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A study is made of the singlet, triplet, and quintet states of B2 below 45,000/cm at the multireference configuration-interaction level. The stronger bonding in B2, as compared with Al2, manifests itself in the potential energy curves. In B2, five of the six states dissociating to the ground state atoms are bound, compared with only two for Al2. Radiative lifetimes are reported for the lowest vibrational level of many of the bound triplet states of B2.
The problem of calculating the position and width of the lowest-lying (L = 0, 1) resonances in the Ps + H scattering system has recently been re-examined by the authors [1]. In the model used, resonances axe assumed generated by bound Rydberg states in the closed re-arranged channel [e(+) + H(-)]. This infinite series of Coulomb bound states are shifted somewhat by the coupling with the open scattering channel [Ps + H]. Estimates using this approach, first carried out by one of the authors [2] using a simple form of scattering wavefunction, indicated an anticipated small shift of resonance away from the Rydberg energy in the S-wave (L = 0). More recent results by Ho and Yan [3] using the complex-rotation method showed unexpected significant shifting in the P (L = 1) and D (L = 2)-wave resonance energies from their respective unperturbed values. Our re-calculation of the resonances [I I for L = 0 and I indicates that, in each case, reasonably consistent resonance energies are obtained by coupling the two lowest lying states (IS and 2S for L = 0 and 2P and 3P for L = 1). For each L it is the higher state (2S and 3P, respectively) that produces the resonance. The lower state (1S and 2P, respectively) is effective only in increasing the non-resonant phase shift. In this work we extend the model to L = 2 (D-waves). Our results show that, unlike the S and P-waves, the 313-state alone produces a resonant energy that is very close to the result of Yan and Ho [3]. Inclusion of the 4D-state produces a second resonance in the scattering system shifted up slightly from its unperturbed Rydberg energy.
Consider the calculation of the oscillator strength of th B yielded by X electronic transition in CH3. The X state is strongly bound, but in the B state, CH3 is pre-dissociated by H atom tunneling through a potential energy barrier to form CH2+H. If we turn off pre-dissociation by making the potential outside of the barrier repulsive, the calculated 0-0 oscillator strength for CD3 from high quality ab initio potential and transition moment data along with accurate ro-vibrational wavefunctions is 0.0212, which is a factor of two greater than experiment. This discrepancy is largely due to the neglect of pre-dissociation. In this poster we explore techniques for including pre-dissociation in the calculations.
The N2(+) potential energies have been determined from a complete active space self-consistent field calculation with active 2s and 2p electrons. A (6s 4p 3d 1f) Gaussian basis set was used together with additional higher angular momentum and diffuse functions. The calculated potential energy curves for the states 4Sigma(mu)(+), 4Pi(g), and 6Sigma(g)(+), for which there are no spectroscopic observations, are presented. The corresponding spectroscopic constants have been determined from a polynomial curve fit to the computed energies near the well minima and are shown. The 6Sigma(g)(+) state is found to be significantly bound, with a minimum at 1.72 A.
This paper presents a novel, safe tracking control design method that learns the parameters of an uncertain Euler-Lagrange (EL) system online using adaptive learning laws. A barrier function (BF) is first used to transform the full-state constrained EL-dynamics into an equivalent unconstrained dynamics. An adaptive tracking controller is then developed along with the parameter update law in the transformed state space such that the states remain bounded for all time within a prescribed bound. A stability analysis is developed that considers the EL-dynamics’ uncertainty, yielding a semi-globally uniformly ultimately bounded (SGUUB) tracking error and the parameter estimation error. The controller design is validated in simulations using a two-link planar manipulator. The results show the proposed method’s ability to track the reference trajectory while remaining inside each of the predefined state bounds.
Realistic error bounds for reduced-state model-reference controller
A standard perturbation expansion in the atom-radiation field interaction is used to calculate the two photon excitation cross section for 1s(2) 2s(2) 2p(4) p3 to 1s(2) 2s(2) 2p(3) (s4) 3p p3 transition in atomic oxygen. The summation over bound and continuum intermediate states is handled by solving the equivalent inhomogeneous differential equation. Exact summation results differ by a factor of 2 from a rough estimate obtained by limiting the intermediate state summation to one bound state. Higher order electron correlation effects are also examined.
Systems modeled as partially observable Markov decision processes (POMDPs) can be tracked quickly with three restrictions: all actions are grouped together, the out-degree of each system state is bounded by a constant, and the number of non-zero elements in the belief state is bounded by a (different) constant. With these restrictions, the tracking algorithm operates in constant time and linear space. The first restriction assumes that the action itself is unobservable. The second restriction defines a subclass of POMDPs that covers however a wide range of problems. The third restriction is an approximation technique that can lead to a potentially vexing problem: an observation may be received that has probability according to the restricted belief state. This problem of impossibility will cause the belief state to collapse. In this paper we discuss the tradeoffs between the constant bound on the belief state and the quality of the solution. We concentrate on strategies for overcoming the impossibility problem and demonstrate initial experimental results that indicate promising directions.
