysis and we found that there was a significant difference in the LLE measure of the actual data and the surrogate data.

Epileptic seizures are thought to be generated and to evolve through an underlying anomaly of synchronization in the activity of groups of neuronal populations. The related dynamic scenario of state transitions is revealed by detecting changes in the dynamical properties of Electroencephalography (EEG) signals. The recruitment procedure ending with the crisis can be explored through a spatial-temporal plot from which to extract suitable descriptors that are able to monitor and quantify the evolving synchronization level from the EEG tracings. In this paper, a spatial-temporal analysis of EEG recordings based on the concept of permutation entropy (PE) is proposed. The performance of PE are tested on a database of 24 patients affected by absence (generalized) seizures. The results achieved are compared to the dynamical behavior of the EEG of 40 healthy subjects. Being PE a feature which is dependent on two parameters, an extensive study of the sensitivity of the performance of PE with respect to the parameters' setting was carried out on scalp EEG. Once the optimal PE configuration was determined, its ability to detect the different brain states was evaluated. According to the results here presented, it seems that the widely accepted model of "jump" transition to absence seizure should be in some cases coupled (or substituted) by a gradual transition model characteristic of self-organizing networks. Indeed, it appears that the transition to the epileptic status is heralded before the preictal state, ever since the interictal stages. As a matter of fact, within the limits of the analyzed database, the frontal-temporal scalp areas appear constantly associated to PE levels higher compared to the remaining electrodes, whereas the parieto-occipital areas appear associated to lower PE values. The EEG of healthy subjects neither shows any similar dynamic behavior nor exhibits any recurrent portrait in PE topography.

The model simulates the activity of three neural populations using a Lotka–Volterra predator–prey system and, based on neuro-anatomical and neuro-physiological recent findings, assumes that a functional thalamo-cortical gate should be crossed by 'queuing' thalamic signals and that a sleep promoting substance acts as a modulator. The resultant activity accounts for the sleep stage transitions. In accordance with sleep cycles timing, the model proves to be able to reproduce the clustering and randomness of those peculiar transient synchronized EEG patterns (TSEP) described in normal human sleep and supposed to be related to the dynamic building up of NREM sleep until its stabilization against perturbations.

A generalized optimal current lattice model (GOCLM) for traffic flow is proposed to describe the motion of the dynamical traffic flow with a consideration of multi-interaction of the front lattice sites. In order to verify the reasonability of the new model, the stability condition is obtained by the use of linear stability theory. The modified KdV (Korteweg–de Vries) equation is derived by the use of the nonlinear analysis method and the kink-antikink soliton solution is obtained near the critical point. The propagation velocities of density waves are calculated for different numbers of the front interactions. A numerical simulation is carried out to check out the performance of GOCLM for traffic flow. The simulation results show that GOCLM is better than the previous models in suppressing the traffic jams.

We proposed a new car-following model named as total generalized optimal velocity model (TGOVM) based on the analysis of the previous models. TGOVM is superior to the previous models in stabilizing the uniform traffic flow by considering all the front influencing factors: headways, relative velocities, and interactions. The linear analysis result showed its superiority to the GOVM, FLOVM, and FLRVM. The nonlinear analysis method is adopted to analyze this model, which described by a differential-difference equation. The modified Korteweg-de Vries (KdV) equation is derived and the kink-antikink soliton solution is obtained near the critical point. The simulation results show that the stabilization is enhanced by the improvement.

An extended optimal velocity (OV) difference model is proposed in a cooperative driving system by considering multiple OV differences. The stability condition of the proposed model is obtained by applying the linear stability theory. The results show that the increase in number of cars that precede and their OV differences lead to the more stable traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions, respectively. To verify these theoretical results, the numerical simulation is carried out. The theoretical and numerical results show that the stabilization of traffic flow is enhanced by considering multiple OV differences. The traffic jams can be suppressed by taking more information of cars ahead.

Considering the effect of density difference, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of pedestrian flow varies with the reaction coefficient of density difference. Based on nonlinear analysis method, the Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable regions, respectively. The results show that jams may be alleviated by considering the effect of density difference. The findings also indicate that in the process of building and subway station design, a series of auxiliary facilities should be considered in order to alleviate the possible pedestrian jams.

Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equation are derived to describe soliton waves and the kink–antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.

Financial market is a complex evolved dynamic system with high volatilities and noises, and the modeling and analyzing of financial time series are regarded as the rather challenging tasks in financial research. In this work, by applying the Potts dynamic system, a random agent-based financial time series model is developed in an attempt to uncover the empirical laws in finance, where the Potts model is introduced to imitate the trading interactions among the investing agents. Based on the computer simulation in conjunction with the statistical analysis and the nonlinear analysis, we present numerical research to investigate the fluctuation behaviors of the proposed time series model. Furthermore, in order to get a robust conclusion, we consider the daily returns of Shanghai Composite Index and Shenzhen Component Index, and the comparison analysis of return behaviors between the simulation data and the actual data is exhibited.

