Final Energy Distribution Research Articles

Shakedown of metallic sandwich beams when subjected to repeated impact loadings

When a monolithic metallic beam/plate subjected to repeated dynamic loadings with fixed impact level experiences elastoplastic deformation, its measurable deformations may cease to develop for further repetitions of the same dynamic load: this phenomenon was referred to as “pseudo-shakedown” in previous studies (Jones, 2014; Shen and Jones, 1992). Would pseudo-shakedown occur in a metallic sandwich structure under repeated shock loadings remains elusive. A combined experimental and numerical study was carried out to explore whether dynamic shakedown could occur in all-metallic ultralightweight corrugated core sandwich beams. For repeated impact tests, the sandwich beams were fabricated via the sequential process of cutting-stamping-vacuum brazing. When subjected to repeated impact loads (achieved via aluminum foam projectiles launched from a light gas gun), the dynamic responses of each sandwich specimen - including structural evolutions, beam deflections, and deformation/failure modes - were measured. Experimental results revealed that, depending upon the level of impact momentum applied to the sandwich beam, either dynamic shakedown or progressive failure could occur. The method of finite elements (FE) was subsequently employed to simulate the repeated shock tests, which was validated against experimental measurements, with good agreement achieved. To explore the physical mechanisms underlying the observed dynamic shakedown, the FE results of final plastic energy and effective plastic strain distribution in the sandwich beam were extracted and analyzed. When shakedown occurred, the measurable permanent deformation of the sandwich beam kept a relatively stable state, but its plastic energy remained positive, which is different from its monolithic beam/plate counterpart (i.e., plastic energy dropping to zero during dynamic shakedown). Such difference is mainly attributed to stress concentration occurring at the connecting joint points between the corrugated core and face sheets of sandwich and clamped endings, which produces plastic deformations that are difficult to reflect in overall large deformations of the beam. Consequently, the dynamic shakedown of metallic corrugated core sandwich beam captured in this study appears to be inexhaustive and hence may be termed as the “apparent pseudo-shakedown” (with danger lurking in the welding joints as well as clamped endings). Finally, based on a simplified bi-linear hardening constitutive law, the mechanisms underlying the dynamic shakedown of sandwich beam were further discussed from a purely base material point of view.

Curvature Sensing-Based Pupil Alignment Method for Large-Aperture Telescopes

In optical systems, pupil alignment is an important component of wavefront sensing, closed-loop feedback, and imaging vignetting control because it directly affects the detection limit of the system and thus the realization of scientific goals. This study proposes the use of the energy transfer characteristics of the pupil edge to determine the misalignment of each pupil. The mechanism involves decoupling the influence of each pupil from the final exit pupil energy distribution by using aperture coding without the addition of other optical paths. The degree to which the pupil is aligned is characterized by the normalized point source sensitivity (PSSn). The pupil misalignment PSSn increased from 0.75 to 0.83. The results of this study can be used to perform tomographic detection of pupil alignment and obtain high-quality telescopic images.

Continuous thermomajorization and a complete set of laws for Markovian thermal processes

The standard dynamical approach to quantum thermodynamics is based on Markovian master equations describing the thermalization of a system weakly coupled to a large environment, and on tools such as entropy production relations. Here we develop a new framework overcoming the limitations that the current dynamical and information theory approaches encounter when applied to this setting. More precisely, we introduce the notion of continuous thermomajorization, and employ it to obtain necessary and sufficient conditions for the existence of a Markovian thermal process transforming between given initial and final energy distributions of the system. These lead to a complete set of generalized entropy production inequalities including the standard one as a special case. Importantly, these conditions can be reduced to a finitely verifiable set of constraints governing non-equilibrium transformations under master equations. What is more, the framework is also constructive, i.e., it returns explicit protocols realizing any allowed transformation. These protocols use as building blocks elementary thermalizations, which we prove to be universal controls. Finally, we also present an algorithm constructing the full set of energy distributions achievable from a given initial state via Markovian thermal processes and provide a $\texttt{Mathematica}$ implementation solving $d=6$ on a laptop computer in minutes.

