A new method for computing the state transition matrix
State transition matrix computation method with efficient algorithm for orbit prediction in n-body gravitational field
Weiss, E. H.↗
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A study of the effects of state transition matrix approximations
The effects of using an approximate state transition matrix in orbit estimation are investigated. The approximate state transition matrix results when higher order geopotential terms in the equations of motion are ignored in the formation of the variational equations. Two methods of orbit estimation are considered: the differential correction procedure (DC) and the extended Kalman filter (EKF). The system used for the study is the Research & Development version of the Goddard Trajectory Determination System. The effects of the approximation are analyzed on a number of orbits. These orbits of various inclinations and semimajor axes. Other parameters studied include geopotential models and DC arc length.
May, J. A.↗
The structure and energetics of the HCN-HNC transition state
The optimum geometries and quadratic force constants of HCN, HNC and the transition state connecting them have been determined at the single- and double-excitation coupled-cluster (CCSD) and CCSD(T) levels of theory. Energy differences were evaluated using the CCSD and CCSD(T) methods in conjunction with large atomic natural orbital basis sets containing g-type basis functions on the heavy atoms and f-type functions on hydrogen. The most reliable structure obtained for the transition state has bond distances of 1.194, 1.188, and 1.389 A for r(CN), r(CH), and r(NH), respectively. Including a correction for zero-point vibrational energies, the transition state is predicted to be 44.6 + or - 1.0 kcal/mol above the HCN isomer, while HNC is predicted to be 14.4 + or - 1.0 kcal/mol above HCN. The latter value is in excellent agreement with the most recent experimental determination (14.8 + or - 2.0 kcal/mol).
Lee, Timothy J.↗
The Galactic Black Hole Transient H1743-322 During Outburst Decay Connections Between Timing Noise, State Transitions, And Radio Emission
Multiwavelength observations of Galactic black hole transients during outburst decay are instrumental for our understanding of the accretion geometry and the formation of outflows around black hole systems. H1743-322, a black hole transient observed intensely in X-rays and also covered in the radio band during its 2003 decay, provides clues about the changes in accretion geometry during state transitions and also the general properties of X-ray emission during the intermediate and low-hard states. In this work, we report on the evolution of spectral and temporal properties in X-rays and the flux in the radio band, with the goal of understanding the nature of state transitions observed in this source. We concentrate on the transition from the thermal dominant state to the intermediate state that occurs on a timescale of 1 day. We show that the state transition is associated with a sudden increase in power-law flux. We determine that the ratio of the power-law flux to the overall flux in the 3-25 keV band must exceed 0.6 for us to observe strong timing noise. Even after the state transition, once this ratio was below 0.6, the system transited back to the thermal dominant state for 1 day. We show that the emission from the compact radio core does not turn on during the transition from the thermal dominant state to the intermediate state but does turn on when the source reaches the low-hard state, as seen in 4U 1543-47 and GX 339-4. We find that the photon index correlates strongly with the QPO frequency and anticorrelates with the rms amplitude of variability. We also show that the variability is more likely to be associated with the power-law emission than the disk emission.
Kalemci, E.↗
An Analytical State Transition Matrix for Orbits Perturbed by an Oblate Spheroid
An analytical state transition matrix and its inverse, which include the short period and secular effects of the second zonal harmonic, were developed from the nonsingular PS satellite theory. The fact that the independent variable in the PS theory is not time is in no respect disadvantageous, since any explicit analytical solution must be expressed in the true or eccentric anomaly. This is shown to be the case for the simple conic matrix. The PS theory allows for a concise, accurate, and algorithmically simple state transition matrix. The improvement over the conic matrix ranges from 2 to 4 digits accuracy.
Mueller, A. C.↗
Full CI studies of the collinear transition state for the reaction F + H2 yields HF + H
Full CI calculations on the collinear transition state for the reaction F + H2 yields HF + H are reported. The full CI results are compared with those obtained from single-reference and multireference CI calculations and from single-reference CPF calculations. In general, only those methods which attempt to account for the effects of higher excitations, such as CPF or CI plus the Davidson correction, yield a transition-state location and barrier height in good agreement with the full CI. In an extended basis, the effect of higher excitations is estimated to lower the barrier by as much as 1.5 kcal/mol; such an effect would essentially eliminate the present discrepancy between theory and experiment.
