SMARANDACHE NUMBER RELATED TRIANGLES

Given a triangle in Euclidean geometry it is well known that there exist an infinity of triangles each of which is similar to the given one. In Section I we make certain observations on Smarandache numbers

Quantum Mechanics of Extended Objects

We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this representation is used to demonstrate the quantization of spacetime. The quantum mechanics of extended objects is then applied to two paradigm examples, namely, the fuzzy (extended object) harmonic oscillator and the Yukawa potential. In the second example, we theoretically predict the phenomenological coupling constant of the $\omega$ meson, which mediates the short range and repulsive nucleon force, as well as the repulsive core radius.Comment: RevTex, 24 pages, 1 eps and 5 ps figures, format change

Numerical Modelling Study of Behaviour of Consolidated Strata Around Tunnel

Tunnelling in densely populated areas and under existing buildings is common in most of the cities around the world. Upon excavation there are changes that take place in the soil /rock mass and these changes can have an impact on the surface structures. In this paper an attempt is made to assess the behavior of the tunnel in given environment and the associated displacements due to tunneling in a highly consolidated soil/rock mass with two different conditions of earth pressure coefficient. A case study of a tunnel in South India was taken up for studies. 3-dimensional Distinct Element Modelling code was used for the analysis. In the first stage, earth pressure coefficient Ko of 2.2 was taken for the top layers and 1.8 for bottom layers. In the second stage, a value of 2.2 was considered throughout the model. In the third stage displacement generated in the transverse direction, in the presence and absence of the building load was taken into consideration and analysed. Vertical displacements were found to be of considerable magnitude at the crown, showing a decreasing trend towards the surface. Horizontal displacements were of negligible magnitude along the depth. However, maximum displacement was noted at the springing level of the tunnel. Models incorporating weight of buildings showed no noticeable increase in the settlements, as the soil/rock mass is already consolidated.Keywords: Numerical modeling; 3 Dimensional; Distinct Element code; Earth pressure coefficient