Solitary Waves of Maxwell's Equations in Nonlinear Anisotropic Media

Abstract

The (1 + 1)-D solitary wave solutions of Maxwell's equations in nonlinearity induced anisotropic media (in liquids such as carbon disulphide, and in crystals, etc.) are investigated. We find that there is no arbitrarily linearly polarized (in the x-y plane perpendicular to the propagation direction z) soliton solution from Maxwell's equations except that with linear polarization either in alignment with or orthogonal to the geometric axis of the light induced refractive index change. This contradicts the prediction of the vector nonlinear Schroedinger equation (an approximation of Maxwell's equations) which yields soliton solutions with an arbitrary linear polarization. However, Maxwell's equations are found to admit stable elliptically polarized solitary wave solutions which reduce to the stable circularly polarized solitary wave solutions of the vector nonlinear Schroedinger equation when the induced refractive index change approaches zero.     

Investigation of the Soret effect in copper nanoparticle colloids by self-phase modulation and Z-scan

A theoretical investigation is reported on the photo-thermal response of copper nanoparticle colloids in the presence of thermal and mass diffusion processes. The absorbed laser beam energy is converted into heat and generates a temperature gradient, which causes nanoparticle concentration variation in the fluid. Transverse spatial redistribution of the nanoparticles induces changes in absorption and refraction of the medium. Experimentally, the photo-thermal response was determined by measuring absorption and refraction changes of the nanoparticle colloids using the far-field diffraction patterns and Z-scan technique. This allowed evaluation of the Soret coefficient of the nanoparticle colloids and excellent agreement is found in measuring this coefficient using both the far-field diffraction pattern and Z-scan technique.     

Application of nano-sized cobalt on ZSM-5 zeolite as an active catalyst in Fischer–Tropsch synthesis

In this study the catalytic behavior of Co/HZSM-5 in Fischer–Tropsch synthesis (FTS) has been examined in order to optimize the operating conditions for acquiring maximum selectivity. Catalysts consisted of various quantities of cobalt particles supported on HZSM-5 zeolite were prepared by impregnation method. In order to investigate the effects of operating parameters on catalytic performance and to estimate the optimum conditions, experiments were designed using L-16 Taguchi method. All experimental runs were carried out in a fixed bed reactor under isobaric condition (2 MPa). According to the Taguchi model and considering the impact of the operating parameters on the process output and performing certain validation tests, the optimum operating conditions for the process were determined as T = 513 K, space velocity = 1.1 h^?1, Co on HZSM-5 = 11.6%, H₂/CO = 1.7.In the next step, a kinetic model for FTS based on carbide mechanism was presented applying the synthesized catalyst under the optimum conditions. This model is a combination of kinetic rates of hydrocarbon formation and the relations for the growth probability and olefin re-adsorption factor.     

Development of Fixed Frequency Beam Steering Wide Band Leaky Wave Cavity Antenna

A complete design of substrate integrated leaky wave cavity antenna for fixed frequency beam steering is presented. The antenna consists of a small rectangular metallic tapered cavity fed by hook-shaped element and covered by the substrate. The steering of the beam in the desired direction is achieved by controlling the taper of the cavity. The beam is scanned at fixed frequency by changing position of the microstrip lines on the substrate. The substrate placed on the cavity resolves the problem of input impedance mismatch. The pertinent features of the antenna are compactness, broadband, and fixed-frequency beam steering capability.     

Rehabilitating acid soils for increasing crop productivity through low-cost liming material

Productivity of red and lateritic soils is low because of their acidity and deficiencies in few essential nutrients viz., nitrogen, phosphorus, calcium, zinc, boron, molybdenum etc. We compared the effectiveness of basic slag, a low-cost liming material, with that of calcite as an ameliorant for these soils using mustard followed by rice as test crops. Experiments were conducted with three levels of each of basic slag and calcite along with a control on farmers' fields at 14 different locations. Influence of farmyard manure (FYM) and poultry manure (PM) on the effectiveness of the slag was also tested. On an average, basic slag performed better than calcite in increasing yields of both mustard and rice and left over higher amounts of available Ca, Si and Zn in residual soils. The slag also improved N, P, K and Ca nutrition of mustard and Si and Zn nutrition of rice with a favorable benefit:cost (B:C) ratio over the calcite (4.82 vs. 1.44). Effectiveness of the basic slag improved when it was applied in combination with FYM or PM (B:C, 5.83 and 6.27). Basic slag can, therefore, be advocated for use in the acidic red and lateritic soils for economically improving their productivity.     

A spatially explicit model of postdisaster housing recovery

Although postdisaster housing recovery is an important player in community recovery, its modeling is still in its infancy. This research aims to provide a spatial regression model for predicting households’ recovery decisions based on publicly available data. For this purpose, a hierarchical Bayesian geostatistical model with random spatial effects was developed. To calibrate the model, households’ data that were collected from Staten Island, New York, in the aftermath of Hurricane Sandy were used. The model revealed that on the scale of census tract, residents with higher income or larger household size were significantly less likely to reconstruct. In contrast, odds of reconstruction rose with increase of long‐term residents. The model outputs were also employed to develop a reconstruction propensity score for each census tract. The score predicts probability of reconstruction/repair in each tract versus others. The model was validated through comparison of the propensity scores with the distribution of Community Development Block Grant Disaster Recovery assistance and its resultant reconstruction. The validation indicated capability of the model to predict the potential hotspots of reconstruction. Accordingly, the propensity score can serve as a decision‐support tool to tailor recovery policies.