Abstract:
We demonstrate the use of photonic crystal fiber (PCF) joined in between two single mode fibers (SMF) as a concentration sensor. To realize this, one micrometer length PCF of hexagonal lattice is sandwiched between two SMF having one micrometer length each. To maximize the coupling between SMF and PCF, the core diameters are made equal. Then the output from a given input through this structure is analyzed with respect to different concentrations in the air holes of PCF using Finite Difference Time Domain (FDTD) method. It is found that the variation of electric field intensity at the output is linear with respect to concentration of alcohol.

Abstract:
We in this paper propose a model to increase the diffraction efficiency of a holographic grating at 1550 nm for multiplexing application. To use such a grating, polarization dependence loss is introduced analytically and then optimized for its minimum value A configuration of holographic grating is proposed based on both maximum diffraction efficiency and minimum polarization dependence loss. The proposed grating is expected to find importance in optoelectronic multichip module.

Abstract:
Ever since its introduction in the second decade of the past century, the economic order quantity (EOQ) model has been the subject of extensive investigations and extensions by academicians. The physical characteristics of stocked items dictate the nature of inventory policies implemented to manage and control. The question is how reliable are the EOQ models when items stocked deteriorate one time. This paper introduces a modified EOQ model in which it assumes that a percentage of the on-hand inventory is wasted due to deterioration. There is hidden cost not account for when modeling inventory cost. We study the problem of promotion for a deteriorating item subject to loss of these deteriorated units. The objective of this paper is to determine the optimal time length, optimal units lost due to deterioration, the promotional effort and the replenishment quantity so that the net profit is maximized and the numerical analysis show that an appropriate promotion policy can benefit the retailer and that promotion policy is important, especially for deteriorating items. Furthermore crisp decision making is shown to be superior to crisp decision making without promotional effort cost in terms of profit maximization.

Abstract:
Wepropose to measure the concentration of potassium chloride using photonic crystal fiber having circular air holes of diameter 400 nm. The principle of measurement is based on the linear variation of the transmitted field emerging from the PCF with respect to concentration of potassium chloride. Field distribution in photonic crystal structure is simulated using plane wave expansion (PWE) method. Simulation result reveals that the intensity of transmitted light varies linearly with respect to concentration of potassium chloride filled in the air holes.

Abstract:
Large tonnages of chromite tailing were discarded during processing of chromite ore in the
conventional circuit. A typical chromite plant tailing was treated in wilfley table for the recovery
of chromite values. Optimisation study was carried out for the process parameters of wilfley
table using empirical models, developed from the experimental data. It was found that grade and
recovery (% Cr_{2}O_{3}) in the concentrate fraction majorly depended on the variation of deck tilt
angle. To achieve high grade (>45%) with acceptable recovery (>40%), set of optimisation
condition of parameters have derived which resulted large quantity of wash water (>5lpm of
flow rate) is necessary. Validation of the empirical models were done with set of tests which
resulted good agreement with the predict values (R2 is 0.96 and 0.99 for the grade and recovery
respectively).

Abstract:
The High Tension Roll Separator (HTRS) is one of the main electrostatic unit operations employed to separate titanium minerals like ilmenite, rutile and leucoxene which behave as conducting from zircon, sillimanite, garnet and monazite which behave as non-conducting minerals when a high potential difference is applied. Three process inputs, namely roll speed, feed material temperature and roll speed have been optimized. Experiments were conducted based on the Box- Behnken factorial design; the results were analyzed using response surface methodology (RSM). A new term, called Operational Quality Index (OQI) has been defined as a process output, which is maximized by quadratic programming, to obtain the optimum operating conditions. The maximum value of OQI obtained under the constraints of grade >96% and recovery >98% is 195.53, at the following operating conditions—Temperature: 102°C, Feed Rate: 1.75 tph and Roll Speed: 132 rpm. Under these conditions, the grade and recovery obtained are 96.6% and 98.9% respectively.

Abstract:
In this article, we obtain conditions for the oscillation of vector solutions to the first-order systems of linear difference equations $$displaylines{ x(n+1)=a(n)x+b(n)y cr y(n+1)=c(n)x+d(n)y }$$ and $$displaylines{ x(n+1)=a(n)x+b(n)y+f_1(n) cr y(n+1)=c(n)x+d(n)y+f_2(n) }$$ where $a(n), b(n), c(n), d(n) $ and $f_i(n), i=1, 2$ are real valued functions defined for $n geq 0$.

Abstract:
We study front propagation in the reversible reaction-diffusion system A + A <-> A on a 1-d lattice. Extending the idea of leading particle in studying the motion of the front we write a master equation in the stochastically moving frame attached to this particle. This approach provides a systematic way to improve on estimates of front speed obtained earlier. We also find that the leading particle performs a correlated random walk and this correlation needs to be taken into account to get correct value of the front diffusion coefficient.

Abstract:
We study front propagation in the irreversible epidemic model $A+B\to 2A$ in one dimension. Here, we allow the particles $A$ and $B$ to diffuse with rates $D_A$ and $D_B$, which, in general, may be different. We find analytic estimates for the front velocity by writing truncated master equation in a frame moving with the rightmost $A$ particle. The results obtained are in reasonable agreement with the simulation results and are amenable to systematic improvement. We also observe a crossover from the linear dependence of front velocity $V$ on $D_A$ for smaller values of $D_A$ to $V\propto \sqrt{D_A}$ for larger $D_A$, but numerically still significantly different from the mean field value. The deviations reflect the role of internal fluctuations which is neglected in the mean field description.

Abstract:
We study front propagation in the reaction diffusion process $A\leftrightarrow2A$ on one dimensional lattice with hard core interaction between the particles. We propose a two site self consistent method (TSSCM) to make analytic estimates for the front velocity and are in excellent agreement with the simulation results for all parameter regimes. We expect that the simplicity of the method will allow one to use this technique for estimating the front velocity in other reaction diffusion processes as well.