N. Balakrishnan

University of Nevada, Las Vegas, Las Vegas, Nevada, United States

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Publications (132)338.37 Total impact

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    ABSTRACT: Rate coefficients for collisional processes such as rotational and vibrational excitation are essential inputs in many astrophysical models. When rate coefficients are unknown, they are often estimated using known values from other systems. The most common example is to use He-collider rate coefficients to estimate values for other colliders, typically H$_2$, using scaling arguments based on the reduced mass of the collision system. This procedure is often justified by the assumption that the inelastic cross section is independent of the collider. Here we explore the validity of this approach focusing on rotational inelastic transitions for collisions of H, para-H$_2$, $^3$He, and $^4$He with CO in its vibrational ground state. We compare rate coefficients obtained via explicit calculations to those deduced by standard reduced-mass scaling. Not surprisingly, inelastic cross sections and rate coefficients are found to depend sensitively on both the reduced mass and the interaction potential energy surface. We demonstrate that standard reduced-mass scaling is not valid on physical and mathematical grounds, and as a consequence, the common approach of multiplying a rate coefficient for a molecule-He collision system by the constant factor of ~1.4 to estimate the rate coefficient for para-H$_2$ collisions is deemed unreliable. Furthermore, we test an alternative analytic scaling approach based on the strength of the interaction potential and the reduced mass of the collision systems. Any scaling approach, however, may be problematic when low-energy resonances are present; explicit calculations or measurements of rate coefficients are to be preferred.
    The Astrophysical Journal 06/2014; 790(2). · 6.73 Impact Factor
  • G B Pradhan, N Balakrishnan, Brian K Kendrick
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    ABSTRACT: The effect of initial vibrational excitation of the D2 molecule on the quantum dynamics of the O(1D)+D2 reaction is investigated as a function of collision energy. The potential energy surface of Dobbyn and Knowles (1997 Mol. Phys. 91 1107) and a time-independent quantum mechanical method based on hyperspherical coordinates have been adopted for the dynamics calculations. Results for elastic, inelastic, and reactive scattering over collision energies ranging from the ultracold to thermal regimes are reported for total angular momentum quantum number J = 0. Calculations show that the collisional outcome of the O(1D)+D2 reaction is not strongly influenced by the initial vibrational excitation of the D2 molecule similar to its H2 counterpart. A J-shifting approximation is used to calculate the initial state selected reactive rate coefficients over the temperature range T = 1 − 500 K. The reactive rate coefficients for D2(v = 0) are found to be in excellent agreement with available experimental results. The temperature dependence of the kinetic isotope effect is also investigated and its value at room temperature is found to be in good agreement with available theoretical and experimental results.
    Journal of Physics B Atomic Molecular and Optical Physics 06/2014; 47(13):135202. · 2.03 Impact Factor
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    ABSTRACT: Collision-induced energy transfer involving H2 molecules plays an important role in many areas of physics. Kinetic models often require a complete set of state-to-state rate coefficients for H2+H2 collisions in order to interpret results from spectroscopic observations or to make quantitative predictions. Recent progress in full-dimensional quantum dynamics using the numerically exact close-coupling (CC) formulation has provided good agreement with existing experimental data for low-lying states of H2 and increased the number of state-to-state cross sections that may be reliably determined over a broad range of energies. Nevertheless, there exist many possible initial states (e.g., states with high rotational excitation) that still remain elusive from a computational standpoint even at relatively low collision energies. In these cases, the coupled-states (CS) approximation offers an alternative full-dimensional formulation. We assess the accuracy of the CS approximation for H2+H2 collisions by comparison with benchmark results obtained using the CC formulation. The results are used to provide insight into the orientation effects of the various internal energy transfer mechanisms. A statistical CS approximation is also investigated and cross sections are reported for transitions which would otherwise be impractical to compute.
