15 research outputs found
Entropy of chains placed on the square lattice
We obtain the entropy of flexible linear chains composed of M monomers placed
on the square lattice using a transfer matrix approach. An excluded volume
interaction is included by considering the chains to be self-and mutually
avoiding, and a fraction rho of the sites are occupied by monomers. We solve
the problem exactly on stripes of increasing width m and then extrapolate our
results to the two-dimensional limit to infinity using finite-size scaling. The
extrapolated results for several finite values of M and in the polymer limit M
to infinity for the cases where all lattice sites are occupied (rho=1) and for
the partially filled case rho<1 are compared with earlier results. These
results are exact for dimers (M=2) and full occupation (\rho=1) and derived
from series expansions, mean-field like approximations, and transfer matrix
calculations for some other cases. For small values of M, as well as for the
polymer limit M to infinity, rather precise estimates of the entropy are
obtained.Comment: 6 pages, 7 figure
Thomas-Fermi theory of an inhomogeneous electron liquid generalized to incorporate density gradients
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Comparison of Numerical Methods for Solving the Second-Order Differential Equations of Molecular Scattering Theory
The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to the same level of accuracy. The results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions. Such a hybrid program was developed and found to be at least 1.5 to 2.0 times faster than any individual method
Two applications of the Divide & Conquer principle in the molecular sciences
Brinkmann G, Dress A, Perrey SW, Stoye J. Two applications of the Divide & Conquer principle in the molecular sciences. Mathematical programming. 1997;79(1-3):71-97.In this paper, two problems from the molecular sciences are addressed: the enumeration of fullerene-type isomers and the alignment of biosequences. We report on two algorithms dealing with these problems both of which are based on the well-known and widely used Divide & Conquer principle. In other words, our algorithms attack the original problems by associating with them an appropriate number of much simpler problems whose solutions can be "glued together" to yield solutions of the original, rather complex tasks. The considerable improvements achieved this way exemplify that the present day molecular sciences offer many worthwile opportunities for the effective use of fundamental algorithmic principles and architectures