Universality and Specificity of Fractal Dimension of Fractured Surfaces in Materials

After calculation on the fracture angles under various conditions of specific surface energies with different symmetry operations of rotation, the complicated behavior of dependence of fractal dimension on the structure of crystal is shown. It is found that the crack propagates along the weakest crystal plane no matter what the direction of the maximum stress is if the anisotropy is sufficiently strong; and then, the fractal dimension of the fractured surfaces might be determined by the approximate fractal structure already existed in the material. Specificity of the fractal dimension of fractured surfaces would be easy to appear in this case. Reversely, the crack propagates along the direction of the maximum stress no matter what direction of the weakest crystal plane is if the anisotropy is sufficiently weak. Universality of the fractal dimension of fractured surfaces would be possible to appear in this case. In many real materials, universality and specificity of the materials are associated. The fractal dimension measured may more or less be influenced by the structure of materials and it shows its universality through the specificity of materials.

Plotting the Clarifying Curves and Determination of the Specific Amount of Settled Material during the Initial Period to Sedimentation in Stationary Column of Aqueous Suspensions of Solids

The present paper presents an algorithm and a program for plotting the clarifying curves and for determination of the specific amount of settled material during the initial period based on data obtained from sedimentation experiments in stationary column of aqueous suspensions of solids particles with different concentrations. The algorithm and program have been developed for an interactive, rapid and convenient processing of the data obtained from sedimentation experiments in stationary column of aqueous suspensions of solids particles and allow obtaining with accuracy of precise and expressive graphs which characterize the behaviour of aqueous suspensions to sedimentation in stationary column. Sedimentation study of different aqueous suspensions of solids particles in stationary column is of great importance for experimentally determining the important parameters required to design and exploitation clarifiers and sludge thickeners from waste water treatment plants.

Interlayer transport of an electron in bilayer graphene with phonon-induced lattice distortion in the presence of biased potential

The interlayer transport of an electron in bilayer graphene influenced by a phonon in the presence of a biased potential is investigated using the tight-binding approach. The in-plane optical mode E2g and out-of-plane optical mode B1g associated with the applied biased potential are considered to compute and discuss the interlayer transport probability of an electron initially localized on the bottom layer at the Dirac point in the Brillouin zone. Without the biased potential, the interlayer transport probability is equal to 0.5 regardless of the phonon displacement except for a few special cases. Applying a biased potential to the layers, we find that in different phonon modes the function of the transport probability with respect to the applied biased potential and phonon displacement is complex and various, but on the whole the transport probability decreases with the increase in the absolute value of the applied biased potential. These phenomena are discussed in detail in this paper.