Numerical Solvability of Hammerstein Integral Equations of Mixed Type

We consider a mixed Hammerstein integral equation of the form where –<a<b<, y, f_i and k_i, (1im) are known functionsand x is a solution to be determined. In this paper, we obtainexistence, uniqueness, and numerical solvability of (I) undercertain smoothness assumptions on the known functions y, f_iand k_i.     

Second harmonic generation from corona-poled polymer thin films of Y-shape chromophore with different isolation groups

We characterize thermal stability fof second harmonic generation (SHG) properties of four different Y-type polymers poled using corona poling method. These polymers are based on donor–acceptor–donor-type repeating unit with different aromatic moieties acting as donors and dicyanomethylene acting as an acceptor through conjugated bridge. The donor varies from different substituted benzene to phenothiazine. Polymer containing phenothiazine as donor showed higher SHG intensity and high temperature stability due to rigid repeating unit of phenothiazine compared to others with benzene in the main chain.     

SOLVING A CROP PROBLEM BY AN OPTIMAL CONTROL METHOD

ABSTRACT. A system of ordinary differential equations coupled with a parabolic partial differential equation is studied in order to understand an interaction between two crops and a pathogen. Two different types of crops are planted in same field in some pattern so that the spread of pathogen can be controlled. The pathogen prefers to eat one crop. The other crop, which is not preferred by the pathogen, is introduced to control the spread of pathogen in the farming land. The “optimal” initial planting pattern is sought to maximize plant yields while minimizing the variation in the planting pattern. The optimal pattern is characterized by a variation inequality involving the solutions of the optimality system. Numerical examples are given to illustrate the results.     

Thermoelastic properties of minerals at high temperature

The knowledge of elasticity of the minerals is useful for interpreting the structure and composition of the lower mantle and also in seismic studies. The purpose of the present study is to discuss a simple and straightforward method for evaluating thermoelastic properties of minerals at high temperatures. We have extended the Kumar’s formulation by taking into the account the concept of anharmonicity in minerals above the Debye temperature (θ _D). In our present study, we have investigated the thermophysical properties of two minerals (pyrope-rich garnet and MgAl₂O₄) under high temperatures and calculated the second-order elastic constant (C _ij ) and bulk modulus (K _T) of the above minerals, in two cases first by taking Anderson–Gruneisen parameter (δ _T) as temperature-independent and then by treating δ _T as temperature-dependent parameter. The results obtained when δ _T is temperature-dependent are in close agreement with experimental data.     

Numerical simulation of immiscible liquid-liquid flow in microchannels using lattice Boltzmann method

Immiscible kerosene-water two-phase flows in microchannels connected by a T-junction were numerically studied by a Lattice Boltzmann (LB) method based on field mediators.The two-phase flow lattice Boltzmann model was first validated and improved by several test cases of a still droplet.The five distinct flow regimes of the kerosene-water system,previously identified in the experiments from Zhao et al.,were reproduced.The quantitative and qualitative agreement between the simulations and the experimental dat...     

Dielectric relaxation and hydrogen bonding studies of 1,3-propanediol–dioxane mixtures using time domain reflectometry technique

The complex permittivity, static dielectric constant and relaxation time for 1,3-propanediol, 1,4-dioxane and their mixtures have been studied using time domain reflectometry (TDR). The excess permittivity, excess inverse relaxation time and Kirkwood correlation factor have also been determined at various concentrations of dioxane. Hydrogen bonded theory was applied to compute the correlation terms for the mixtures. The Bruggeman model for the nonlinear case has been fitted to the dielectric data for mixtures.     

OPTIMAL DYNAMIC HARVEST OF A MOBILE RENEWABLE RESOURCE

Abstract We present a mathematical model for the growth, movement, and harvesting of a renewable resource, and characterize the spatiotemporal distribution of harvest effort which maximizes the present value of harvest (yield) over a finite time horizon. We derive the optimality system for this model and show that the yield‐maximizing solution often includes one or more no‐take reserves that change in size over time. We explore how the results change with varying parameter values. The results inform ongoing debate about the use of reserves, and are increasingly relevant as technology enables enforcement of spatially structured harvest constraints.