A theory of normed simulations

In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general purpose theorem provers. Moreover, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a lower-level specification can be simulated by at most one step in the higher-level one, for any related pair of states. In earlier work we demonstrated that normed simulations are quite useful as a vehicle for the formalization of refinement proofs via theorem provers. Here we show that normed simulations also have pleasant theoretical properties: (1) under some reasonable assumptions, it is decidable whether a given relation is a normed forward simulation, provided tautology checking is decidable for the underlying logic; (2) at the semantic level, normed forward and backward simulations together form a complete proof method for establishing behavior inclusion, provided that the higher-level specification has finite invisible nondeterminism.Comment: 31 pages, 10figure

Random walks - a sequential approach

In this paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its as- sociated sequential partial sum process under non-standard sampling. The asymptotic behavior differs substantially from the stationary situation, if there is a unit root (random walk component). To obtain meaningful asymptotic results we consider local nonpara- metric alternatives for the drift component. It turns out that the rate of convergence at which the drift vanishes determines whether the asymptotic properties of the monitoring procedure are determined by a deterministic or random function. Further, we provide a theoretical result about the optimal kernel for a given alternative

The fine-grained phase-space structure of Cold Dark Matter halos

We present a new and completely general technique for calculating the fine-grained phase-space structure of dark matter throughout the Galactic halo. Our goal is to understand this structure on the scales relevant for direct and indirect detection experiments. Our method is based on evaluating the geodesic deviation equation along the trajectories of individual DM particles. It requires no assumptions about the symmetry or stationarity of the halo formation process. In this paper we study general static potentials which exhibit more complex behaviour than the separable potentials studied previously. For ellipsoidal logarithmic potentials with a core, phase mixing is sensitive to the resonance structure, as indicated by the number of independent orbital frequencies. Regions of chaotic mixing can be identified by the very rapid decrease in the real space density of the associated dark matter streams. We also study the evolution of stream density in ellipsoidal NFW halos with radially varying isopotential shape, showing that if such a model is applied to the Galactic halo, at least $10^5$ streams are expected near the Sun. The most novel aspect of our approach is that general non-static systems can be studied through implementation in a cosmological N-body code. Such an implementation allows a robust and accurate evaluation of the enhancements in annihilation radiation due to fine-scale structure such as caustics. We embed the scheme in the current state-of-the-art code GADGET-3 and present tests which demonstrate that N-body discreteness effects can be kept under control in realistic configurations.Comment: 20 pages, 24 figures, submitted to MNRA

On Norm-Based Estimations for Domains of Attraction in Nonlinear Time-Delay Systems

For nonlinear time-delay systems, domains of attraction are rarely studied despite their importance for technological applications. The present paper provides methodological hints for the determination of an upper bound on the radius of attraction by numerical means. Thereby, the respective Banach space for initial functions has to be selected and primary initial functions have to be chosen. The latter are used in time-forward simulations to determine a first upper bound on the radius of attraction. Thereafter, this upper bound is refined by secondary initial functions, which result a posteriori from the preceding simulations. Additionally, a bifurcation analysis should be undertaken. This analysis results in a possible improvement of the previous estimation. An example of a time-delayed swing equation demonstrates the various aspects.Comment: 33 pages, 8 figures, "This is a pre-print of an article published in 'Nonlinear Dynamics'. The final authenticated version is available online at https://doi.org/10.1007/s11071-020-05620-8

Semi-classical approach to J/ψJ/\psi suppression in high energy heavy-ion collisions

We study the heavy quark/antiquark pair dynamics in strongly-coupled quark gluon plasma. A semi-classical approach, based on the Wigner distribution and Langevin dynamics, is applied to a color screened $c{\bar c}$ pair, in a hydrodynamically cooling fireball, to evaluate the total $J/\psi$ suppression at both RHIC and LHC energies. Although its limitation is observed, this approach results to a $J/\psi$ suppression of around 0.30 at RHIC and 0.25 at LHC.Comment: 4 pages, 6 figures, Proceeding for International Conference on Strangeness in Quark Matter 2013 (SQM 2013) at Birmingha