What Drives Energy Eciency in Africa? Insights from 12 Selected Countries Using Incremental Decomposition Analysis

This paper examines why Africa, and Sub-Saharan Africa (SSA) in particular, has some of the worse energy efficiency indicators in the world. It examines the relationship between total primary energy supply (TPES), final energy consumption, and transmission and distribution (T&D) losses on the continent. We apply the Sun-Shaley incremental decomposition method of logarithmic mean divisia index (LMDI to twelve (12) African countries using data from 2000 to 2016 to decompose TPES into the effects of changes in final energy consumption (FEC), population change (POP), carbon dioxide (CO2) emissions, and economic activity measured by gross domestic product (GDP), and their impact on energy efficiency. The method provides a precise decomposition analysis and incremental results that can be added to study the long-run impacts without any information missing in between. The findings show that the study countries have worsening energy efficiency indicators with energy intensity (EI) as high as 55%, coupled with an inefficient transformation of primary energy supply to final consumption, culminating in significant systems losses. It was further discovered that countries that have more significant proportions of renewables sources in their energy mix have lower transmission and distribution losses. This study serves as a guide to the policy discourse regarding the energy efficiency situation in Africa. Environmental Policy Energy efficiency total primary energy supply decomposition analysis Sub-Saharan Africa

Dynamics Studies of O2 Collision on Pt(111) Using a Global Potential Energy Surface

The dynamics of O2 collision on Pt(111) has been studied by molecular dynamics simulations using a global potential energy surface (PES), which was developed by fitting ∼4800 plane-wave density functional theory points using the permutation invariant polynomial-neural network method. The simulations were performed for the normal and off-normal incidences at a wide range of incident energies and surface temperatures. A generalized Langevin oscillator model was used to incorporate the molecule–surface coupling that plays an important role in this collision process. The trapping probability, final energy distribution, scattering angle distributions of scattered molecules, and the energy transfer to surface distribution were determined and analyzed. The PES shows an activated path to the chemisorption states, as the trapping probability directly increases with incident energy (larger than 0.1 eV) to reach a maximum and then decreases at high incident energy. The trapping probability obviously reduces by raising surface temperature at low incident energy because the initial kinetic energy of molecule is more likely to be dissipated into surface motions than molecular internal ro-vibrational modes. Additional parallel momentum of off-normal incidence leads to a strong suppression of the trapping probability, caused by the energetic corrugation of the lateral barrier heights. The scattering angular distributions are found to be quasispecular and the final translational energy slightly increases with scattering angle deviating significantly from the hard-cube model, indicating the nonconservation of parallel momentum during the collision on the corrugate PES.

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ТРЕХМЕРНЫХ ВОЛНОВЫХ АТТРАКТОРОВ

Internal and inertial waves obey very specific dispersion relation, which defines the direction of wave propagation with respect to the gravity or axis of rotation, but which does no define the wavelength. Particular cases of scale effects are described in (Brouzet et al., 2017). In closed geometrics the presence of a monochromatic wavemaker can produce wave beams, which after multiple reflections from the boundaries may approach a closed loop – the wave attractor. In ideal fluids the concentration of energy on the wave attractor can grow without any limits. In viscous stratified or rotating fluids the concentration will be balanced with dissipation due to viscosity, which results in appearance of wave attractors of finite width. The characterization of the flow with the Reynolds number based on the boundary conditions is questionable in this case, since on the attractor the velocity can be several times magnified. When the wave beam is reflected from an inclined plane, the horizontal component of velocity rotates, as was first described by O. Phillips, while preserving the angle with the gravity or axis of rotation. With the help of ray tracing it can be shown that due to this effect the three-dimensional accumulation of wave energy can occur. First qualitative and quantitative correspondence of laboratory and numerical simulation of wave attractors in the pseudo-2D laboratory tank with trapezoidal section was described in (Brouzet et al., 2016), and importance of dissipation on the lateral boundaries was shown (F. Beckebanze et al., 2018). For high Schdmidt number there appear the folded structures, which can interact with the background wave motion (Sibgatullin, Kalugin 2016). In (Brouzet et al., 2016b), (Dauxois et al., 2018) cascade of triadic resonances in (1,1) produced by a wave attractor was demonstrated. Three-dimensional accumulation of wave energy in trapezoidal frustum with a localized wavemaker was investigated in (Pillet et al., 2018). Numerical simulations of the present work had showed the importance of phase shift in transversal direction. An attractor can have the same form as the 2D attractor in any given longitudinal cut, but the phase of oscillation can change up to counter-phase. Interplay of 3D concentration of waves beams, dissipation and phase shifting impact the final energy distribution in transversal direction. First three-dimensional simulations (Sibgatullin et al., 2017) of tidal and symmetric forcing on the rotating layer of fluid with inclined walls showed three-dimensional twisted structure of waves attractors for precession of one boundary of the layer in opposite direction to the rotation of the layer. With growth of the amplitude of the external forcing the the instability of triadic resonance appears, but in contrast to the internal wave attractors, triadic resonances take place in azimuthal (transversal to the trapeze) section. The turbulent regimes generated by the background wave attractors are studied, with analysis of full power income and total dissipation. The research was supported by the Program of Fundamental Research of the Presidium of the Russian Academy of Sciences No. 26

