This chapter also elucidates the issue of particle-particle contact in a multiphase system. The focus is, however, different than in the previous chapters. Those chapters considered the modelling of collision processes where the objective was to explore the collision dynamics (e.g., deformation and velocity). In this chapter, however, we study heat conduction between particles. This indicates that the particles have different temperatures as they collide. First, we examine a mathematical model for heat conduction if the collision is elastic. Later, it is shown how the same strategy can be used if there is a permanent (plastic) deformation during a collision. Finally, consider dissipative forces.

This chapter explains the hard-sphere model of particle-particle collision. This model exploits impulse equations that directly relate the pre-collisional and post-collisional velocities of the particles. Thus, this model does not track the deformation history that was done in the prior chapters. As a result, we obtain ready analytical solutions so that the computational time is short. First, the chapter shows a standard hard-sphere model for a “mechanical” collision of two bodies. Different strategies are presented, such as the so-called two- and three-parameter hard-sphere model. Later, an extension of these models is shown that also accounts for adhesive interactions. Although, due to its simplicity, the hard-sphere model may not account for various physical phenomena between colliding particles, it may still be used in many applications. In this chapter, the reader is again provided with a computer code.

The rapid development of mega-constellations raises difficult issues of international law, including liability for collisions involving satellites. Establishing ‘causation’ – that the actions of one satellite operator caused a specific collision with another space object and resulted in damage – could be a challenge, especially in the context of knock-on collisions where debris from an initial collision later collides with one or more spacecraft, including satellites. A further challenge is determining, in the absence of binding international rules on the design and operation of satellites, what is ‘reasonable’ behaviour and therefore what constitutes ‘negligence’. This chapter also addresses the interference to astronomy that is increasingly resulting from light and radio spectrum pollution from satellites. A full interpretation of the Outer Space Treaty leads to the conclusion that states are already required to take certain steps, including conducting an environmental impact assessment, before licensing mega-constellations, because of the obligation of ‘due regard to the corresponding interests of all other States Parties to the Treaty’.

Relativistic collision kinematics is examined. Relativistic and non-relativistic collisional processes in plasmas are treated in detail.

The Dawn orbiter mission has revealed the mineralogical and chemical composition of Vesta’s surface materials and constraints on its interior structure. The surface is composed of breccias of basalt and ultramafic rocks, contaminated by exogenic carbonaceous chondrite.At the center of the asteroid is a metallic core about half the diameter of the body, and gravity data provide information on the thicknesses and densities of the mantle and crust.Huge, overlapping impact basins expose rocks of the lower crust and mantle. Howardite–eucrite–diogenite (HED) meteorites are samples of Vesta, mostly excavated by the giant impacts and delivered to Earth via an orbital resonance with Jupiter.Petrologic and geochemical studies of HEDs constrain interpretations of Dawn’s spectral and geochemical data, and offer otherwise unobtainable insights into the asteroid’s origin, bulk composition, global differentiation, impact history, and geochronology.Major unresolved questions include whether Vesta had an early magma ocean, as well as the source of “missing” olivine in mantle rocks, and a possible role for fluids. As the sole surviving rocky protoplanet, Vesta provides a unique perspective on the nebular raw materials that accreted to form the terrestrial planets.

Having described motion, we can now explain it. We introduce the conserved 4-momentum, and with it the ideas of energy-momentum, conserved mass, and scattering.

In Chapter 7, A Survey of Chosen-Prefix Collision Attacks, Marc Stevens surveys the technical advances, impact and usage of collision attacks for the most widely used cryptographic hash functions. Cryptographic hash function are the Swiss army knives within cryptography and are used in many applications including digital signature schemes, message authentication codes, password hashing, cryptocurrencies and content-addressable storage. Stevens was one of the driving forces in turning initial weaknesses in the compression function into practical attacks against various widely deployed protocols relying on hash function collision resistance for their security. In Chapter 7 he explains how each scenario involves the development of slightly different ideas to exploit weaknesses in especially MD5.

Social institutions collided from 1000 to 1600 CE, halting population growth. Gaia brought the Medieval Warm Era, nourishing prosperity from 800 to 1200 CE, until the Black Plague infected the Old World. The sixteenth-century mortality wave of the Americas reinforced population shrinkage; declining agriculture reinforced the cooling of the Little Ice Age. Meanwhile, earlier prosperity had encouraged ambitions among warriors: their bellicose emotions revealed links of social and biological human nature as they destroyed empires in China and the Mediterranean. The Mongols regime supported commerce and knowledge exchange, yet their legacy brought further warfare. Maritime encounters brought other collisions, especially after the tenth century. Transoceanic routes, completing the global trade network, spread disease, conflict, and mortality. Inherited representations of the world met with challenge: the major religions each experienced doctrinal schisms. The sixteenth century, while it offered innovative elements of global expansion, also reproduced the collisions of previous centuries, revealing the inherent challenges and limits to the human order.

Seventeenth-century empires of east and west built four types of profitable colonies. They maintained port cities, labor systems, and trade in precious metals. A comparison of oceanic shipping shows that, while Europeans dominated long-haul routes, Asian shipping dominated the dense Indian Ocean trade. Capitalism entered this scene, gradually gaining global leadership. Its most basic institution was the profit-making enterprise, combining local and international trade. A second institution, the proprietors’ association, linked entrepreneurs to pressure states at home and abroad for pro-enterprise policy in commerce, taxation, diplomacy, and war. Such associations gained an early start in the Netherlands and thereafter in England. A Dutch–English alliance then created a third capitalistic institution, a network of national proprietors’ associations able to sustain pro-capitalist policy among states even as they warred. The chapter concludes with exploration of global cultural exchange and early signals of nationalism and democracy. The changes in economy, culture, and politics relied both on current agency and deep antecedents worldwide.

Chapter 5 focuses on the formation of rocky planetary-scale bodies, including terrestrial planets, super-Earths, and giant planet cores. The concepts of gravitational focusing, shear and dispersion dominated encounters, and catastrophic disruption are introduced. A simple "particle in a box" statistical model for planetary growth is described, along with the ideas of orderly, runaway, and oligarchic growth. Factors that determine the planetesimal velocity dispersion, including viscous stirring, dynamical friction, and gas drag, are discussed. The regimes of pebble accretion, the conditions under which it operates, and the pebble accretion rate, are discussed. The standard model for the final assembly of the Solar System's terrestrial planets is outlined.