Journal of Multiscale Modelling

In this paper, we present a dynamically adaptive wavelet method for solving Schrodinger equation on one-dimensional, two-dimensional and on the sphere. Solving one-dimensional and two-dimensional Schrodinger equations are based on Daubechies wavelet with finite difference method on an arbitrary grid, and for spherical Schrodinger equation is based on spherical wavelet over an optimal spherical geodesic grid. The method is applied to the solution of Schrodinger equation for computational efficiency and achieve accuracy with controlling spatial grid adaptation — high resolution computations are performed only in regions where a solution varies greatly (i.e., near steep gradients, or near-singularities) and a much coarser grid where the solution varies slowly. Thereupon the dynamic adaptive wavelet method is useful to analyze local structure of solution with very less number of computational cost than any other methods. The prowess and computational efficiency of the adaptive wavelet method is demonstrated for the solution of Schrodinger equation on one-dimensional, two-dimensional and on the sphere.

Cytosolic free calcium concentration is a key regulatory factor and perhaps the most widely used means of controlling cellular function. Calcium can enter cells through different pathways which are activated by specific stimuli including membrane depolarization, chemical signals and calcium depletion of intracellular stores. One of the important components of oocyte maturation is differentiation of the Ca²⁺ signaling machinery which is essential for egg activation after fertilization. Eggs acquire the ability to produce the fertilization-specific calcium signal during oocyte maturation. The calcium concentration patterns required during different stages of oocyte maturation are still not completely known. Also the mechanisms involved in calcium dynamics in oocyte cell are still not well understood. In view of above a two dimensional FEM model has been proposed to study calcium distribution in an oocyte cell. The parameters such as buffers, ryanodine receptor, SERCA pump and voltage gated calcium channel are incorporated in the model. Based on the biophysical conditions the initial and boundary conditions have been framed. The model is transformed into variational form and Ritz finite element method has been employed to obtain the solution. A program has been developed in MATLAB 7.10 for the entire problem and executed to obtain numerical results. The numerical results have been used to study the effect of buffers, RyR, SERCA pump and VGCC on calcium distribution in an oocyte cell.

In this research work we have modeled, simulated and compared the electronic charge transport for Metal-Semiconductor-Metal interfaces of Graphene Nano Ribbons (GNR) with different geometries using First-Principle calculations and Non-Equilibrium Green's Function (NEGF) method. We modeled junctions of Armchair GNR strip sandwiched between two Zigzag strips with (Z-A-Z) and Zigzag GNR strip sandwiched between two Armchair strips with (A-Z-A) using semi-empirical Extended Huckle Theory (EHT) within the framework of Non-Equilibrium Green Function (NEGF). I-V characteristics of the interfaces were visualized for various transport parameters. The distinct changes in conductance and I-V curves reported as the Width across layers, Channel length (Central part) was varied at different bias voltages from -1V to 1 V with steps of 0.25 V. From the simulated results we observed that the conductance through A-Z-A graphene junction is in the range of 10^-13 Siemens whereas the conductance through Z-A-Z graphene junction is in the range of 10^-5 Siemens. These suggested conductance controlled mechanisms for the charge transport in the graphene interfaces with different geometries is important for the design of graphene based nano scale electronic devices like Graphene FETs, Sensors.

To predict the behaviour of thermal physiology of a finite biological tissue in severe cold climatic conditions, a mathematical model has been established based on Pennes' bio-heat transfer equation with oscillatory boundary condition and time dependent heat source term. Crank-Nicholson scheme has been employed to obtain the solution of the boundary value problem to understand the change in stable temperature profiles at the peripheral tissues of human body subjected to forced convection due to cold. Thermal stress at these regions with respect to different input parameters has been computed under extreme environmental conditions using MATLAB Software. The results have shown a relative significance and provide a reasonable outcome in terms of variable metabolic heat generation and oscillatory heat source. The oscillations of the temperature profiles from the mean temperatures were computed in relation with tissue medium and other physiological parameters.