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You can often get more insight by deriving a well-known result in a different way. Let us reflect a bit more about Langevin's approach. What happens if we use the assumption of quite high viscosity b /m l/T) right from the beginning Then neglecting m ~x/ dt 2 compared with 'Y dx/ dt, instead of (8.22) we can write



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PriceWaterhouseCoopers has a process for designing an enterprise security framework that incorporates many of the elements of this pattern [PWC01]. It tailors a security process based on the business requirements and factors of an enterprise. It includes asset inventory collection and information classification. Mint Business Solutions has defined an approach to security in the context of best practice in enterprise information management [MBS03]. Within this broad

dx dt =F,

(11.14)

(8.29)

100 6

where F == 'YF. Now let us try to obtain the properties of F without using the thermal equilibrium result (8.25) explicitly. The question we ask is: What properties must F have for this simple Langevin equation to be equivalent to the diffusion equation (8.20) deduced by Einstein The ensemble average of F can be given in terms of that of x by averaging (8.29):

_ 2PT xT=Q' (11.15)

Table 6.4 Establishing security properties for the museum:





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(F(t))

REQUIRED SECURITY PROPERTIES Confidentiality (HR, management, individual) Integrity (HR, individual only) Availability (HR and management) Accountability (changes in HR) Museum financial/ insurance data, partner financial data Confidentiality Integrity Basic accounting Confidentiality Integrity Basic accounting Museum/partner relationships Protect acquisition and transport plans and strategies Protect scheduling data Insurance policy constraints Museum charter requirements Intellectual property Enterprise/employee relations Enterprise/public reputation Contractual obligations Financial reporting laws

dt (x).

Like z in (11.9), all these ratios are bounded by 0 and 1. The four-momentum fractions in Fig. 11.7 are

(8.30)

Confidentiality (restricted to narrow group)

We can calculate (x) if we determine the probability distribution p(x, t) that obeys Einstein's diffusion equation (8.20). Assuming that the particle starts at the origin at t = 0, you can show (Problem 8.2) that the solution of (8.20) is given by

forq, for '1, forgo (11.16)

Enterprise/public reputation Museum charter requirements Partner reputations for loan exhibits Insurance policy constraints Enterprise/employee relations Enterprise/public relations Enterprise/employee relations Laws Enterprise/public reputation Insurance policy constraints Enterprise/partner relations Costs

(2.62)

q,(t) ::::::

Integrity Accountability (for any change)

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The variables are defined relative to the most energetic jet, for example, the q jet in Fig. 11.7. Its direction is referred to as the" thrust axis." The q, q, and g are coplanar in the plane y = O. Longitudinal and transverse momentum conservation are embodied in (11.16), but energy conservation introduces the additional requirement that (11.17) The zero mass of the '1 and g leads to the further constraints [see (11.16)]

A~vr cos (1ft) .

Availability (safety)

In other words, the swing oscillates 90 degrees out of phase with our pushing. Our push is stronger when the swing is at its point of minimum height and weaker when it is at its point of maximum height. This is exactly what you experience when pushing a child on a swing. As the swing approaches you, you must decrease the intensity of the force so that it vanishes when the swing reaches its point of maximum height. Far away from resonance (i.e., Iw VA), q,(t) :::::: 0 and the swing does not move. Figure 2.6 plots the average of the square of (2.61) over one oscillation period against w for a value of / 100 times smaller than the natural frequency. Notice that it decreases quickly as the frequency becomes different from the natural frequency. The sharp peak in Figure 2.6 is typical of resonant phenomena. To solve (2.56) for any driving force, it is convenient to solve it first for an impulse force c5(t - t'). This solution is called the Green's function, G(tlt'), after George Green, a nineteenth-century mathematician from Nottingham, England. The equation for the Green's function is

2 x~ -x T q 2 x I. = 0 '

(2.63)

framework, they base their security approach on the ISO standard 17799. This standard identifies a set of controls that include:

18For weak damping the natural frequency is approximately the same as the natural frequency with no damping.

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