Noise, thermal

Many special-purpose electrical thermometers have been developed, either for use in practical temperature measurement, or as research devices for the study of temperature and temperature scales. Among the latter are thermometers which respond to thermal noise (Johnson noise) and thermometers based on the temperature dependence of the speed of sound. 

The function / incorporates the screening effect of the surfactant, and is the surfactant density. The exponent x can be derived from the observation that the total interface area at late times should be proportional to p. In two dimensions, this implies R t) oc 1/ps and hence x = /n. The scaling form (20) was found to describe consistently data from Langevin simulations of systems with conserved order parameter (with n = 1/3) [217], systems which evolve according to hydrodynamic equations (with n = 1/2) [218], and also data from molecular dynamics of a microscopic off-lattice model (with n= 1/2) [155]. The data collapse has not been quite as good in Langevin simulations which include thermal noise [218]. 

Von Neumann s and Brilloun s assertions are both certainly very plausible ones, in view of the fact that each mechanical degree of freedom used to store one bit of information (such as a capacitor, for example) involves at least an amount of kT of thermal noise which must then apparently be overcome to reliably read or manipulate the given bit of information [benn82]. We have inserted the word apparently in quotes, however, because this supposition is now known to be false ... 

In any particular situation, it is usually possible to give a variety of reasons why the observed quantity behaves in an erratic manner. The observed quantity may be critically dependent on certain parameters and the observed fluctuations attributed to slight variations of these parameters. The implication here is that the observed fluctuations appear erratic only because we have not taken the trouble to make a sufficiently precise analysis of the situation to disclose the pattern the observations are following. It is also possible, in some situations, to adopt the viewpoint that certain aspects of the phenomenon being studied are inherently unknowable and that the best physical laws we can devise to explain the phenomenon will have some form of randomness or unpredictability built into them. Such is the case, for example, with thermal noise voltages, which are believed to be governed by the probabilistic laws of quantum physics. 

Sums of Independent Random Variables.—Sums of statistically independent random variables play a very important role in the theory of random processes. The reason for this is twofold sums of statistically independent random variables turn out to have some rather remarkable mathematical properties and, moreover, many physical quantities, such as thermal noise voltages or measurement fluctuations, can be usefully thought of as being sums of a large number of small, presumably independent quantities. Accordingly, this section will be devoted to a brief discussion of some of the more important properties of sums of independent random variables. 

As our first example we shall define what is known as a gaussian Markov process. This process, as we shall see later, is a good model for thermal noise or vacuum-tube-generated noise that has been passed through an RC filter with time constant a 1. We begin by defining two functions / and Q as follows... 

Internal thermal noise of mirrors. Mirror substrates are transparent material cylinders. They are affected by thermal noise and each one of their modes of vibration can be represented by an harmonic oscillator. The study of thermal noise in solids is a complex task, made difficult because no... 

The value should be that of single polymer chain elasticity caused by entropic contribution. At first glance, the force data fluctuated a great deal. However, this fluctuation was due to the thermal noise imposed on the cantilever. A simple estimation told us that the root-mean-square (RMS) noise in the force signal (AF-lS-b pN) for an extension length from 300 to 350 nm was almost comparable with the thermal noise, AF= -21.6 pN. 

An important early paper on fluctuation processes is that of Harry Nyquist (1928), who suggested an equation linking the mean-square amplitude of thermal noise in an electrical circuit to the resistance R of the noise EMF (or current) generator ... 

The mean-square amplitude of nonequilibrium noise, quite in contrast to that of equilibrium thermal noise, may reach rather high values for instance, hundreds of millivolts during anodic polarization of semiconductors (Parkhutik and Timashev, 2000). 

Ideally, any procedure for signal enhancement should be preceded by a characterization of the noise and the deterministic part of the signal. Spectrum (a) in Fig. 40.18 is the power spectrum of white noise which contains all frequencies with approximately the same power. Examples of white noise are shot noise in photomultiplier tubes and thermal noise occurring in resistors. In spectrum (b), the power (and thus the magnitude of the Fourier coefficients) is inversely proportional to the frequency (amplitude 1/v). This type of noise is often called 1//... 

The IDL is dependent on various factors such as sensitivity of the detector for the analyte of interest and electronic and detector (instrumental) noise of various origins, e.g., thermal noise, shot noise, flicker (1 //) noise, environmenfal noise, efc. Several books and articles have been published on fhe different types of instrumental noise, e.g., Skoog and Leary s Principles of Instrumental Analysis . ... 

The viscoelastic effects on the morphology and dynamics of microphase separation of diblock copolymers was simulated by Huo et al. [ 126] based on Tanaka s viscoelastic model [127] in the presence and absence of additional thermal noise. Their results indicate that for

bulk modulus of both blocks, the area fraction of the A-rich phase remains constant during the microphase separation process. For each block randomly oriented lamellae are preferred. 

Another important property of PMTs is the pulse height distribution. The amplification of individual photoelectrons by the PMT is a stochastic process that causes variations in the gain of individual photoelectrons. As a result significant jitter in the amplitude of the output pulses is observed, see Fig. 3.6. These pulse height variations can be more than a factor of 10. The lowest pulse heights mainly consist of (thermal) noise, indicated by the dashed line in Fig. 3.6. The pulse height distribution exhibits a peak corresponding to detected photons. The threshold level of the... 

Optical receiver noise can arise partly from fundamental photon noise and partly from thermal noise in the receiver circuit. For CO2 detection, it was assumed that the optical receiver was an extended InGaAs detector, followed... 

The power which must be supplied to the thermistor to measure its resistance depends on the noise level and on the detection system. The latter is the main responsible for the total noise (a few nV/v/Hz), since the resistors are at low temperature and, hence, then-thermal noise can be usually neglected (see eq. (9.17)). 

This eliminates the amplifier and transmission line noise superimposed on the thermal noise, since the respective noise voltages are uncorrelated. 

Examples are given in References 249 and 250 of about 100 ions detected in a single scan. This is about the practical detection limit for image current detection due to thermal noise in the detection system. Bradykinin has been detected from a sample concentration of 3 nM [249] and detection of sub-femtomole levels on a column is readily obtained [251]. 

Therefore the flicker noise is expected to grow with 7 as the device size is scaled down. In deep submicron MOSFETs the corner frequency at which thermal noise equals flicker noise may be as large as 100 MHz, indicating that, at low frequency, 1/f noise is the most severe noise source which affects sensor performance. 

When constituted of metals, thermopiles exhibit a very low noise, in particular only thermal noise if the voltage amplifier used for signal amplification has a very high input impedance. 

To detect the reflected signal in the presence of thermal white noise, the correlation process (matched filtering) is used according to the fundamentals given above. The received signal will be detected when its power is higher than the thermal noise power P/v multiplied by detectability factor D, e.g. 

In the receiver some noise is added ( receiver noise ), arising from thermal activity generated within the components of the receiver. For distant scatterers the return signal is often so weak that this thermal noise can become a significant issue. We write... 

Thermally stimulated creep (TSCr) method, 21 742-743 Thermally stimulated current spectrometry (TSC), 21 743 Thermal mass meters, 20 681 Thermal mechanical analysis (TMA), of polyester fibers, 20 21 Thermal motion, in silicon-based semiconductors, 22 237-238 Thermal noise, silicon-based semiconductors and, 22 237 Thermal oxidation, 10 77-78, 79 in VOC control, 20 683-685 Thermal oxidation rates, silicon, 22 490 Thermal oxidizers... 

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