Bayesian Machine Learning Approach to the Quantification of Uncertainties on Ab Initio Potential Energy Surfaces.

This work introduces a novel methodology for the quantification of uncertainties associated with potential energy surfaces (PESs) computed from first-principles quantum mechanical calculations. The methodology relies on Bayesian inference and machine learning techniques to construct a stochastic PES and to express the inadequacies associated with the ab initio data points and their fit. By combining high fidelity calculations and reduced-order modeling, the resulting stochastic surface is efficiently forward propagated via quasi-classical trajectory and master equation calculations. In this way, the PES contribution to the uncertainty on predefined quantities of interest (QoIs) is explicitly determined. This study is done at both microscopic (e.g., rovibrational-specific rate coefficients) and macroscopic (e.g., thermal and chemical relaxation properties) levels. A correlation analysis is finally applied to identify the PES regions that require further refinement, based on their effects on the QoI reliability. The methodology is applied to the study of singlet (11A') and quintet (25A') PESs describing the interaction between O2 molecules and O atoms in their ground electronic state. The investigation of the singlet surface reveals a negligible uncertainty on the kinetic properties and relaxation times, which are found to be in excellent agreement with the ones previously published in the literature. On the other hand, the methodology demonstrated significant uncertainty on the quintet surface, due to inaccuracies in the description of the exchange barrier and the repulsive wall. When forward propagated, this uncertainty is responsible for the variability of 1 order of magnitude in the vibrational relaxation time and of factor four in the exchange reaction rate coefficient, both at 2500 K.

Construction of a coarse-grain quasi-classical trajectory method. I. Theory and application to N2-N2 system.

This work aims to construct a reduced order model for energy transfer and dissociation in non-equilibrium nitrogen mixtures. The objective is twofold: to present the Coarse-Grain Quasi-Classical Trajectory (CG-QCT) method, a novel framework for constructing a reduced order model for diatom-diatom systems; and to analyze the physics of non-equilibrium relaxation of the nitrogen molecules undergoing dissociation in an ideal chemical reactor. The CG-QCT method couples the construction of the reduced order model under the coarse-grain model framework with the quasi-classical trajectory calculations to directly construct the reduced model without the need for computing the individual rovibrational specific kinetic data. In the coarse-grain model, the energy states are lumped together into groups containing states with similar properties, and the distribution of states within each of these groups is prescribed by a Boltzmann distribution at the local translational temperature. The required grouped kinetic properties are obtained directly by the QCT calculations. Two grouping strategies are considered: energy-based grouping, in which states of similar internal energy are lumped together, and vibrational grouping, in which states with the same vibrational quantum number are grouped together. A zero-dimensional chemical reactor simulation, in which the molecules are instantaneously heated, forcing the system into strong non-equilibrium, is used to study the differences between the two grouping strategies. The comparison of the numerical results against available experimental data demonstrates that the energy-based grouping is more suitable to capture dissociation, while the energy transfer process is better described with a vibrational grouping scheme. The dissociation process is found to be strongly dependent on the behavior of the high energy states, which contribute up to 50% of the dissociating molecules. Furthermore, up to 40% of the energy required to dissociate the molecules comes from the rotational mode, underscoring the importance of accounting for this mode when constructing non-equilibrium kinetic models. In contrast, the relaxation process is governed primarily by low energy states, which exhibit significantly slower transitions in the vibrational binning model due to the prevalence of mode separation in these states.

Energy transfer models in nitrogen plasmas: analysis of N2(X¹Σg⁺)-N(4S(u))-e⁻ interaction.

