Application of Brouwer's artificial-satellite theory to computation of the state transition matrix
Application of Brouwer artificial satellite theory to computation of state transition matrix
Born, G. H.↗
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An analytical state transition matrix for an orbit perturbed by oblateness
A new analytical state transition matrix is presented. This transition matrix contains the two-body terms and the secular and short periodic terms due to the J2 oblateness perturbation. The matrix is derived from a satellite theory which uses a set of 8 canonical elements with the true anomaly as the independent variable. This theory was chosen because of its accuracy and concise formulation. It presents no problems concerning the accuracy of the mean motion, which is typical for classical satellite theories. Numerical experiments show the J2 transition matrix to be superior to the simple two-body matrix.
Mueller, A. C.↗
Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories
Here, the accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH 3 ) molecule and the nucleophilic substitution (S N 2) reaction F – + CH 3 F → FCH 3 + F – . We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.
Iyer, Gopal R.↗
Restricted Partition Function Semiclassical Transition State Theory (RPF-SCTST): Applications to Reactions Involving Hydrogen Cyanide, Hydrogen Peroxide, and Formaldehyde Oxide
We demonstrate the efficiency of the numerical calculation of thermal semiclassical transition state theory (SCTST) rates across several representative chemical reactions using the restricted partition function (RPF)─viz a function that depends only on the imaginary action associated with a reaction. Here, we treat the potential energy surfaces (PESs) through fourth order expansions around the saddle point and integrate the Hamiltonian up to second order in employing vibrational perturbation theory. We apply this formalism to uni- and bimolecular reactions with different─though relatively high─barrier heights to uncover the influence of the barrier properties, minimal energies, and separability of the rotational motion on rate constants and tunneling corrections. Although all modes are coupled within the RPF, we found in our numerical examples that the rotational component in the absence of significant rotational distortions can be separated from the vibrational contributions. Moreover, a classical treatment of the rotational contribution is adequate over the temperature range from approximately 100 to 1000 K. We also found that the choice of DFT basis set can lead to variations in rate constants of up to an order of magnitude. Lastly, different schemes for counting eligible energy levels result in rate constants that differ by no more than a factor of 2, with the remaining discrepancies attributed to the treatment of near-convergent levels in perturbation theory.
74 ATOMIC AND MOLECULAR PHYSICS↗
A Numerical Method for Computing the State Transition Matrix Using Poincare Integral Invariants
The Poincare integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a new numerical procedure for obtaining the state transition matrix (STM), which can be applied to both conservative and nonconservative systems. The method is analogous to a finite difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. We discuss the mathematical similarities between this new STM and existing methods, show numerical results for orbital motion and uncertainty propagation, and discuss new insights afforded by the Hamiltonian properties of phase flow.
state transition matrix↗
Approximate Cartesian state transition matrix
Based on a Taylor series expansion, an easily-computed approximation to the Cartesian state transition matrix is presented for a general velocity-independent force field. Suitable for the short time intervals encountered in onboard navigation applications of the extended Kalman filter, it provides approximately five decimal digits of accuracy for earth orbiting spacecraft with update intervals of one minute, and better accuracy for shorter intervals.
Markley, F. L.↗
Using integrals of the state transition matrix for efficient transient-response computations
An iterative technique for the computation of lower-order state systems with poles at the origin (such as aircraft lateral dynamics) or with time-polynomial inputs is developed and demonstrated. The integrated input or output signals are computed using the integrals of the state transition matrix, thus reducing the system order and computation time. In an application to the lateral response of a DC-8 aircraft (Grunwald, 1981), this method required only 7824 multiplication or addition operations (at fourth order) to achieve the accuracy obtained in 15,012 operations by a conventional sixth-order computation.
Grunwald, A. J.↗
A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix
A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.
