Papers by Paras Mal Agrawal
The Journal of Chemical Physics, 1989
The Journal of Physical Chemistry, 1995
The reaction dynamics of vinyl bromide decomposition in perfect, face-centered cubic xenon and kr... more The reaction dynamics of vinyl bromide decomposition in perfect, face-centered cubic xenon and krypton matrices at 12 K and in xenon lattices with 10 and 20% vacant sites are computed using trajectory methods with an analytic potential for the electronic ground state of vinyl bromide. The total potential is written as the summation of a pairwise lattice potential, pairwise lattice-vinyl bromide interactions, and the gas-phase vinyl bromide potential. Product yield ratios, rate coefficients for vibrational energy transfer to the lattice phonon modes, and total decomposition rate coefficients are computed as a function of initial vinyl bromide energy. At low levels of excitation, three-center HBr dissociation is the only observed decomposition channel. This result is in accord with the data obtained from recent photolysis experiments. At higher energies, threecenter H2 elimination becomes important. When the excitation energy exceeds 6.0 eV, three-center H2 elimination becomes the major reaction channel. The relative importance of C-Br and C-H bond cleavage to produce Br and H atoms is greatly reduced in the matrix environment. Such processes become important only at higher energies. Molecular hydrogen elimination is also suppressed by the matrix, but the relative yield of HBr is enhanced compared to the gas-phase result. Limited calculations using Kr matrices suggest that the results are insensitive to matrix composition. The energy transfer rate coefficients are found to decrease exponentially with the percentage of vacancies in the lattice. The total vinyl bromide decomposition rates increase as the percentage of lattice vacancies increases, but the gas-phase rates are not approached even when 20% of the lattice sites are vacant. It is concluded that the molecular hydrogen seen in the matrix photolysis of vinyl bromide is produced by photolytic reactions of the HBr/acetylene products produced by the primary decomposition.
SSRN Electronic Journal, 2010
In physics, at the beginning of the twentieth century it was recognized that some experiments cou... more In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics but the same could be explained by the newly discovered quantum theory. It resulted into a new mechanics called quantum mechanics that revolutionized the scientific and technological developments. Again at the beginning of the twenty-first century, it is being recognized that some experiments related with the human decision making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quantum interference equation to illustrate the quantum approach. The explanation of disjunction effect experiments of Tversky and Shafir(1992) has been chosen to demonstrate the necessity of a quantum model. Further to suggest the possibility of application of the quantum theory to the business related decisions, some terms such as price operator, state of mind of the acquiring firm, etc. are introduced and discussed in context of the merger/acquisition of business firms. The possibility of the development in the areas such as quantum finance, quantum management, application of quantum mechanics to the human dynamics related with health care management, etc. is also indicated.
Tribology International, 2010
A phenomenological model of polishing hemispherical silicon asperities with spherical diamond abr... more A phenomenological model of polishing hemispherical silicon asperities with spherical diamond abrasives is presented. Removal of the asperity material is quantitatively determined by a removal rate constant K. It is based on our molecular dynamics (MD) simulation studies considering the probability of removal of asperity atoms by an abrasive. The dependence of the removal rate constant K on the diameter and velocity of abrasives, number of asperities and abrasives per unit area, and cutting depth has been investigated. The rate constant K is found to be insensitive to the density of asperities, but linearly dependent on the density of abrasives.
The Journal of Physical Chemistry B, 2006
The calculated crystal density at room conditions is about 10% lower than the measured value, whi... more The calculated crystal density at room conditions is about 10% lower than the measured value, while the lattice parameters and thermodynamic melting point are within about 5% at ambient pressure. The chair and inverted chair conformation, bond lengths, and bond angles of the RDX molecule are accurately predicted; however, there are some inaccuracies in the calculated orientations of the NO 2 groups. The SRT-AMBER force field predicts overall reasonable results, but modifications, probably in the torsional parameters, are needed for a more accurate force field.
