Wave, characteristics

Consider the pyruvic acid system in Scheme XV. Let HA and A represent pyruvic acid and pyruvate, respectively, and suppose the system is buffered. At a pH well below the pX of HA, a single polarographic wave characteristic of the reduction of HA is observed. At a pH well above the pX, a wave (at a much more reducing potential) is observed that is characteristic of the reduction of A. ... 

We are used to thinking of electrons as particles. As it turns out, electrons display both particle properties and wave properties. The French physicist Louis de Broglie first suggested that electrons display wave-particle duality like that exhibited by photons. De Broglie reasoned from nature s tendency toward symmetry If things that behave like waves (light) have particle characteristics, then things that behave like particles (electrons) should also have wave characteristics. 

The de Broglie equation predicts that eveiy particle has wave characteristics. The wave properties of subatomic particles such as electrons and neutrons play important roles in their behavior, but larger particles such as Ping-Pong balls or automobiles do not behave like waves. The reason is the scale of the waves. For all except subatomic particles, the wavelengths involved are so short that we are unable to detect the wave properties. Example illustrates this. 

Absorption and emission spectroscopies provide experimental values for the quantized energies of atomic electrons. The theory of quantum mechanics provides a mathematical explanation that links quantized energies to the wave characteristics of electrons. These wave properties of atomic electrons are described by the Schrddinger equation, a complicated mathematical equation with numerous terms describing the kinetic and potential energies of the atom. 

Figure 22.4 Idealised EEG-like patterns in sleep and waking. When we are awake and aroused the EEG is desynchronised (a). As we become drowsy and pass into sleep the EEG waves become more synchronised with 8-12 Hz alpha waves (b), sleep spindles then appear (c) before the EEG becomes even more synchronised with slow (about 1-2 Hz) high-voltage waves characteristic of deep slow-wave sleep (SWS). About every 90 min this pattern is disrupted and the EEG becomes more like that in arousal (d) except that the subject remains asleep. This phase of sleep is also characterised by rolling, rapid eye movements, the so-called REM sleep. SWS is consequently also known as non-REM sleep. These tracings have been drawn to show the main features of the different EEG phases of sleep and as such are much simpler than those that are actually recorded...

Cyclic voltammetry, square-wave voltammetry, and controlled potential electrolysis were used to study the electrochemical oxidation behavior of niclosamide at a glassy carbon electrode. The number of electrons transferred, the wave characteristics, the diffusion coefficient and reversibility of the reactions were investigated. Following optimization of voltammetric parameters, pH, and reproducibility, a linear calibration curve over the range 1 x 10 6 to 1 x 10 4 mol/dm3 niclosamide was achieved. The detection limit was found to be 8 x 10 7 mol/dm3. This voltammetric method was applied for the determination of niclosamide in tablets [33]. 

The substantial effect of secondary breakup of droplets on the final droplet size distributions in sprays has been reported by many researchers, particularly for overheated hydrocarbon fuel sprays. 557 A quantitative analysis of the secondary breakup process must deal with the aerodynamic effects caused by the flow around each individual, moving droplet, introducing additional difficulty in theoretical treatment. Aslanov and Shamshev 557 presented an elementary mathematical model of this highly transient phenomenon, formulated on the basis of the theory of hydrodynamic instability on the droplet-gas interface. The model and approach may be used to make estimations of the range of droplet sizes and to calculate droplet breakup in high-speed flows behind shock waves, characteristic of detonation spray processes. 

Although there are numerous published investigations in which records of the wavy surface profile have been obtained, e.g. (H9, D16, Sll), not many of these have been analyzed for information on wavelengths, most being concerned with wave-size (height) distributions. However, it may be noted that the experimental wavelengths of Kapitsa and Kapitsa (K10) show a trend in the direction of the data reported above, even at very small Reynolds numbers (lVa < 25). It seems, therefore, that the Kapitsa theory is applicable only at very small flow rates, as far as wave characteristics are concerned, in the case of the free flow of wavy films. Allen (A3) has reported a similar conclusion. 

The experimental results show that c/n decreases up to a certain flow rate at which it was found that Arwe = 0.8, after which a different behavior is exhibited, with an increase in c/V, as ArRe increases. At NRe = 280, a further break was observed this is due to the onset of turbulence in the film, which alters the manner in which u varies with ArRe. Hence, as in the case of the wavelengths, there appears to be an important change in the wave characteristics near the critical Weber number of unity. 

Thomas and Portalski (T14), 1958 Experimental study of water film flowing inside tube 1.96 X 98 cm., Nr, = 141-493, counterflow of air. Data on film thicknesses, pressure drop, wave characteristics. 

