On the functional representation of bond energy functions

Ab initio calculations are used to test the ability of various representations to reproduce bond energies. It is found that expansion in 1/R, where R is the bond length, is remarkably efficient and is consistently better than the usual R expansion. A quadratic form in 1/R is better than a cubic representation in R and sometimes even as good as a quartic representation. A cubic function in 1/R is, in all cases studied, better performing than the quartic expansion in R. It is also found that parameters derived with the 1/R expansion are defined more sharply than those derived for the R expansion. It is suggested that the 1/R expansion may be computationally more efficient for simulations of large biomolecules and for constructions of reactive force fields than the standard bond functions. © 1994 by John Wiley & Sons, Inc.     

Geometry-dependent atomic charges: Methodology and application to alkanes,aldehydes, ketones,and amides

A general methodology for deriving geometry-dependent atomic charges is presented. The main ingredient of the method is a model that describes the molecular dipole moment in terms of geometry-dependent point charges. The parameters of the model are determined from ab initio calculations of molecular dipole moments and their Cartesian derivatives at various molecular geometries. Transferability of the parameters is built into the model by fitting ab initio calculations for various molecules simultaneously. The results show that charge flux along the bonds is a major contributing factor to the geometry dependence of the atomic charges, with additional contributions from fluxes along valence angles and adjacent bonds. Torsion flux is found to be smaller in magnitude than the bond and valence angle fluxes but is not always unimportant. A set of electrostatic parameters is presented for alkanes, aldehydes, ketones, and amides. Transferability of these parameters for a host of molecules is established to within 3 ?5% error in the predicted dipole moments. A possible extension of the method to include atomic dipoles is outlined. With the inclusion of such atomic dipoles and with the set of transferable point charges and charge flux parameters, it is demonstrated that molecular electrostatic potentials as well as electrostatic forces on nuclei can be reproduced much better than is possible with other models (such as potential derived charges). © 1995 by John Wiley & Sons, Inc.     

Simulations of lipid crystals: Characterization of potential energy functions and parameters for lecithin molecules

We evaluate an empirical potential energy function and associated parameters for classical molecular dynamics simulations of lecithins, a common class of lipid. The physical accuracy of the force field was tested through its application to molecular dynamics simulations of the known crystal structures of lipid molecules. Average atomic positions and molecular conformation are well maintained during the simulations despite considerable thermal motion. Calculated isotropic temperature factors correlate highly with those from experiment.     

Modal interaction and bifurcations in two degree of freedom duffing oscillators

A methodology is first presented for analyzing long time response of periodically exited nonlinear oscillators. Namely, a systematic procedure is employed for determining periodic steady state response, including harmonic and superharmonic components. The stability analysis of the located periodic motions is also performed, utilizing results of Froquet theory. This methodology is then applied to a special class of two degree of freedom nonlinear oscillators, subjected to harmonic excitation. The numberical results presented in the second part of this study illustrate effects caused by the interaction of the modes as well as effects of the nonlinearities on the steady state response of these oscillators. In addition, sequences of bifurcations are analyzed for softening systems, leading to unbounded response of the model examined. Finally, the importance of higher harmonics on the response of systems with strongly nonlinear characteristics is investigated.     

Predicting aflatoxin and fumonisin in shelled corn lots using poor-quality grade components

A study was conducted to determine if aflatoxin and fumonisin are concentrated in the poor-quality grade components of shelled corn. Four 1.0 kg test samples were each taken from 23 lots of shelled corn marketed in North Carolina. Inspectors from the Federal Grain Inspection Service divided each test sample into 3 grade components: (1) damaged kernels (DM), (2) broken corn and foreign material (BCFM), and )3) whole kernels (WH). The aflatoxin and fumonisin concentration was measured in each component and a mass balance equation was used to calculate the total concentration of each mycotoxin in each test sample. Averaged across all test samples, the aflatoxin concentrations in the DM, BCFM, and WH components were 1300.3, 455.2, and 37.3 ppb, respectively. Averaged across all test samples, the fumonisin concentrations in the DM, BCFM, and WH components were 148.3, 51.3, and 1.8 ppm, respectively. The DM and BCFM components combined accounted for only 5.0% of the test sample mass, but accounted for 59.8 and 77.5% of the total aflatoxin and fumonisin mass in the test sample, respectively. Both aflatoxin mass (ng) and aflatoxin concentration (ng/g) in the combined DM and BCFM components had high correlations with aflatoxin concentration in the lot. The highest correlation occurred when aflatoxin mass (ng) in the combined DM and BCFM components was related to aflatoxin concentration in the lot (0.964). Similar results were obtained for fumonisin. This study indicated that measuring either aflatoxin or fumonisin in the combined DM and BCFM grade components could be used as a screening method to predict either aflatoxin or fumonisin in a bulk lot of shelled corn.     

Distribution among sample test results when testing shelled corn lots for fumonisin.

The statistical distribution known as the compound gamma function was studied for suitability in describing the distribution of sample test results associated with testing lots of shelled corn for fumonisin. Thirty-two 1.1 kg test samples were taken from each of 16 contaminated lots of shelled corn. An observed distribution consisted of 32 sample fumonisin test results for each lot. The mean fumonisin concentration, c, and the variance, s2, among the 32 sample fumonisin test results along with the parameters for the compound gamma function were determined for each of the 16 observed distributions. The 16 observed distributions of sample fumonisin test results were compared with the compound gamma function using the Power Divergence test. The null hypothesis that the observed distribution could have resulted from sampling a family of compound gamma distributions was not rejected at the 5% significance level for 15 of the 16 lots studied. Parameters of the compound gamma distribution were calculated from the 32-fumonisin sample test results using the method of moments. Using regression analysis, equations were developed that related the parameters of the compound gamma distribution to fumonisin concentration and the variance associated with a fumonisin test procedure. An operating characteristic curve was developed for a fumonisin sampling plan to demonstrate the use of the compound gamma function.     

On Banach spaces whose dual balls are not weak∗ sequentially compact

Theorem 1. LetX be a Banach space. (a) IfX ^∗ has a closed subspace in which no normalized sequence converges weak^∗ to zero, thenl ₁ is isomorphic to a subspace ofX. (b) IfX ^∗ contains a bounded sequence which has no weak^∗ convergent subsequence, thenX contains a separable subspace whose dual is not separable. The second-named author was supported in part by NSF-MPS 72-04634-A03.     

Complemented isometric copies of in dual Banach spaces

Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .