Thick disks are common in spiral and S0 galaxies and seem to be an inherent part of galaxy formation and evolution. Our own Milky Way is host to an old thick disk. The stars associated with this disk are enhanced in the α-elements relative to similar stars present in the thin disk. The Milky Way thin disk also appears to be younger than the thick disk. Elementalabundance trends in stellar samples associated with the thin and thick disks in the Milky Way are reviewed. Special attention is paid to how such samples are selected. Our current understanding of the elemental abundances and ages in the Milky Way thick and thin disks is summarized and discussed. The need for differential studies is stressed. Finally, formation scenarios for the thick disk are briefly discussed in the light of the current observational picture.

I review current models of star formation and discuss potential effects of high metallicity. Our current paradigm for star formation is that it is a dynamical process in which molecular clouds and regions of star formation form on their local dynamical times. Molecular clouds are characterised by turbulent motions, which, together with gravity, lead to their fragmentation and the formation of individual stars. The resulting distribution of stellar masses can be most easily understood as a combination of fragmentation, continued accretion to form higher-mass stars and dynamical interactions. Regions of high metallicity are likely to differ in terms of their star formation in three main areas: the formation of molecular gas on grains; the cooling processes which determine the characteristic stellar mass; and the higher opacity of dust grains, which increases the effects of radiation pressure in limiting the growth of massive stars by accretion. Characterising star formation in regions of high metallicity will allow accurate determinations of these effects.

We present the results of our recent abundance survey of the Galactic thick disk. We selected from the Hipparcos catalog 176 sample stars satisfying the following criteria: they are nearby (d ≤ 150 pc) subgiants and dwarfs, of spectral types F and G, and with thick-disk kinematics (VLSR ≤ −40 kms−1, │WLSR│ ≤ 30 kms−1). Assuming that the velocity distribution of each stellar population is Gaussian, we assigned stars with a probability P ≤ 70% to one of the three components. This resulted in 95 thick-disk stars, 17 thin-disk stars, and 24 halo stars. The remaining 40 objects cannot be unambiguously assigned to one of the three components.

We derived abundances for 23 elements from C to Eu. The thick-disk abundance patterns are compared with earlier results from the thin-disk survey of Reddy et al. (2003). The levels of α-elements (O, Mg, Si, Ca, and Ti), thought to be produced dominantly in Type-ii supernovae, are enhanced in thick-disk stars relative to the values found for thin-disk members in the range −0.3 > [Fe/H] > −1.2. The scatter in the abundance ratios [X/Fe] at a given [Fe/H] for thick-disk stars is consistent with the predicted dispersion due to measurement errors, as is the case for the thin disk, suggesting a lack of “cosmic” scatter. The observed compositions seem consistent with a model of galaxy formation by mergers in a ∧ CDM universe.

The Bologna Open Cluster Chemical Evolution (BOCCE) project is intended to study the disk of our Galaxy using open clusters as tracers of its properties. We are building a large sample of clusters, deriving homogeneously their distance, age, reddening, and detailed chemical composition. Among our sample we have several objects more metal-rich than the Sun and we present here first results of the analysis for NGC 6819, IC 4651, NGC 6134, NGC 6791, and NGC 6253, the last two being the most metal-rich open clusters known.

The subject of statics often appears in later chapters in other books, after force and torque have been discussed. However, the way that force and torque are used in statics problems is fairly minimal, at least compared with what we'll be doing later in this book. Therefore, since we won't be needing much of the machinery that we'll be developing later on, I'll introduce here the bare minimum of force and torque concepts necessary for statics problems. This will open up a whole class of problems for us. But even though the underlying principles of statics are quick to state, statics problems can be unexpectedly tricky. So be sure to tackle a lot of them to make sure you understand things.

Balancing forces

A “static”. setup is one where all the objects are motionless. If an object remains motionless, then Newton's second law, F = ma (which we'll discuss in great detail in the next chapter), tells us that the total external force acting on the object must be zero. The converse is not true, of course. The total external force on an object is also zero if it moves with constant nonzero velocity. But we'll deal only with statics problems here. The whole goal in a statics problem is to find out what the various forces have to be so that there is zero net force acting on each object (and zero net torque, too, but that's the topic of Section 2.2).

1. Is there such a thing as a perfectly rigid object?

1. 2. How do you synchronize two clocks that are at rest with respect to each other?

In Chapter 8, we discussed situations where the direction of the vector L remained constant, and only its magnitude changed. In this chapter, we will look at more general situations where the direction of L is allowed to change. The vector nature of L will prove to be vital here, and we will arrive at all sorts of strange results for spinning tops and such things. This chapter is rather long, alas, but the general outline is that the first three sections cover general theory, then Section 9.4 introduces some actual physical setups, and then Section 9.6 begins the discussion of tops.

Preliminaries concerning rotations

The form of general motion

Before getting started, we should make sure we're all on the same page concerning a few important things about rotations. Because rotations generally involve three dimensions, they can often be hard to visualize. A rough drawing on a piece of paper might not do the trick. For this reason, this chapter is one of the more difficult ones in this book. But to ease into it, the next few pages consist of some definitions and helpful theorems. This first theorem describes the general form of any motion. You might consider it obvious, but it's a little tricky to prove.

The twin paradox appeared in Chapters 11 and 14, both in the text and in various problems. To summarize, the twin paradox deals with twin A who stays on the earth, and twin B who travels quickly to a distant star and back. When they meet up again, they discover that B is younger. This is true because A can use the standard special-relativistic time-dilation result to say that B's clock runs slow by a factor γ.

The “paradox” arises from the fact that the situation seems symmetrical. That is, it seems as though each twin should be able to consider herself to be at rest, so that she sees the other twin's clock running slow. So why does B turn out to be younger? The resolution to the paradox is that the setup is in fact not symmetrical, because B must turn around and thus undergo acceleration. She is therefore not always in an inertial frame, so she cannot always apply the simple special-relativistic time-dilation result.

While the above reasoning is sufficient to get rid of the paradox, it isn't quite complete, because (a) it doesn't explain how the result from B's point of view quantitatively agrees with the result from A's point of view, and (b) the paradox can actually be formulated without any mention of acceleration, in which case slightly different reasoning applies.

This book has one purpose: to help you understand four of the most influential equations in all of science. If you need a testament to the power of Maxwell's Equations, look around you – radio, television, radar, wireless Internet access, and Bluetooth technology are a few examples of contemporary technology rooted in electromagnetic field theory. Little wonder that the readers of Physics World selected Maxwell's Equations as “the most important equations of all time.”

How is this book different from the dozens of other texts on electricity and magnetism? Most importantly, the focus is exclusively on Maxwell's Equations, which means you won't have to wade through hundreds of pages of related topics to get to the essential concepts. This leaves room for in-depth explanations of the most relevant features, such as the difference between charge-based and induced electric fields, the physical meaning of divergence and curl, and the usefulness of both the integral and differential forms of each equation.

You'll also find the presentation to be very different from that of other books. Each chapter begins with an “expanded view” of one of Maxwell's Equations, in which the meaning of each term is clearly called out. If you've already studied Maxwell's Equations and you're just looking for a quick review, these expanded views may be all you need. But if you're a bit unclear on any aspect of Maxwell's Equations, you'll find a detailed explanation of every symbol (including the mathematical operators) in the sections following each expanded view.