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Remnants of 2.1–1.8 Ga orogens can be recognized in nearly every craton assembled within reconstructions of the Rodinia supercontinent, although no particular pattern of laterally extensive orogenic belts emerges. These cratons may be the fragments of an older supercontinent formed in response to the collision and accretion of even older cratons during the early Earth history. Paleomagnetic constraints have played a limited role in many previous reconstructions of the early Precambrian supercontinent mainly because of the poor age control and a large scatter of the paleomagnetic poles. The geometry of giant radiating dyke swarms and orogenic belts provide important constraints for the reconstruction of the Pre-Rodinian supercontinent. Some early unmetamorphosed and undeformed mafic dyke swarms in North China, Southern Peninsular India and North America share coeval age of ~ 1.85 Ga. If these continents are assembled, the overall pattern exhibited by the mafic dyke swarms appears to constitute a giant radiating swarm, with a piercing point between the Cuddapah rift in South India and the Xiong'er aulacogen in North China. This suggests that the North China Craton, Indian Craton and Canadian Shield may be fragmented from the same landmass. The reconstruction of ~ 1.85 Ga giant radiating dyke swarm attempted in this paper suggests that the North China Craton, India Craton and Canadian Shield were united together to form a landmass within the Columbia supercontinent before its extension and break-up. The 1.90–1.85 Ga Andean-style North Orogenic Belt suggests that a subduction zone existed on the northern margin of the North China Craton. Wopmay Orogenic Belt developed in a 1.88–1.84 Ga continental volcano-plutonic arc, which is interpreted as the product of eastward subduction of oceanic lithosphere. The Transantarctica Orogenic Belt in East Antarctica may be another candidate to be linked with the subduction zone. The North Orogenic, Wopmay Orogenic and Transantarctica Orogenic Belts could be connected to form a continuous subduction zone. The orogenic comparison strengthens the configuration of the Columbia supercontinent proposed by the reconstruction of the giant radiating dyke swarm. The Laurentia, West Australia and East Antarctica were relatively stable from 1.85 Ga to 1.20 Ga as inferred from the data on dyke swarms, magmatism and the paleomagnetism. These continents constituted the core of the Columbia supercontinent in the Late Paleoproterozoic time. The North China Craton and Indian Craton were however separated from the Columbia supercontinent during the Mesoproterozoic time.

The 1.3– 1.2 Ga fan- shaped Mackenzie dyke swarm and other similar- aged dyke swarms in the Canadian Shield constitute the subswarms of a Late Mesoproterozoic giant radiating swarm. The Late Mesoproterozoic mafic dyke swarms in Australia and East Antarctica might constitute additional subswarms of the giant radiating dyke swarm. A possible Late Mesoproterozoic mantle plume is placed at the focal area of the giant radiating dyke swarm between North America and the landmass (West Australia– East Antarctica). This mantle plume triggered the continuous extension at ca. 1.3–1.2 Ga, which extended into much of Columbia and led to the final fragmentation of the Columbia supercontinent.

Mafic dyke swarms and aulacogens are major anorogenic extensional events in the Late Paleoproterozoic North China Craton (NCC). The N–NNW mafic dyke swarms are widespread in the NCC, whose ages span between 1.83 and 1.77 Ga. The similar ages and orientations of ∼ 1.8 Ga dyke swarms in the NCC demonstrate that the amalgamated NCC experienced widespread extension at this time. Based on the width statistics of dyke swarms on ten survey lines, an average crustal extension ratio of 0.35% was found for the NCC. The small magnitude of overall extension suggests that the mafic dyke swarms were emplaced into the elastic fractures, and indicates that the NCC had become a brittle plate prior to the emplacement of the mafic dyke swarms. Precisely dated mafic dyke swarms, when used as paleostress indicators, can be employed in the paleostress field reconstruction of Precambrian cratons. Two dimensional finite element modeling (2-D FEM) of the NCC, in which the various blocks were assigned densities and elastic constants, shows that north–south compression favors dyke intrusion along generally N–NW lines, and that deviations in dyke trends can be explained by the effects of boundary constraints and the physical properties of the crust. The best fitting model can be considered a plausible representation of the tectonic force acting on the NCC that produces the intraplate stress field that is most consistent with the observed orientation of dyke swarms. The results of modeling of the Late Paleoproterozoic stress field suggest a common tectonic setting for the emplacement of mafic dyke swarms in the Central Orogenic Zone, Western and East Blocks of the NCC. The results also show that the north–south tectonic forces play an important role in determining the paleostress field in the NCC. The widespread extension of the NCC resulted from the north–south tectonic forces which may be related to the break-up of the Late Paleoproterozoic supercontinent. The paleostress field modeling provides a possible approach to consider the supercontinent paleostress reconstruction and to reveal the mechanisms of the supercontinent break-up.

The dominant rock types in the khondalite suite in the Archean to Early Proterozoic granulite belt of north-central China are sillimanite-garnet gneiss (SGG), quartz-garnet gneiss (QGG), and quartz-feldspar gneiss (QFG). Field and geochemical results from the China khondalites and khondalites from other locations (including those from the type locality in India) are not consistent with a paleosol protolith. Major and trace element distributions in the SGG and QGG suggest shale and feldspathic sandstone protoliths, respectively. REE distributions including negative Eu anomalies in both rock groups are remarkably similar to those in Phanerozoic shales. Element distributions in QFG, including highly fractionated REE patterns, are similar to Archean TTG and these rocks are interpreted to have felsic volcanic protoliths. Sediment protoliths of the SGG and QGG may have been derived from sources in which granite and a smaller amount of basalt dominated, but they cannot have had significant contribution from Archean TTG sources. The China khondalite protoliths appear to have been deposited in a cratonic basin along the northwest margin of the North China craton. Although the khondalites from China and elsewhere chiefly have sedimentary protoliths, different compositions and lithologic proportions between khondalite suites indicate variable sediment provenance, intensity of paleoweathering, and tectonic settings.

Modelling grease as a four-parameter non-Newtonian fluid and making use of a weighted residual method, a modified Reynolds equation is derived, in which a parameter characterizing the non-Newtonian effect is incorporated. A numerically complete solution is achieved by adopting Christensen and Prakash's rigid stamp model. An iteration scheme is employed until finally the non-Newtonian effect parameter calculated under average shear rate converges satisfactorily. By regressing numerical results, a central film thickness formula for grease lubrication is fitted. The agreement between theoretical and experimental results is good.