Actions for axisymmetric potentials

We give an algorithm for the economical calculation of angles and actions for stars in axisymmetric potentials. We test the algorithm by integrating orbits in a realistic model of the Galactic potential, and find that, even for orbits characteristic of thick-disc stars, the errors in the actions are typically smaller than 2 percent. We describe a scheme for obtaining actions by interpolation on tabulated values that significantly accelerates the process of calculating observables quantities, such as density and velocity moments, from a distribution function.Comment: 5 pages accepted for publication in MNRA

Numerical Study of Competing Spin-Glass and Ferromagnetic Order

Two and three dimensional random Ising models with a Gaussian distribution of couplings with variance $J$ and non-vanishing mean value $J_0$ are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the ($J_0,J$) plane after rescaling can be collapsed on two curves: one for $J_0/J > r_c$ and other for $J_0/J < r_c$. In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions respectively. No evidence for an extra phase is found.Comment: a bit more data is taken, 5 pages, 4 eps figures included, to appear in PR

Automatic Abstraction in SMT-Based Unbounded Software Model Checking

Software model checkers based on under-approximations and SMT solvers are very successful at verifying safety (i.e. reachability) properties. They combine two key ideas -- (a) "concreteness": a counterexample in an under-approximation is a counterexample in the original program as well, and (b) "generalization": a proof of safety of an under-approximation, produced by an SMT solver, are generalizable to proofs of safety of the original program. In this paper, we present a combination of "automatic abstraction" with the under-approximation-driven framework. We explore two iterative approaches for obtaining and refining abstractions -- "proof based" and "counterexample based" -- and show how they can be combined into a unified algorithm. To the best of our knowledge, this is the first application of Proof-Based Abstraction, primarily used to verify hardware, to Software Verification. We have implemented a prototype of the framework using Z3, and evaluate it on many benchmarks from the Software Verification Competition. We show experimentally that our combination is quite effective on hard instances.Comment: Extended version of a paper in the proceedings of CAV 201

The Astrophysical Multipurpose Software Environment

We present the open source Astrophysical Multi-purpose Software Environment (AMUSE, www.amusecode.org), a component library for performing astrophysical simulations involving different physical domains and scales. It couples existing codes within a Python framework based on a communication layer using MPI. The interfaces are standardized for each domain and their implementation based on MPI guarantees that the whole framework is well-suited for distributed computation. It includes facilities for unit handling and data storage. Currently it includes codes for gravitational dynamics, stellar evolution, hydrodynamics and radiative transfer. Within each domain the interfaces to the codes are as similar as possible. We describe the design and implementation of AMUSE, as well as the main components and community codes currently supported and we discuss the code interactions facilitated by the framework. Additionally, we demonstrate how AMUSE can be used to resolve complex astrophysical problems by presenting example applications.Comment: 23 pages, 25 figures, accepted for A&

Einselection and Decoherence from an Information Theory Perspective

We introduce and investigate a simple model of conditional quantum dynamics. It allows for a discussion of the information-theoretic aspects of quantum measurements, decoherence, and environment-induced superselection (einselection).Comment: Proceedings of the Planck constant centenary meeting. Uses annalen.cls and fleqn.st

Short Range Ising Spin Glasses: a critical exponent study

The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension $d_{f}=2.58$, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff renormalization-group scheme. The order parameter critical exponent $\beta$ is directly estimated from the data of the local Edwards- Anderson (EA) order parameter, obtained through an exact recursion procedure. The scaling of the EA order parameter, leading to estimates of the $\nu$ exponent of the correlation length is also performed. Four distinct initial distributions of the quenched coupling constants (Gaussian, bimodal, uniform and exponential) are considered. Deviations from a universal behaviour are observed and analysed in the framework of the renormalized flow in a two dimensional appropriate parameter space.Comment: 9 pages, 01 figure (ps

A new approach to the study of the ground-state properties of 2D Ising spin glass

A new approach known as flat histogram method is used to study the +/-J Ising spin glass in two dimensions. Temperature dependence of the energy, the entropy, and other physical quantities can be easily calculated and we give the results for the zero-temperature limit. For the ground-state energy and entropy of an infinite system size, we estimate e0 = -1.4007 +/- 0.0085 and s0 = 0.0709 +/- 0.006, respectively. Both of them agree well with previous calculations. The time to find the ground-states as well as the tunneling times of the algorithm are also reported and compared with other methods.Comment: 11 pages, 4 figure

Simulating the universe on an intercontinental grid of supercomputers

Understanding the universe is hampered by the elusiveness of its most common constituent, cold dark matter. Almost impossible to observe, dark matter can be studied effectively by means of simulation and there is probably no other research field where simulation has led to so much progress in the last decade. Cosmological N-body simulations are an essential tool for evolving density perturbations in the nonlinear regime. Simulating the formation of large-scale structures in the universe, however, is still a challenge due to the enormous dynamic range in spatial and temporal coordinates, and due to the enormous computer resources required. The dynamic range is generally dealt with by the hybridization of numerical techniques. We deal with the computational requirements by connecting two supercomputers via an optical network and make them operate as a single machine. This is challenging, if only for the fact that the supercomputers of our choice are separated by half the planet, as one is located in Amsterdam and the other is in Tokyo. The co-scheduling of the two computers and the 'gridification' of the code enables us to achieve a 90% efficiency for this distributed intercontinental supercomputer.Comment: Accepted for publication in IEEE Compute

Generating Non-Linear Interpolants by Semidefinite Programming

Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work for discovering interpolants for propositional logic, quantifier-free fragments of first-order theories and their combinations have been proposed. However, little work focuses on discovering polynomial interpolants in the literature. In this paper, we provide an approach for constructing non-linear interpolants based on semidefinite programming, and show how to apply such results to the verification of programs by examples.Comment: 22 pages, 4 figure