9 papers
Evaluation of Coulomb potential in a triclinic cell with periodic boundary conditions
Sandeep Tyagi
Lekner and Sperb's work on the evaluation of Coulomb energy and forces under periodic boundary conditions is generalized that makes it possible to use a triclinic unit cell in simu…
Rapid evaluation of the periodic Green's function in d dimensions
Sandeep Tyagi
A method is given to obtain the Green's function for the Poisson equation in any arbitrary integer dimension under periodic boundary conditions. We obtain recursion relations which…
Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces
Sandeep Tyagi
A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions.…
Interpolation of the Josephson interaction in highly anisotropic superconductors from a solution of the two dimensional sine-Gordon equation
Yadin Y. Goldschmidt, Sandeep Tyagi
In this paper we solve numerically the two dimensional elliptic sine-Gordon equation with appropriate boundary conditions. These boundary conditions are chosen to correspond to the…
New series representation for Madelung constant
Sandeep Tyagi
A new series representation of the Madelung constant is given. We represent Madelung constant as a sum of an exact term plus an exponentially fast converging series. The remarkable…
Coulomb potentials in two and three dimensions under periodic boundary conditions
Sandeep Tyagi
A method to sum over logarithmic potential in 2D and Coulomb potential in 3D with periodic boundary conditions in all directions is given. We consider the most general form of unit…