Wave behavior

Observations of smooth spalls in iron provided an early, dramatic demonstration of the importance of release wave behaviors. In 1956, Dally [61E01] reported the existence of remarkably smooth fracture surfaces in explosively compressed steel. The existence of these smooth spalls was a sensitive function of the sample thickness. Analysis and experiments by Erkman [61E01] confirmed that the smooth spalls were associated with interaction of release-wave shocks and shocks from reduction of pressure at free surfaces. These release shocks are a consequence of differences in compressibility at pressures just below and just above the 13 GPa transformation. 

Given the various release-wave behaviors summarized above, it is clear that release waves may often dominate wave profiles, and failure to consider their influences can lead to incorrect interpretation of observed materials responses, especially those in which samples are preserved for post-shock... 

A class of partial differential equations first proposed by Erwin Schrodinger in 1926 to account for the so-called quantized wave behavior of molecules, atoms, nuclei, and electrons. Solutions to the Schrodinger equation are wave functions based on Louis de Broglie s proposal in 1924 that all matter has a dual nature, having properties of both particles and waves. These solutions are... 

Detonation Wave Behavior in Permissible Explosives. See Ref 46, listed on p D726... 

Our intent here is not to suggest a solution method but rather to use the stream-function-vorticity formulation to comment further on the mathematical characteristics of the Navier-Stokes equations. In this form the hyperbolic behavior of the pressure has been lost from the system. For low-speed flow the pressure gradients are so small that they do not measurably affect the net pressure from a thermodynamic point of view. Therefore the pressure of the system can simply be provided as a fixed parameter that enters the equation of state. Thus pressure influences density, still accommodating variations in temperature and composition. Since the pressure or the pressure gradients simply do not appear anywhere else in the system, pressure-wave behavior has been effectively filtered out of the system. Consequently acoustic behavior or high-speed flow cannot be modeled using this approach. 

Taylor and Kennedy (T8), 1961 Discussion of onset of wave formation and wave behavior in open-channel flow. 

To analyze the shock wave behavior in a gas-solid flow, several assumptions are made ... 

FIGURE 61 Specific-heat contribution y (H) of the vortex-core electrons in the mixed state (normalized by the Sommerfeld parameter y ) of the YxLui xNi2B2C samples from Figure 60 as function of the applied magnetic field. The dotted straight line y(H) H corresponds to the usual s-wave behavior in the dirty limit. 

To prove the. v-wave character of the superconductivity, we first present /j+SR data acquired in a high-quality YBa2Cu3C>6.95 crystal at applied magnetic fields of 0.05, 1.0, 3.0, and 6.0 Tesla. The measured temperature- and field-dependences of the second moment of the local field distribution, self-consistent analysis in which deviations from i-wave symmetry are attributed to weak fluxon de-pinning phenomena, rather than to d-wave effects. We show that the purported intrinsic d-wave behavior previously claimed for muon experiments is actually not due to d- waves but is an extrinsic phenomenon caused by flux de-pinning.9... 

Instead of forcing the data to conform to the d-wave picture, we take the approach that the deviations from. v-wave behavior are due to quantifiable phenomena, most notably temperature-dependent fhixon de-pinning. Since the maximum temperature for the data acquired at each held is below the melting curve (see Fig. 4 of Ref. 11), the vortex lattice is subject to pinning, as occurs in very clean crystals where the flux lattice becomes locked-in by weak pinning at oxygen vacancies and/or other defects. 

But according to the present approach, they behave as quantum states in Hilbert space. These latter can be diffracted and modulated interference patterns. This latter is taken as the signal of wave behavior in the standard textbooks. But, as water waves in a pond designed to mimic a two-slit setup... 

Wave/particle duality is the postulate that all objects of physical reality possess both localized (particle) and distributed (wave) properties. Due to their low rest mass, electrons exhibit both particle and wave behavior on the scale of length of atoms (nanometers). Thus, every electron has a wavelength associated with it. This wavelength is called the de Broglie wavelength Adb,... 

The interstitial region between these spheres is represented by a constant potential valve (the muffin-tin constant or muffin-tin zero). This is the region of unscattered electron propagation, in which simple plane-wave or spherical-wave behavior describes the electron wave-field. The plane-wave description is computationally advantageous when dealing with multiple scattering by periodic lattices, since such lattices diffract any plane wave into other well-defined plane waves. This approach is often useful even with non-periodic overlayers adsorbed on an otherwise periodic substrate. 

If production of an oxidizing hole in the da orbital is the important factor in the photochemical reaction, then electrochemical veneration of such a hole should produce a highly reactive intermediate mat would mimic the initial step in the 3(da po) photoreaction. Several of the binuclear complexes undergo reversible one-electron oxidations in noncoordinating solvents (22-24). The complex Rh2(TMB)42+ possesses a quasireversible one-electron oxidation at 0.74 V (Electrochemical measurements for [Rh2(TMB)4](PF6)2 CH2CI2/TBAPF6 (0.1 M), glassy carbon electrode, 25°C, SSCE reference electrode). Electrochemical oxidation of Rh2(TMB)42+ in the presence of 1,4-cyclohexadiene exhibits an enhanced anodic current with loss of the cathodic wave, behavior indicative of an electrocatalytic process (25). Bulk electrolysis of Rh2(TMB)42+ in an excess of 1,4-cyclohexadiene results in the formation of benzene and two protons (Equation 4). 

This paper deals with thermal wave behavior during frmisient heat conduction in a film (solid plate) subjected to a laser heat source with various time characteristics from botii side surfaces. Emphasis is placed on the effect of the time characteristics of the laser heat source (constant, pulsed and periodic) on tiiermal wave propagation. Analytical solutions are obtained by memis of a numerical technique based on MacCormack s predictor-corrector scheme to solve the non-Fourier, hyperbolic heat conduction equation. 

Wave behavior of light Diffraction and interference effects of superimposed waves... 

The wave model fails to account for phenomena associated with the absorption and emission of radiant energy. For these processes, electromagnetic radiation can be treated as discrete packets of energy or particles called photons or quanta. These dual views of radiation as particles and waves are not mutually exclusive but are complementary. In fact, the energy of a photon is directly proportional to its frequency, as we shall see. Similarly, this duality applies to streams of electrons, protons, and other elementary particles, which can produce interference and diffraction effects that are typically associated with wave behavior. 

The wave behavior of electrons is exploited in the electron microscope. This instrument allows magnification of objects far too small to be seen with an ordinary light microscope. 

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