Variational Integrators for the Gravitational N-Body Problem

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive block power of two timesteps does not increase the error in symplecticity. In contrast to other high-order, symplectic, individual timestep, momentum-preserving algorithms, the algorithm takes only forward timesteps. We compare a code integrating an N-body system using the algorithm with a direct-summation force calculation to standard stellar cluster simulation codes. We find that our algorithm has about 1.5 orders of magnitude better symplecticity and momentum conservation errors than standard algorithms for equivalent numbers of force evaluations and equivalent energy conservation errors.Comment: 31 pages, 8 figures. v2: Revised individual-timestepping description, expanded comparison with other methods, corrected error in predictor equation. ApJ, in pres

Variational Integrators for Almost-Integrable Systems

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These integrators exploit that epsilon << 1 to increase their accuracy by constructing discrete Lagrangians based on the assumption that the integrator trajectory is close to that of the integrable system. Several of the integrators we present are equivalent to well-known symplectic integrators for the equivalent perturbed Hamiltonian systems, but their construction and error analysis is significantly simpler in the variational framework. One novel method we present, involving a weighted time-averaging of the perturbing terms, removes all errors from the integration at O(epsilon). This last method is implicit, and involves evaluating a potentially expensive time-integral, but for some systems and some error tolerances it can significantly outperform traditional simulation methods.Comment: 14 pages, 4 figures. Version 2: added informative example; as accepted by Celestial Mechanics and Dynamical Astronom

Evolutionary Channels for the Formation of Double Neutron Stars

We analyze binary population models of double-neutron stars and compare results to the accurately measured orbital periods and eccentricities of the eight known such systems in our Galaxy. In contrast to past similar studies, we especially focus on the dominant evolutionary channels (we identify three); for the first time, we use a detailed understanding of the evolutionary history of three double neutron stars as actual constraints on the population models. We find that the evolutionary constraints derived from the double pulsar are particularly tight, and less than half of the examined models survive the full set of constraints. The top-likelihood surviving models yield constraints on the key binary evolution parameters, but most interestingly reveal (i) the need for electron-capture supernovae from relatively low-mass degenerate, progenitor cores, and (ii) the most likely evolutionary paths for the rest of the known double neutron stars. In particular, we find that J1913+16 likely went through a phase of Case BB mass transfer, and J1906+0746 and J1756-2251 are consistent with having been formed in electron-capture supernovae.Comment: 17 pages, 9 figure

European Youth Cybercrime, Online Harm and Online Risk Taking: 2022 Research Report

Researching cybercriminality to design new methods to prevent, investigate and mitigate cybercriminal behaviour. This is one of the largest studies to date exploring youth cybercriminality. The survey is informed by 5 key disciplines: cyberpsychology, criminology, psychology, neuroscience, and digital anthropology Results confirm that cybercrime and cyberdeviance is prevalent-survey finds that two thirds (69%) of European youth self-report to have committed at least one form of cybercrime or online harm or risk taking, and just under half 47.76% (N=3808) report to have engaged in criminal behaviour online, from summer of 2020 to the summer of 2021 Survey finds that males are more likely (74%) than females (65%) to self-report having been involved in at least one form of cybercrime or online harm or risk taking in the last year and results confirm that the majority of cybercrime and cyberdeviant behaviours are gendered. Survey analysis demonstrates that cybercriminal and online harm or risk taking behaviours form a cluster of 11 behaviours that are highly interrelated (CcCd-Cluster) and that cybercrime and online harm or risk taking behaviours represent a spectrum (CcCd-Spectrum) A significant shift from a siloed, categorical approach is needed in terms of how cybercrimes are conceptualised, investigated, and legislated

CC-DRIVER Policy Brief No. 8: European Youth Survey

This policy brief contains key findings from the CC-DRIVER 2021 European Youth Survey and corresponding conclusions. This brief is designed for all professionals working within the area of cybercrime and key stakeholders, including LEAs, Academics, Criminal Justice, Policy Makers, and Educators. The lack of clarity surrounding the term cybercrime has significant impact on society, cybercrime policy, legal intervention, and academic research. No single classification system fully encapsulated cybercrime concepts or accurately reflected the nebulous nature of cybercrime acts. There is remaining ambiguity as to what exactly constitutes a cybercrime, and it is likely that a clear conceptualisation of cybercrime will continue to be challenged. This review presents key cybercrime definitions, categorisations of cybercrime and typologies of cybercrime. This review presents a new framework with which to conceptualise cybercrime

Variances: A Canary in the Coal Mine for Zoning Reform?

There is perhaps no area of land use law where practice departs more from legal doctrine than the realm of zoning variances. According to the legal doctrine, variances are to be granted sparingly, providing a “safety valve” that alleviates unique hardships encountered by a property owner. In practice, variances are granted at high rates—often around ninety percent of applications are approved—and, in some jurisdictions, in high volumes. In such cases, variances effectively serve as a rezoning, enabling jurisdictions to permit otherwise prohibited uses and allow growth and development to occur without addressing needed zoning reforms. By allowing neighbors the opportunity to weigh in on the smallest of changes, with little attention to the relevant legal doctrine, they also create significant uncertainty, delay, and cost for property owners. This problem is particularly acute in the City of Boston, where the city grants thousands of variances each year. In this symposium contribution, we share the results of an empirical study of variance decisions in Boston. We compare Boston to three neighboring jurisdictions: Cambridge, Brookline, and Somerville. We find that variances in Boston are, consistent with prior studies elsewhere, granted at a very high rate. Looking at the substance of these decisions, we find that little attention is given to the legal requirements for a variance. Instead, decisions are shaped by a desire to help individual applicants, a willingness to permit development consistent with the neighborhood, and the policy preferences of board members. This study suggests a number of lessons for reformers. Variance decisions shed light on particularly onerous elements of local zoning, revealing targets for reform. The process itself highlights how local residents understand zoning and their expectations regarding their own role in land use decision-making. In jurisdictions that rely heavily on variances to permit new development, reformers will need to grapple with how they might substitute the voice residents currently exercise through the variance process