Internal State Distribution Research Articles

The contour integral method for Feynman-Kac equation with two internal states

We develop the contour integral method for numerically solving the Feynman-Kac equation with two internal states Xu and Deng (2018) [23], describing the functional distribution of particle's internal states. The striking benefits are obtained, including spectral accuracy, low computational complexity, small memory requirement, etc. We perform the error estimates and stability analyses, which are confirmed by numerical experiments.

Reduced-dimensionality nonlinear distributed-parameter observer for fuel cell systems

To ensure reliable and efficient operation of fuel cell systems, it is important to monitor them online. However, placing sensors inside the fuel cell is often challenging, so virtual sensing using an efficient state observer is used in this study. Detecting local internal phenomena, such as reactants’ starvation, membrane dryout/flooding, and nitrogen accumulation, requires knowledge of the spatial distribution of internal states. Lumped-parameter models are not suitable for this, as they use a single variable to describe parameters such as hydrogen concentration. Instead, a high-order distributed-parameter fuel cell model is used to predict the spatial profiles of various internal states. An observer algorithm is employed to correct the predicted quantities using a few measurements taken at the system boundary. This update step only considers dominant dynamics from a reduced model to adjust all system states accordingly, making it computationally efficient and robust. The observer algorithm’s performance was verified against a high-fidelity model through detailed simulations.

Structural and Heat Transfer Model Analysis of Wall-Mounted Solar Chimney Inlets and Outlets in Single-Story Buildings

Wall-mounted solar chimneys use solar radiation to heat the air inside the chimney cavity and use thermal pressure to create natural convection. Applying this principle allows for the indoor ventilation of a building without energy consumption. However, in wall-mounted solar chimney designs, different air inlet and outlet design dimensions can have varying degrees of impact on the effectiveness of wall-mounted solar chimney ventilation. In order to analyze the internal airflow state and airflow temperature field distribution of wall-mounted solar chimneys, physical models of wall-mounted solar chimneys with six different air outlet-to-inlet cross-sectional area ratios were developed in this research work. Before numerical simulation analysis, heat transfer analysis of the wall-mounted solar chimney’s structural components and airflow channels was carried out, and corresponding mathematical heat transfer models were established. The internal flow state and temperature distribution characteristics of a wall-mounted solar chimney were analyzed by steady-state simulations using the computational fluid dynamics software, Ansys Fluent. Finally, transient simulation calculation analysis was conducted under six different S-value models to investigate the variation in the natural ventilation of a single-story building’s wall-mounted solar chimney for a whole day. The study showed that under the same simulation conditions, 80% ≤ S < 100% effectively avoided the formation of vortices in the internal airflow of the wall-mounted solar chimneys and kept the ventilation effect of wall-mounted solar chimneys at a high level. The results of this study provide a reference for the optimization of research on the design of the air inlet and outlet structures of wall-mounted solar chimneys for single-story buildings.

A fast two-phase non-isothermal reduced-order model for accelerating PEM fuel cell design development

A reduced-order model (ROM) is developed for proton exchange membrane fuel cells (PEMFCs) considering the non-isothermal two-phase effects, with the goal of enhancing computational efficiency and thus accelerating fuel cell design development. Using analytical order reduction and approximation methods, the fluxes and source terms in conventional 1D conservation equations are reduced to six computing nodes at the interfaces between each cell component. The errors associated with order reduction are minimized by introducing new approximation methods for the potential distribution, the transport properties, and the membrane hydration status. The trade-off between model accuracy and computational efficiency is studied by comparing the simulation results and computational times of the new model with a full 1D model. The new model is nearly two orders of magnitude faster without sacrificing too much accuracy (<4% difference) compared to the 1D model. The new model is then used to analyze the influence of the membrane electrode assembly (MEA) design on cell performance and internal state distributions, offering insights into MEA structural optimization. The model can be readily extended to account for more detailed physico-chemical processes, such as Knudsen diffusion or the influence of micro-porous layers, and it can be an effective tool for understanding and designing PEMFCs.