Potential curves for the ground state and the first excited state of NaAr were determined. The van der Waals molecule NaAr was prepared by supersonic free jet expansion of a mixture of sodium, argon, and helium. The electronic transition from the ground state to the first excited state A2pi was excited by a tunable dye laser and the resulting fluorescence was studied. The dispersed fluorescence spectra show discrete and diffuse features, corresponding to transitions from excited vibrational levels of the A state to bound and unbound levels of the x state. The characteristic reflection structure in the bound-free spectra permits an unambiguous assignment of the vibrational numbering in the A state, and this assignment together with previously measured spectroscopic constants are used to calculate the potential curve of the A state. The discrete structure in the fluorescence spectra is used to determine the potential curve of the x state in the well region, and the repulsive part of the X curve is then deduced through trial-and-error simulation of the bound-free spectra.
Recombination of ground-state oxygen atoms populates six different bound electronic states of molecular oxygen. Of the six optical transitions expected between the three upper states at 4 to 4.5 electron volts and the two lowest states, five have been observed in the afterglow of a conventional helium-oxygen microwave discharge in both (O-16)2 and (O-18)2, three of them for the first time in gas-phase spectra. Generation of these emissions from oxygen atoms in a system free of molecular oxygen establishes that atom recombination is the production mechanism.
Excited state energy upper bounds in second order perturbation theory using Hylleraas variational principle
Synchrotron radiation light source measurements were conducted in the 105-155 nm region to obtain the photoabsorption and fluorescence cross sections of C2H2, and the quantum yield for producing the C2H-asterisk fluorescence from C2H2's photodissociation was measured in the 106-136.5 nm region. The products of the radiative lifetime quenching rate constant increase with excitation wavelengths. The data obtained on lifetimes, quenchings, and fluorescence spectra point to an upper state of the C2H-asterisk fluorescence that is well bound, while the lower state is a repulsive or weak-bound state.
Energy levels and electric dipole radiative transitions were determined for O III. The wavefunctions for the bound and continuum states were derived by solving coupled integrodifferential equations in the close-coupling approximation with the aid of two methods, the R-matrix and linear algebraic methods. Configuration interaction wavefunctions are presented for eight states of the O IV target with configurations of 2s(x)sp(y) (x + y = 3). Oscillator strengths are calculated for the transitions between, and photoionization cross sections from, bound states of O III with configurations of 2s(x)2p(y)nl (for n of not greater than 10 and l of not greater than 3).
Solution of Boltzmann, and rate equations for bound electronic states in nonequilibrium magnetohydrodynamic plasma
Eight doublet and eight quartet states of ClOO were investigated by ab initio CI techniques. The potential energy surfaces of the four lowest energy doublet states of both A-double-prime and A-prime symmetry indicate that only the 1 2A-double-prime state is bound. In contrast to the model provided by the HO2 radical, all of the excited doublet states investigated were repulsive with respect to dissociation to Cl + O2 and metastable or bound with respect to dissociation to ClO + O. The transitions to the excited states investigated span the visible and near UV spectral regions, but the transition moments indicate that they are very weak. Since the photolysis products are the same as those of the rapid thermal dissociation, photolysis is not expected to be an important atmospheric process. The soft bending potential for the 1 2A-prime state and the shape of the 1 4A-double-prime state in the entrance channel of the ClO + O yields Cl + O2 reaction provide a qualitative explanation for the underprediction of the low temperature reaction rate by previous trajectory calculations.
Symbolic execution is a program analysis technique that is used for many purposes, one of which is test-case generation. For loop-free programs, this generates a test-set that achieves path coverage. Program loops, however, imply exponential growth of the number of paths in the best case and non-termination in the worst case. In practice, the number of loop unwindings needs to be bounded for analysis. We consider symbolic execution in the context of the tool Symbolic Pathfinder. This tool extends the model-checker Java Pathfinder and relies on its bounded state-space exploration for termination. We present an implementation of k-bounded loop unwinding, which increases the amount of user-control over the symbolic execution of loops. Bounded unwinding can be viewed as a naive way to prune paths through loops. When using symbolic execution for test-case generation, naively pruning paths is likely at the cost of coverage. In order to improve coverage of branches within a loop body, we present a technique that semi-automatically concretizes variables used in a loop. The basic technique is limited and we therefore present annotations to manually steer symbolic execution towards certain branches, as well as ideas on how the technique can be extended to be more widely applicable.