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Richard Burridge’s volume could not have come at a better time. In the aftermath of the COVID pandemic, his discourse is on the virtual church and the celebration of Holy Communion online. Some Christian churches have gladly embraced the concept of online meetings and still allow their members to attend services in this way. Other Christian churches do not support online Holy Communion. Instead, they support online church services only, without the Eucharist. Burridge’s book provides a raison d’etre for online forms of Christian worship.

The nature of the high-speed rupture or the main shock of the Burridge–Knopoff spring-block model in two dimensions obeying the rate- and state-dependent friction law is studied by means of extensive computer simulations. It is found that the rupture propagation in larger events is highly anisotropic and irregular in shape on longer length scales, although the model is completely uniform and the emergent rupture-propagation velocity is nearly constant everywhere at the rupture front. The manner of the rupture propagation sometimes mimics the successive ruptures of neighbouring ‘asperities’ observed in real, large earthquakes. Large events tend to be unilateral, with its epicentre lying at the rim of its rupture zone. The epicentre site of a large event is also located next to the rim of the rupture zone of some past event. Event-size distributions are computed and discussed in comparison with those of the corresponding one-dimensional model. The magnitude distribution exhibits a power-law behaviour resembling the Gutenberg–Richter law for smaller magnitudes, which changes over to a more characteristic behaviour for larger magnitudes. For very large events, the rupture-length distribution exhibits mutually different behaviours in one dimension and in two dimensions, reflecting the difference in the underlying geometry. This article is part of the theme issue ‘Statistical physics of fracture and earthquakes’.

Although over eighty percent of the country is Muslim, Indonesia is marked by an extraordinary diversity in language, ancestry, culture, religion and ways of life. This book focuses on the Christian Dani of West Papua, providing a social and ethnographic history of the most important indigenous population in the troubled province. It presents a fascinating overview of the Dani’s conversion to Christianity, examining the social, religious and political uses to which they have put their new religion. Based on independent research carried out over many years among the Dani people, the book provides an abundance of new material on religious and political events in West Papua. Underlining the heart of Christian-Muslim rivalries, the book questions the fate of religion in late-modern times.

This paper deals with the numerical approximation of a stick–slip system, known in the literature as Burridge–Knopoff model , proposed as a simplified description of the mechanisms generating earthquakes. Modelling of friction is crucial and we consider here the so-called velocity-weakening form. The aim of the article is twofold. Firstly, we establish the effectiveness of the classical Predictor–Corrector strategy . To our knowledge, such approach has never been applied to the model under investigation. In the first part, we determine the reliability of the proposed strategy by comparing the results with a collection of significant computational tests, starting from the simplest configuration to the more complicated (and more realistic) ones, with the numerical outputs obtained by different algorithms. Particular emphasis is laid on the Gutenberg–Richter statistical law, a classical empirical benchmark for seismic events. The second part is inspired by the result by Muratov (Phys Rev 59:3847–3857, 1999) providing evidence for the existence of traveling solutions for a corresponding continuum version of the Burridge–Knopoff model. In this direction, we aim to find some appropriate estimate for the crucial object describing the wave, namely its propagation speed . To this aim, motivated by LeVeque and Yee (J Comput Phys 86:187–210, 1990) (a paper dealing with the different topic of conservation laws), we apply a space-averaged quantity (which depends on time) for determining asymptotically an explicit numerical estimate for the velocity, which we decide to name LeVeque–Yee formula after the authors’ name of the original paper. As expected, for the Burridge–Knopoff, due to its inherent discontinuity of the process, it is not possible to attach to a single seismic event any specific propagation speed. More regularity is expected by performing some temporal averaging in the spirit of the Cesàro mean . In this direction, we observe the numerical evidence of the almost convergence of the wave speeds for the Burridge–Knopoff model of earthquakes.

Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conducted with the crack propagating along a weak interface. A parametric study is conducted with respect to varying impact speeds ranging from 5 m/s to 60 m/s and cohesive strengths from 4 to 35 MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999) Science 284:1337–1340]. The simulations are capable of handling crack growth with crack-tip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between \\[\\sqrt 2 c_{S}\\] (cS is the shear wave speed) and cD (cD is the dilatational wave speed) of the bulk material. The Burridge–Andrews mechanism for transition of the crack-tip velocity from sub-Rayleigh to intersonic speed of the bulk material is observed for impact speeds ranging from 9.5 to 60 m/s (for normal and shear cohesive strengths of 24 MPa). Within the intersonic regime, sustained crack-tip velocities between 1.66 cS (or 0.82 cD) and 1.94 cS (or 0.95 cD) were obtained. For the cases simulated in this work, within the stable intersonic regime, the lowest intersonic crack-tip velocity obtained was 1.66 cS (or 0.82 cD).

Burridge and Knopoff proposed a mass-spring model to explore interface dynamics along a fault during an earthquake. The Burridge and Knopoff (BK) model is composed of a series of blocks of equal mass connected to each other by springs of same stiffness. The blocks also are attached to a rigid driver via another set of springs that pulls them at a constant velocity against a rigid substrate. They studied dynamics of interface for an especial case with ten blocks and a specific set of fault properties. In our study effects of Coulomb and rate-state dependent friction laws on the dynamics of a single block BK model is investigated. The model dynamics is formulated as a system of coupled nonlinear ordinary differential equations in state-space form which lends itself to numerical integration methods, e.g. Runge-Kutta procedure for solution. The results show that the rate and state dependent friction law has the potential of triggering dynamic patterns that are different from those under Coulomb law.

We generate conservation laws for the Burridge–Knopoff equation which model nonlinear dynamics of earthquake faults by a new conservation theorem proposed recently by Ibragimov. One can employ this new general theorem for every differential equation (or systems) and derive new local and nonlocal conservation laws. Nonlocal conservation laws comprise nonlocal variables defined by the adjoint equations to the Burridge–Knopoff equation.

[...]once upon a time\" tells us to expect a fairy tale and \"here is the news\" to expect a report on the day's significant activities, the \"sui generis\" approach to the gospels invited the expectation that we would learn about the early Church, not the life of a historical figure. Unlike most writers on New Testament ethics, who focus on the teaching, such as the Sermon on the Mount, Burridge gives extended attention to the ethic derived from the narrative of the deeds of Jesus.

I am pleased to have the opportunity to participate in this debate on a book that I have watched in the making, from a distance, over the past ten years or more. Richard Burridge was a faithful participant in the New Testament Ethics Seminar at the Studiorum Novi Testamenti Societas, a seminar that I had the privilege of co-chairing, along with Wolfgang Schrage and Andreas Lindemann. During the years of that working group Richard presented early drafts of material that adumbrated the basic themes of Imitating Jesus . Consequently, he and I have been discussing our common interests in these matters for quite a while. Anyone who reads Richard's substantial new work alongside my earlier book, The Moral Vision of the New Testament , will see that we don't always agree, but there are actually a fair number of commonalities – perhaps more commonalities than would be conveyed by a casual survey of Richard's explicit references to my work.

\"So in south-east Australia we found quite a lot of movement, you can go from Sydney to southern Tasmania to Phillip Island and the penguin colonies are all genetically indistinguishable,\" she said. \"But then around the area of Kangaroo Island you can move only 30 kilometres between two different colonies and they'll be genetically different.\" \"It could be just because that's where the penguins have happened to meet, as they've expanded back out from the east and the west,\" she said.