    The Journal of Chemical Physics 02/2014; 140(6):064308. · 3.12 Impact Factor
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    ABSTRACT: Quantum scattering calculations are reported for state-to-state vibrational relaxation and reactive scattering in O + OH(v = 2 - 3, j = 0) collisions on the electronically adiabatic ground state (2)A'' potential energy surface of the HO2 molecule. The time-independent Schrödinger equation in hyperspherical coordinates is solved to determine energy dependent probabilities and cross sections over collision energies ranging from ultracold to 0.35 eV and for total angular momentum quantum number J = 0. A J-shifting approximation is then used to compute initial state selected reactive rate coefficients in the temperature range T = 1 - 400 K. Results are found to be in reasonable agreement with available quasiclassical trajectory calculations. Results indicate that rate coefficients for O2 formation increase with increasing the OH vibrational level except at low and ultralow temperatures where OH(v = 0) exhibits a slightly different trend. It is found that vibrational relaxation of OH in v = 2 and v = 3 vibrational levels is dominated by a multi-quantum process.
    The Journal of Chemical Physics 11/2013; 139(19):194305. · 3.12 Impact Factor
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    ABSTRACT: New quantum scattering calculations for rotational deexcitation transitions of CO induced by H collisions using two CO-H potential energy surfaces (PESs) from Shepler et al. (2007) are reported. State-to-state rate coefficients are computed for temperatures ranging from 1 to 3000 K for CO($v=0,j$) deexcitation from $j=1-5$ to all lower $j^\prime$ levels, with $j$ being the rotational quantum number. Different resonance structures in the cross sections are attributed to the differences in the anisotropy and the long-range van der Waals well depths of the two PESs. These differences affect rate coefficients at low temperatures and give an indication of the uncertainty of the results. Significant discrepancies are found between the current rate coefficients and previous results computed using earlier potentials, while the current results satisfy expected propensity rules. Astrophysical applications to modeling far infrared and submillimeter observations are briefly discussed.
    The Astrophysical Journal 05/2013; 771(1). · 6.73 Impact Factor
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    ABSTRACT: Quantum scattering calculations of vibration-vibration (VV) and vibration-translation (VT) energy transfer for non-reactive H2-H2 collisions on a full-dimensional potential energy surface are reported for energies ranging from the ultracold to the thermal regime. The efficiency of VV and VT transfer is known to strongly correlate with the energy gap between the initial and final states. In H2(v = 1, j = 0) + H2(v = 0, j = 1) collisions, the inelastic cross section at low energies is dominated by a VV process leading to H2(v = 0, j = 0) + H2(v = 1, j = 1) products. At energies above the opening of the v = 1, j = 2 rotational channel, pure rotational excitation of the para-H2 molecule leading to the formation of H2(v = 1, j = 2) + H2(v = 0, j = 1) dominates the inelastic cross section. For vibrationally excited H2 in the v = 2 vibrational level colliding with H2(v = 0), the efficiency of both VV and VT process is examined. It is found that the VV process leading to the formation of 2H2(v = 1) molecules dominates over the VT process leading to H2(v = 1) + H2(v = 0) products, consistent with available experimental data, but in contrast to earlier semiclassical results. Overall, VV processes are found to be more efficient than VT processes, for both distinguishable and indistinguishable H2-H2 collisions confirming room temperature measurements for v = 1 and v = 2.
    The Journal of Chemical Physics 03/2013; 138(10):104302. · 3.12 Impact Factor
  • G.B.Pradhan, N. Balakrishnan, B.K.Kendrick
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    ABSTRACT: A quantum dynamics study of the O((1)D) + H2(v = 0 - 2, j = 0) system has been carried out using the potential energy surfaces of Dobbyn and Knowles [Mol. Phys. 91, 1107 (1997)]. A time-independent quantum mechanical method based on hyperspherical coordinates is adopted for the dynamics calculations. Energy dependent cross section, probability, and rate coefficients are computed for the elastic, inelastic, and reactive channels over collision energies ranging from the ultracold to thermal regimes and for total angular momentum quantum number J = 0. The effect of initial vibrational excitation of the H2 molecule on vibrational and rotational populations of the OH product is investigated as a function of the collision energy. Comparison of results for vibrational levels v = 0 - 2 of H2 demonstrates that the vibrational excitation of H2 and its non-reactive relaxation pathway play a minor role in the overall collisional outcome of O((1)D) and H2. It is also found that while the state-resolved product vibrational distributions are sensitive to the initial collision energy and H2 vibrational level, the product rotational distribution depicts an inverted population that is largely insensitive to initial conditions. Rate coefficients evaluated using a J-shifting approximation show reasonable agreement with available theoretical and experimental results suggesting that the J-shifting approximation may be used to evaluate the rate coefficients for O((1)D) + H2 reaction.
