X-ray Version of Davisson-Germer Experiment

Application of unitcell defined boundary conditions leads to the question on the formation of standing waves within unitcell. We design and propose X-ray version of Davisson-Germer experiment as the answer. In the proposed experiment, a tunable synchrotron beam replaces the variable de Broglie wavelength of incident electron beam. Among the two series of Davisson-Germer peaks from original experiments available in literature, first series shown in figure 1 demonstrates standing wave description and the second series shown in figure 2 demonstrates running wave description. Both running waves and standing waves cannot simultaneously exist within the unitcell and the proposed experiment alone can resolve between the two. The experiment can be conducted on a macromolecular crystal also.

Dynamics of two gas bubbles in liquid in an ultrasonic traveling wave

The influence of the liquid viscosity and compressibility on the dynamics of two air bubbles (with equilibrium radii of 5 μm) in water at room conditions under the action of a plane ultrasonic wave traveling along the line of the bubble centers (the wavelength is 5000 μm, the amplitude is 0.3 bar) is studied. The initial distance between the centers of the bubbles is six bubble radii. A mathematical model is used, which is fourth-order accurate in terms of the ratio of the radius of the bubbles to the distance between them. It is shown that the spatial displacements of the bubbles are determined mainly by their hydrodynamic interaction. The influence of the liquid viscosity and compressibility is generally significant, and the viscosity affects much more. Without account of the liquid viscosity and compressibility, the bubbles collide with each other after the action of 4.5 running-wave lengths. With taking into account the liquid compressibility, the bubbles under the same action remain remote at a distance on the order of their equilibrium radii, while with additionally allowing for the liquid viscosity, their spacing is kept close to the initial one.

SOLUSI NUMERIK PERSAMAAN GELOMBANG KORTEWIEG DE VRIES (KDV)

One of KdV wave form is 𝑢𝑡 + 6𝑢𝑢𝑥 + 𝑢𝑥𝑥𝑥 = 0. This paper deals with finding numerical solutions of KdV’s equation which form a running wave 𝑢(𝑥, 𝑡) = 𝑢(𝑥 − 𝜆𝑡), by using Stepeest DescentMethod which is charged on Hamilton 𝐻(𝑢) and Momentum 𝑀(𝑢). By using MAPLE software, we obtain numerical solutions of KdV equation in the form of running wave profile