arXiv subjects

N. Balakrishnan

Publications and source records attributed to N. Balakrishnan.

At least 55 records · Page 3Linked to original sources

arXiv2015

Collisional quenching of highly rotationally excited HF

Collisional excitation rate coefficients play an important role in the dynamics of energy transfer in the interstellar medium. In particular, accurate rotational excitation rates are needed to interpret microwave and infrared observations of the interstellar gas for nonlocal thermodynamic equilibrium line formation. Theoretical cross sections and rate coefficients for collisional deexcitation of rotationally excited HF in the vibrational ground state are reported. The quantum-mechanical close-coupling approach implemented in the nonreactive scattering code MOLSCAT was applied in the cross section and rate coefficient calculations on an accurate 2D HF-He potential energy surface. Estimates of rate coefficients for H and H$_2$ colliders were obtained from the HF-He collisional data with a reduced-potential scaling approach. The calculation of state-to-state rotational quenching cross sections for HF due to He with initial rotational levels up to $j=20$ were performed for kinetic energies from 10$^{-5}$ to 15000 cm$^{-1}$. State-to-state rate coefficients for temperatures between 0.1 and 3000 K are also presented. The comparison of the present results with previous work for lowly-excited rotational levels reveals significant differences. In estimating HF-H$_2$ rate coefficients, the reduced-potential method is found to be more reliable than the standard reduced-mass approach. The current state-to-state rate coefficient calculations are the most comprehensive to date for HF-He collisions. We attribute the differences between previously reported and our results to differences in the adopted interaction potential energy surfaces. The new He rate coefficients can be used in a variety of applications. The estimated H$_2$ and H collision rates can also augment the smaller datasets previously developed for H$_2$ and electrons.

astro-ph.SR↗

arXiv2015

Quantum dynamics of CO-H$_2$ in full dimensionality

Accurate rate coefficients for molecular vibrational transitions due to collisions with H$_2$, critical for interpreting infrared astronomical observations, are lacking for most molecules. Quantum calculations are the primary source of such data, but reliable values that consider all internal degrees of freedom of the collision complex have only been reported for H$_2$-H$_2$ due to the difficulty of the computations. Here we present essentially exact full-dimensional dynamics computations for rovibrational quenching of CO due to H$_2$ impact. Using a high-level six-dimensional potential surface, time-independent scattering calculations, within a full angular-momentum-coupling formulation, were performed for the deexcitation of vibrationally excited CO. Agreement with experimentally-determined results confirms the accuracy of the potential and scattering computations, representing the largest of such calculations performed to date. This investigation advances computational quantum dynamics studies representing initial steps toward obtaining CO-H$_2$ rovibrational quenching data needed for astrophysical modeling.

astro-ph.SR↗

arXiv2014

Ultracold chemistry with alkali-metal-rare-earth molecules

A first principles study of the dynamics of $^6$Li($^{2}$S) + $^6$Li$^{174}$Yb($^2Σ^+$)$ \to ^6$Li$_2(^1Σ^+$) + $^{174}$Yb($^1$S) reaction is presented at cold and ultracold temperatures. The computations involve determination and analytic fitting of a three-dimensional potential energy surface for the Li$_2$Yb system and quantum dynamics calculations of varying complexities, ranging from exact quantum dynamics within the close-coupling scheme, to statistical quantum treatment, and universal models. It is demonstrated that the two simplified methods yield zero-temperature limiting reaction rate coefficients in reasonable agreement with the full close-coupling calculations. The effect of the three-body term in the interaction potential is explored by comparing quantum dynamics results from a pairwise potential that neglects the three-body term to that derived from the full interaction potential. Inclusion of the three-body term in the close-coupling calculations was found to reduce the limiting rate coefficients by a factor of two. The reaction exoergicity populates vibrational levels as high as $v=19$ of the $^6$Li$_2$ molecule in the limit of zero collision energy. Product vibrational distributions from the close-coupling calculations reveal sensitivity to inclusion of three-body forces in the interaction potential. Overall, the results indicate that a simplified model based on the long-range potential is able to yield reliable values of the total reaction rate coefficient in the ultracold limit but a more rigorous approach based on statistical quantum or quantum close-coupling methods is desirable when product rovibrational distribution is required.

physics.chem-ph↗

arXiv2014

Quantum Defect Theory for Cold Chemistry with Product Quantum State Resolution

We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short-range with quantum defect theory at long-range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for D+H$_2\to$ HD+H collisions with rovibrational quantum state resolution of the HD product, is shown to be accurate for a wide range of collision energies and initial conditions. The hybrid CC-MQDT formalism may provide an alternative approach to full CC calculations for cold and ultracold reactions.

physics.atom-ph↗

arXiv2014

Multichannel quantum defect theory for ro-vibrational transitions in ultracold molecule-molecule collisions