    The Journal of Chemical Physics 01/2013; 138(16):164310. · 3.12 Impact Factor
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    ABSTRACT: Highly efficient and specific energy transfer mechanisms that involve rotation-rotation, vibration-vibration, and vibration-rotation exchange in diatomic molecules are examined theoretically in ultracold H_{2}, D_{2}, and HD self-collisions as a function of initial vibrational level v. The three quasiresonant mechanisms are found to operate for all vibrational levels and yield complex scattering lengths which vary smoothly with v. Exceptions to this trend occur at select high values of v where the scattering lengths are modulated by orders of magnitude corresponding to the location of an s-wave zero-energy resonance in "vibration space." The quasiresonant mechanisms, which are not very sensitive to the details of the interaction potential, generally control the final distribution of molecular states for any given initial distribution. The zero-energy resonances are more sensitive to the potential and may be used to vibrationally "tune" the interaction strength, similar to methods which vary applied external fields.
    Physical Review Letters 12/2012; 109(23):233201. · 7.73 Impact Factor
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    ABSTRACT: The quasi-resonant rotation-rotation (QRRR) mechanism is studied theoretically in ultracold H2, D2, and HD self-collisions as a function of initial vibrational level v. In the QRRR mechanism, the collision partners swap internal rotational excitation resulting in large cross sections and scattering lengths. The efficiency of the QRRR mechanism is a consequence of conservation of total system internal rotational angular momentum and near conservation of internal energy. Extending to high vibrational excitation, we find that the QRRR mechanism identified for H2(v=1)+H2(v'=0) by Qu'em'ener et al. [1] persists with scattering lengths, both real and imaginary, varying smoothly with v. However, exceptions occur at select high values of v where the scattering lengths are enhanced by orders of magnitude corresponding to the location of a zero-energy resonance in ``vibration space." Similar trends are seen for D2 and HD self-collisions. If the QRRR mechanism operates in other ultracold dimer-dimer collision systems, then vibrational excitation may be used to ``tune" the interaction strength similar to methods which use external fields or theoretical variation of the reduced mass.[4pt] [1] G. Qu'em'ener et al., Phys. Rev. A 77, 030704(R) (2008).
    06/2012;
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    ABSTRACT: We report quantum calculations of rovibrational transitions in H2 + H2 collisions on different ab initio potential surfaces (PESs). The PESs employed include the six-dimensional interaction potential of Hinde [1] and a hybrid potential constructed from the Hinde potential and the high accuracy 4-dimensional PES of Patkowski et al. [2]. Results show that vibrational relaxation cross sections are sensitive to details of the potentials at low energies but the sensitivity is significantly suppressed for quasiresonant transitions that involve small energy gaps and that conserve the total rotational angular momentum of the colliding molecules. Additionally, we present results for H2(v=2) + H2(v = 0) collisions and explore competition between vibration-vibration (VV) transfer leading to H2(v=1) +H2(v=1) products and vibration-translation (VT) transfer yielding H2(v=1) + H2(v=0) products. Results show that the VV process dominates over the VT process, in agreement with available experimental data. [1] Robert J. Hinde, J. Chem. Phys. 128, 154308 (2008). [2] K. Patkowski, W. Cencek, P.Jankowski, K. Szalewicz, J. B. Mehl, G. Garberoglio, and A. H. Harvey, J. Chem. Phys. 129, 094304 (2008).
