By J. M. Ziman
Initially released in 1979, this e-book discusses how the actual and chemical homes of disordered platforms reminiscent of drinks, glasses, alloys, amorphous semiconductors, polymer strategies and magnetic fabrics could be defined via theories in keeping with quite a few mathematical versions, together with random assemblies of demanding spheres, tetrahedrally-bonded networks and lattices of 'spins'. The textual content describes those versions and a few of the mathematical theories wherein the observable homes are derived. options and ideas corresponding to the suggest box and coherent approximations, graphical summation, percolation, scaling and the renormalisation staff are defined and utilized. This booklet can be of worth to somebody with an curiosity in theoretical and experimental physics.
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Additional resources for Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems
For both series a single-shot precision and an autocorrelation can be given. Additionally, a cross-correlation can be computed that indicates whether noise affects the measurements of both time intervals completely independently or in a correlated fashion. In a linear delay-line for instance the delay variations of the first delay elements affects the arrival time at all subsequent nodes. Hence, there is a correlation of the arrival times for all measurements during which the common delay elements are passed.
By replacing all delay elements by multiplexers with one input connected to the loop and the other one used as a dummy input this problem can be circumvented. However, area and power consumption are increased and the resolution is degraded. In practice there is a trade-off between non-linearity caused by a long delay-line and the structural non-linearity from the loop itself. The latter one can be reduced by a careful layout and reasonable sizing of the multiplexer. An advanced architecture that measures and eliminates this non-linearity is proposed in the following section.
12 VLSB ≤ ε < 12 VLSB , the quantization error of a TDC is not mean free (0 ≤ ε < TLSB ). 6) In a controlled TDC the reference time according to this definition corresponds usually to the time reference TR of the control loop (ref. 4). 10) In the frequency domain the constant component ε yields a DC spectral line. The variable component results in spectral power with f > 0. e. its power spectral density is flat. This is justified for non-periodic signals that change sufficiently fast. 12) The DC component of the quantization error has been neglected.