The Journal of Physical Chemistry B, 2006
Physical properties of condensed-phase 1,3,3-trinitroazetidine (TNAZ) have been computed with mol... more Physical properties of condensed-phase 1,3,3-trinitroazetidine (TNAZ) have been computed with molecular dynamics (MD) and a nonreactive, fully flexible force field formulated by combining the intramolecular interactions obtained from the Generalized AMBER Force Field and the rigid-molecule force field developed by Sorescu-Rice-Thompson [J. Phys. Chem. B 1997, 101, 798] (AMBER-SRT). The results are compared with MD calculations, using the AMBER force field. The predicted densities of crystalline TNAZ from both force fields are about 10% lower than the experimental value. The calculated thermodynamic melting point at 1 atm from the AMBER-SRT force field is 390 K, in good agreement with the measured value of 374 K, while the AMBER force field predicts a thermodynamic melting point of 462 K. The lattice parameters and the molecular and crystal structures calculated with the AMBER-SRT force field are in excellent agreement with experiment. Simulations with the AMBER-SRT force field were also used to generate the isotherm of TNAZ up to 4 GPa and the bulk modulus and its pressure derivative.
Surface Science, 2002
The hopping self diffusion coefficient of an adatom on the (1 0 0), (1 1 0) and (1 1 1) surfaces ... more The hopping self diffusion coefficient of an adatom on the (1 0 0), (1 1 0) and (1 1 1) surfaces of nine FCC metals have been investigated using Monte Carlo variational transition state theory and the Lennard-Jones (L-J) interactions. The metals that have been studied are Ag, Al, Au, Cu, Ir, Ni, Pd, Pt and Rh. The potential parameters for the L-J interactions have been determined from the known experimental values of cohesive energies and lattice constants. The ratio, R, of the cohesive energy to the activation energy for diffusive hopping on the (1 1 1) and (1 0 0) surfaces are found to be 30 and 6, respectively. For diffusive hopping on the (1 1 0) surface, R depends on the direction of diffusion: R is 5 and 2.8 along the ½1 1 0 and [0 0 1] directions, respectively. The pre-exponential factor, D 0 , for these metals is found to vary within a factor of three from the corresponding average value, ðD 0 Þ av for a given surface and diffusion channel. Also, the pre-exponential factors corresponding to diffusion on the (1 1 1), (1 0 0), (1 1 0)½1 1 0 and (1 1 0)[0 0 1] surfaces are found to satisfy an empirical expression in terms of R, lattice constant, and the distance between the two nearest binding sites. The results on the activation energies and pre-exponential factors are compared with other experimental and theoretical data.
Surface Science, 1987
The effects of (a) surface relaxation to the " bath" modes of the bulk, (b) the number of lattice... more The effects of (a) surface relaxation to the " bath" modes of the bulk, (b) the number of lattice atoms explicitly considered in the primary reaction zone, (c) lattice force constants, and (d) the functional form of the lattice potential upon the dynamics of H 2 chemisorption on a Si(lll) surface have been investigated. The H z sticking probabilities, energy transfer rates out of the newly formed Si-H bond, and instantaneous surface mobilities have been computed. The sticking probabilities are virtually independent of surface relaxation, the size of the lattice model, and the nature of the lattice potential. Si-H vibrational energy transfer rates are increased and surface mobilities are decreased by inclusion of relaxation. However, the magnitude of these effects is less than a factor of two. Variation of the lattice potential is likewise found to exert a small effect upon the Si-H energy transfer rates and surface mobilities. The origin of these effects appears to be related to resonance effects between the Si-H vibrational motion and the phonon modes of the lattice. The results suggest that a three-layer lattice model with 25 atoms in the primary reaction zone is sufficient for this system. When primary zones of this size are employed, surface relaxation to the "bath" modes of the bulk are not of major importance for semiconductor systems at low temperatures.
Physical Review B, 2005
Molecular dynamics simulations of silicon melting reported in the literature using Tersoff's pote... more Molecular dynamics simulations of silicon melting reported in the literature using Tersoff's potential give melting temperatures about 50% higher than the experimental value. To address this discrepancy, we have proposed a modification to the values of the parameters of the Tersoff potential. This modification involves a change in the magnitude of 3 of the 12 parameters in the Tersoff potential as an effective means for bringing down the melting point close to the experimental value. The melting point is determined by performing Monte Carlo simulations using the empirical void-nucleated melting procedure. In addition to an agreement of the computed melting point with the experiment, the modified parameters also bring the density of the liquid and the solid at the melting point into good agreement with the experiment without significantly altering the density and energy values of the solid crystal at room temperature. The coordination number and specific heat of the liquid are also found to be in better agreement with the experiment when the modified set of parameters is used. A comparison of density over a wide range of temperatures shows that the density of the solid predicted by the Tersoff potential with the modified parameters is larger than that given by the unmodified parameters. This difference, however, is not appreciable at room temperature; it increases with temperature and is about 1% at the melting point. The computed cohesive energy of the solid, the point defect energy corresponding to a vacancy, and the surface energy values for ͑100͒ and ͑111͒ surfaces are also found to be nearly the same for the modified as well as the unmodified parameters.