Multichannel quantum defect theory (MQDT) has been widely applied to resonant and non-resonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full-close coupling (CC) calculations when spin, hyperfine and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for H$_2$-H$_2$ collisions in full-dimensionality, is shown to adequately reproduce cross sections for quasi-resonant rotational and vibrational transitions in the ultracold (1$μ$K) and $\sim$ 1-10 K regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range $K$-matrix evaluated in the ultracold regime (1$μ$K) can adequately characterize cross sections in the mK-K regime when no shape resonances are present. The hybrid CC-MQDT formalism provides an alternative approach to full CC calculations at considerably less computational expense for cold and ultracold molecular scattering.

physics.atom-ph↗

arXiv2014

On the Validity of Collider-Mass Scaling for Molecular Rotational Excitation

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.

astro-ph.GA↗

arXiv2013

Quantum Calculation of Inelastic CO Collisions with H: I. rotational quenching of low-lying rotational levels

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.

astro-ph.SR↗

arXiv2012

Some Pitman Closeness Properties Pertinent to Symmetric Populations

In this paper, we focus on Pitman closeness probabilities when the estimators are symmetrically distributed about the unknown parameter $θ$. We first consider two symmetric estimators $\hatθ_1$ and $\hatθ_2$ and obtain necessary and sufficient conditions for $\hatθ_1$ to be Pitman closer to the common median $θ$ than $\hatθ_2$. We then establish some properties in the context of estimation under Pitman closeness criterion. We define a Pitman closeness probability which measures the frequency with which an individual order statistic is Pitman closer to $θ$ than some symmetric estimator. We show that, for symmetric populations, the sample median is Pitman closer to the population median than any other symmetrically distributed estimator of $θ$. Finally, we discuss the use of Pitman closeness probabilities in the determination of an optimal ranked set sampling scheme (denoted by RSS) for the estimation of the population median when the underlying distribution is symmetric. We show that the best RSS scheme from symmetric populations in the sense of Pitman closeness is the median and randomized median RSS for the cases of odd and even sample sizes, respectively.

math.ST↗

arXiv2012

Pareto analysis based on records

Estimation of the parameters of an exponential distribution based on record data has been treated by Samaniego and Whitaker (1986) and Doostparast (2009). Recently, Doostparast and Balakrishnan (2011) obtained optimal confidence intervals as well as uniformly most powerful tests for one- and two-sided hypotheses concerning location and scale parameters based on record data from a two-parameter exponential model. In this paper, we derive optimal statistical procedures including point and interval estimation as well as most powerful tests based on record data from a two-parameter Pareto model. For illustrative purpose, a data set on annual wages of a sample production-line workers in a large industrial firm is analyzed using the proposed procedures.

math.ST↗

arXiv2010

Rotational quenching of CO due to H$_2$ collisions

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 $|Δj|$. 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.

astro-ph.SR↗

arXiv2009

New multi-sample nonparametric tests for panel count data

This paper considers the problem of multi-sample nonparametric comparison of counting processes with panel count data, which arise naturally when recurrent events are considered. Such data frequently occur in medical follow-up studies and reliability experiments, for example. For the problem considered, we construct two new classes of nonparametric test statistics based on the accumulated weighted differences between the rates of increase of the estimated mean functions of the counting processes over observation times, wherein the nonparametric maximum likelihood approach is used to estimate the mean function instead of the nonparametric maximum pseudo-likelihood. The asymptotic distributions of the proposed statistics are derived and their finite-sample properties are examined through Monte Carlo simulations. The simulation results show that the proposed methods work quite well and are more powerful than the existing test procedures. Two real data sets are analyzed and presented as illustrative examples.

math.ST↗

arXiv2008

Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen

Pranab K. Sen has contributed extensively to many areas of Statistics including order statistics, nonparametrics, robust inference, sequential methods, asymptotics, biostatistics, clinical trials, bioenvironmental studies and bioinformatics. His long list of over 600 publications and 22 books and volumes along with numerous citations during the past 5 decades bear testimony to his work. All three of us have had the good fortune of being associated with him in different capacities. He has given professional and personal advice on many occasions to all of us, and we feel that our lives have certainly been enriched by our association with him. He has been over the years a friend, philosopher and a guide to us, and still continues to be one! While parametric statistical inference remains ever so popular, semi-parametric, Bayesian and nonparametric inferential methods have attracted great attention from numerous applied scientists because of their weaker assumptions, which make them naturally robust and so more appropriate in real-life applications. This clearly signals for ``beyond parametrics'' approaches which include nonparametrics, semi-parametrics, Bayes methods and many others. Motivated by this feature, and his drive in the ``beyond parametrics'' area, we thought that it will be only appropriate for a volume in honor of Pranab Kumar Sen to focus on this aspect of statistical inference and its applications. With this in mind, we have put together this volume in order to (i) review some of the recent developments in this direction, (ii) focus on some new methodologies and highlight their applications, and (iii) suggest some interesting open problems and possible new directions for further research.

math.ST↗

arXiv2008

Pranab Kumar Sen: Life and works

In this article, we describe briefly the highlights and various accomplishments in the personal as well as the academic life of Professor Pranab Kumar Sen.

math.ST↗

arXiv2008

Rotational quenching rate coefficients for H_2 in collisions with H_2 from 2 to 10,000 K

