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The innermost region of the Milky Way harbors the central molecular zone (CMZ). This region contains a large amount of molecular gas but a poor star formation rate considering the densities achieved by the gas in this region. We used the arepo code to perform a hydrodynamic and star formation simulation of the Galaxy, where a Ferrers bar was adiabatically introduced. During the stage of bar imposition, the bar strength excites density waves close to the inner Lindblad resonance guiding material toward the inner Galaxy, driving the formation of a ring that we qualitatively associate with the CMZ. During the simulation, we identified that the ring passes three main phases, namely: formation, instability, and quasi-stationary stages. During the whole evolution, and particularly in the quasi-stationary stage, we observe that the ring is associated with the x2 family of periodic orbits. Additionally, we found that most of the star formation occurs during the ring formation stage, while it drastically decreases in the instability stage. Finally, we found that when the gas has settled in a stable x2 orbit, the star formation takes place mostly after the dense gas passes the apocenter, triggering the conveyor-belt mechanism described in previous studies.
This chapter uses the ideas of hydrodynamics introduced in the last chapter to formulate the hydrodynamic theory of the flocking problem (i.e., the “Toner–Tu” equations).
I present a purely dynamical derivation of the Mermin–Wagner–Hohenberg theorem, and compare it with the standard equilibrium derivation. This also provides an opportunity to introduce diffusion equations and gradient expansions, both of which play a large role in what follows.
I introduce, and describe in detail, the dynamical renormalization group, using the KPZ equation as an example. In addition to spelling out the mechanics of the technique in great detail, I also emphasize its philosophical importance, as the answer to Einstein’s famous question “Why is the universe intelligible?” and its role as a guide to the formulation of hydrodynamic theories.
This chapter treats incompressible flocks in two dimensions, and shows that they map onto both equilibrium two-dimensional smectics, and our old friend the KPZ equation (albeit in one dimension), as well as a peculiar type of constrained magnet. Exact scaling laws are again found, this time by exploiting these mappings.
This chapter applies the dynamical renormalization group introduced in Chapter 4 to the flocking problem, and uses it to show that nonlinear terms in the dynamics are “relevant,” and change the dynamics in precisely the way needed to circumvent the Mermin–Wagner–Hohenberg theorem.
In creatures ranging from birds to fish to wildebeest, we observe the collective and coherent motion of large numbers of organisms, known as 'flocking.' John Toner, one of the founders of the field of active matter, uses the hydrodynamic theory of flocking to explain why a crowd of people can all walk, but not point, in the same direction. Assuming a basic undergraduate-level understanding of statistical mechanics, the text introduces readers to dry active matter and describes the current status of this rapidly developing field. Through the application of powerful techniques from theoretical condensed matter physics, such as hydrodynamic theories, the gradient expansion, and the renormalization group, readers are given the knowledge and tools to explore and understand this exciting field of research. This book will be valuable to graduate students and researchers in physics, mathematics, and biology with an interest in the hydrodynamic theory of flocking.
Odd Radio Circles (ORCs) are a class of low surface brightness, circular objects approximately one arcminute in diameter. ORCs were recently discovered in the Australian Square Kilometre Array Pathfinder (ASKAP) data and subsequently confirmed with follow-up observations on other instruments, yet their origins remain uncertain. In this paper, we suggest that ORCs could be remnant lobes of powerful radio galaxies, re-energised by the passage of a shock. Using relativistic hydrodynamic simulations with synchrotron emission calculated in post-processing, we show that buoyant evolution of remnant radio lobes is alone too slow to produce the observed ORC morphology. However, the passage of a shock can produce both filled and edge-brightnened ORC-like morphologies for a wide variety of shock and observing orientations. Circular ORCs are predicted to have host galaxies near the geometric centre of the radio emission, consistent with observations of these objects. Significantly offset hosts are possible for elliptical ORCs, potentially causing challenges for accurate host galaxy identification. Observed ORC number counts are broadly consistent with a paradigm in which moderately powerful radio galaxies are their progenitors.
An open problem of the derivation of the relativistic Vlasov equation for systems of charged particles moving with velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is illustrated on the non-relativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. The key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.
Both observations and theoretical studies have convincingly shown that outflows (i.e., wind and jet) are common phenomena from black hole accretion systems with various accretion rates, although the physical driving mechanisms are not exactly same for different accretion modes. Outflows are not only important in the dynamics of black hole accretion, but also play an important role in AGN feedback; therefore it is crucial to investigate their main physical properties including mass flux and velocity. In this paper we summarize recent studies in investigating the properties and driving mechanisms from black hole accretion flows with various accretion rates.