Photon spectrum and angle distribution for photon scattering with relativistic Maxwellian electrons

Description of photon scattering with relativistic Maxwellian electrons is numerically complex, and computationally time consuming for the final photon energy and angle distribution. A Monte Carlo method is used to simulate photon scattering with relativistic Maxwellian electrons. The main idea of this method is to transform the interaction of photonmoving electrons in the laboratory coordinate system into that in a new coordinate system in which the electrons are at rest, then to use the exact Klein-Nishina formula to describe this interaction and obtain the outgoing photon energy and angle, finally, to transform it into the primary laboratory coordinate system. In sum, there are eight steps, i.e.two two-dimensional (2D) transforms and two three-dimensional (3D) transforms and two Lorentz transforms, and two sampling. Repeating this process, summarizing and averaging all computed energy values and angles, the distribution of scattered energy and angle can be obtained.</br>A Monte Carlo processor is developed to simulate a photon of any energy interacting with electrons at any temperature. Some typical cases are simulated. The computed results indicate that the photon spectrum is different from that of the photon scattering with rest electrons remarkably, especially for a low energy photon scattering with the high temperature electrons. The main phenomena are Doppler broading and blue shifting. The moving electron can extend the distribution of the outgoing photon energy, and for a low energy photon scattering with the high temperature electrons, the photon maybe obtains the energy from electrons with significant probability. The angle distribution is very complicated, and it is determined by the incident photon energy, the outgoing photon energy, and the electron temperature. This processor can calculate the energy scattering differential cross-sections or energy-angle scattering double differential cross-sections, and provide the data in a tabulated form for other transport methods.

Stochastic Electron Acceleration by the Whistler Instability in a Growing Magnetic Field

Abstract We use 2D particle-in-cell simulations to study the effect of the saturated whistler instability on the viscous heating and nonthermal acceleration of electrons in a shearing, collisionless plasma with a growing magnetic field, . In this setup, an electron pressure anisotropy with naturally arises due to the adiabatic invariance of the electron magnetic moment ( and are the pressures parallel and perpendicular to ). If the anisotropy is large enough, then the whistler instability arises, efficiently scattering the electrons and limiting ( ). In this context, taps into the plasma velocity shear, producing electron heating by the so-called anisotropic viscosity. In our simulations, we permanently drive the growth of by externally imposing a plasma shear, allowing us to self-consistently capture the long-term, saturated whistler instability evolution. We find that besides the viscous heating, the scattering by whistler modes can stochastically accelerate electrons to nonthermal energies. This acceleration is most prominent when initially , gradually decreasing its efficiency for larger values of ( ). If initially , then the final electron energy distribution can be approximately described by a thermal component, plus a power-law tail with a spectral index of ∼3.7. In these cases, the nonthermal tail accounts for of the electrons and for of their kinetic energy. We discuss the implications of our results for electron heating and acceleration in low-collisionality astrophysical environments, such as low-luminosity accretion flows.

Mode Specific Electronic Friction in Dissociative Chemisorption on Metal Surfaces: H_{2} on Ag(111).