Experimental and Numerical Investigation of the Damage Characteristics of Rocks under Ballistic Penetration

Rock penetration is an inevitable problem in the study of drilling and projectile penetration. The penetration resistance of red sandstone and limestone was investigated at projectile speeds ranging from 600–1200 m/s. The damage characteristics of these rocks were studied via experimental tests and numerical simulations. The damage condition of the target surface, internal damage state and crack distribution were obtained. It was concluded that the maximum error of the numerical simulation and experimental results was not more than 10%. The penetration resistance of limestone was approximately 23.8% stronger than that of red sandstone. However, the energy absorption effect of limestone was weaker than that of red sandstone, and large cracks can be more easily formed. The compaction area of red sandstone was softer, with obvious crack compaction in the crater area, and particle detachment can more easily occur. Red sandstone was more sensitive to the impact angle of the projectile. With oblique penetration, the projectile was more likely to deflect inside the red sandstone target.

Study of He*/Ne*+Ar, Kr, N2, H2, D2 Chemi-Ionization Reactions by Electron Velocity-Map Imaging.

The chemi-ionization of Ar, Kr, N2, H2, and D2 by Ne(3P2) and of Ar, Kr, and N2 by He(3S1) was studied by electron velocity map imaging (e-VMI) in a crossed molecular beam experiment. A curved magnetic hexapole was used to state-select the metastable species. Collision energies of 60 meV were obtained by individually controlling the beam velocities of both reactants. The chemi-ionization of atoms and molecules can proceed along different channels, among them Penning ionization and associative ionization. The evolution of the reaction is influenced by the internal redistribution of energy, which happens at the first reaction step that involves the emission of an electron. We designed and built an e-VMI spectrometer in order to investigate the electron kinetic energy distribution, which is related to the internal state distribution of the ionic reaction products. The analysis of the electron kinetic energy distributions allows an estimation of the ratio between the two-reaction channel Penning and associative ionization. In the molecular cases the vibrational or electronic excitation enhanced the conversion of internal energy into the translational energy of the forming ions, thus influencing the reaction outcome.

Theoretical Study of the Energy Disposal Mechanism and the State-Resolved Quantum Dynamics of the H + LiH+ → H2 + Li+ Reaction.

Despite several studies in the literature, the detailed quantum state-to-state level mechanism of the astrophysically important exoergic barrierless H + LiH+ → H2 + Li+ reaction is yet to be understood. In this work, we have investigated the energy disposal mechanism of the reaction in terms of integral reaction cross section, product internal state distributions, differential cross section, and rate constant. Fully converged and Coriolis coupled quantum mechanical calculations based on a time-dependent wave packet method have been performed at the state-to-state level on the ab initio electronic ground state potential energy surface (PES) constructed by Martinazzo et al. (J. Chem. Phys. 2003, 119, 11241-11248). The agreement between the present quantum mechanical and previous quasi-classical results is found even at very low relative translational energies of reagents. A non-statistical inverse Boltzmann vibrational distribution for the product is found. This is attributed to the "attractive" nature of the underlying PES, which facilitates the excess energy release mostly as product vibration (60-80%). The energy disposal in products is found to be unaffected by the rovibrational excitation of the reagent diatom due to the weak coupling between the vibrational modes of the reagent and the product. The mild effect of collision energy on the product energy disposal is ascribed to the effective coupling between the translational modes of the reagent and the product. It is found that the collisions lead to the formation of the product H2 in its rovibrationally excited levels.

Consistent kinetic-continuum dissociation model I. Kinetic formulation.

In this article, we propose a generalized non-equilibrium chemical kinetics model from ab initio simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air chemistry. First, we present a simple cross section model for dissociation that captures recent ab initio data accurately. The cross section model is analytically integrated over Boltzmann distributions and general non-Boltzmann distributions to derive a general non-equilibrium dissociation model. The general non-Boltzmann model systematically incorporates key physics such as dependence on translational energy, rotational energy, vibrational energy, internal energy, centrifugal barrier, and non-Boltzmann effects such as overpopulation and depletion of high energy states. The model is shown to reproduce the rates from quasi-classical trajectory calculations for Boltzmann distributions of internal energy states. The reduced rates in a non-equilibrium steady state due to depletion of high internal energy states are also predicted well by the model. Furthermore, the model predicts the enhanced rates as observed due to significant overpopulation of high vibrational states relative to Boltzmann distributions while the gas is in non-equilibrium in the transient phase. The model provides a computationally inexpensive way of incorporating non-equilibrium chemistry without incurring additional cost in the existing computational tools. Further comparisons of the model are carried out in Paper II, where simplifications to the model are proposed based on the results.

A quantum wavepacket study of state-to-state photodissociation dynamics of HOBr/DOBr

Photodissociation of HOBr is an important step in the reaction network of the depletion of ozone in stratosphere. Here, we report the first three-dimensional potential energy surfaces for the lowest three singlet states for HOBr, based on high level multi reference configuration interaction calculations. Quantum dynamics calculations are performed with a real wavepacket method, yielding not only absorption spectra but also internal state and angular distributions of the photodissociation fragments. Our results agree quantitatively with the measured total absorption cross sections of HOBr in the ultraviolet region and reproduce well the observed vibrationally cold and rotationally hot OH/OD fragments via photodissociation of HOBr/DOBr at 266 nm. In addition, we predict that the recoil anisotropy parameters for OH/OD are close to the limiting value of a parallel transition, suggesting a rapid dissociation process at 266 nm following an in-plane transition from the ground state (11A′) to the 21A′ state. This is consistent with the experimental conclusion derived from the measured rotational alignment. However, spin and electronic angular momenta need to be taken into account in the future to achieve a more quantitative agreement with experiment. Our work is expected to motivate further experimental investigations for this benchmark system.

Roaming Reactions and Dynamics in the van der Waals Region.

Roaming reactions were first clearly identified in photodissociation of formaldehyde 15 years ago, and roaming dynamics are now recognized as a universal aspect of chemical reactivity. These reactions typically involve frustrated near-dissociation of a quasibound system to radical fragments, followed by reorientation at long range and intramolecular abstraction. The consequences can be unexpected formation of molecular products, depletion of the radical pool in chemical systems, and formation of products with unusual internal state distributions. In this review, I examine some current aspects of roaming reactions with an emphasis on experimental results, focusing on possible quantum effects in roaming and roaming dynamics in bimolecular systems. These considerations lead to a more inclusive definition of roaming reactions as those for which key dynamics take place at long range.

Ethylene Intersystem Crossing Caught in the Act by Photofragment Sulfur Atoms

Ethylene, C2H4, the simplest π-bonded molecule, is of enormous fundamental and commercial importance. Its lowest triplet state, in which the CH2 moieties occupy perpendicular planes, is well known from theory, but there has been no definitive experimental observation of this species. Here, velocity map imaging of the sulfur atoms in ethylene sulfide (c-C2H4S) photodissociation at 217 nm is used to reveal the internal state distribution of co-product ethylene. While both S (1D) and S (3P) translational energy distributions display three distinct regions that find their origins in singlet and triplet excited states of c-C2H4S, respectively, the S (3P) distribution is dominated by a fourth, low-recoil region. In this region, the distribution is fully isotropic at a recoil of 9 ± 1 kcal/mol, corresponding to the opening of the triplet ethylene channel. Multireference calculations suggest that this photodissociation pathway is mediated by a hot, transient biradical CH2CH2S that strongly favors CH2-hindered rotations in the predissociated complex. This photochemical ring-opening mechanism is invoked to account for the vibrational features observed in this low-recoil region, which are attributed to triplet ethylene relaxing to the torsional saddle point on the ground-state singlet surface. This study thereby gives for the first time the experimental confirmation of an adiabatic singlet-triplet splitting of 66 ± 1 kcal/mol and a torsional barrier height of 64 ± 1 kcal/mol in ethylene.

Real-space laser-induced fluorescence imaging applied to gas-liquid interfacial scattering

We describe the real-space imaging of the products of molecular scattering, applied to collisions of hydroxyl radicals with low-vapor-pressure-liquid surfaces. A pulsed molecular beam of OD (for technical reasons) with a mean laboratory-frame kinetic energy of 29.5 kJ mol−1 was directed at continually refreshed surfaces of the representative liquids perfluoropolyether, squalane, and squalene. Laser-induced fluorescence (LIF) was excited by pulsed laser light shaped into a planar sheet, tuned to selected rovibronic transitions in the OD A–X band. The LIF emission was imaged and intensified before being captured by an external camera. Sequences of images allowed the evolution of the incident packet and scattered plumes of OD molecules to be observed. The results confirm previous observations of the internal-state distributions of the scattered OD and its differential survival probability on different liquid surfaces. New measurements of the angular distributions found them all to be broad and approximately symmetric, independent of the angle of incidence. This is interpreted as implying a high degree of atomic-scale roughness, rather than a predominant trapping-desorption mechanism, because of the other observed signatures of impulsive scattering; these include the degree of OD rotational excitation, superthermal speeds, and the correlation of speed with scattering angle. This approach has considerable potential to be applied in related gas-surface scattering experiments. It is immune from the difficulties of some other imaging methods that involve charged-particle detection and allows a spatially extended region of the scattering plane perpendicular to the surface to be imaged.