Shallowly submerged oscillating structures may be found in wave energy devices or semi-submersible vessels. Predicting the force on such structures is critical for design purposes, but complicated due to nonlinear phenomena which can occur in shallow water, including wave breaking and bore formation. Such effects are particularly important around the first ‘resonance’ frequency of the fluid on top of the device, where linear theory predicts large flows on/off the cylinder and corresponding surface elevations and forces. In an effort to create a reliable and efficient model to predict the hydrodynamic force on a shallowly submerged truncated vertical cylinder, an axisymmetric nonlinear hybrid model is developed for forced heave oscillations. The flow above the cylinder is modelled using the nonlinear shallow water equations, and linear potential flow theory is used in the surrounding fluid. The model is compared with experimental results for forced heave oscillations and performs well for predicting the heave force. It is then used to examine linearised heave force for increasing amplitudes of (prescribed) harmonic heave motion. There is a significant reduction in the peaks of radiation damping and added mass coefficients with increasing amplitude, and associated shifts in the frequencies of the peaks.
Hydroinformatics is a technology that combines information and communications technologies together with various disciplinary optimization and simulation models that focus on the management of water. This paper reviews the historical development of hydroinformatics and summarizes the current state of this technology. It describes the range of modeling tools and applications currently described in hydroinformatics literature. The paper concludes with some speculations about possible future developments in hydroinformatics.
We present the Cosmological Double Radio Active Galactic Nuclei (CosmoDRAGoN) project: a large suite of simulated AGN jets in cosmological environments. These environments sample the intra-cluster media of galaxy clusters that form in cosmological smooth particle hydrodynamics (SPH) simulations, which we then use as inputs for grid-based hydrodynamic simulations of radio jets. Initially conical jets are injected with a range of jet powers, speeds (both relativistic and non-relativistic), and opening angles; we follow their collimation and propagation on scales of tens to hundreds of kiloparsecs, and calculate spatially resolved synthetic radio spectra in post-processing. In this paper, we present a technical overview of the project, and key early science results from six representative simulations which produce radio sources with both core- (Fanaroff-Riley Type I) and edge-brightened (Fanaroff-Riley Type II) radio morphologies. Our simulations highlight the importance of accurate representation of both jets and environments for radio morphology, radio spectra, and feedback the jets provide to their surroundings.
This chapter discusses two different approaches to describing fluid flow: a Lagrangian approach (following a fluid element as it moves) and a Eulerian approach (watching fluid pass through a fixed volume in space). Understanding each of these descriptions of flow is needed to fully understand the dynamics of fluids. This chapter is devoted to diving into the differences between the two descriptions of fluid motion. Understanding this chapter will help tremendously in the understanding of the upcoming chapters when the Navier–Stokes equations and energy equation are discussed. This chapter will introduce the material derivative. It is extremely important to understand this derivative before the Navier–Stokes equations themselves are tackled.
In the previous chapter, the forces acting on a moving fluid element were exhaustively studied. Using Newtons second law of motion, the Navier–Stokes equations for both compressible and incompressible flows were obtained. This chapter uses an alternative approach to developing the Navier–Stokes equations. Namely, by starting from a Eulerian description (as opposed to a Lagrangian description), the integral form and conservation form of the Navier–Stokes equations are developed. The continuity and Navier–Stokes equations in its various forms are tabulated and reviewed in this chapter. This chapter ends by solving some very simple, yet common, problems involving the incompressible Navier–Stokes equations.
This chapter develops the Navier–Stokes equations using a Lagrangian description. In doing so, the concept of a stress tensor and its role in the overall force balance on a fluid element is discussed. In addition, the various terms in the stress tensor as well as the individual force terms in the Navier–Stokes equations are investigated. The chapter ends with a discussion on the incompressible Navier–Stokes equations.
This chapter serves as an introduction to the concept of conservation and how conservation principles are used in fluid mechanics. The conservation principle is then applied to mass and an equation known as the continuity equation is developed. Various mathematical operations such as the dot product, the divergence, and the divergence theorem are introduced along the way. The continuity equation is discussed and the idea of an incompressible flow is introduced. Some examples using mass conservation are also given.
In this chapter, a concept known as scaling is introduced. Scaling (also known as nondimensionalization) is essentially a form of dimensional analysis. Dimensional analysis is a general term used to describe a means of analyzing a system based off the units of the problem (e.g. kilogram for mass, kelvin for temperature, meter for length, coulomb for electric change, etc.). The concepts of this chapter, while not entirely about the fluid equations per se, is arguably the most useful in understanding the various concepts of fluid mechanics. In addition, the concepts discussed within this chapter can be extended to other areas of physics, particularly areas that are heavily reliant on differential equations (which is most of physics and engineering).