    06/2012;
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    ABSTRACT: Along with H2, HD has been found to play an important role in the cooling of the primordial gas for the formation of the first stars and galaxies. It has also been observed in a variety of cool molecular astrophysical environments. The rate of cooling by HD molecules requires knowledge of collisional rate coefficients with the primary impactors, H, He, and H2. To improve knowledge of the collisional properties of HD, we present rate coefficients for the He-HD collision system over a range of collision energies from 10–5 to 5 × 103 cm–1. Fully quantum mechanical scattering calculations were performed for initial HD rovibrational states of j = 0 and 1 for v = 0-17 which utilized accurate diatom rovibrational wave functions. Rate coefficients of all Δv = 0, –1, and –2 transitions are reported. Significant discrepancies with previous calculations, which adopted a small basis and harmonic HD wave functions for excited vibrational levels, were found for the highest previously considered vibrational state of v = 3. Applications of the He-HD rate coefficients in various astrophysical environments are briefly discussed.
    The Astrophysical Journal 12/2011; 744(1):62. · 6.73 Impact Factor
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    ABSTRACT: Building on recent advances in ultrafast lasers and methods to slow molecules, an experiment is proposed to produce translationally cold CO2 super-rotors (j∼200) by combining an optical centrifuge with helium-buffer-gas cooling. Quantum mechanical calculations of the complex scattering length for He-CO2 collisions demonstrate that the efficiency of rotational quenching decreases rapidly with increasing rotational excitation j in the ultracold regime. Extrapolating to helium cryogenic temperatures, rotational quenching is predicted to remain inefficient up to ∼1 K, allowing for the possible creation of a beam of translationally cold, rotationally hot molecules.
    Physical Review A 10/2011; 84(5). · 3.04 Impact Factor
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    ABSTRACT: We report a quantum dynamics study of O + OH (v = 1, j = 0) collisions on its ground electronic state, employing two different potential energy surfaces: the DIMKP surface by Kendrick and Pack, and the XXZLG surface by Xu et al. A time-independent quantum mechanical method based on hyperspherical coordinates has been adopted for the dynamics calculations. Energy-dependent probabilities and rate coefficients are computed for the elastic, inelastic, and reactive channels over the collision energy range E(coll) = 10(-10)-0.35 eV, for J = 0 total angular momentum. Initial state-selected reaction rate coefficients are also calculated from the J = 0 reaction probabilities by applying a J-shifting approximation, for temperatures in the range T = 10(-6)-700 K. Our results show that the dynamics of the collisional process and its outcome are strongly influenced by long-range forces, and chemical reactivity is found to be sensitive to the choice of the potential energy surface. For O + OH (v = 1, j = 0) collisions at low temperatures, vibrational relaxation of OH competes with reactive scattering. Since long-range interactions can facilitate vibrational relaxation processes, we find that the DIMKP potential (which explicitly includes van der Waals dispersion terms) favours vibrational relaxation over chemical reaction at low temperatures. On the DIMKP potential in the ultracold regime, the reaction rate coefficient for O + OH (v = 1, j = 0) is found to be a factor of thirteen lower than that for O + OH (v = 0, j = 0). This significantly high reactivity of OH (v = 0, j = 0), compared to that of OH (v = 1, j = 0), is attributed to enhancement caused by the presence of a HO(2) quasibound state (scattering resonance) with energy near the O + OH (v = 0, j = 0) dissociation threshold. In contrast, the XXZLG potential does not contain explicit van der Waals terms, being just an extrapolation by a nearly constant function at large O-OH distances. Therefore, long-range potential couplings are absent in calculations using the XXZLG surface, which does not induce vibrational relaxation as efficiently as the DIMKP potential. The XXZLG potential leads to a slightly higher reactivity (a factor of 1.4 higher) for O + OH (v = 1, j = 0) compared to that for O + OH (v = 0, j = 0) at ultracold temperatures. Overall, both potential surfaces yield comparable values of reaction rate coefficients at low temperatures for the O + OH (v = 1, j = 0) reaction.
    Physical Chemistry Chemical Physics 06/2011; 13(42):19067-76. · 4.20 Impact Factor
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    ABSTRACT: We present a full dimensional quantum mechanical treatment of collisions between two H(2) molecules over a wide range of energies. Elastic and state-to-state inelastic cross sections for ortho-H(2) + para-H(2) and ortho-H(2) + ortho-H(2) collisions have been computed for different initial rovibrational levels of the molecules. For rovibrationally excited molecules, it has been found that state-to-state transitions are highly specific. Inelastic collisions that conserve the total rotational angular momentum of the diatoms and that involve small changes in the internal energy are found to be highly efficient. The effectiveness of these quasiresonant processes increases with decreasing collision energy and they become highly state-selective at ultracold temperatures. They are found to be more dominant for rotational energy exchange than for vibrational transitions. For non-reactive collisions between ortho- and para-H(2) molecules for which rotational energy exchange is forbidden, the quasiresonant mechanism involves a purely vibrational energy transfer albeit with less efficiency. When inelastic collisions are dominated by a quasiresonant transition calculations using a reduced basis set involving only the quasiresonant channels yield nearly identical results as the full basis set calculation leading to dramatic savings in computational cost.
    The Journal of Chemical Physics 06/2011; 134(21):214303. · 3.12 Impact Factor
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    ABSTRACT: As most of the gas in the Universe is not in thermal equilibrium, accurate modeling and interpretation of observations requires understanding of a variety of collisional processes. Rate coefficients describing such processes can usually be measured and/or calculated, but the enormous enhancements in the spectral line resolution and sensitivity expected from ALMA, SOFIA, Herschel, and other FIR/submm telescopes place unquenchable demands on the collisional data. As a consequence, the construction of reliable collisional data sets for astrophysical/astrochemical modeling faces a number of challenges: i) Due to the voluminous quantity of required data, theory must provide the bulk of the results with experiment serving as benchmarks. ii) The accuracy of the scattering calculations are directly dependent on the reliability and availability of the quantum chemical data. iii) Database construction requires consistent and appropriate funding which is typically lacking. We review these issues in the context of our ongoing collaborative work on computations of rovibrational excitation of H_2, HD, CO, H_2O, CO_2, NH_3, and CH_4 due to H, He, and H_2 collisions and their role in the modeling of various astrophysical environments. This work was partially supported by NASA grants NNG05GD81G, NNG06GC94G, NNX07AP12G, and NNX10AD56G, and NSF grants PHY-0554794, PHY-0855470, PHY-0854838, and AST-0607733.
    05/2011;
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    ABSTRACT: We report quantum dynamics calculations of rotational and vibrational energy transfer in collisions between two para-H(2) molecules over collision energies spanning from the ultracold limit to thermal energies. Results obtained using a recent full-dimensional H(2)-H(2) potential energy surface (PES) developed by Hinde [J. Chem. Phys. 128, 154308 (2008)] are compared with those derived from the Boothroyd, Martin, Keogh, and Peterson (BMKP) PES [J. Chem. Phys. 116, 666 (2002)]. For vibrational relaxation of H(2)(v=1,j=0) by collisions with H(2)(v=0,j=0) as well as rotational excitations in collisions between ground state H(2) molecules, the PES of Hinde is found to yield results in better agreement with available experimental data. A highly efficient near-resonant energy transfer mechanism that conserves internal rotational angular momentum and was identified in our previous study of the H(2)-H(2) system [Phys. Rev. A 77, 030704(R) (2008)] using the BMKP PES is also found to be reproduced by the Hinde PES, demonstrating that the process is largely insensitive to the details of the PES. In the absence of the near-resonance mechanism, vibrational relaxation is driven by the anisotropy of the potential energy surface. Based on a comparison of results obtained using the Hinde and BMKP PESs with available experimental data, it appears that the Hinde PES provides a more accurate description of rotational and vibrational transitions in H(2)-H(2) collisions, at least for vibrational quantum numbers v ≤ 1.