Vibrational predissociation of the phenol-water dimer: a view from the water.

The vibrational predissociation (VP) dynamics of the phenol-water (PhOH-H2O) dimer were studied by detecting H2O fragments and using velocity map imaging (VMI) to infer the internal energy distributions of PhOH cofragments, pair-correlated with selected rotational levels of the H2O fragments. Following infrared (IR) laser excitation of the hydrogen-bonded OH stretch fundamental of PhOH (Pathway 1) or the asymmetric OH stretch localized on H2O (Pathway 2), dissociation to H2O + PhOH was observed. H2O fragments were monitored state-selectively by using 2+1 Resonance-Enhanced Multiphoton Ionization (REMPI) combined with time-of-flight mass spectrometry (TOF-MS). VMI of H2O in selected rotational levels was used to derive center-of-mass (c.m.) translational energy (ET) distributions. The pair-correlated internal energy distributions of the PhOH cofragments derived via Pathway 1 were well described by a statistical prior distribution. On the other hand, the corresponding distributions obtained via Pathway 2 show a propensity to populate higher-energy rovibrational levels of PhOH than expected from a statistical distribution and agree better with an energy-gap model. The REMPI spectra of the H2O fragments from both pathways could be fit by Boltzmann plots truncated at the maximum allowed energy, with a higher temperature for Pathway 2 than that for Pathway 1. We conclude that the VP dynamics depends on the OH stretch level initially excited.

Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F.

Anion photoelectron imaging is a very efficient method for the study of energy states of bound negative ions, neutral species and interactions of unbound electrons with neutral molecules/atoms. State-of-the-art in vacuo anion generation techniques allow application to a broad range of atomic, molecular, and cluster anion systems. These are separated and selected using time-of-flight mass spectrometry. Electrons are removed by linearly polarized photons (photo detachment) using table-top laser sources which provide ready access to excitation energies from the infra-red to the near ultraviolet. Detecting the photoelectrons with a velocity mapped imaging lens and position sensitive detector means that, in principle, every photoelectron reaches the detector and the detection efficiency is uniform for all kinetic energies. Photoelectron spectra extracted from the images via mathematical reconstruction using an inverse Abel transformation reveal details of the anion internal energy state distribution and the resultant neutral energy states. At low electron kinetic energy, typical resolution is sufficient to reveal energy level differences on the order of a few millielectron-volts, i.e., different vibrational levels for molecular species or spin-orbit splitting in atoms. Photoelectron angular distributions extracted from the inverse Abel transformation represent the signatures of the bound electron orbital, allowing more detailed probing of electronic structure. The spectra and angular distributions also encode details of the interactions between the outgoing electron and the residual neutral species subsequent to excitation. The technique is illustrated by the application to an atomic anion (F-), but it can also be applied to the measurement of molecular anion spectroscopy, the study of low lying anion resonances (as an alternative to scattering experiments) and femtosecond (fs) time resolved studies of the dynamic evolution of anions.

Entanglement of the molecular photodissociation products at avoided crossings and conical intersections

This is a quantum mechanical study of the entanglement between pyrrolyl radical and the H-atom formed in the photodissociation of pyrrole. The parent molecule is photoexcited into the low lying 1πσ∗ states interacting with the ground electronic state via avoided crossings or conical intersections. The entanglement, studied in the time independent and the time dependent frameworks, is quantified using the von Neumann entropy which can be expressed in terms of the normalized internal state distributions of the pyrrolyl product. It is demonstrated that the von Neumann entropy is sensitive to the coupling between two electronic states and is substantially affected by Fano resonances in the dissociating molecule. The entropy generated at a conical intersection is generally larger than at an avoided crossing, although the main qualitative features are similar in both cases.

