Vol. 3, No. 2 (2019): Regular Issue

We study the disproportional effect of non-uniformity on a system of photovoltaic cell network. When a cell is partially shaded, besides the loss from the shaded cell, the power output of the whole cell network is significantly affected. Although this effect is well known in the solar cell community, the theoretical analysis has relied on one or more approximations or specially defined functions. In this paper, we present a parametric formulation of photovoltaic cells in which the output voltage and current relationships are described by explicit functions parametrized by the voltage over the cell diode. No additional approximations or specially defined functions are required to study the output characteristics. We further show that the model remains unchanged when applied to a network of many identical PV cells either in parallel or in series; the parameters for the network can be obtained from those of the cell. Incorporating interpolation in calculation, the model can be used to study a network with dissimilar cells, specifically a network with a partially shaded cell. We show that the voltage over the shaded cell becomes negative and power is dissipated over the shaded cell. The model is also conveniently used to study the network output characteristics when bypass diodes are included in the PV network.

We propose computationally feasible statistical algorithms for the automated assessment of isolation and integration of urban locations and neighborhoods by using maps acquired from the OpenStreeMap service. Integration and isolation de ned by observing the properties of scale-dependent random walks on city street maps are not always opposites. While isolation worsens economic and social mo- bility prospects in sprawling metropolitan areas, some secluded places homing the wealthiest can be characterized as being in integrated isolation in the city.

Free vibration of beam is an important issue in structural engineering because of its various physical applications in the real field. In this paper, the free vibration of a nonlinear beam rest on a nonlinear elastic foundation is studied. A mathematical modeling for the free vibration of beam rest on nonlinear elastic foundation is presented. A modified harmonic balance is used to investigate the nonlinear free vibration response of beam. The main advantage of the method is that the unknown coefficients are expressed in power series of a new parameter. However, in a classical harmonic balance method the values of the unknown coefficients are determined by solving a set of complicated algebraic equations truncating higher order nonlinear terms. The results obtained by the proposed method have been compared with corresponding numerical results to verify the accuracy of method. Besides, the effects of various elastic foundation coefficients have been examined.

In this paper, a local theory for stability and bifurcation of equilibriums for nonlinear dynamical systems is presented. The stability and bifurcation on specific eigenvectors of the linearized system at equilibrium is discussed. The higher-order singularity and stability for nonlinear systems on the specic eigenvectors are developed. The Hopf bifurcation based on the transformation of the Fourier series base is also discussed. The stability and bifurcation of equilibriums in low-dimensional dynamical systems is discussed for a better understanding of stability and bifurcation theory. The Lyapunov function stability is briey discussed, and the extended Lyapunov stability theory is presented.

The form of the lower part of the vector eld erroneously leads to the conclusion/statement that the original system in 1st order has no linear counterpart, which is untrue. In here, the decomposition to linear and nonlinear part of the 1st order original system it is shown. The eigenvalues of the matrix associated with the linear part are all zero, therefore it cannot be claimed Lyapunov's conclusion that the system in low energies can be approximated with the linear counterpart. Also, two typographic errors have been corrected. The corrections and the additions not only don't affect the value of the rest part of the published article but also enhance the value of the original manuscript. More precisely, since the original system in low energies cannot be approximated by the solution of the linear counterpart, the followed approach to describe the dynamics of the spinning shaft with linearization around the equilibria of the restricted system which are the rigid body motions, is of higher significance.