Operations Research, 2013
In physics, at the beginning of the twentieth century it was recognized that some experiments cou... more In physics, at the beginning of the twentieth century it was recognized that some experiments could not be explained by the conventional classical mechanics, but the same could be explained by the newly discovered quantum theory. It resulted in a new mechanics called quantum mechanics that revolutionized scientific and technological developments. Again, at the beginning of the twenty-first century, it is being recognized that some experiments related to the human decision-making processes could not be explained by the conventional classical decision theory but the same could be explained by the models based on quantum mechanics. It is now recognized that we need quantum mechanics in psychology as well as in economics and finance. In this paper we attempt to advance and explain the present understanding of applicability of quantum mechanics to the human decision-making processes. Using the postulates analogous to the postulates of quantum mechanics, we show the derivation of the quan...
The Journal of Chemical Physics, 1981
The results of an infinite-order sudden theory modified by the inclusion of an explicit exit-chan... more The results of an infinite-order sudden theory modified by the inclusion of an explicit exit-channel velocity dependence of the scattering cross section (IOSAM) are compared with standard IOSA results having a scattering cross section independent of exit-channel velocity and with the experimental data reported by Barnes et al. for the HF–Ar system. Calculations of σ(j′←1) and σ(j′←2) are reported at three relative translational energies using two different potential-energy surface formulations, a pairwise additive Lennard-Jones (12,6) potential, and an SCF ab initio surface augmented by an attractive van der Waals term. In general, the IOSAM results on the LJ (12,6) surface are found to be in good to excellent accord with experiment for transitions with ΔJ≳0. For transitions with Δj<0, the agreement between theory and experiment is poor. The results obtained on the unadjusted SCF surface have the correct qualitative trends, but the degree of agreement with experiment is significa...
The Journal of Chemical Physics, 1981
The effect of potential surface topography upon elastic and inelastic scattering has been investi... more The effect of potential surface topography upon elastic and inelastic scattering has been investigated using the infinite-order sudden approximation (IOSA) to compute total differential and integral cross sections, state-to-state cross sections, and the relaxation rates of depleted levels in the (He, CO2) and (3He, CO2) rigid rotor systems on six different potential energy surfaces that include three surfaces obtained from electrom–gas type calculations, two ab initio SCF surfaces, and one surface (KPK) obtained by empirical fitting to the measured total differential cross section. It is found that the total elastic, inelastic, and differential cross sections are very sensitive to the long-range attractive terms in the potential, and the differential cross sections are also found to be significantly dependent upon the topography of the repulsive regions of the surface. Consequently, differential cross sections are very sensitive probes of surface topography and should be the data of...
The Journal of Chemical Physics, 1989
The dynamics of silicon-atom diffusion on a reconstructed Si(111)-(7×7) surface have been investi... more The dynamics of silicon-atom diffusion on a reconstructed Si(111)-(7×7) surface have been investigated using variational phase-space theory methods with a previously described [J. Chem. Phys. (to be published)] potential-energy surface. A four-layer lattice model of the Binnig et al. (7×7) reconstruction containing 291 atoms is employed for the surface. Canonical Markov walks with importance sampling incorporated are used to evaluate the flux across both right-circular and right-elliptical cylindrical dividing surfaces separating adsorption sites. This flux is minimized with respect to the parameters of the dividing surface to obtain the best estimate of the classical jump frequencies. The minimum jump frequencies so obtained are corrected for recrossings of the dividing surface by the calculation of trajectories that start from phase-space points obtained in the random walk that lie within a specified distance w of the dividing surface. The corrected jump frequencies are then used ...
The Journal of Chemical Physics, 1990
The x-axis wavelength scale on Fig. 1 is labeled incorrectly. The x-ray scale should go from 224.... more The x-axis wavelength scale on Fig. 1 is labeled incorrectly. The x-ray scale should go from 224.44 om on the left to 224.94 nm on the right with tick marks every 0.05 nm (not 0.1 nm as in the published figure). We thank Frank Holland for pointing out this error.