The relaxation of N2(X¹Σg⁺) molecules in a background gas composed of N((4)S(u)) atoms and free electrons is studied by using an ideal isochoric and isothermic chemical reactor. A rovibrational state-to-state model is developed to study energy transfer process induced by free electron and atomic collisions. The required cross sections and the corresponding rate coefficients are taken from two well-known kinetic databases: NASA Ames kinetic mechanism for the description of the N2(X¹Σg⁺)-N((4)S(u)) processes and the Phys4Entry database for the electron driven processes, N2(X¹Σg⁺)-e(-). The evolution of the population densities of each individual rovibrational level is explicitly determined via the numerical solution of the master equation for temperatures ranging from 10000 to 30,000 K. It was found that the distribution of the rovibrational energy levels of N2(X¹Σg⁺) is strongly influenced by the electron driven collisional processes, which promote the excitation of the low lying vibrational levels. The macroscopic vibrational energy relaxation is governed by the molecule-atom collisions, when free electrons, initially cold are relaxing to the final heat-bath temperature. Thus, the main role of the free electrons is to ensure the equilibration of vibrational and free electron excitation, thus validating the existence of the local equilibrium T(V)-T(e). However, if electrons and heavy particles are assumed to be in equilibrium at the heat bath temperature, electron driven processes dominate the vibrational relaxation. Finally, we have assessed the validity of the Landau-Teller model for the description of the inelastic energy transfer between molecules and free electrons. In the case of free-electron temperatures lower than 10,000 K, Landau-Teller relaxation model gives an accurate description of the vibrational relaxation, while at higher temperatures the error in the predictions can be significant and the model should not be used.

Nonequilibrium shock-heated nitrogen flows using a rovibrational state-to-state method.

A rovibrational collisional model is developed to study the internal energy excitation and dissociation processes behind a strong shock wave in a nitrogen flow. The reaction rate coefficients are obtained from the ab initio database of the NASA Ames Research Center. The master equation is coupled with a one-dimensional flow solver to study the nonequilibrium phenomena encountered in the gas during a hyperbolic reentry into Earth's atmosphere. The analysis of the populations of the rovibrational levels demonstrates how rotational and vibrational relaxation proceed at the same rate. This contrasts with the common misconception that translational and rotational relaxation occur concurrently. A significant part of the relaxation process occurs in non-quasi-steady-state conditions. Exchange processes are found to have a significant impact on the relaxation of the gas, while predissociation has a negligible effect. The results obtained by means of the full rovibrational collisional model are used to assess the validity of reduced order models (vibrational collisional and multitemperature) which are based on the same kinetic database. It is found that thermalization and dissociation are drastically overestimated by the reduced order models. The reasons of the failure differ in the two cases. In the vibrational collisional model the overestimation of the dissociation is a consequence of the assumption of equilibrium between the rotational energy and the translational energy. The multitemperature model fails to predict the correct thermochemical relaxation due to the failure of the quasi-steady-state assumption, used to derive the phenomenological rate coefficient for dissociation.

Thermally driven molecular linear motors: a molecular dynamics study.

We conduct molecular dynamics simulations of a molecular linear motor consisting of coaxial carbon nanotubes with a long outer carbon nanotube confining and guiding the motion of an inner short, capsulelike nanotube. The simulations indicate that the motion of the capsule can be controlled by thermophoretic forces induced by thermal gradients. The simulations find large terminal velocities of 100-400 nm/ns for imposed thermal gradients in the range of 1-3 K/nm. Moreover, the results indicate that the thermophoretic force is velocity dependent and its magnitude decreases for increasing velocity.

Casimir forces between arbitrary compact objects.

We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations. The objects' shape and composition enter only through their scattering matrices. The result is exact when all multipoles are included, and converges rapidly. A low frequency expansion yields the energy as a series in the ratio of the objects' size to their separation. As an example, we obtain this series for two dielectric spheres and the full interaction at all separations for perfectly conducting spheres.

Parity doubling and SU(2)LxSU(2)R restoration in the hadron spectrum.

We construct the most general nonlinear representation of chiral SU(2)LxSU(2)R broken down spontaneously to the isospin SU(2), on a pair of hadrons of same spin and isospin and opposite parity. We show that any such representation is equivalent, through a hadron field transformation, to two irreducible representations on two hadrons of opposite parity with different masses and axial-vector couplings. This implies that chiral symmetry realized in the Nambu-Goldstone mode does not predict the existence of degenerate multiplets of hadrons of opposite parity nor any relations between their couplings or masses.

Casimir Interaction between a plate and a cylinder.

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate sphere, where it is known at large separations. The force has an unexpectedly weak decay approximately L/[H3 ln(H/R)] at large plate-cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.

Attractive Casimir forces in a closed geometry.

We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence.

Hydrodynamic properties of carbon nanotubes.

