Modeling of Hydrogen Storage Materials: A Reactive Force Field for NaH

Parameterization of a reactive force field for NaH is done using ab initio derived data. The parameterized force field(ReaxFFNaH) is used to study the dynamics governing hydrogen desorption in NaH. During the abstraction process of surface molecular hydrogen charge transfer is found to be well described by the parameterized force field. To gain more insight into the mechanism governing structural transformation of NaH during thermal decomposition a heating run in a molecular dynamics simulation is done. The result shows that a clear signature of hydrogen desorption is the fall in potential energy surface during heating

Phase-Fitted Runge–Kutta Pairs of Orders 8(7)

A new phase fitted Runge–Kutta pair of orders 8(7) which is a modification of a well known explicit Runge–Kutta pair for the integration of periodic initial value problems is presented. Numerical experiments show the efficiency of the new pair in a wide range of oscillatory problems. © 2017 Elsevier B.V

Direct estimation of SIR model parameters through second-order finite differences

SIR model is widely used for modeling the infectious diseases. This is a system of ordinary differential equations (ODEs). The numbers of susceptible, infectious, or immunized individuals are the compartments in these equations and change in time. Two parameters are the factor of differentiating these models. Here, we are not interested in solving the ODEs describing a certain SIR model. Given the observed data, we try to estimate the parameters that determine the model. For this, we propose a least squares approach using second-order centered differences for replacing the derivatives appeared in the ODEs. Then we arrive at a simple linear system that can be solved explicitly and furnish the approximations of the parameters. Numerical results over various artificial data verify the simplicity and accuracy of the new method. © 2020 John Wiley & Sons, Ltd

Perturbing singular systems and the correlating of uncorrelated random sequences

A stochastic process may be used to combine sequences with zero autocorrelation to give an autocorrelated sequence. We study this simple paradigm of irreversible mixing. © 2007 American Institute of Physics

Eighth order, phase-fitted, six-step methods for solving y″= f(x, y)

A family of explicit, semi-symmetric, eighth-order, six-step methods for the numerical solution of y″= f(x, y) is considered. This family can be derived through interpolation techniques and only two stages (function evaluations) are spent per step. A method is given with variable coefficients. This variance is based in the requirement to nullify the errors when solving the standard simple oscillator. We conclude with numerical tests over a set of problems justifying our effort of dealing with the new method. © 2019, Springer Nature Switzerland AG

Explicit Runge–Kutta methods for starting integration of Lane–Emden problem

Traditionally, when constructing explicit Runge–Kutta methods we demand the satisfaction of the trivial simplifying assumption. Thus, f 1 =f(x 0 ,y 0 ) is always used as the first stage of these methods when applied to the Initial Value Problem (IVP): y ′ (x)=f(x,y), y(x 0 )=y 0 . Here we examine the case with f 1 =f(x 0 +c 1 h,y 0 ),(h: the step) and c 1 ≠ 0. We derive the order conditions for arbitrary order and construct a 5th order method at the standard cost of six stages per step. This method is found to outperform other classical Runge–Kutta pairs with orders 5(4) when applied to problems with singularity at the beginning (e.g. Lane–Emden problem). © 201