In this paper, a modified full velocity difference model (FVDM) based on car-following theory is proposed with the consideration of velocity deviation which represents the inexact judgement of velocity. The stability condition is obtained by the use of linear stability analysis. It is shown that the stability of traffic flow varies with the deviation extent of velocity. The Burgers, Korteweg-de Vries (KdV) and modified K-dV (MKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The numerical simulations show a good agreement with the analytical results, such as density wave, hysteresis loop, acceleration, deceleration and so on. The results show that traffic congestion can be suppressed by taking the positive effect of velocity deviation into account. By taking the positive effect of high estimate of velocity into account, the unrealistic high deceleration and negative velocity which occur in FVDM will be eliminated in the proposed model.

In this paper, a new car-following model considering effect of the driver’s forecast behavior is proposed based on the full velocity difference model (FVDM). Using the new model, we investigate the starting process of the vehicle motion under a traffic signal and find that the delay time of vehicle motion is reduced. Then the stability condition of the new model is derived and the modified Korteweg–de Vries (mKdV) equation is constructed to describe the traffic behavior near the critical point. Numerical simulation is compatible with the analysis of theory such as density wave, hysteresis loop, which shows that the new model is reasonable. The results show that considering the effect of driver’s forecast behavior can help to enhance the stability of traffic flow.

In order to investigate the effect of driver’s memory during a period of time upon traffic dynamics, an extended lattice hydrodynamic model for traffic flow is proposed and studied analytically and numerically in this paper. The linear stability analysis reveals that the time length of driver’s memory has an important effect on stability of traffic flow. The factor will lead to the occurrence of traffic congestion. Three typical nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equation are derived to describe the evolution of density wave for traffic flow in three different regions, which are stable, meta-stable and unstable region, respectively. The simulations are given to illustrate and clarify the analytical results. The results indicate that the time length of driver’s memory has a negative effect upon stability of traffic flow.

This work introduces an analytical technique for determining solutions to a highly nonlinear Duffing-harmonic oscillator model problem. The parametric solutions of Duffing oscillator vibrations for an undamped case are achieved analytically in terms of Adomian polynomials by implementing the straightforward approach of the Laplace Transformation, known as the Laplace Decomposition Procedure (LDP). Possible plots of both numerical and analytical results sketched for various parameters are also presented to support our discussion. These graphs demonstrate variations of position-time, speed-time, and speed-position for an undamped Duffing oscillator case. When analyzed in general, they can provide vibration pattern descriptions for a variety of physical and engineering system configurations. We also examine their physical structures and behavioral characteristics within the conceptual framework of chaotic formalism.

Reflexology is a 4000-year-old art of healing practiced in ancient India, China and Egypt. In the beginning of the 20th century, it spread to the Western world. Reflexologic clinics and massage centers can be found all around the world. In spite of the widespread popularity, to the best of our knowledge, no serious research work has been done in this area, although much scientific research work has been carried out in other Eastern techniques like meditation and yoga. This is why a humble attempt is done in this work to quantitatively assess the effect of reflexological stimulation from a systems point of view. In this work, nonlinear techniques have been used to assess the complexity of EEG with and without reflexological stimulation. We prefer the nonlinear approach, as we believe that the effects are taking place in a subtle way, since there is no direct correlation between reflexological points and modern neuroanatomy.

This study examines the relationship between economic growth and participation in global value chains (GVCs) and demonstrates that the U-shaped nonlinear pattern of GVCs could be more effective than the simple linear pattern of GVCs in terms of economic growth in high- and middle-income economies. The U-shaped nonlinear pattern expresses that an economy decreases foreign dominated GVCs (increases domestic value chains) for building local value chains and then raises the GVCs participation to benefit at a better position in GVCs. This paper investigates a panel of 63 advanced and emerging economies and obtained significant evidence by using systemic quantitative analysis. This research suggests that emerging markets should decrease foreign-dominated GVCs (increase high value-added domestic value chain) and then raise the participation of the GVC for economic growth.

We analyse time series of the Aerosol Index, a parameter related to the aerosol content and retrieved by satellite observations. In particular, we consider data recorded on oriental part of Sahara. A stochastic equation describes the behaviour of the Aerosol Index as occurs in Italy, but out of a stochastic resonance regime. We prove that, in the oriental part of Sahara, local dust source is simply linear superimposed to noise so that a stochastic resonance regime is not set. Furthermore, we find that the local dust emission strongly influences the Aerosol Index data and it is responsible for about 78% of the annual periodicity in the signal.

In recent years, the influence of drivers' behaviors on traffic flow has attracted considerable attention according to Transportation Cyber Physical Systems. In this paper, an extended car-following model is presented by considering drivers' timid or aggressive characteristics. The impact of drivers' timid or aggressive characteristics on the stability of traffic flow has been analyzed through linear stability theory and nonlinear reductive perturbation method. Numerical simulation shows that the propagating behavior of traffic density waves near the critical point can be described by the kink–antikink soliton of the mKdV equation. The good agreement between the numerical simulation and the analytical results shows that drivers' characteristics play an important role in traffic jamming transition.

In this study, a new car-following model is established aiming to predict the variation of vehicle headways on urban road. The linear stability condition is derived corresponding to the prevision of headway in moving. The modified Korteweg–de Vries (mKdV) equation is deduced through the nonlinear analysis. The kink–antikink soliton solution of the mKdV equation can interpret the urban traffic jams near the critical point under the prevision of vehicle headway. Moreover, it is clear that the prevision of headway effect did improve the stability of urban traffic flow since the traffic jams are alleviated efficiently by taking into account the prevision of headway term in numerical simulations, which are consistent with the theoretical analysis.