Rate coefficients for rotational transitions in H_2 induced by H_2 impact are presented. Extensive quantum mechanical coupled-channel calculations based on a recently published (H_2)_2 potential energy surface were performed. The potential energy surface used here is presumed to be more reliable than surfaces used in previous work. Rotational transition cross sections with initial levels J <= 8 were computed for collision energies ranging between 0.0001 and 2.5 eV, and the corresponding rate coefficients were calculated for the temperature range 2 < T <10,000 K. In general, agreement with earlier calculations, which were limited to 100-6000 K, is good though discrepancies are found at the lowest and highest temperatures. Low-density-limit cooling functions due to para- and ortho-H_2 collisions are obtained from the collisional rate coefficients. Implications of the new results for non-thermal H_2 rotational distributions in molecular regions are also investigated.

astro-ph↗

arXiv2007

Low energy H+CO scattering revisited: CO rotational excitation with new potential surfaces

A recent modeling study of brightness ratios for CO rotational transitions in gas typical of the diffuse ISM by Liszt found the role of H collisions to be more important than previously assumed. This conclusion was based on quantum scattering calculations using the so-called WKS potential energy surface (PES) which reported a large cross section for the important 0->1 rotational transition. New close-coupling (CC) rigid-rotor calculations for CO(v=0,J=0) excitation by H are performed on four different PESs. Two of the PESs are obtained in this work using state-of-the-art quantum chemistry techniques at the CCSD(T) and MRCI levels of theory. Cross sections for the J=0->1, as well as other odd Delta J, transitions are significantly suppressed compared to even Delta J transitions in thermal energy CC calculations using the CCSD(T) and MRCI surfaces. This is consistent with a expected even Delta J propensity and in contrast to CC calculations using the earlier WKS PES which predict a dominating 0->1 transition. The current results suggest that the original astrophysical assumption that excitation of CO by H_2 dominates the kinetics of CO in diffuse ISM gas is likely to remain valid.

astro-ph↗

arXiv2006

State-to-state rotational transitions in H$_2$+H$_2$ collisions at low temperatures

We present quantum mechanical close-coupling calculations of collisions between two hydrogen molecules over a wide range of energies, extending from the ultracold limit to the super-thermal region. The two most recently published potential energy surfaces for the H$_2$-H$_2$ complex, the so-called DJ (Diep and Johnson, 2000) and BMKP (Boothroyd et al., 2002) surfaces, are quantitatively evaluated and compared through the investigation of rotational transitions in H$_2$+H$_2$ collisions within rigid rotor approximation. The BMKP surface is expected to be an improvement, approaching chemical accuracy, over all conformations of the potential energy surface compared to previous calculations of H$_2$-H$_2$ interaction. We found significant differences in rotational excitation/de-excitation cross sections computed on the two surfaces in collisions between two para-H$_2$ molecules. The discrepancy persists over a large range of energies from the ultracold regime to thermal energies and occurs for several low-lying initial rotational levels. Good agreement is found with experiment (Maté et al., 2005) for the lowest rotational excitation process, but only with the use of the DJ potential. Rate coefficients computed with the BMKP potential are an order of magnitude smaller.

physics.atom-ph↗

arXiv2005

Heavy atom tunneling in chemical reactions: study of H + LiF collisions

The H+LiF(X 1Sigma+,v=0-2,j=0)-->HF(X 1Sigma+,v',j')+Li(2S) bimolecular process is investigated by means of quantum scattering calculations on the chemically accurate X 2A' LiHF potential energy surface of Aguado et al. [J. Chem. Phys. 119, 10088 (2003)]. Calculations have been performed for zero total angular momentum for translational energies from 10-7 to 10-1 eV. Initial-state selected reaction probabilities and cross sections are characterized by resonances originating from the decay of metastable states of the H...F-Li and Li...F-H van der Waals complexes. Extensive assignment of the resonances has been carried out by performing quasibound states calculations in the entrance and exit channel wells. Chemical reactivity is found to be significantly enhanced by vibrational excitation at low temperatures, although reactivity appears much less favorable than non-reactive processes due to the inefficient tunneling of the relatively heavy fluorine atom strongly bound in van der Waals complexes.

physics.chem-ph↗

arXiv2004

Quantum dynamics of the Li+HF-->H+LiF reaction at ultralow temperatures

Quantum mechanical calculations are reported for the Li+HF(v=0,1,j=0)-->H+LiF(v',j') bimolecular scattering process at low and ultralow temperatures. Calculations have been performed for zero total angular momentum using a recent high accuracy potential energy surface for the X 2A' electronic ground state. For Li+HF(v=0,j=0), the reaction is dominated by resonances due to the decay of metastable states of the Li...F-H van der Waals complex. Assignment of these resonances has been carried out by calculating the eigenenergies of the quasibound states. We also find that while chemical reactivity is greatly enhanced by vibrational excitation the resonances get mostly washed out in the reaction of vibrationally excited HF with Li atoms. In addition, we find that at low energies, the reaction is significantly suppressed due to the formation of rather deeply bound van der Waals complexes and the less efficient tunneling of the relatively heavy fluorine atom.

physics.chem-ph↗