Electronic friction and the ensuing nonadiabatic energy loss play an important role in chemical reaction dynamics at metal surfaces. Using molecular dynamics with electronic friction evaluated on the fly from density functional theory, we find strong mode dependence and a dominance of nonadiabatic energy loss along the bond stretch coordinate for scattering and dissociative chemisorption of H_{2} on the Ag(111) surface. Exemplary trajectories with varying initial conditions indicate that this mode specificity translates into modulated energy loss during a dissociative chemisorption event. Despite minor nonadiabatic energy loss of about 5%, the directionality of friction forces induces dynamical steering that affects individual reaction outcomes, specifically for low-incidence energies and vibrationally excited molecules. Mode-specific friction induces enhanced loss of rovibrational rather than translational energy and will be most visible in its effect on final energy distributions in molecular scattering experiments.

Work distributions for random sudden quantum quenches.

The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.

ON THE DISTRIBUTION OF PARTICLE ACCELERATION SITES IN PLASMOID-DOMINATED RELATIVISTIC MAGNETIC RECONNECTION

We investigate the distribution of particle acceleration sites, independently of the actual acceleration mechanism, during plasmoid-dominated, relativistic collisionless magnetic reconnection by analyzing the results of a particle-in-cell numerical simulation. The simulation is initiated with Harris-type current layers in pair plasma with no guide magnetic field, negligible radiative losses, no initial perturbation, and using periodic boundary conditions. We find that the plasmoids develop a robust internal structure, with colder dense cores and hotter outer shells, that is recovered after each plasmoid merger on a dynamical time scale. We use spacetime diagrams of the reconnection layers to probe the evolution of plasmoids, and in this context we investigate the individual particle histories for a representative sample of energetic electrons. We distinguish three classes of particle acceleration sites associated with (1) magnetic X-points, (2) regions between merging plasmoids, and (3) the trailing edges of accelerating plasmoids. We evaluate the contribution of each class of acceleration sites to the final energy distribution of energetic electrons -- magnetic X-points dominate at moderate energies, and the regions between merging plasmoids dominate at higher energies. We also identify the dominant acceleration scenarios, in order of decreasing importance -- (1) single acceleration between merging plasmoids, (2) single acceleration at a magnetic X-point, and (3) acceleration at a magnetic X-point followed by acceleration in a plasmoid. Particle acceleration is absent only in the vicinity of stationary plasmoids. The effect of magnetic mirrors due to plasmoid contraction does not appear to be significant in relativistic reconnection.

Violent relaxation of ellipsoidal clouds

An isolated, initially cold and ellipsoidal cloud of self-gravitating particles represents a relatively simple system to study the effects of the deviations from spherical symmetry in the mechanism of violent relaxation. Initial deviations from spherical symmetry are shown to play a dynamical role that is equivalent to that of density fluctuations in the case of an initially spherical cloud. Indeed, these deviations control the amount of particles energy change and thus determine the properties of the final energy distribution, particularly the appearance of two species of particles: bound and free. Ejection of mass and energy from the system together with the formation of a density profile decaying as $\rho(r) \sim r^{-4}$ and a Keplerian radial velocity dispersion profile, are the prominent features similar to those observed after the violent relaxation of spherical clouds. In addition, we find that ejected particles are characterized by highly non-spherical shapes, whose features can be traced in the initial deviations from spherical symmetry that are amplified during the dynamical evolution: particles can indeed form anisotropic configurations, like bars and/or disks, even though the initial cloud was very close to spherical.

Tunneling dynamics of the NH3 (Ã) state observed by time-resolved photoelectron and H atom kinetic energy spectroscopies.

We have investigated the effects of quantum tunneling on the photodissociation dynamics of ammonia, following below and above barrier photoexcitation of low-lying levels of the ν'(2) umbrella mode of the NH(3) à state (NH(3) (Ã)). This barrier separates the local minimum of the vertical Franck–Condon region from the NH(3) (Ã)/NH(3) (X̃) conical intersection (CI) which can be accessed along the N–H stretch coordinate. Two complementary techniques, time-resolved photoelectron spectroscopy (TR-PES) and time-resolved total kinetic energy release spectroscopy (TR-TKER), have been utilized to directly measure, for the first time, vibrational level dependent excited state lifetimes and N–H dissociation time scales as well as photoproduct final energy distributions. Interestingly, ν'(2) even/odd dependencies are observed in the measured time constants and NH(2) internal energy spectra, which are attributed to tunneling through a barrier, whose magnitude is dependent on the planarity of NH(3) in the à state and direct versus indirect dissociation at the NH(3) (Ã)/NH(3) (X̃) conical intersection.

