Self-gravity in curved mesh elements

The local character of self-gravity along with the number of spatial dimensions are critical issues when computing the potential and forces inside massive systems like stars and disks. This appears from the discretisation scale where each cell of the numerical grid is a self-interacting body in itself. There is apparently no closed-form expression yet giving the potential of a three-dimensional homogeneous cylindrical or spherical cell, in contrast with the Cartesian case. By using Green’s theorem, we show that the potential integral for such polar-type 3D sectors—initially, a volume integral with singular kernel—can be converted into a regular line-integral running over the lateral contour, thereby generalising a formula already known under axial symmetry. It therefore is a step towards the obtention of another potential/density pair. The new kernel is a finite function of the cell’s shape (with the simplest form in cylindrical geometry), and mixes incomplete elliptic integrals, inverse trigonometric and hyperbolic functions. The contour integral is easy to compute; it is valid in the whole physical space, exterior and interior to the sector itself and works in fact for a wide variety of shapes of astrophysical interest (e.g. sectors of tori or flared discs). This result is suited to easily providing reference solutions, and to reconstructing potential and forces in inhomogeneous systems by superposition. The contour integrals for the 3 components of the acceleration vector are explicitely given.     

The transportation sector and low-carbon growth pathways: modelling urban,infrastructure, and spatial determinants of mobility

This article contributes to the controversial debate over the effect of spatial organization on CO₂ emissions by investigating the potential of infrastructure measures that favour lower mobility in achieving the transition to a low-carbon economy. The energy–economy–environment (E3) IMACLIM-R model is used to provide a detailed representation of passenger and freight transportation. Unlike many of the E3 models used to simulate mitigation options, IMACLIM-R represents both the technological and behavioural determinants of mobility. By comparing business-as-usual, carbon price only, and carbon price combined with transport policy scenarios, it is demonstrated that the measures that foster a modal shift towards low-carbon modes and a decoupling of mobility needs from economic activity significantly modify the sectoral distribution of mitigation efforts and reduce the level of carbon tax necessary to reach a given climate target relative to a ‘carbon price only’ policy.

Policy relevance

Curbing carbon emissions from transport activities is necessary in order to reach mitigation targets, but it poses a challenge for policy makers. The transport sector has two peculiarities: a weak ability to react to standard pricing measures (which encourages richer policy interventions) and a dependence on long-lived infrastructure (which imposes a delay between policy interventions and effective action). To address these problems, a framework is proposed for analysing the role of transport-specific measures adopted complementarily to carbon pricing in the context of international climate policies. Consideration is given to alternative approaches such as infrastructure measures designed to control mobility through less mobility-intensive denser agglomerations, investment reorientation towards public mode, and logistics reorganization towards less mobility-dependent production processes. Such measures can significantly reduce transport emissions in the long term and hence would moderate an increase in the carbon price and reduce its more important detrimental impacts on the economy.     

Analysis of the effect of trees on block propagation using a DEM model: implications for rockfall modelling

The objective of this research was to use numerical models based on mechanical approaches to improve the integration of the protective role of forests against rockfall into block propagation models. A model based on the discrete element method (DEM) was developed to take into account the complex mechanical processes involved during the impact of a block on a tree. This modelling approach requires the definition of many input parameters and cannot be directly integrated into block propagation models. A global sensitivity analysis identified the leading parameters of the block kinematics after impact (i.e. block energy reduction, trajectory changes, and rotational velocity): the impact velocity, the tree diameter, and the impact point horizontal location (i.e. eccentricity). Comparisons with the previous experimental and numerical studies of block impacts on trees demonstrated the applicability of the DEM model and showed some of the limitations of earlier approaches. Our sensitivity analysis highlights the significant influence of the impact velocity on the reduction of the block’s kinetic energy. Previous approaches usually also focus on parameters such as impact height, impact vertical incidence, and tree species, whose importance is only minor according to the present results. This suggests that the integration of forest effects into block propagation models could be both improved and simplified. The DEM model can also be used as an alternative to classical approaches for the integration of forest effects by directly coupling it with block propagation models. This direct coupling only requires the additional definition of the location and the diameter of each tree. Indeed, the input parameters related to the mechanical properties of the stem and the block/stem interaction in the DEM model can be set to average values because they are not leading parameters. The other input parameters are already defined or calculated in the block propagation model.