    The Journal of Chemical Physics 01/2011; 134(1):014301. · 3.12 Impact Factor
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    ABSTRACT: Rate coefficients for state-to-state rotational transitions in CO induced by both para- and ortho-H$_2$ collisions are presented. The results were obtained using the close-coupling method and the coupled-states approximation, with the CO-H$_2$ interaction potential of Jankowski & Szalewicz (2005). Rate coefficients are presented for temperatures between 1 and 3000 K, and for CO($v=0,j$) quenching from $j=1-40$ to all lower $j^\prime$ levels. Comparisons with previous calculations using an earlier potential show some discrepancies, especially at low temperatures and for rotational transitions involving large $|\Delta j|$. The differences in the well depths of the van der Waals interactions in the two potential surfaces lead to different resonance structures in the energy dependence of the cross sections which influence the low temperature rate coefficients. Applications to far infrared observations of astrophysical environments are briefly discussed. Comment: 28 pages, 10 figures
    The Astrophysical Journal 04/2010; 718:1062. · 6.73 Impact Factor
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    ABSTRACT: Elastic and rotationally inelastic processes are studied for collisions of rotationally excited CO2 with He. In the ultracold limit, complex scattering lengths were computed for rotational levels up to j=200 using the close-coupling method and the coupled-states approximation. As illustrative examples, some cross sections are also presented. This work was motivated by recent experimental efforts to generate highly excited CO2 rotational states with an optical centrifuge [1] and the possibility of translationally cooling carbon dioxide with helium buffer-gas techniques. Experiments with rotationally excited and cold CO2 may be feasible as the ratio of the real to imaginary components of the scattering length exceeds ˜30 for j=200. [4pt] [1] A. S. Mullin, L. Yuan, S. Teitelbaum, and A. Robinson, APS Bulletin, DAMOP Abstract E1.00016 (2009).
    03/2010;
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    Goulven Quéméner, Naduvalath Balakrishnan, Alexander Dalgarno
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    ABSTRACT: This paper summarizes the recent theoretical works on inelastic collisions and chemical reactions at cold and ultracold temperatures involving neutral or ionic systems of atoms and molecules. Tables of zero-temperature rate constants of various molecules are provided. Comment: 28 pages, 25 figures
    01/2010;
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    ABSTRACT: We examine the effect of theoretically varying the collision-system reduced mass in collisions of He with vibrationally excited molecular hydrogen and observe zero-energy resonances for select atomic “hydrogen” masses less than 1 u or a “helium” mass of 1.95 u. Complex scattering lengths, state-to-state vibrational quenching cross sections, and a low-energy elastic scattering resonance are all studied as a function of collision-system reduced mass. Experimental observations of these phenomena in the cold and ultracold regimes for collisions of 3He and 4He with H2, HD, HT, and DT should be feasible in the near future.
    Physical Review A 01/2010; 81(1). · 3.04 Impact Factor

Publication Stats

1k Citations
338.37 Total Impact Points

Institutions

  • 2003–2014
    • University of Nevada, Las Vegas
      • Department of Chemistry
      Las Vegas, Nevada, United States
  • 2005–2012
    • University of Georgia
      • • Center for Simulational Physics
      • • Department of Physics and Astronomy
      Athens, GA, United States
  • 1997–2009
    • Harvard-Smithsonian Center for Astrophysics
      • Institute for Theoretical Atomic, Molecular and Optical Physics
      Cambridge, MA, United States
  • 2006
    • St. Cloud State University
      Saint Cloud, Minnesota, United States
  • 2005–2006
    • University of Kentucky
      • Department of Physics & Astronomy
      Lexington, KY, United States
  • 2000
    • Louisiana Tech University
      Louisiana, United States