The Journal of Chemical Physics, 1988
The recombination dynamics for the SiH2+SiH2→H2Si=SiH2 reaction are studied by quasiclassical tra... more The recombination dynamics for the SiH2+SiH2→H2Si=SiH2 reaction are studied by quasiclassical trajectory methods using a global potential-energy surface fitted to the available experimental data and the results of various ab initio calculations. The potential surface is written as the sum of 18 many-body terms whose functional forms are motivated by chemical and physical considerations. The surface contains 41 parameters which are fitted to calculated geometries, fundamental vibrational frequencies, and energies for H2Si=SiH2, H2Si=SiH, H2Si=Si, HSi=Si, Si2, H2, and SiH2, and to various calculated and/or measured reaction barrier heights and activation energies. In general, the equilibrium bond lengths and angles given by the global surface are in agreement with ab i n i t i o results to within 0.03 Å and 0.5°, respectively. The calculated exothermicities for various reactions involving silicon and hydrogen atoms are in excellent agreement with previous MP4 calculations and with exp...
The Journal of Chemical Physics, 1996
The power spectrum line shapes for oscillators undergoing a continuous modulation of the vibratio... more The power spectrum line shapes for oscillators undergoing a continuous modulation of the vibrational frequency are investigated. It is shown that the single, sharp line normally characteristic of such systems broadens and exhibits a wealth of fine structure components. The characteristic fine structure pattern is one of decreasing amplitude and spacing. This continuous frequency modulation (CFM) effect has been examined for a series of model oscillators that includes harmonic systems with linear and exponential variation of the frequency without amplitude damping, a harmonic system with exponential damping of both the resonant frequency and the amplitude, and a Morse oscillator whose kinetic energy is being exponentially damped. An analytic expression for the power spectrum of a harmonic oscillator whose frequency is varying linearly with time is derived. This result demonstrates that the position of the fine structure extrema depends linearly upon the initial oscillator frequency a...
The Journal of Chemical Physics, 2006
The neural network (NN) procedure to interpolate ab initio data for the purpose of molecular dyna... more The neural network (NN) procedure to interpolate ab initio data for the purpose of molecular dynamics (MD) simulations has been tested on the SiO2 system. Unlike other similar NN studies, here, we studied the dissociation of SiO2 without the initial use of any empirical potential. During the dissociation of SiO2 into Si+O or Si+O2, the spin multiplicity of the system changes from singlet to triplet in the first reaction and from singlet to pentet in the second. This paper employs four potential surfaces. The first is a NN fit [NN(STP)] to a database comprising the lowest of the singlet, triplet, and pentet energies obtained from density functional calculations in 6673 nuclear configurations. The other three potential surfaces are obtained from NN fits to the singlet, triplet, and pentet-state energies. The dissociation dynamics on the singlet-state and NN(STP) surfaces are reported. The results obtained using the singlet surface correspond to those expected if the reaction were to o...
The Journal of Chemical Physics, 2005
A new approach involving neural networks combined with molecular dynamics has been used for the d... more A new approach involving neural networks combined with molecular dynamics has been used for the determination of reaction probabilities as a function of various input parameters for the reactions associated with the chemical-vapor deposition of carbon dimers on a diamond (100) surface. The data generated by the simulations have been used to train and test neural networks. The probabilities of chemisorption, scattering, and desorption as a function of input parameters, such as rotational energy, translational energy, and direction of the incident velocity vector of the carbon dimer, have been considered. The very good agreement obtained between the predictions of neural networks and those provided by molecular dynamics and the fact that, after training the network, the determination of the interpolated probabilities as a function of various input parameters involves only the evaluation of simple analytical expressions rather than computationally intensive algorithms show that neural ...
The Journal of Chemical Physics, 1991
The dynamics of silicon-atom diffusion on the dimer–adatom-stacking fault model (DAS) of the reco... more The dynamics of silicon-atom diffusion on the dimer–adatom-stacking fault model (DAS) of the reconstructed Si(111)-(7×7) surface suggested by Takayanagi et al. have been investigated using variational phase-space theory methods. The site-to-site jump frequency is obtained from the variationally minimized total flux across a right cylindrical dividing surface whose cross section in the surface plane is formed from straight line and elliptical segments. This minimized flux is corrected for surface recrossings by the computation of trajectories starting from phase-space points in the transition-state region that are obtained in the Markov walk used to evaluate the phase-space integrals in the expression for the total classical flux. The jump frequencies are used as input to the set of differential equations that describes the diffusion rates on the DAS surface. Values of the diffusion coefficient D are computed from the slopes of plots of the time variation of the root-mean-square disp...
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Papers by Paras Mal Agrawal