Sharif Digital Repository

Several schemes for discretization of first and second derivatives are available in Smoothed Particle Hydrodynamics (SPH). Here, four schemes for approximation of the first derivative and three schemes for the second derivative are examined using a theoretical analysis based on Taylor series expansion both for regular and irregular particle distributions. Estimation of terms in the truncation errors shows that only the renormalized (the first-order consistent) scheme has acceptable convergence properties to approximate the first derivative. None of the second derivative schemes has the first-order consistency. Therefore, they converge only when the particle spacing decreases much faster than... 

In this paper, a very simple periodic ridge on a symmetric slab waveguide is used for implementing an on-chip CMOS-compatible second-order spatial differentiator. The reflection and transmission coefficients of this structure show that the second derivative is performed in the transmission when the optical beam normally incidents on the periodic ridge. Simulations confirm that the reason behind the second-order spatial differentiation of the incoming beam is the excitation of the guided mode of the periodic ridge. A Maxwell’s equation solver that utilizes the finite element method (FEM) is used to simulate this structure, and an eigenmode solver is utilized for the validation. The results of... 

The main aim of this article is to find the optimum positions of the stabilizers that reduces the vibration and leads to the largest weight on bit (WOB) in drill strings. In this work, the potential energy of drill strings has been derived by considering the drill string weight and WOB. The potential energy of this continuous system is considered as a multi-degree-of-freedom system by the mode summation method. The equilibrium position of the system and its stability is determined by finding the roots of the first derivative and the sign of the second derivative of the potential energy, respectively. Using this formulation, the best positions of stabilizers that lead to the largest WOB can... 

Vulnerability of power electronic converters in DC microgrids in case of fault occurrence in DC cables necessitates using a fast fault detection and isolation scheme. In this paper, a modified, fast and selective protection scheme has been presented, which provides the required tripping of low voltage DC (LVDC) microgrids. This protection scheme has been developed based on the natural characteristics of the fault current, in which the first and second derivatives of the fault current have been employed to define thresholds for discriminating between faulted and non-faulted situations. To enhance fault detection capability of the protection scheme, definition of thresholds have been improved... 

Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) can lead to non-physical oscillations in the pressure and density fields when simulating incompressible flow problems. This in turn may result in tensile instability and sometimes divergence. In this paper, it is shown that this difficulty originates from the specific form of spatial discretization used for the pressure term when solving the mass conservation equation. After describing the pressure-velocity decoupling problem associated with the so-called colocated grid methods, a modified approach is presented that overcomes this problem using a different discretization scheme for the second derivative of pressure. The modified... 

This paper presents a new scheme to apply artificial neural network (ANN) in prediction of static recrystallization (SRX) kinetics. Firstly, based on empirical data of SRX kinetics, a mathematical model is suggested to construct a neural network. Then, an appropriate neural network is trained on the basis of the first and the second derivatives of recrystallized fraction with respect to time. Finally, a thermo-mechanical finite element analysis is coupled with the proposed ANN to predict static recrystallization kinetics in hot rolling process of AA5083. To verify the model, the predicted results and the experimental data are compared and it is observed that there is a good consistency... 

Using the work hardening rate-strain curves, an effective mathematical model has been developed to predict the stress-strain curves of alloy steel during hot deformation up to the peak stress regardless of the level of the strain, weather smaller or larger than the critical strain. This model is expressed in terms of peak stress, peak strain and one temperature-sensitive parameter, S. In addition, one new model, which is a function of peak strain, was proposed to predict the critical strain for the initiation of dynamic recrystallization using the second derivative of work hardening rate with respect to stress. Besides the theoretical study, the analysis is used to determine the... 

The numerical solution to the parabolized Navier-Stokes (PNS) and globally iterated PNS (IPNS) equations for accurate computation of hypersonic axisymmetric flowfields is obtained by using the fourth-order compact finite-difference method. The PNS and IPNS equations in the general curvilinear coordinates are solved by using the implicit finite-difference algorithm of Beam and Warming type with a high-order compact accuracy. A shock-fitting procedure is utilized in both compact PNS and IPNS schemes to obtain accurate solutions in the vicinity of the shock. The main advantage of the present formulation is that the basic flow variables and their first and second derivatives are simultaneously... 

In this paper, a novel temperature-dependent multi-scale method is developed to investigate the role of temperature on surface effects in the analysis of nano-scale materials. In order to evaluate the temperature effect in the micro-scale (atomic) level, the temperature related Cauchy-Born hypothesis is implemented by employing the Helmholtz free energy, as the energy density of equivalent continua relating to the inter-atomic potential. The multi-scale technique is applied in atomistic level (nano-scale) to exhibit the temperature related characteristics. The first Piola-Kirchhoff stress and tangential stiffness tensor are computed, as the first and second derivatives of the free energy...