A survey of low-velocity collisional features in Saturn's F ring

Small (~50km scale), irregular features seen in Cassini images to be emanating from Saturn's F ring have been termed mini-jets by Attree et al. (2012). One particular mini-jet was tracked over half an orbital period, revealing its evolution with time and suggesting a collision with a local moonlet as its origin. In addition to these data we present here a much more detailed analysis of the full catalogue of over 800 F ring mini-jets, examining their distribution, morphology and lifetimes in order to place constraints on the underlying moonlet population. We find mini-jets randomly located in longitude around the ring, with little correlation to the moon Prometheus, and randomly distributed in time, over the full Cassini tour to date. They have a tendency to cluster together, forming complicated `multiple' structures, and have typical lifetimes of ~1d. Repeated observations of some features show significant evolution, including the creation of new mini-jets, implying repeated collisions by the same object. This suggests a population of <~1km radius objects with some internal strength and orbits spread over 100km in semi-major axis relative to the F ring but with the majority within 20km. These objects likely formed in the ring under, and were subsequently scattered onto differing orbits by, the perturbing action of Prometheus. This reinforces the idea of the F ring as a region with a complex balance between collisions, disruption and accretion.Comment: 21 pages, 12 figures. Accepted for publication in Icarus. Supplementary information available at http://www.maths.qmul.ac.uk/~attree/mini-jets

Few cycle pulse propagation

We present a comprehensive framework for treating the nonlinear interaction of few-cycle pulses using an envelope description that goes beyond the traditional SVEA method. This is applied to a range of simulations that demonstrate how the effect of a $\chi^{(2)}$ nonlinearity differs between the many-cycle and few-cycle cases. Our approach, which includes diffraction, dispersion, multiple fields, and a wide range of nonlinearities, builds upon the work of Brabec and Krausz[1] and Porras[2]. No approximations are made until the final stage when a particular problem is considered. The original version (v1) of this arXiv paper is close to the published Phys.Rev.A. version, and much smaller in size.Comment: 9 pages, 14 figure

Reversible boolean networks II: Phase transition, oscillation, and local structures

We continue our consideration of a class of models describing the reversible dynamics of $N$ Boolean variables, each with $K$ inputs. We investigate in detail the behavior of the Hamming distance as well as of the distribution of orbit lengths as $N$ and $K$ are varied. We present numerical evidence for a phase transition in the behavior of the Hamming distance at a critical value $K_c\approx 1.65$ and also an analytic theory that yields the exact bounds on $1.5 \le K_c \le 2.$ We also discuss the large oscillations that we observe in the Hamming distance for $K<K_c$ as a function of time as well as in the distribution of cycle lengths as a function of cycle length for moderate $K$ both greater than and less than $K_c$. We propose that local structures, or subsets of spins whose dynamics are not fully coupled to the other spins in the system, play a crucial role in generating these oscillations. The simplest of these structures are linear chains, called linkages, and rings, called circuits. We discuss the properties of the linkages in some detail, and sketch the properties of circuits. We argue that the observed oscillation phenomena can be largely understood in terms of these local structures.Comment: 31 pages, 15 figures, 2 table

Tracking the Orbital and Super-orbital Periods of SMC X-1

The High Mass X-ray Binary (HMXB) SMC X-1 demonstrates an orbital variation of 3.89 days and a super-orbital variation with an average length of 55 days. As we show here, however, the length of the super-orbital cycle varies by almost a factor of two, even across adjacent cycles. To study both the orbital and super-orbital variation we utilize lightcurves from the Rossi X-ray Timing Explorer All Sky Monitor (RXTE-ASM). We employ the orbital ephemeris from Wojdowski et al. (1998) to obtain the average orbital profile, and we show that this profile exhibits complex modulation during non-eclipse phases. Additionally, a very interesting ``bounceback'' in X-ray count rate is seen during mid-orbital eclipse phases, with a softening of the emission during these periods. This bounceback has not been previously identified in pointed observations. We then define a super-orbital ephemeris (the phase of the super-orbital cycle as a function of date) based on the ASM lightcurve and analyze the trend and distribution of super-orbital cycle lengths. SMC X-1 exhibits a bimodal distribution of these lengths, similar to what has been observed in other systems (e.g., Her X-1), but with more dramatic changes in cycle length. There is some hint, but not conclusive evidence, for a dependence of the super-orbital cycle length upon the underlying orbital period, as has been observed previously for Her X-1 and Cyg X-2. Using our super-orbital ephemeris we are also able to create an average super-orbital profile over the 71 observed cycles, for which we witness overall hardening of the spectrum during low count rate times. We combine the orbital and super-orbital ephemerides to study the correlation between the orbital and super-orbital variations in the system.Comment: 10 pages, using emulateapj style. To be published in the Astrophysical Journa

Limits on the Network Sensitivity Function for Multi-Agent Systems on a Graph

This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems