FLiMS: a fast lightweight 2-way merger for sorting

In this paper, we present FLiMS, a highly-efficient and simple parallel algorithm for merging two sorted lists residing in banked and/or wide memory. On FPGAs, its implementation uses fewer hardware resources than the state-of-the-art alternatives, due to the reduced number of comparators and elimination of redundant logic found on prior attempts. In combination with the distributed nature of the selector stage, a higher performance is achieved for the same amount of parallelism or higher. This is useful in many applications such as in parallel merge trees to achieve high-throughput sorting, where the resource utilisation of the merger is critical for building larger trees and internalising the workload for faster computation. Also presented are efficient variations of FLiMS for optimizing throughput for skewed datasets, achieving stable sorting or using fewer dequeue signals. FLiMS is also shown to perform well as conventional software on modern CPUs supporting single-instruction multiple-data (SIMD) instructions, surpassing the performance of some standard libraries for sorting

Detecting chaos in particle accelerators through the frequency map analysis method

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.Comment: Submitted for publication in Chaos, Focus Issue: Chaos Detection Methods and Predictabilit

Experimental survey of FPGA-based monolithic switches and a novel queue balancer

This paper studies small to medium-sized monolithic switches for FPGA implementation and presents a novel switch design that achieves high algorithmic performance and FPGA implementation efficiency. Crossbar switches based on virtual output queues (VOQs) and variations have been rather popular for implementing switches on FPGAs, with applications in network switches, memory interconnects, network-on-chip (NoC) routers etc. The implementation efficiency of crossbar-based switches is well-documented on ASICs, though we show that their disadvantages can outweigh their advantages on FPGAs. One of the most important challenges in such input-queued switches is the requirement for iterative scheduling algorithms. In contrast to ASICs, this is more harmful on FPGAs, as the reduced operating frequency and narrower packets cannot “hide” multiple iterations of scheduling that are required to achieve a modest scheduling performance.Our proposed design uses an output-queued switch internally for simplifying scheduling, and a queue balancing technique to avoid queue fragmentation and reduce the need for memory-sharing VOQs. Its implementation approaches the scheduling performance of a state-of-the-art FPGA-based switch, while requiring considerably fewer resources

Efficient queue-balancing switch for FPGAs

This paper presents a novel FPGA-based switch design that achieves high algorithmic performance and an efficient FPGA implementation. Crossbar switches based on virtual output queues (VOQs) and variations have been rather popular for implementing switches on FPGAs, with applications to network-on-chip (NoC) routers and network switches. The efficiency of VOQs is well-documented on ASICs, though we show that their disadvantages can outweigh their advantages on FPGAs. Our proposed design uses an output-queued switch internally for simplifying scheduling, and a queue balancing technique to avoid queue fragmentation and reduce the need for memory-sharing VOQs. Our implementation approaches the scheduling performance of the state-of-the-art, while requiring considerably fewer FPGA resources

Probing a regular orbit with spectral dynamics

We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis code of Carpintero & Aguilar to determine the nature of an orbit (irregular, regular, resonant, periodic) from a short-time numerical integration. If the orbit is regular, we approximate it by a truncated Fourier time series of a few tens of terms per coordinate. Switching to a description in action-angle variables, this corresponds to a reconstruction of the underlying invariant torus. We then relate the uniform distribution of a regular orbit on its torus to the non-uniform distribution in the space of observables by a simple Jacobian transformation between the two sets of coordinates. This allows us to compute, in a cell-independent way, all the physical quantities needed in the study of the orbit, including the density and in the line-of-sight velocity distribution, with much increased accuracy. The resulting flexibility in the determination of the orbital properties, and the drastic reduction of storage space for the orbit library, provide a significant improvement in the practical application of Schwarzschild's orbit superposition method for constructing galaxy models. We test and apply our method to two-dimensional orbits in elongated discs, and to the meridional motion in axisymmetric potentials, and show that for a given accuracy, the spectral dynamics formalism requires an order of magnitude fewer computations than the more traditional approaches.Comment: 13 pages, 18 eps figures, submitted to MNRA

Measurements of coherent tune shifts and head-tail growth rates at the CERN SPS

As part of an ongoing effort to monitor SPS impedance changes with regard to LHC, the coherent tune shifts and head-tail growth rates in the SPS were measured for single proton bunches at 26 GeV. From these measurements the real and imaginary components of the transverse broadband impedance can be estimated

A unified framework for the orbital structure of bars and triaxial ellipsoids

We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these bars are classified both visually and with a new automated orbit classification method based on frequency analysis. The well-known prograde x1 orbit family originates from the same parent orbit as the box orbits in stationary and rotating triaxial ellipsoids. However, only a small fraction of bar orbits (~4%) have predominately prograde motion like their periodic parent orbit. Most bar orbits arising from the x1 orbit have little net angular momentum in the bar frame, making them equivalent to box orbits in rotating triaxial potentials. In these simulations a small fraction of bar orbits (~7%) are long-axis tubes that behave exactly like those in triaxial ellipsoids: they are tipped about the intermediate axis owing to the Coriolis force, with the sense of tipping determined by the sign of their angular momentum about the long axis. No orbits parented by prograde periodic x2 orbits are found in the pure bar model, but a tiny population (~2%) of short-axis tube orbits parented by retrograde x4 orbits are found. When a central point mass representing a supermassive black hole (SMBH) is grown adiabatically at the center of the bar, those orbits that lie in the immediate vicinity of the SMBH are transformed into precessing Keplerian orbits that belong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH, the inflow of mass and outward transport of angular momentum transform some x1 and long-axis tube orbits into prograde short-axis tubes. This study has important implications for future attempts to constrain the masses of SMBHs in barred galaxies using orbit-based methods like the Schwarzschild orbit superposition scheme and for understanding the observed features in barred galaxies

Global Dynamics in Galactic Triaxial Systems I

In this paper we present a theoretical analysis of the global dynamics in a triaxial galactic system using a 3D integrable Hamiltonian as a simple representation. We include a thorough discussion on the effect of adding a generic non--integrable perturbation to the global dynamics of the system. We adopt the triaxial Stackel Hamiltonian as the integrable model and compute its resonance structure in order to understand its global dynamics when a perturbation is introduced. Also do we take profit of this example in order to provide a theoretical discussion about diffussive processes taking place in phase space.Comment: Accepted A&

Orbital Instabilities in a Triaxial Cusp Potential

This paper constructs an analytic form for a triaxial potential that describes the dynamics of a wide variety of astrophysical systems, including the inner portions of dark matter halos, the central regions of galactic bulges, and young embedded star clusters. Specifically, this potential results from a density profile of the form $\rho (m) \propto m^{-1}$, where the radial coordinate is generalized to triaxial form so that $m^2 = x^2/a^2 + y^2/b^2 + z^2/c^2$. Using the resulting analytic form of the potential, and the corresponding force laws, we construct orbit solutions and show that a robust orbit instability exists in these systems. For orbits initially confined to any of the three principal planes, the motion in the perpendicular direction can be unstable. We discuss the range of parameter space for which these orbits are unstable, find the growth rates and saturation levels of the instability, and develop a set of analytic model equations that elucidate the essential physics of the instability mechanism. This orbit instability has a large number of astrophysical implications and applications, including understanding the formation of dark matter halos, the structure of galactic bulges, the survival of tidal streams, and the early evolution of embedded star clusters.Comment: 50 pages, accepted for publication in Ap