Structure of solid monolayers and multilayers of n -hexane on graphite

We present all-atom molecular dynamics simulations ofn-hexane on the basal plane of graphite at monolayer and multilayer coverages. In keeping with experimental data, we find the presence of ordered adsorbed layers both at single monolayer coverage and when the adsorbed layer coexists with excess liquid adsorbate. Using a simulation method that does not impose any particular periodicity on the adsorbed layer, we quantitatively compare our results to the results of neutron diffraction experiments and find a structural transition from a uniaxially incommensurate lattice to a fully commensurate structure on increasing the coverage from a monolayer to a multilayer. The zig-zag backbone planes of all the alkane molecules lie parallel to the graphite surface at the multilayer coverage, while a few molecules are observed to attain the perpendicular orientation at monolayer coverage. Dedicated to Professor C N R Rao on his 70th birthday     

Rovibrational matrix elements of polarizability of HD, HT and DT molecules

Fresh computations of rovibrational matrix elements of the polarizability α[=(α_||+2α_⊥)/3] and the polarizability anisotropy γ(=α_||−α_⊥) of the heteronuclear isotopomers, HD, HT, and DT, of the hydrogen molecule are presented. The computations combine the most accurate polarizability functions α(R) and γ(R) (R being the bond distance) on the one hand and the most accurate adiabatic potential on the other. The calculations are extended to the product operators xα and xγ where x is the centre of mass to centre of charge separation in the heteronuclear species. The latter matrix elements are needed, additionally, for elucidating the absorption intensities of some of the zero-phonon rovibrational transitions peculiar to the heteronuclear species in the crystalline phase.     

Phase transfer of highly monodisperse iron oxide nanocrystals with Pluronic F127 for biomedical applications

Iron oxide nanoparticles made from the thermal decomposition method are highly uniform in all respects (size, shape, composition and crystallography), making them ideal candidates for many bioapplications. The surfactant coating on the as-synthesized nanoparticles renders the nanoparticles insoluble in aqueous solutions. For biological applications nanoparticles must be water soluble. Here we demonstrate the phase transfer of our nanoparticles with the biocompatible copolymer Pluronic F127. Transmission electron microscopy, Fourier transform infrared spectroscopy and dynamic light scattering indicate that the nanoparticles are coated discretely. Magnetic measurements show that the nanoparticles remain superparamagnetic with saturation magnetization ∼96% of the maximum theoretical value.     

Simultaneous best approximation by three polynomials

Let [a, b] be any interval and let p₀, p₁, p_k be any three polynomials of degrees 0, 1, k, respectively, where k 2. A set of necessary and sufficient conditions for the existence of an f in C[a, b] such that p_i is the best approximation to f from the space of all polynomials of degree less than or equal to i, for all i = 0, 1, k, is given.     

Information recovery from black holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss. First Award in the 2006 Essay Competition of the Gravity Research Foundation.     

A finite difference approach to the equations of age-dependent population dynamics

We establish the convergence of the finite difference scheme for the nonlinear equations of population dynamics proposed by Guertin and MacCamy. The applicability of the discrete equations to establish qualitative properties of the solution to the continuous problem is also illustrated.     

Vibrational spectra of (NH4)3ZnCl5

IR and Raman spectra of (NH₄)₃ZnCl₅ have been recorded. The observed spectra have been analysed on the basis of the vibrations of ZnCl ₄ ²⁻ and NH ₄ ⁺ ions. The appearance of multiple Raman bands indicates the presence of two different types of ammonium ions. The effect of anisotropic crystalline field over the ZnCl₄ and NH₄ tetrahedra is also discussed. The assignment of internal modes has been verified by the potential energy distribution calculations.     

Chvátal closures for mixed integer programming problems

Chvátal introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality. This viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems. The basic ingredient in these cutting-plane proofs is that for a polyhedronP and integral vectorw, if max(wx|x P, wx integer} =t, thenwx t is valid for all integral vectors inP. We consider the variant of this step where the requirement thatwx be integer may be replaced by the requirement that be integer for some other integral vector . The cutting-plane proofs thus obtained may be seen either as an abstraction of Gomory's mixed integer cutting-plane technique or as a proof version of a simple class of the disjunctive cutting planes studied by Balas and Jeroslow. Our main result is that for a given polyhedronP, the set of vectors that satisfy every cutting plane forP with respect to a specified subset of integer variables is again a polyhedron. This allows us to obtain a finite recursive procedure for generating the mixed integer hull of a polyhedron, analogous to the process of repeatedly taking Chvátal closures in the integer programming case. These results are illustrated with a number of examples from combinatorial optimization. Our work can be seen as a continuation of that of Nemhauser and Wolsey on mixed integer cutting planes.Supported by Sonderforschungsbereich 303 (DFG) and by NSF Grant Number ECS-8611841.Supported by NSF Grant Number ECS-8418392 and Sonderforschungsbereich 303 (DFG), Institut für Ökonometrie und Operations Research, Universität Bonn, FR Germany.     

New theoretical insight into the interactions and properties of formic acid: development of a quantum-based pair potential for formic acid

We performed ab initio quantum-chemical studies for the development of intra- and intermolecular interaction potentials for formic acid for use in molecular-dynamics simulations of formic acid molecular crystal. The formic acid structures considered in the ab initio studies include both the cis and trans monomers which are the conformers that have been postulated as part of chains constituting liquid and crystal phases under extreme conditions. Although the cis to trans transformation is not energetically favored, the trans isomer was found as a component of stable gas-phase species. Our decomposition scheme for the interaction energy indicates that the hydrogen-bonded complexes are dominated by the Hartree-Fock forces while parallel clusters are stabilized by the electron correlation energy. The calculated three-body and higher interactions are found to be negligible, thus rationalizing the development of an atom-atom pair potential for formic acid based on high-level ab initio calculations of small formic acid clusters. Here we present an atom-atom pair potential that includes both intra- and inter molecular degrees of freedom for formic acid. The newly developed pair potential is used to examine formic acid in the condensed phase via molecular-dynamics simulations. The isothermal compression under hydrostatic pressure obtained from molecular-dynamics simulations is in good agreement with experiment. Further, the calculated equilibrium melting temperature is found to be in good agreement with experiment.