Bartels, Robert E.↗
Modeling Magnetic Disk Wind State Transitions in Black Hole X-Ray Binaries
We analyze three prototypical black hole X-ray binaries, 4U 1630–472, GRO J1655–40, and H1743–322, in an effort to systematically understand the intrinsic state transition of the observed accretion disk winds between wind-on and wind-off states by utilizing state-of-the-art Chandra/HETGS archival data from multi-epoch observations. We apply our magnetically driven wind models in the context of magnetohydrodynamic(MHD)calculations to constrain(1)their global density slope(p),(2)their density (n17) at the foot point of the inner most launching radius, and(3)the abundances of heavier elements(AFe,S,Si). Incorporating the MHD winds into xstar photoionization calculations in a self-consistent manner, we create a library of synthetic absorption spectra given the observed X-ray continua. Our analysis clearly indicates a characteristic bimodal transition of multi-ion X-ray winds; i.e., the wind density gradient is found to steepen(fro mp∼1.2–1.4 to∼1.4–1.5)while its density normalization declines as the source transitions from the wind-onto the wind-off state. The model implies that the ionized wind remains physically present even in the wind-off state, despite its apparent absence in the observed spectra. Super solar abundances for heavier elements are also favored. Our global multi-ion wind models, taking into account soft X-ray ions as well as Fe K absorbers, show that the internal wind condition plays an important role in wind transitions besides photoionization changes. Simulated XRISM/Resolve and Athena/X-IFU spectra are presented to demonstrate a high fidelity of the multi-ion wind model for a better understanding of these powerful ionized winds in the coming decades
Keigo Fukumura↗
Rotational state-to-state transition rate coefficients for H 2 O + H 2 O collisions at nonequilibrium conditions
Aims.The goal is to develop a database of rate coefficients for rotational state-to-state transitions in H 2 O + H 2 O collisions that is suitable for the modeling of energy transfer in nonequilibrium conditions, in which the distribution of rotational states of H 2 O deviates from local thermodynamic equilibrium. Methods.A two-temperature model was employed that assumed that although there is no equilibrium between all possible degrees of freedom in the system, the translational and rotational degrees of freedom can be expected to achieve their own equilibria independently, and that they can be approximately characterized by Boltzmann distributions at two different temperatures,T kin andT rot . Results.Upon introducing our new parameterization of the collisional rates, taking into account their dependence on bothT kin andT rot , we find a change of up to 20% in the H 2 O rotational level populations for both ortho and para-H 2 O for the part of the cometary coma where the nonequilibrium regime occurs.
Astronomy & Astrophysics↗
Radio astronomical determination of ground state transition frequencies of CH
From a comparison of the spectra of CH and other molecules toward the continuum source Cas A and four dark clouds, the ground state transition frequencies of CH have been determined and are reported. The relative errors in these frequencies are about twice as small as those obtained earlier by radio astronomical methods for the two main lines of ground state OH.
Rydbeck, O. E. H.↗
A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties
A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.
Bartels, Robert E.↗
Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models
A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.
Low Thrust↗
The protonation of N2O reexamined - A case study on the reliability of various electron correlation methods for minima and transition states
The protonation of N2O and the intramolecular proton transfer in N2OH(+) are studied using various basis sets and a variety of methods, including second-order many-body perturbation theory (MP2), singles and doubles coupled cluster (CCSD), the augmented coupled cluster (CCSD/T/), and complete active space self-consistent field (CASSCF) methods. For geometries, MP2 leads to serious errors even for HNNO(+); for the transition state, only CCSD/T/ produces a reliable geometry due to serious nondynamical correlation effects. The proton affinity at 298.15 K is estimated at 137.6 kcal/mol, in close agreement with recent experimental determinations of 137.3 +/- 1 kcal/mol.
Martin, J. M. L.↗
Anaerobic benzene oxidation in Geotalea daltonii involves activation by methylation and is regulated by the transition state regulator AbrB
ABSTRACT Benzene is a widespread groundwater contaminant that persists under anoxic conditions. The aim of this study was to more accurately investigate anaerobic microbial degradation pathways to predict benzene fate and transport. Preliminary genomic analysis of Geotalea daltonii strain FRC-32, isolated from contaminated groundwater, revealed the presence of putative aromatic-degrading genes. G. daltonii was subsequently shown to conserve energy for growth on benzene as the sole electron donor and fumarate or nitrate as the electron acceptor. The hbs gene, encoding for 3-hydroxybenzylsuccinate synthase (Hbs), a homolog of the radical-forming, toluene-activating benzylsuccinate synthase (Bss), was upregulated during benzene oxidation in G. daltonii , while the bss gene was upregulated during toluene oxidation. Addition of benzene to the G. daltonii whole-cell lysate resulted in toluene formation, indicating that methylation of benzene was occurring. Complementation of σ 54 - (deficient) E. coli transformed with the bss operon restored its ability to grow in the presence of toluene, revealing bss to be regulated by σ 54 . Binding sites for σ 70 and the transition state regulator AbrB were identified in the promoter region of the σ 54 -encoding gene rpoN, and binding was confirmed. Induced expression of abrB during benzene and toluene degradation caused G. daltonii cultures to transition to the death phase. Our results suggested that G. daltonii can anaerobically oxidize benzene by methylation, which is regulated by σ 54 and AbrB. Our findings further indicated that the benzene, toluene, and benzoate degradation pathways converge into a single metabolic pathway, representing a uniquely efficient approach to anaerobic aromatic degradation in G. daltonii . IMPORTANCE The contamination of anaerobic subsurface environments including groundwater with toxic aromatic hydrocarbons, specifically benzene, toluene, ethylbenzene, and xylene, has become a global issue. Subsurface groundwater is largely anoxic, and further study is needed to understand the natural attenuation of these compounds. This study elucidated a metabolic pathway utilized by the bacterium Geotalea daltonii capable of anaerobically degrading the recalcitrant molecule benzene using a unique activation mechanism involving methylation. The identification of aromatic-degrading genes and AbrB as a regulator of the anaerobic benzene and toluene degradation pathways provides insights into the mechanisms employed by G. daltonii to modulate metabolic pathways as necessary to thrive in anoxic contaminated groundwater. Our findings contribute to the understanding of novel anaerobic benzene degradation pathways that could potentially be harnessed to develop improved strategies for bioremediation of groundwater contaminants.
