An efficient hybrid method for stochastic reaction-diffusion biochemical systems with delay

Many chemical reactions, such as gene transcription and translation in living cells, need a certain time to finish once they are initiated. Simulating stochastic models of reaction-diffusion systems with delay can be computationally expensive. In the present paper, a novel hybrid algorithm is proposed to accelerate the stochastic simulation of delayed reaction-diffusion systems. The delayed reactions may be of consuming or non-consuming delay type. The algorithm is designed for moderately stiff systems in which the events can be partitioned into slow and fast subsets according to their propensities. The proposed algorithm is applied to three benchmark problems and the results are compared with those of the delayed Inhomogeneous Stochastic Simulation Algorithm. The numerical results show that the new hybrid algorithm achieves considerable speed-up in the run time and very good accuracy

Free Vibration Analysis of Functionally Graded Nanocomposite Beams on Elastic Foundation Using a Mesh-Free Method

Abstract The use of Carbon Nanotubes as the reinforcing constituent for polymer matrix composites in place of conventional fibers has led to the emergence of a new generation of advanced composite materials. In this paper, the free vibration of functionally graded nanocomposite beams on elastic foundations are studied. Three different types of Carbon Nanotubes distributions in the polymer matrix material are studied; Uniform distribution, symmetrically functionally graded distribution and unsymmetrically functionally graded distribution. The analysis is carried out by a mesh-free method using the two-dimensional theory of elasticity. The Moving Least Square shape functions are implemented to approximate the displacement field. Due to the absence of the Kronecker delta property of the shape functions, a transformation technique is used to apply the essential boundary conditions. After validation, the effects of different design parameters such as Carbon Nanotubes distribution, slenderness ratios, boundary conditions and foundation stiffness on the vibrational behavior of the structure are investigated. It can be seen that from a design perspective, the vibrational response of a FG structure may be controlled in two ways; one way is through changing the distribution of the CNT’s in the matrix material and the other way is by changing stiffness of the elastic foundation on which it is resting. A notable observation is that increasing the stiffness of the foundation will move the neutral axis away from the foundation support of the beam. The current approach can serve as a benchmark against which other semi-analytical and numerical methods based on classical beam theories can be compared

Free Vibration Analysis of Functionally Graded Nanocomposite Beams on Elastic Foundation Using a Mesh-Free Method

<div><p>Abstract The use of Carbon Nanotubes as the reinforcing constituent for polymer matrix composites in place of conventional fibers has led to the emergence of a new generation of advanced composite materials. In this paper, the free vibration of functionally graded nanocomposite beams on elastic foundations are studied. Three different types of Carbon Nanotubes distributions in the polymer matrix material are studied; Uniform distribution, symmetrically functionally graded distribution and unsymmetrically functionally graded distribution. The analysis is carried out by a mesh-free method using the two-dimensional theory of elasticity. The Moving Least Square shape functions are implemented to approximate the displacement field. Due to the absence of the Kronecker delta property of the shape functions, a transformation technique is used to apply the essential boundary conditions. After validation, the effects of different design parameters such as Carbon Nanotubes distribution, slenderness ratios, boundary conditions and foundation stiffness on the vibrational behavior of the structure are investigated. It can be seen that from a design perspective, the vibrational response of a FG structure may be controlled in two ways; one way is through changing the distribution of the CNT’s in the matrix material and the other way is by changing stiffness of the elastic foundation on which it is resting. A notable observation is that increasing the stiffness of the foundation will move the neutral axis away from the foundation support of the beam. The current approach can serve as a benchmark against which other semi-analytical and numerical methods based on classical beam theories can be compared.</p></div