Sensitivity of Measured Fission Yields on Prompt-neutron Corrections

Although the number of emitted prompt neutrons from the fission fragments increases as a function of excitation energy, it is not fully understood whether the increase in ν¯ (A) as a function of En is mass dependent. The share of excitation energies among the fragments is still under debate, but there are reasons to believe that the excess in neutron emission originates only from the heavy fragments, leaving ν¯light (A) almost unchanged. We have investigated the consequences of a mass-dependent increase in ν¯ (A) on the final mass and energy distributions. The analysis have been performed on experimentally measured data on 234U (n, f). The assumptions concerning ν¯ (A) are essential when analysing measurements based on the 2E-technique, and impact significantly on the measured observables. For example, the post-neutron emission mass yield distribution revealed changes up to 10–30 %. The outcome of this work pinpoints the urgent need to determine ν¯ (A) experimentally, and in particular, how ν¯ (A) changes as a function of incident neutron energy. Many fission yields in the data libraries could be largely affected, since their analysis is based on a different assumption concerning the neutron emission.

Quasiclassical trajectory studies of 18O(3P) + NO2 isotope exchange and reaction to O2 + NO on D and D1 potentials

We report quasiclassical trajectory calculations for the bimolecular reaction (18)O((3)P) + NO2 on the recent potential energy surfaces of the ground (D0) and first excited (D1) states of NO3 [B. Fu, J. M. Bowman, H. Xiao, S. Maeda, and K. Morokuma, J. Chem. Theory. Comput. 9, 893 (2013)]. The branching ratio of isotope exchange versus O2 + NO formation, as well as the product angular distributions and energy and rovibrational state distributions are presented. The calculations are done at the collision energy of relevance to recent crossed beam experiments [K. A. Mar, A. L. Van Wyngarden, C.-W. Liang, Y. T. Lee, J. J. Lin, and K. A. Boering, J. Chem. Phys. 137, 044302 (2012)]. Very good agreement is achieved between the current calculations and these experiments for the branching ratio and final translational energy and angular distributions of isotope exchange products (16)O((3)P) + NO2 and O2 + NO formation products. The reactant (18)O atom results in (18)O(16)O but not N(18)O for the O2 + NO formation product channel, consistent with the experiment. In addition, the detailed vibrational and rotational state information of diatomic molecules calculated currently for the (34)O2 + NO formation channel on D0 and D1 states are in qualitative agreement with the previous experimental and theoretical results of the photodissociation of NO3 and are consistent with older thermal bimolecular kinetics measurements.

Simulation of angular and energy distributions for heavy evaporation residues using statistical model approximations and TRIM code

A Monte Carlo approach has been developed for simulations of the angular and energy distributions for heavy evaporation residues (ER) produced in heavy ion fusion-evaporation reactions. The approach uses statistical model approximations of the HIVAP code for the calculations of initial angular and energy distributions inside a target, which are determined by neutron evaporation from an excited compound nucleus. Further step in the simulation of transmission of ER heavy atoms through a target layer is performed with the TRIM code that gives final angle and energy distributions at the exit from the target. Both the simulations (neutron evaporation and transmission through solid media) have been separately considered and good agreement has been obtained between the results of simulations and available experimental data. Some applications of the approach have been also considered.

Theoretical Study of Ion Acceleration by Double-Layer Formation in Multicharged Laser-Produced Plasmas

A theoretical study about the ion acceleration in low-energy (10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> W/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) laser-produced plasma is presented. Calculations have been implemented following a 1-D particle-in cell method. We describe the plasma-vacuum expansion dynamics and the ion acceleration due to the so-called double-layer formation. Observed results show that, regardless of the initial temperature and density of the plasma, postheating is needed to obtain average values of final ion kinetic energy distributions similar to the experimental results. This confirms that, with nanosecond pulsed lasers, the plasma is strongly heated by the laser pulse tail.