Bullows, James E.↗
Transition-state lattice modes and the breakdown of adiabatic tunneling for hydrogen and deuterium in bcc Nb
Interstitial hydrogen and deuterium in body-centered-cubic metals constitute archetypal quantum tunneling systems. Their relevance has been renewed by the connection between hydrogenic tunneling in Nb and defect-induced decoherence in superconducting qubits, motivating a predictive microscopic theory. Existing theoretical treatments invoke an adiabatic separation between the light interstitial and the host lattice, an assumption whose validity has not been rigorously established for hydrogenic species. Here, we show that the experimentally measured tunnel splittings of O-trapped H and D in bcc Nb are quantitatively reproduced only within a five-dimensional (5D) Lattice-Renormalized Born-Oppenheimer (LRBO) framework. This approach treats three interstitial modes and two judiciously selected lattice modes, which includes a transition-state mode, on equal quantum footing. By recasting nested Born-Oppenheimer hierarchies within this same formalism and benchmarking against modern \textit{ab initio} potential energy surfaces, we show that adiabatic separation of the light particle from lattice dynamics is satisfied only in the positive-muon ($μ^{+}$) mass limit. In contrast, tunneling for H and D is fundamentally a collective, nonadiabatic process mediated by anharmonic lattice couplings. Finally, we show that the breakdown of adiabaticity can be anticipated from simple energy estimates involving the ground-state light-particle energy evaluated at a small number of fixed lattice configurations, providing a practical criterion for assessing the validity of adiabatic tunneling theories in other systems.
Pritchard, P. Graham [Northwestern U.]↗
A Coupled-Cluster Study of XON (X=H, F, Cl), and the XON (left and right arrow) XNO Transition States
The XON molecules (X=H, F, and Cl) have been studied using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, CCSD(T), in conjunction with a double polarized triple-zeta basis set. The equilibrium geometries, dipole moments, harmonic vibrational frequencies and infrared intensities have been predicted. The X-O bond distance is shown to be abnormally long for X=F and Cl, and this is attributed to the degree of ionic bonding and the stability of NO(+). Based on Mulliken population analyses, it is shown that there is a significant degree of X(-), ON(+) ionic bonding character for FON and ClON, whereas for HON the ionic character is reduced and best described as H(+), NO(-). The stability of the XON molecule relative to the XNO isomer is shown to increase in the order HON<FON<ClON, although even ClON is 27.0 plus or minus 1.0 kcal/mol (0 K) less stable than ClNO. The XON (left and right arrow) XNO transition states are also investigated. FON and ClON possess the lowest barrier heights to isomerization (7.2 plus or minus 1.0 kcal/mol at 0 K), but these are sufficiently large to suggest that isomerization should not be rapid at low temperatures.
Lee, Timothy↗
A NICER Look at the State Transitions of the Black Hole Candidate MAXI J1535-571 During its Reflares
The black hole candidate and X-ray binary MAXI J1535−571 was discovered in 2017 September. During the decay of its discovery outburst, and before returning to quiescence, the source underwent at least four reflaring events, with peak luminosities of ∼1035–36 erg s−1 (d/4.1 kpc)2. To investigate the nature of these flares, we analysed a sample of NICER (Neutron star Interior Composition Explorer) observations taken with almost daily cadence. In this work, we present the detailed spectral and timing analysis of the evolution of the four reflares. The higher sensitivity of NICER at lower energies, in comparison with other X-ray detectors, allowed us to constrain the disc component of the spectrum at ∼0.5 keV. We found that during each reflare the source appears to trace out a q-shaped track in the hardness–intensity diagram similar to those observed in black hole binaries during full outbursts. MAXI J1535−571 transits between the hard state (valleys) and softer states (peaks) during these flares. Moreover, the Comptonized component is undetected at the peak of the first reflare, while the disc component is undetected during the valleys. Assuming the most likely distance of 4.1 kpc, we find that the hard-to-soft transitions take place at the lowest luminosities ever observed in a black hole transient, while the soft-to-hard transitions occur at some of the lowest luminosities ever reported for such systems.
V A Cuneo↗