Guk-Chol Ri | Searcharxiv

arXiv2017

Influence of halide composition on the structural, electronic, and optical properties of mixed CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$ perovskites calculated using the virtual crystal approximation method

We investigate the structural, electronic and optical properties of mixed bromide-iodide lead perovskite solar cell CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$ by means of the virtual crystal approximation (VCA) within density functional theory (DFT). Optimizing the atomic positions and lattice parameters increasing the bromide content $x$ from 0.0 to 1.0, we fit the calculated lattice parameter and energy band gap to the linear and quadratic function of Br content, respectively, which are in good agreement with the experiment, respecting the Vegard's law. With the calculated exciton binding energy and light absorption coefficient, we make sure that VCA gives consistent results with the experiment, and the mixed halide perovskites are suitable for generating the charge carriers by light absorption and conducting the carriers easily due to their strong photon absorption coefficient, low exciton bindign energy, and high carrier mobility at low Br contents. Furthermore analyzing the bonding lengths between Pb and X (I$_{1-x}$Br$_x$: virtual atom) as well as C and N, we stress that the stability of perovskite solar cell is definitely improved at $x$=0.2.

cond-mat.mtrl-sci↗

arXiv2016

Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients

The existence of solutions to Cauchy type problems of linear Riemann-Liouville fractional differential equations with variable coefficients is considered in a space of integrable functions. First, we consider the existence and uniqueness of solution for a Cauchy type problem with special initial conditions in the space of integrable functions. Then we provide an example of the problem that has no solution in the space of integrable functions. We give a solving method and a representation of solutions for the Cauchy type problem. Last we give some examples.

math.CA↗

arXiv2013

Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and $n$ terms

This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.

math-ph↗