Prediction of bond dissociation energies and transition state barriers by a modified complete basis set model chemistry

The complete basis set model chemistries CBS-4 and CBS-q were modified using density functional theory for the geometry optimization step of these methods. The accuracy of predicted bond dissociation energies and transition state barrier heights was investigated based on geometry optimizations using the B3LYP functional with basis set sizes ranging from 3-21G(d,p) to 6-311G(d,p). Transition state barrier heights can be obtained at CBS-q with B3LYP/6-31G(d,p) geometries with rms error of 1.7 kcal/mol within a test set of ten transition state species. The method should be applicable to molecules with up to eight or more heavy atoms. Use of B3LYP/6-311G(d,p) for geometry optimizations leads to further improvement of CBS-q barrier heights with a rms error of 1.4 kcal/mol. For reference, the CBS-QCI/APNO model chemistry was evaluated and is shown to provide very reliable predictions of barrier heights (rms error=1.0 kcal/mol)

Robust Adaptive Control Barrier Functions: An Adaptive & Data-Driven Approach to Safety (Extended Version)

A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new adaptive data-driven safety paradigm is merged with a recent adaptive control algorithm for systems nominally contracting in closed-loop. This unification is more general than other safety controllers as closed-loop contraction does not require the system be invertible or in a particular form. Additionally, the approach is less expensive than nonlinear model predictive control as it does not require a full desired trajectory, but rather only a desired terminal state. The approach is illustrated on the pitch dynamics of an aircraft with uncertain nonlinear aerodynamics.Comment: Added aCBF non-Lipschitz example and discussion on approach implementatio

Collapse Barriers and Halo Abundance: Testing the Excursion Set Ansatz

Our heuristic understanding of the abundance of dark matter halos centers around the concept of a density threshold, or "barrier", for gravitational collapse. If one adopts the ansatz that regions of the linearly evolved density field smoothed on mass scale M with an overdensity that exceeds the barrier will undergo gravitational collapse into halos of mass M, the corresponding abundance of such halos can be estimated simply as a fraction of the mass density satisfying the collapse criterion divided by the mass M. The key ingredient of this ansatz is therefore the functional form of the collapse barrier as a function of mass M or, equivalently, of the variance sigma^2(M). Several such barriers based on the spherical, Zel'dovich, and ellipsoidal collapse models have been extensively discussed. Using large scale cosmological simulations, we show that the relation between the linear overdensity and the mass variance for regions that collapse to form halos by the present epoch resembles expectations from dynamical models of ellipsoidal collapse. However, we also show that using such a collapse barrier with the excursion set ansatz predicts a halo mass function inconsistent with that measured directly in cosmological simulations. This inconsistency demonstrates a failure of the excursion set ansatz as a physical model for halo collapse. We discuss implications of our results for understanding the collapse epoch for halos as a function of mass, and avenues for improving consistency between analytical models for the collapse epoch and the results of cosmological simulations.Comment: Version accepted by ApJ, scheduled for May 2009, v696. High-res version available at http://kicp.uchicago.edu/~brant/astro-ph/excursion_set_ansatz/robertson_excursion_set_ansatz.pd

Effects of correlation between merging steps on the global halo formation

The excursion set theory of halo formation is modified by adopting the fractional Brownian motion, to account for possible correlation between merging steps. We worked out analytically the conditional mass function, halo merging rate and formation time distribution in the spherical collapse model. We also developed an approximation for the ellipsoidal collapse model and applied it to the calculation of the conditional mass function and the halo formation time distribution. For models in which the steps are positively correlated, the halo merger rate is enhanced when the accreted mass is less than $\sim 25M^*$, while for the negatively correlated case this rate is reduced. Compared with the standard model in which the steps are uncorrelated, the models with positively correlated steps produce more aged population in small mass halos and more younger population in large mass halos, while for the models with negatively correlated steps the opposite is true. An examination of simulation results shows that a weakly positive correlation between successive merging steps appears to fit best. We have also found a systematic effect in the measured mass function due to the finite volume of simulations. In future work, this will be included in the halo model to accurately predict the three point correlation function estimated from simulations.Comment: 8 pages, submitted to MNRA

Quantum Tunneling in the Wigner Representation

Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various initial state preparations and local potential barriers. It is manifestly causal and includes time-lag effects and quantum spreading. Specific features of quantum dynamics which disappear in the standard semi-classical approximation are revealed. The propagator may be applied to calculation of the final momentum and coordinate distributions, for particles transmitted through or reflected from the potential barrier, as well as for elucidating the tunneling time problem.Comment: 18 pages, LATEX, no figure

Precision measurement of the local bias of dark matter halos

We present accurate measurements of the linear, quadratic, and cubic local bias of dark matter halos, using curved "separate universe" N-body simulations which effectively incorporate an infinite-wavelength overdensity. This can be seen as an exact implementation of the peak-background split argument. We compare the results with the linear and quadratic bias measured from the halo-matter power spectrum and bispectrum, and find good agreement. On the other hand, the standard peak-background split applied to the Sheth & Tormen (1999) and Tinker et al. (2008) halo mass functions matches the measured linear bias parameter only at the level of 10%. The prediction from the excursion set-peaks approach performs much better, which can be attributed to the stochastic moving barrier employed in the excursion set-peaks prediction. We also provide convenient fitting formulas for the nonlinear bias parameters $b_2(b_1)$ and $b_3(b_1)$, which work well over a range of redshifts.Comment: 23 pages, 8 figures; v2 : added references (sec. 1, 4, 5), results at higher redshifts on fig. 4 and updated fitting formulas (eqs 5.2-5.3), v3 : clarifications throughout, version accepted by JCA