We study water flowing past an array of single walled carbon nanotubes using nonequilibrium molecular dynamics simulations. For carbon nanotubes mounted with a tube spacing of 16.4 x 16.4 nm and diameters of 1.25 and 2.50 nm, respectively, we find drag coefficients in reasonable agreement with the macroscopic, Stokes-Oseen solution. The slip length is -0.11 nm for the 1.25 nm carbon nanotube, and 0.49 for the 2.50 nm tube for a flow speed of 50 m/s, respectively, and 0.28 nm for the 2.50 nm tube at 200 m/s. A slanted flow configuration with a stream- and spanwise velocity component of 100 ms(-1) recovers the two-dimensional results, but exhibits a significant 88 nm slip along the axis of the tube. These results indicate that slip depends on the particular flow configuration.

Casimir effect and geometric optics.

We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. We reproduce the standard result for parallel plates and agree over a wide range of parameters with a recent numerical treatment of the sphere and plate with Dirichlet boundary conditions. Our approach improves upon the proximity force approximation. It can be generalized easily to other geometries, other boundary conditions, to the computation of Casimir energy densities, and to many other situations.

Quantum energies of interfaces.

We present a method for computing the one-loop, renormalized quantum energies of symmetrical interfaces of arbitrary dimension and codimension using elementary scattering data. Internal consistency requires finite-energy sum rules relating phase shifts to bound state energies.

Tracheobronchial injuries after blunt chest trauma in children--hidden pathology.

BACKGROUND: Blunt thoracic injuries in children are unique because the pliability of the chest wall allows transmission of massive external force directly into the mediastinum. Children presenting after blunt chest trauma may have complete disruption of the airway with little external sign of injury. Without prompt diagnosis and appropriate treatment, the risk for progressive respiratory failure is high. METHODS: Four children with tracheobronchial injuries were referred to a pediatric trauma center from 1994 to 1997. All children, age 18 months to 13 years, suffered unusual crush injuries. All diagnoses were based on unresolved pneumothorax or pneumomediastinum. RESULTS: Bronchoscopy identified the location of injury as posterior trachea (n = 1) and right mainstem bronchus (n = 2). A tertiary bronchial injury (n = 1) was missed by initial tracheogram and subsequent bronchoscopy but identified during surgical exploration. All children survived after thoracotomy and primary repair of the injury. CONCLUSIONS: Tracheobronchial disruption is a rare, life-threatening injury. Suspicion should be high when pneumomediastinum and pneumothorax are refractory to adequate pleural drainage. Flexible bronchoscopy with intubation distal to the injury may be necessary to prevent loss of the airway. Advance preparation should include setups for bronchoscopy, thoracotomy, and cardiopulmonary bypass. Patient survival depends on preparation and prompt surgical intervention.

Rapid assay of cytotoxicity using Tetramitus flagellates.

A simple test for measuring cytotoxic agents has been developed using the flagellate phenotype of Tetramitus rostratus. The test measures dose-dependent inhibition of cell division by individual agents such as 4-nitroquinoline-N-oxide and other mutagens. Dose-response data are given also for mixtures including coal tar pitch condensate, centrifuged particles obtained from tap water, and water concentrates prepared with XAD-2 resin. Because Tetramitus flagellates have a gullet and are particle-feeders, the assay allows for cytotoxic measurements of whole particles without prior extraction or solvent substitution procedures. The cytotoxic activities observed may reflect genotoxic activity, since all chemicals that produced a positive response are genotoxic in other test systems.

Electroconvulsive therapy and major depression in Down's syndrome.

The authors treated two patients who had Down's syndrome and major depression with a combination of inpatient and outpatient electroconvulsive therapy (ECT). They found only 10 other similar published cases, although none involved outpatient ECT. Their experience, in conjunction with that reported in the literature, indicates that ECT is a safe and effective treatment for depressed mentally retarded individuals, including those who respond poorly to antidepressants.

Urinary mutagen levels in smokers.

Urinary mutagen levels were measured over an 8-week period in a group of 13 smokers. Individual urinary mutagen levels were observed to be relatively constant and while there was a general correlation between mutagen excretion levels and cigarette consumption, individuals' excretion levels could not be predicted on the basis of either the numbers of cigarettes smoked or the tar content of the cigarettes.