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satisfy it for d = 4, the significance of which we shall discuss later.) The conclusion is that mean-field theory is not reliable quantitatively, and predicts too high a degree of universality. However, we do learn some important lessons from it: First, we learn that it is possible to understand qualitatively, and even to some extent quantitatively, how a perfectly regular function such as the Landau free energy can lead to a singular Gibbs free energy. The point is that, while 1/1(m, H, T) is a regular function of its arguments, the value iii that minimizes 1/1 may be a singular function of Hand T. The mean-field theory shows how such singularities can arise in a physically instructive way. Second, we learn about universality, even if mean-field theory overstates it. The fact that the critical exponents are independent of the parameters in the Landau free energy suggests the critical phenomena are not sensitive to the details of the microscopic Hamiltonian, but possibly only to general structures, such as the number of "slow" degrees of freedom (i.e., order parameters) and the dimensionality of space. These lessons have given impetus and direction to the more refined treatments that we shall study later.

The Van der Waals equation of state can be regarded as a mean-field theory of gas-liquid transitions. That is, we can find a Landau free energy that gives the desired equation upon minimizing with ~espect to the order parameter. We do this by working backward. The Van der Waals equation in universal form is

(2.35)

The free energy of the solution can be obtained from the definition A = U - TS. To this end we first discuss the internal energy of the solution. It is a function of T, P, no, n 1. Further, it is assumed to be a homogeneous function of no and n 1. That is, if no and n 1 are simultaneously increased by a certain factor, U increases by the same factor. By making a Taylor series expansion we can write

U(T, P, no, n 1) = U(T, P, no,O)

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U(T, P, no, n 1) = nouo(T,

In this chapter and the prior one, you have studied line-based patterns: that is, trendlines and channels. Understanding and using these is essential to good charting. But these straight-line patterns are relatively easy to nd, and there are many other kinds of patterns that are important to your knowledge of technical analysis but may not be so obvious. In the next chapter, we will begin this journey into more ambiguous patterns by studying rounded tops and rounded bottoms. These are patterns which can help you predict reversals of a security from which you can pro t.

p) + n1u1(T, p)

+ n1v1(T, P)

(2.36)

When you launch Microsoft Word, a blank document appears, ready for you to start typing. If you repeatedly type the same text in your documents, for example, your company name, you can add this text to Word s Quick Parts Gallery; then, the next time you need to add the text to a document, you can select it from the gallery instead of retyping it.

V(T, P, no, n 1) = novo(T, P) (2.37)

where Uo and Vo are the internal energy per mole and volume per mole of the pure solvent respectively. On the other hand, U 1 and VI have no comparably simple interpretation. Let us now consider the entropy of the solution. Imagine that the solution undergoes an infinitesimal reversible transformation, with no and n 1 held fixed. The change in entropy is the exact differential

dS = -

dQ = -(dU + PdV) = no [ -(duo + Pdvo) + - -(du + Pdv ) 1 1 1 1

nIl]

Two of the most important events that occur repeatedly in technical analysis are breakouts and reversals A breakout is the act of a price escaping from a relatively tight price range either to the upside (a breakout above resistance) or the downside (a failure below support) A reversal is the act of a price changing directly either from (a) up to down, or (b) from down to up What is going on in each case is the same an escape from a price range The terminology differs only to state what has happened prior to that escape Breakouts and reversals are crucial events to discern on a chart since they can make you money, and two of the most common patterns found on charts that relate to these events are rounded tops (at the peak of a chart) and saucers (at the bottom).

+ Pdvo),

dS l = r(du 1 + Pdu 1)

S(T, P, no, n 1) = noso(T, P)

+ n1s1(T, p) + ;\(no, n 1)

Press to delete characters to the left of the cursor. Press to delete characters to the right of the cursor.

(2.38)

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