Fractional compound Poisson processes with multiple internal states

For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and functional distributions of the trajectories of particles; in particular, the equations governing the functional distribution of internal states are also obtained. The dynamics of the stochastic processes are analyzed and the applications, calculating the distribution of the first passage time and the distribution of the fraction of the occupation time, of the equations are given. For the further application of the newly built models, we make very detailed discussions on the none-immediately-repeated stochastic process, e.g., the random walk of smart animals.

Imaging the Photodissociation Dynamics of Nitrous Acid (HONO): The Role of Torsion.

We present the findings of the first imaging study of trans-HONO and cis-HONO photodissociation through the [Formula: see text] band and [Formula: see text] band of the Ã1A″-X̃1A' transition. The NO photofragment was probed by (1 + 1) resonance-enhanced multiphoton ionization and studied using the direct-current slice imaging technique with our finite slice reconstruction method. The NO state-specific translational energy distributions show some rotational structure corresponding to the internal state distribution in the OH cofragment. All images showed a perpendicular angular distribution with a recoil anisotropy parameter from ca. -0.6 to -0.8. In both bands, cis-HONO showed greater anisotropy than trans-HONO. Deviation from the limiting value expected for a pure perpendicular dissociation is ascribed to deviation of the transition moment from normal to the heavy atom plane owing to OH torsion, rather than lifetime effects assumed in the large body of previous work.

Translational and Rotational Energy Distributions of NO Photodesorbed from Au(100)

We report velocity and internal state distributions of nitric oxide photodesorbed from an Au(100) single crystal using 355 and 266 nm photons. The velocity distributions were measured in all three dimensions independently using our novel 3D-velocity map imaging setup. Combined with the internal energy distributions we reveal two distinct desorption mechanisms for the photodesorption of NO from gold dependent on the photon wavelength. The 355 nm desorption is dominated by a nonthermal mechanism due to excitation of an electron from the gold substrate to the adsorbed NO; this leads to a superthermal and noticeably narrow velocity distribution and a rotational state distribution that positively correlates with the velocity distribution and can be described by a rotational temperature appreciably above the surface temperature. Desorption with 266 nm photons leads to a slower average speed and wider angular distribution and rotational temperatures not too far off the surface temperature. We conclude that in th...

Final State Resolved Quantum Predissociation Dynamics of SO2(C̃1B2) and Its Isotopomers via a Crossing with a Singlet Repulsive State.

The fragmentation dynamics of predissociative SO2(C̃1B2) is investigated on an accurate adiabatic potential energy surface (PES) determined from high level ab initio data. This singlet PES features non-C2v equilibrium geometries for SO2, which are separated from the SO(X̃3Σ-) + O(3P) dissociation limit by a barrier resulting from a conical intersection with a repulsive singlet state. The ro-vibrational state distribution of the SO fragment is determined quantum mechanically for many predissociative states of several sulfur isotopomers of SO2. Significant rotational and vibrational excitations are found in the SO fragment. It is shown that these fragment internal state distributions are strongly dependent on the predissociative vibronic states, and the excitation typically increases with the photon energy.

Master Equation Analysis of Thermal and Nonthermal Microwave Effects.

Master equation is a successful model to describe the conventional heating reaction, it is expanded to capture the "microwave effect" in this work. The work equation of "microwave effect" included master equation presents the direct heating, indirect heating, and nonthermal effect about the microwave field. The modified master equation provides a clear physics picture to the nonthermal microwave effect: (1) The absorption and the emission of the microwave, which is dominated by the transition dipole moment between two corresponding states and the intensity of the microwave field, provides a new path to change the reaction rate constants. (2) In the strong microwave field, the distribution of internal states of the molecules will deviate from the equilibrium distribution, and the system temperature defined in the conventional heating reaction is no longer available. According to the general form of "microwave effect" included master equation, a two states model for unimolecular dissociation is proposed and is used to discuss the microwave nonthermal effect particularly. The average rate constants can be increased up to 2400 times for some given cases without the temperature changed in the two states model. Additionally, the simulation of a model system was executed using our State Specified Master Equation package. Three important conclusions can be obtained in present work: (1) A reasonable definition of the nonthermal microwave effect is given in the work equation of "microwave effect" included master equation. (2) Nonthermal microwave effect possibly exists theoretically. (3) The reaction rate constants perhaps can be changed obviously by the microwave field for the non-RRKM and the mode-specified reactions.