Numerical approximations for population growth model by rational Chebyshev and Hermite functions collocation approach: A comparison

This paper aims to compare rational Chebyshev (RC) and Hermite functions (HF) collocation approach to solve Volterra's model for population growth of a species within a closed system. This model is a nonlinear integro‐differential equation where the integral term represents the effect of toxin. This approach is based on orthogonal functions, which will be defined. The collocation method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare these methods with some other numerical results and show that the present approach is applicable for solving nonlinear integro‐differential equations. Copyright © 2010 John Wiley & Sons, Ltd.     

Infrared spectra of acetylene–water complexes: C2D2–H2O,C2D2–HDO,and C2D2–D2O

Infrared spectra of C₂D₂–water complexes are studied in the 4.1 μm region of the C₂D₂ ν₃ fundamental band using a tunable diode laser source to probe a pulsed supersonic slit jet. Relatively large vibrational red shifts (?27.7 to ?28.0 cm^?1) are observed which are more easily interpretable than for the analogous C₂H₂ vibration thanks to the absence of Fermi resonance effects for C₂D₂. Noticeable homogeneous line broadening leads to estimates of upper state predissociation lifetimes of about 0.5, 0.9 and 1.1 ns for C₂D₂–H₂O, –HDO, and –D₂O, respectively. Transitions involving K_a = 0 and 1 levels are observed for C₂D₂–HDO, but there is a puzzling absence of K_a = 1 for C₂D₂–H₂O and C₂D₂–D₂O.     

Study of optical properties in a cubic quantum dot

In this paper, the effect of hydrostatic pressure on both the intersubband optical absorption coefficients and the refractive index changes is studied for typical GaAs/Al _x  Ga_1?x As cubic quantum dot. We use analytical expressions for the linear and third-order nonlinear intersubband absorption coefficients and refractive index changes obtained by the compact-density matrix formalism. The linear, third-order nonlinear, and total intersubband absorption coefficients and refractive index changes are calculated at different pressures as a function of the photon energy with known values of box length (L), the incident optical intensity (I), and Al concentration (x). According to the results obtained from the present work, we have found that the pressure plays an important role in the intersubband optical absorption coefficient and refractive index changes in a cubic quantum dot.     

A molecular dynamics study of effective parameters on nano-droplet surface tension

The main purpose of this paper is to numerically study the effect of droplet radius, temperature, and surface wettability on droplet surface tension. Moreover, the validity of Young-Laplace equation (Y-L) for nano-droplet is examined. Simulations of droplet surrounded by its vapor and droplet on solid surface are carried out and the results are compared to each other in order to comprehend the role of surface wettability on droplet surface tension. The pair potential for the liquid-liquid and liquid-solid interaction is considered using Lennard-Jones model. Different numbers of atoms and surface wettabilities are employed to generate droplet of different radiuses. In addition, contact angle of droplet on solid surface is computed. Pressure tensor and density profile is locally calculated. Furthermore, liquid pressure is evaluated far from the interface using the virial theorem and gas pressure is obtained using an equation of state. In order to calculate the surface tension, two different approaches are employed; Young-Laplace equation and direct molecular dynamics (MD) simulation. The surface tension increases with increase in droplet radius and it is seen that the surface wettability does not directly influence the surface tension.     

Study of stability of variants of ovine prions with different susceptibilities to scrapie

Well-defined set of sheep PrP polymorphisms at positions 136, 154 and 171 define susceptibility to scrapie, ranging from very high susceptibility observed for V136-R154-Q171 (VRQ) variant to resistance for A136-R154-R171 (ARR).To gain insight into the mechanisms of scrapie susceptibility/resistance, the unfolding pathways of the sheep prion protein variants were analysed by differential scanning calorimetry over a wide range of pH. Thermal unfolding occurs, in the 5.0 to 6.0 pH range, through a reversible one-step process while at pH<4.5 and >6.0 unfolding intermediates are formed, which are stable in the 65–80°C range. The observed differences correlate with ovine susceptibility to scrapie.This revised version was published online in November 2005 with corrections to the Cover Date.     

Hypercyclicity on the Algebra of Hilbert-Schmidt Operators

We prove that the Hypercyclicity Criterion for any operator T on a Hilbert space is equivalent to the hypercyclicity of the left multiplication operator induced by T on the algebra of Hilbert-Schmidt operators.