Three-State Trajectory Surface Hopping Studies of the Photodissociation Dynamics of Formaldehyde on ab Initio Potential Energy Surfaces

Full-dimensional, three-state, surface hopping calculations of the photodissociation dynamics of formaldehyde are reported on ab initio potential energy surfaces (PESs) for electronic states S(1), T(1), and S(0). This is the first such study initiated on S(1) with ab initio-calculated spin-orbit couplings among the three states. We employ previous PESs for S(0) and T(1), and a new PES for S(1), which we describe here, as well as new spin-orbit couplings. The time-dependent electronic state populations and the branching ratio of radical products produced from S(0) and T(1) states and that of total radical products and molecular products at three total energies are calculated. Details of the surface hopping dynamics are described, and a novel pathway for isomerization on T(1) via S(0) is reported. Final translational energy distributions of H + HCO products from S(0) and T(1) are also reported as well as the translational energy distribution and final rovibrational distributions of H(2) products from the molecular channel. The present results are compared to previous trajectory calculations initiated from the global minimum of S(0). The roaming pathway leading to low rotational distribution of CO and high vibrational population of H(2) is observed in the present calculations.

A nanoflare distribution generated by repeated relaxations triggered by kink instability

Context: It is thought likely that vast numbers of nanoflares are responsible for the corona having a temperature of millions of degrees. Current observational technologies lack the resolving power to confirm the nanoflare hypothesis. An alternative approach is to construct a magnetohydrodynamic coronal loop model that has the ability to predict nanoflare energy distributions. Aims: This paper presents the initial results generated by such a model. It predicts heating events with a range of sizes, depending on where the instability threshold for linear kink modes is encountered. The aims are to calculate the distribution of event energies and to investigate whether kink instability can be predicted from a single parameter. Methods: The loop is represented as a straight line-tied cylinder. The twisting caused by random photospheric motions is captured by two parameters, representing the ratio of current density to field strength for specific regions of the loop. Dissipation of the loop's magnetic energy begins during the nonlinear stage of the instability, which develops as a consequence of current sheet reconnection. After flaring, the loop evolves to the state of lowest energy where, in accordance with relaxation theory, the ratio of current to field is constant throughout the loop and helicity is conserved. Results: The results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Hence, an energy distribution of the nanoflares produced is collated. Conclusions: The final energy distribution features two nanoflare populations that follow different power laws. The power law index for the higher energy population is more than sufficient for coronal heating.

Collisional Energy Transfer Probability DensitiesP(E,J;E′,J′) for Monatomics Colliding with Large Molecules

Collisional energy transfer remains an important area of uncertainty in master equation simulations. Quasi-classical trajectory (QCT) calculations were used to examine the energy transfer probability density distribution (energy transfer kernel), which depends on translational temperature, on the nature of the collision partners, and on the initial and final total internal energies and angular momenta: P(E, J; E', J'). For this purpose, model potential energy functions were taken from the literature or were formulated for pyrazine + Ar and for ethane + Ar collisions. For each collision pair, batches of 10(5) trajectories were computed with three selected initial vibrational energies and five selected values for initial total angular momentum. Most trajectories were carried out with relative translational energy distributions at 300 K, but some were carried out at 1000 or 1200 K. In addition, some trajectories were computed for artificially "heavy" ethane, in which the H-atoms were assigned masses of 20 amu. The results were binned according to (ΔE, ΔJ), and a least-squares analysis was carried out by omitting the quasi-elastic trajectories from consideration. By trial-and-error, an empirical function was identified that fitted all 45 batches of trajectories with moderate accuracy. The results reveal significant correlations between initial and final energies and angular momenta. In particular, a strong correlation between ΔE and ΔJ depends on the smallest rotational constant in the excited polyatomic. These results show that the final rotational energy distribution is not independent of the initial distribution, showing that the plausible simplifying assumption described by Smith and Gilbert [Int. J. Chem. Kinet. 1988, 20, 307-329] and extended by Miller, Klippenstein, and Raffy [J. Phys. Chem. A 2002, 106, 4904-4913] is invalid for the systems studied.