178 research outputs found
New series representation for Madelung constant
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 result is that even if the series part is
discarded, one obtains Madelung constant correct up to ten good decimal
figures. This, to the best of our knowledge, may be the fastest converging
series representation of the Madelung constant. A few other important
identities are also obtained
Coulomb potentials in two and three dimensions under periodic boundary conditions
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 cells, the rhombic cell in 2D and the triclinic cell
in 3D. For the 3D case, this paper presents a generalization of Sperb's work
[R. Sperb, Mol. Simulation, \textbf{22}, 199-212(1999)]. The expressions
derived in this work converge extremely fast in all region of the simulation
cell. We also obtain results for slab geometry. Furthermore, self-energies for
both 2D as well as 3D cases are derived. Our general formulas can be employed
to obtain Madelung constants for periodic structures.Comment: Generalization of the work done in cond-mat/0405574. To appear in J.
Chem. Physics. A few typos have been correcte
Evaluation of Coulomb potential in a triclinic cell with periodic boundary conditions
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 simulations in 3D rather than just an orthorhombic cell.
The expressions obtained are in a similar form as previously obtained by Lekner
and Sperb for the especial case of orthorhombic cell
Logarithmic interaction under periodic boundary conditions: Closed form formulas for energy and forces
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. The work done here is a generalization of
Glasser's results [M. L. Glasser, J. Math. Phys. 15, 188 (1974)] and is
obtained with a different and simpler method than that by Stremler [M. A.
Stremler, J. Math. Phys. 45, 3584 (2004)]. The simplicity of the formulas
derived here makes them extremely convenient in a computer simulation
Effective way to sum over long range Coulomb potentials in two and three dimensions
I propose a method to calculate logarithmic interaction in two dimensions and
coulomb interaction in three dimensions under periodic boundary conditions.
This paper considers the case of a rectangular cell in two dimensions and an
orthorhombic cell in three dimensions. Unlike the Ewald method, there is no
parameter to be optimized, nor does it involve error functions, thus leading to
the accuracy obtained. This method is similar in approach to that of Sperb [R.
Sperb, Mol. Simulation, 22, 199 (1999).], but the derivation is considerably
simpler and physically appealing. An important aspect of the proposed method is
the faster convergence of the Green function for a particular case as compared
to Sperb's work. The convergence of the sums for the most part of unit cell is
exponential, and hence requires the calculation of only a few dozen terms. In a
very simple way, we also obtain expressions for interaction for systems with
slab geometries. Expressions for the Madelung constant of CsCl and NaCl are
also obtained.Comment: To appear in Phy. Rev.
Interpolation of the Josephson interaction in highly anisotropic superconductors from a solution of the two dimensional sine-Gordon equation
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 Josephson interaction between two adjacent pancakes
belonging to the same flux-line in a highly anisotropic superconductor. An
extrapolation is obtained between the regimes of low and high separation of the
pancakes. The resulting formula is a better candidate for use in numerical
simulations than previously derived formulas.Comment: 18 pages, 9 figure
A Study on Comparative Assessment of Water Quality of Dal and Nigeen Lakes of Jammu and Kashmir, India
The lakes of the Kashmir valley, India are under continuous pressure due to increasing anthropogenic activities. In the present study, an attempt has been made to monitor the quality of two important lakes (Dal and Nigeen) of Jammu and Kashmir (J&K), India. These lakes hold significant ecological, cultural, and economic value, attracting many tourists and serving as vital sources of fresh water for local communities. Five sampling sites were selected in the study area, out of which three are in Dal Lake and two in Nigeen Lake. A comparison of the water quality of both lakes was made in the present investigation based on selected physicochemical parameters like water pH, conductivity (EC), dissolved oxygen (DO), biochemical oxygen demand (BOD), chemical oxygen demand (COD), chloride (Cl-), sulfate (SO42-), nitrate (NO3-) and phosphate (PO43-). The results revealed that the value of most of the parameters was higher in Dal Lake (BOD, EC, COD, and PO43-) while some parameters were found higher in Nigeen Lake (NO3-, DO, Cl- and SO42-). The student t-test showed significant differences (p < 0.05) between the means of most of the studied parameters of both the lake except EC and NO3-. Although all the parameters were within the limits if the trend of pollution continues, then the water quality of both lakes will become unfit for aquatic plants, animals, and tourist activities also. This study highlights the urgent need for effective water management strategies and conservation efforts to preserve the water quality of Dal and Nigeen Lakes
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