Konobeev et al. (K21), 1961 Experimental study of C02 absorption by water film, with upward and downward cocurrent gas/film flow, inside tubes 1.05-1.66 cm. i.d., 20-87 cm. long. Gas velocities 6-86 m./sec. IVko = 5-105. Length and amplitude of surface ripples and local film thicknesses measured. Rate of mass transfer stated to be function of wave characteristics only. 

A significant change in the theoretical treatment of atomic structure occurred in 1924 when Louis de Broglie proposed that an electron and other atomic particles simultaneously possess both wave and particle characteristics and that an atomic particle, such as an electron, has a wavelength X = h/p = h/mv. Shortly thereafter, C.J, Davisson and L.H. Germer showed experimentally the validity of this postulate. Dc Broglie s assumption that wave characteristics are inherent in every atomic particle was quickly followed by the development of quantum mechanics, in its most simple form, quantum mechanics introduces the physical laws associated with the wave properties of electromagnetic radiation into the physical description of a system of atomic particles. By means of quantum mechanics a much more satisfactory explanation of atomic structure can be developed. 

Compare yellow and blue waves for each of their three wave characteristics wavelength, frequency, and energy. 

Good SAW (surface acoustic wave) characteristics are reported for Zn-terminated ZnO films homogeneously etched at low rates [95]. O-terminated crystallites lead to the development of craters which are identifiable in SEM (scanning electron microscopy) due to their higher etching rates. 

Sources of pulsed incoherent radiation are so-called flash lamps, which produce short light pulses of broadband continuous-wave characteristic. Commonly, an intense pulse of short duration is used to generate sufficient concentration of a transient species suitable for spectroscopic observation. 

The flash lamps used in archetypal time-resolved techniques produced an intense pulse of short duration and broadband continuous-wave characteristic, and provided information in a millisecond timescale. Gradual improvements, and especially use of laser sources, allow decrease of resolution times to micro-, nano- and femtoseconds [2,10-12],... 

Years later, physicists proved that electrons do have wave characteristics by producing the interference pattern predicted by de Broglie. Clinton Davisson, working in the United States with his junior partner Lester Germer, and George Thomson in Great Britain made the discovery. For their work, Davisson and Thomson... 

Figure 339 Symmetric (S) and anti-symmetric (A) Lamb wave characteristics. Vertical axis Lamb-wave velocity normalized to transverse bulk-wave velocity. Horizontal axis Product k4 where kt = transverse wavenumber = 27r/At, where At is transverse wavelength and d is plate thickness. (Reprimed with permission. See Ref. [61]. 1967 Plenum Press.)...

The differences between these reefs probably reflect differences in their structural framework and variations in wave characteristics and tidal range in the two environments. Anaerobic reactions in reef interstitial waters may not progress far if reef structures are open and well flushed. If, however, the systems are nearly closed, little fresh reactant will enter via seawater exchange and mass transfer will be limited by the reactants trapped in the reef interstitial waters. An important conclusion of Sansone s studies was that thermodynamic disequilibrium among dissolved species such as CH4 and S04 implies microzonation of chemical reactions. Microzonation resulting in slight differences in reef interstitial water compositions may account for the coexistence of different cement mineralogies in reef structures. 

Sine and cosine functions have the properties that we associate with waves—a well-defined wavelength and amplitude—and we may therefore propose that the wave characteristics of our particle may be described by a combination of sine and cosine functions. A general solution to describe the possible waves in the box would then be... 

The above phenomena me physically miomalous and can be remedied through the introduction of a hyperbolic equation based on a relaxation model for heat conduction, which accounts for a finite thermal propagation speed. Recently, considerable interest has been generated toward the hyperbolic heat conduction (HHC) equation and its potential applications in engineering and technology. A comprehensive survey of the relevant literature is available in reference [6]. Some researchers dealt with wave characteristics and finite propagation speed in transient heat transfer conduction [3], [7], [8], [9] and [10]. Several analytical and numerical solutions of the HHC equation have been presented in the literature. 

This was a revolutionary and quite nebulous suggestion, not easily accepted at the time. If it was not for the intervention of Einstein, excited with the proposal, Louis de Broglie would most likely have failed his doctoral examination. Louis de Broglie found support for his hypothesis and attempted to clarify the wave characteristics of a moving electron by... 

The wave function ijr can be represented by a mathematical expression describing the wave characteristics of an electron in an atom. The Hamiltonian operator,. Hi is a set of mathematical instructions to be performed on if in such a way as to give a result that is a numerical value (the energy of the electron) multiplied by ijr. The details of the Hamiltonian operator need not concern us here elaborate discussions can be found in a variety of physical chemistry texts. The characteristics of the wave function ijr, however, are essential background for understanding the discussion of chemical bonding that will follow. 

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