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This chapter focuses on collective motion of isoscalar nature parameterized by shape variables. The equations of motion are derived from energy conservation as implied by self-consistency. A basic ingredient is the variation of the total static energy with deformation, which at finite thermal excitations has to be calculated for constant entropy. Linear response theory is exploited for the dynamics, especially for separating reactive and dissipative forces. Response functions for intrinsic, nucleonic motion are distinguished from those for collective dynamics. The origin of irreversible behavior due to the decay of simple to more complicated nucleonic configurations is described in detail. In practical applications, dressed single particle states are used in their dependence on temperature. The variation of the transport coefficients for inertia and friction with T obtained this way is confronted with that given in various other models, like in the diabatic one, in common RPA, in the random matrix model, or in the liquid drop model and for wall friction. Implications on rotational motion are discussed.

The successful description of the motion of a rigid body is one of the triumphs of Newtonian mechanics. Having learned in the previous chapter how to specify the position and orientation of a rigid body, this chapter deals with its natural motion under impressed external forces and torques. The dynamical theorems of collective motion are extended using rotation operators. Some basic facts about rigid-body motion are discussed, along with the inertia operator and the spin, inertia dyadic, kinetic energy of a rigid body, meaning of the inertia operator, principal axes, time evolution of the spin, torque-free motion of a symmetric body, Euler angles of the torque-free motion, body with one point fixed, time evolution with one point fixed, work-energy theorems, rotation with a fixed axis, symmetric top with one point fixed, initially clamped symmetric top, approximate treatment of the symmetric top, inertial forces, calculations of the Coriolis force, and the magnetic-Coriolis analogy.

This introductory chapter provides a short historical perspective on the evolution of plasma physics and its fusion energy applications. It also examines the basic concepts and characteristics of plasma and describes the basic equations of models used in the study of collective plasma dynamics. The word “plasma” was introduced into physics in 1928 by Irving Langmuir to designate certain equipotential regions containing an electrically neutral ionized gas in quasi-neutral, dilute gas of free-charged particles. However, it can be argued that plasma physics emerged in the nineteenth-century electrical science studies that involved partially-ionized gases. Significant developments made in the decades that followed ultimately revealed two aspects of a plasma's dynamics—that of single-charged particle motions through binary collisions between charged particles, and collective motions in plasma oscillations.

Moving in groups is integral to the life histories of many animals. The term ‘collective motion’ is used to describe the synchronized motion of groups of animals, such as shoals of fish or flocks of birds, that appear to behave as one body, continually changing shape and direction. Social preferences for relatives, familiar conspecifics, or individuals of similar attributes such as size, personality, or sex exist in many animal species. This chapter reviews how such references, which can be encoded in social networks, could affect the collective motion of animal groups. While empirical data on this topic is scarce, a rich theory is in the process of being developed, creating interesting hypotheses and avenues for future research. The chapter begins with describing the importance of social networks for movement dynamics within populations and highlighting the effects social networks could have on the movement of and between distinct groups. The chapter then reviews the role of social networks on within-group movement dynamics. Next, the importance of considering mechanisms at the individual level is highlighted. The chapter ends with a discussion of the challenges in collecting empirical data to test the hypotheses created by theoretical approaches to date.

According to the modern view, elementary particles (electrons, neutrinos, quarks, etc.) are excitations of some more fundamental medium called the quantum vacuum. This is the new aether of the 21st century. The electromagnetic and gravitational fields, as well as the fields transferring the weak and the strong interactions, all represent different types of collective motion of the quantum vacuum. Among the existing condensed matter systems, the particular quantum liquid, superfluid ³He-A most closely resembles the quantum vacuum of the Standard Model. The most important property of ³He-A is that its quasiparticles are very similar to the chiral elementary particles of the Standard Model (electrons and neutrinos), while its collective modes are very similar to gravitational, electromagnetic and SU (2) gauge fields, and the quanta of these collective modes are analogs of gravitons, photons, and weak bosons. The reason for this similarity between the two systems is a common momentum space topology.

This chapter studies in detail the natural motion of rigid bodies under impressed external forces and torques. The dynamical theorems of collective motion will be extended here by use of the rotation operators. The following sections discuss concepts such as the inertia operator and the spin, the inertia dyadic, and the kinetic energy of a rigid body. Any rigid body will have a system of principal axes. If necessary, three arbitrary body-fixed axes can be chosen, the inertia matrix can be calculated, and then the principal axis eigenvectors can be determined. In many situations of interest, however, the directions of the principal axes can be guessed with relative certainty from the symmetry of the rigid body. A number of rules that can be used are presented here.

Fluid flows are a pervasive presence across most branches of human activity, including daily life. Although the basic equations governing the motion of fluid flows are known for two centuries (1822), since the work of Claude–Louis Navier (1785–1836) and Gabriel Stokes (1819–1903), these equations still set a formidable challenge to the quantitative, and sometimes even qualitative, understanding of the way fluid matter flows in space and time. Meteorological phenomena are among the most popular examples in point, but the challenge extends to many otherinstances of collective fluid motion, both in classical and quantum physics. This Chapter presents the Navier–Stokes equations of fluid mechanics and discuss the main motivations behind the kinetic approach to computational fluid dynamics.