Nonlinear formulation of isotropic piezoelectric Euler-Bernoulli nano-beam is developed based on consistent size-dependent piezoelectricity theory. By considering geometrically nonlinear and axial displacement of the centroid of beam sections, basic nonlinear equations of piezoelectric nanobeam are derived using Hamilton's principle and variational method. Afterwards, in the special case for the formulation derived, hinged-hinged piezoelectric nanobeam is studied, and static deflection as well as free vibrations of the nanobeam under mechanical loads is determined. In this case, results of the linear formulation of the size-dependent theory are compared to those of the linear and nonlinear classical continuum theory.

In this paper, the G2 interpolation by Pythagorean-hodograph (PH) quintic curves in ℝd, d ≥ 2, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension d, they supply a G2 quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method.

Mixed convection flow of second grade fluid bounded by a permeable stretching surface is discussed. Soret and Dufour effects are also present. Series solutions for the resulting problems are made using homotopy analysis method (HAM). Analysis has been carried out for the effects of embedded parameters on the velocity, temperature and concentration fields. Numerical values of Nusselt and Sherwood numbers are computed and discussed.

This paper is dedicated to the memory of the great statistician Melvin J. Hinich, with whom we were in contact about this research prior to his untimely death from a tragic fall. We develop a neoclassical growth model with habit formation to exhibit an equilibrium nonlinear relationship between aggregate consumption growth and income growth. We first provide empirical evidence consistent with this relationship both for the United States and France, and we reject the hypothesis of a random walk for consumption. We then estimate this nonlinear relationship. We find for both countries robust evidence of persistence, nonlinearity, and cyclicity in the relationship between consumption and income.

In five subjects, we measured visual evoked potentials (VEPs) elicited by Vernier targets in which the contrast of the two components of the stimuli were modulated by sinusoids at distinct frequencies f1 and f2. This approach allows for the extraction of VEP signatures of spatial interactions, namely, responses at intermodulation frequencies n1f1 + n2f2, without the need to introduce motion into the stimulus. The most prominent interactions were at the sum frequency f1 + f2, and, for frequency pairs that were sufficiently separated, the difference frequency f1 − f2. These responses had a systematic dependence on the temporal parameters of the stimulus, corresponding to an effective latency of 145 to 165 ms. Fourth-order interactions were also detected, particularly at the frequencies 2f1 ± 2f2. These VEP signatures of interaction were similar to interactions seen for colinear line segments separated by a gap. Thus, for Vernier stimuli devoid of motion, VEP signatures of interaction are readily detected but are not specific to hyperacuity displacements. The distribution of interactions across harmonic orders is consistent with local rectification preceding the spatial interactions. Their effective latencies and dependence on spatial parameters are consistent with interactions within V1 receptive fields or mediated by horizontal connections between cells with a similar orientation tuning within V1.