Fundamental limit

There are certain limitations to the usefulness of nitration in aqueous sulphuric acid. Because of the behaviour of the rate profile for benzene, comparisons should strictly be made below 68% sulphuric acid ( 2.5 fig. 2.5) rates relative to benzene vary in the range 68-80% sulphuric acid, and at the higher end of this range are not entirely measures of relative reactivity. For deactivated compounds this limitation is not very important, but for activated compounds it is linked with a fundamental limit to the significance of the concept of aromatic reactivity as already discussed ( 2.5), nitration in sulphuric acid cannot differentiate amongst compounds not less than about 38 times more reactive than benzene. At this point differentiation disappears because reactions occur at the encounter rate. 

Fundamental Limitations to Beers Law Beer s law is a limiting law that is valid only for low concentrations of analyte. There are two contributions to this fundamental limitation to Beer s law. At higher concentrations the individual particles of analyte no longer behave independently of one another. The resulting interaction between particles of analyte may change the value of 8. A second contribution is that the absorptivity, a, and molar absorptivity, 8, depend on the sample s refractive index. Since the refractive index varies with the analyte s concentration, the values of a and 8 will change. For sufficiently low concentrations of analyte, the refractive index remains essentially constant, and the calibration curve is linear. 

As femtomolar detection of analytes become more routine, the goal is to achieve attomolar (10 molar) analyte detection, corresponding to the detection of thousands of molecules. Detection sensitivity is enhanced if the noise ia the analytical system can be reduced. System noise consists of two types, extrinsic and intrinsic. Intrinsic aoise, which represents a fundamental limitation linked to the probabiHty of finding the analyte species within the excitation and observation regions of the iastmment, cannot be eliminated. However, extrinsic aoise, which stems from light scatteriag and/or transient electronic sources, can be alleviated. 

The most fundamental limitation on pressure is at 15 psig (101.4 kPa). Containers built to pressures exceeding this value are usuaHy caHed pressure vessels and are covered by the American Society of Mechanical Fngineers (ASME) Boiler and Pressure Vessel Code. For aH practical purposes, tanks are defined to have internal pressures below this value. 

The downhole turbine motors that are hydraulically operated have some fundamental limitations. One of these is high rotary speed of the motor and drill bit. The high rotary speeds limit the use of downhole turbine motors when drilling with roller rock bits. The high speed of these direct drive motors shortens the life of the roller rock bit. 

What is remarkable about this very simple appearing rule is that one can show that it is capable of univer.sal computation. This means that with a proper selection of initial conditions (i.e. the initial distribution of live and dead cells). Life can be turned into a general purpose computer. This fact fundamentally limits the overall predictability of Life s behavior. 

The relationships between thermodynamic entropy and Shannon s information-theoretic entropy and between physics and computation have been explored and hotly debated ever since. It is now well known, for example, that computers can, in principle, provide an arbitrary amount of reliable computation per kT of dissipated energy ([benu73], [fredkin82] see also the discussion in section 6.4). Whether a dissipationless computer can be built in practice, remains an open problem. We must also remember that computers are themselves physical (and therefore, ultimately, quantum) devices, so that any exploration of the limitations of computation will be inextricably linked with the fundamental limitations imposed by the laws of physics. 

A discussion of reversible computation, as well as some speculations concerning the fundamental limitations of computation, have already been given in section G.4 we will not repeat that discussion here. In the remaining sections of this chapter we instead wish to focus our attention on somewhat more speculative connections between physics and computation and in what way the universe itself might be thought of as a computer. 

What better place to begin our discussion of physics and information than with a quote from Richard Feynman, who, towards the latter part of his life, became increasingly interested in the nature of computing in general and the fundamental limits of computation in particular. ... 

Interested readers should read Jagdish Mehrah s superb recent scientific biography of Richard Feynman [mehra94]. Chapter 24 of Mehra s book discusses Feynman s ideas about the fundamental limits of computation. 

State-of-the-art polymer LEDs now have operating lifetimes and luminous efficiencies suitable for a wide variety of commercial applications. Furthermore, it is clear that the fundamental limits of polymer LED performance have not yet been reached. With improvements in material synthesis, fabrication techniques, and device design, significant increases in LED performance are to be expected. These improvements should lead to the extensive use of polymer LEDs in future display applications. 

The most fundamental limitation of the method is implicit in Equation 1-9. As all atoms absorb x-rays, the method cannot be specific it cannot ordinarily identify unknown elements in a sample, nor can it ordinarily give reliable analytical results on a sample containing unknown elements. On the other hand, it can usually show whether or not such a sample has an assumed ultimate composition.7... 

Farmer, A., Cade, B.S., Torres-Dowdall, J. (2008). Fundamental limits to the accuracy of deuterium isotopes for identifying the spatial origin of migratory animals. Oecologia, Vol. 158, pp. 183-192. (http //dx.doi.org/10.1007/s00442-008-1143-6)... 

The model has been applied successfully to predicting the performances of bearings, gears, seals, and engines [10-12]. A fundamental limitation of the statistic models is their inability to provide detailed information about local pressure distribution, film thickness fluctuation, and asperity deformation, which are crucial for understanding the mechanisms of lubrication, friction, and surface failure. As an alternative, researchers paid a great interest to the deterministic ML model. 

Williams, R. R., Fundamental Limitations on the Use and Comparison of Signal-to-Noise Ratios, Anal. Chem. 63, 1991, 1638-1643. 

This section emphasizes on flame quenching by stretch, as well as highlights and separately discusses the four aspects of counterflow premixed flame extinction limits, including (1) effect of nonequidiffusion, (2) influence of different boundary conditions, (3) effect of pulsating instability, and (4) relahonship of the fundamental limit of flammability. 

In Chapter 6.3, C-J. Sung examines extinction of counterflow premixed flames. He emphasizes flame quenching by stretch and highlights four aspects of counterflow premixed flame extinction limits effect of nonequidiffusion, parf played by differences in boundary conditions, effect of pulsating insfabilify, and relation to the fundamental limit of flammability. 

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