Bauschlicher, Charles W., Jr.↗
Experimental and theoretical examples of the value and limitations of transition state theory
Value and limitations of transition-state theory (TST) are reviewed. TST analyses of the temperature dependence of the 'direct' reactions CH3 + CH3CHO yields CH4 + CH3CO(1) and O + CH4 yields OH + CH3(2) are presented in detail, and other examples of TST usefulness are recalled. Limitations are discussed for bimolecular processes in terms of 'complex' vs. 'direct' mechanisms. The reaction OH + CO yields CO2 + H is discussed in this context. Limitations for unimolecular processes seem to arise only for simple bond fission processes, and recent advances are noted.
Golden, D. M.↗
State transition storyboards: A tool for designing the Goldstone solar system radar data acquisition system user interface software
Effective user interface design in software systems is a complex task that takes place without adequate modeling tools. By combining state transition diagrams and the storyboard technique of filmmakers, State Transition Storyboards were developed to provide a detailed modeling technique for the Goldstone Solar System Radar Data Acquisition System human-machine interface. Illustrations are included with a description of the modeling technique.
Howard, S. D.↗
The nature and role of quantized transition states in the accurate quantum dynamics of the reaction O + H2 yields OH + H
Accurate quantum mechanical dynamics calculations are reported for the reaction probabilities of O(3P) + H2 yields OH + H with zero total angular momentum on a single potential energy surface. The results show that the reactive flux is gated by quantized transition states up to the highest energy studied, which corresponds to a total energy of 1.90 eV. The quantized transition states are assigned and compared to vibrationally adiabatic barrier maxima; their widths and transmission coefficients are determined; and they are classified as variational, supernumerary of the first kind, and supernumerary of the second kind. Their effects on state-selected and state-to-state reactivity are discussed in detail.
Chatfield, David C.↗
Universal Keplerian state transition matrix
A completely general method for computing the Keplerian state transition matrix in terms of Goodyear's universal variables is presented. This includes a new scheme for solving Kepler's problem which is a necessary first step to computing the transition matrix. The Kepler problem is solved in terms of a new independent variable requiring the evaluation of only one transcendental function. Furthermore, this transcendental function may be conveniently evaluated by means of a Gaussian continued fraction.
Shepperd, S. W.↗
Catching Up on State Transitions in Cygnus X-1
In 2005 February we observed Cygnus X-1 over a period of 10 days quasi-continuously with the Rossi X-ray Timing Explorer and the Ryle telescope. We present the results of the spectral and timing analysis on a timescale of 90 min and show that the behavior of Cyg X-1 is similar to that found during our years long monitoring campaign. As a highlight we present evidence for a full transition from the hard to the soft state that happened during less than three hours. The observation provided a more complete picture of a state transition than before, especially concerning the evolution of the time lags, due to unique transition coverage and analysis with high time resolution.
Boeck, Moritz↗
Rapid accretion state transitions following the tidal disruption event AT2018fyk
Following a tidal disruption event (TDE), the accretion rate can evolve from quiescent to near- Eddington levels and back over months{years timescales. This provides a unique opportunity to study the formation and evolution of the accretion flow around supermassive black holes (SMBHs). We present two years of multi-wavelength monitoring observations of the TDE AT2018fyk at X-ray, UV, optical and radio wavelengths. We identify three distinct accretion states and two state transitions between them. These appear remarkably similar to the behaviour of stellar-mass black holes in outburst. The X-ray spectral properties show a transition from a soft (thermal-dominated) to a hard (power-law dominated) spectral state around Lbol ~few x 10^(-2) LEdd, and the strengthening of the corona over time ~100-200 days after the UV/optical peak. Contemporaneously, the spectral energy distribution (in particular, the UV-to-X-ray spectral slope alphaox ) shows a pronounced softening as the outburst progresses. The X-ray timing properties also show a marked change, initially dominated by variability at long (>day) timescales while a high frequency (~10-3 Hz) component emerges after the transition into the hard state. At late times (~500 days after peak), a second accretion state transition occurs, from the hard into the quiescent state, as identi fied by the sudden collapse of the bolometric (X-ray+UV) emission to levels below 10-3.4 LEdd. Our fi ndings illustrate that TDEs can be used to study the scale (in)variance of accretion processes in individual SMBHs. Consequently, they provide a new avenue to study accretion states over seven orders of magnitude in black hole mass, removing limitations inherent to commonly used ensemble studies.
T. Wevers↗
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.↗
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.↗
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.↗