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Weight function for a crack in an orthotropic medium under normal impact loading

100%

Mukherjee S. , Das S.

tom Vol. 11, no 4

915-928

The paper deals with the investigation of an elastodynamic response of an infinite orthotropic medium containing a central crack under normal impact loading. Laplace and Fourier integral transforms are employed to reduce the dimensional wave propagation problem to the solution of a pair of dual integral equations in the Laplace transform plane. These integral equations are then reduced to integral differential equations which have been solved in the low frequency domain by method of iteration. To determine time dependence of the parameters, these equations are inverted to yield the dynamic stress intensity factor (SIF) for normal point force loading. These results have been used to obtain the SIF at the crack tip which corresponds to the weight function for the crack under normal loading. Analytical expressions of the weight function are used to derive SIF for polynomial loading. Numerical results of normalized SIF for a large normalized time variable and for different concentrated point force loading at an arbitrary location of the crack surface have been calculated for different orthotropic materials. In the present paper, a numerical Laplace inversion technique is used to recover the time dependence of the solution. Finally, the results obtained are displayed graphically.

Two-dimensional numerical analysis on mid-infrared emission from IV-VI lead salt photonic crystal microcavity

80%

Mukherjee S. , Bi G. , Kar J. P. , Shi Z.

2009

tom Vol. 39, nr 3

499-509

An optimal design of two dimensional (2D) hexagonal photonic bandgap (PBG) resonating micro-optical defect cavity on IV-VI lead salt material has been carried out. The nature of both the transverse electric (TE) and transverse magnetic (TM) band structure for the electromagnetic waves in the periodic triangular lattice pattern is formulated by the well-established plane wave expansion (PWE) method. The defect cavity is engineered to resonate at ~4.17 žm in TM bandgap. The field distribution in the defect cavity has been analyzed based on two very efficient and popular schemes - perturbation correction finite difference (FD) method and finite difference time domain (FDTD) mechanism which is truncated by uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC). FD method efficiently solves Helmholtz equations to evaluate the field distribution in the semiconducting waveguide for any single spectral wavelength. The numerical results by FD method are re-established by the FDTD scheme that incorporates a precise numerical analysis within a specified wavelength range.

A uniqueness result on meromorphic functions sharing two sets II

80%

Banerjee A. , Majumder S. , Mukherjee S.

Fasciculi Mathematici

2014

tom Nr 53

17--30

We employ the notion of weighted sharing of sets to deal with the well known question of Gross and obtain a unique-ness result on meromorphic functions sharing two sets which will improve an earlier result of Lahiri [15] and a recent one of Banerjee [2].

Effect of multiple adjoining habitats on avifaunal diversity in an agriculture based-wetland adjacent to the Hooghly River, West Bengal, India

80%

Sau M. , Chakraborty M. , Das R. , Mukherjee S.

tom 40

Refined techniques for the analysis of Asiatic lion Panthera leo persica scats

80%

Mukherjee S. , Goyal S. P. , Chellam R.

tom 39

nr 4

We improved the techniques for determining prey items based on hair characteristics from scats of the free-ranging Asiatic lion Panthera leo persica (Meyer, 1826) in terms of accuracy and time efficiency. Cuticular characteristics of hair are similar in many Indian prey species and are not species specific. A combination of hair characteristics, e.g. hair width, medullary structure, and medulla width expressed as per cent of hair width, are most useful to identify the common mammalian prey species. We found that examination of a minimum of 20 hairs/scat and 30 scats would provide a reliable estimate of the lion's diet based on the per cent occurrence of prey species hair in the scats.