Off-shell t-matrix for an exponential potential with non-local core interaction

The wave function approach of Van Leeuwen and Reiner to the t-matrix is generalized to the case of a non-local potential. The transition matrix element for this potential is obtained. The results are used to compute the s-wave part of the t-matrix for a non-local square well potential combined with an outside exponential potential.     

Noether-Symmetry Analysis using Alternative Lagrangian Representations

We have sought to work with an approach to Noether symmetry analysis which uses the properties of infinitesimal point transformations in the space-time (q, t) variable to establish the association between symmetries and conservation laws of a dynamical system. In this approach symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of two uncoupled Harmonic oscillators and two such oscillators coupled by an interaction. Both these systems can have alternative Lagrangian representations. We have studied in detail how the association between symmetries and conservation laws changes as one alters the analytic or Lagrangian representation. This analysis is carried out with a view to explicitly demonstrate that the correlation between symmetry transformation and corresponding invariant quantity depends crucially on the choice of the analytic representation. PACS 45.20.Jj, 45.20.df, 45.20.dh     

On the supersymmetric nonlinear evolution equations

Supersymmetrization of a nonlinear evolution equation in which the bosonic equation is independent of the fermionic variable and the system is linear in fermionic field goes by the name B-supersymmetrization. We provide B-supersymmetric extension of a number of quasilinear and fully nonlinear evolution equations and demonstrate that the supersymmetric system follows from the usual action principle. We observe that B-supersymmetrization can also be realized using a generalized Noetherian symmetry such that the resulting set of Lagrangian symmetries coincides with symmetries of the field equations. Following this viewpoint we derive conservation laws for the supersymmetric pair of equations. We attempt to realize the bosonic and fermionic fields in terms of bright and dark solitons. The interpretation sought by us has its origin in the classic work of Bateman who introduced a reverse-time system with negative friction to bring linear dissipative systems within the framework of variational principle.     

Evolution of optical pulses in the presence of third-order dispersion

We model the propagation of femtosecond pulses through optical fibres by a nonlinear Schrödinger (NLS) equation involving a perturbing term arising due to third-order dispersion in the medium. The perturbative effect of this higher-order dispersion causes the usual NLS soliton to emit a radiation field. As a result, the given initial pulse propagating through the fibre exhibits nonsolitonic behaviour. We make use of a variational method to demonstrate how an initial pulse by the interaction with the emitted radiation can evolve into a soliton. We also demonstrate that the effect of interaction between the initial pulse and radiation field can be accounted for by including, in the evolution equation, terms associated with self-steepening and stimulated Raman scattering that characterize the optical medium.     

Effects of three-body atomic interaction and optical lattice on solitons in quasi-one-dimensional Bose-Einstein condensate

We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of √1 − bg ₃ with g ₃ the coupling constant of the lattice potential and b = 0.7301.      

The Projection Median of a Set of Points in ℝ<Superscript><Emphasis Type="Italic">d</Emphasis></Superscript>

The projection median of a finite set of points in ℝ² was introduced by Durocher and Kirkpatrick [Computational Geometry: Theory and Applications, Vol. 42 (5), 364–375, 2009]. They proved that the projection median in ℝ² provides a better approximation of the two-dimensional Euclidean median than the center of mass or the rectilinear median, while maintaining a fixed degree of stability. In this paper we study the projection median of a set of points in ℝ ^d for d≥2. Using results from geometric measure theory we show that the d-dimensional projection median provides a (d/π)B(d/2,1/2)-approximation to the d-dimensional Euclidean median, where B(α,β) denotes the Beta function. We also show that the stability of the d-dimensional projection median is at least \frac1(d/p)B(d/2, 1/2)\frac{1}{(d/\pi)B(d/2, 1/2)}, and its breakdown point is 1/2. Based on the stability bound and the breakdown point, we compare the d-dimensional projection median with the rectilinear median and the center of mass, as a candidate for approximating the d-dimensional Euclidean median. For the special case of d=3, our results imply that the three-dimensional projection median is a (3/2)-approximation of the three-dimensional Euclidean median, which settles a conjecture posed by Durocher.     

Uptake of HNO3 on hexane and aviation kerosene soots

The uptake of HNO(3) on aviation kerosene (TC-1) soot was measured as a function of temperature (253-295 K) and the partial pressure of HNO(3), and the uptake of HNO(3) on hexane soot was studied at 295 K and over a limited partial pressure of HNO(3). The HNO(3) uptake was mostly reversible and did not release measurable amounts of gas-phase products such as HONO, NO(3), NO(2) or N(2)O(5). The heat of adsorption of HNO(3) on soot was dependent on the surface coverage. The isosteric heats of adsorption, Delta(0)H(isosteric), were determined as a function of coverage. Delta(0)H(isosteric) values were in the range -16 to -13 kcal mol(-1). The heats of adsorption decrease with increasing coverage. The adsorption data were fit to Freundlich and to Langmuir-Freundlich isotherms. The heterogeneity parameter values were close to 0.5, which suggested that a HNO(3) molecule can occupy two sites on the surface with or without being dissociated and that the soot surface could be nonuniform. Surface FTIR studies on the interaction of soot with HNO(3) did not reveal formation of any minor product such as organic nitrate or nitro compound on the soot surface. Using our measured coverage, we calculate that the partitioning of gas-phase nitric acid to black carbon aerosol is not a significant loss process of HNO(3) in the atmosphere.     

Mechanical property evaluation of glass–jute fiber reinforced polymer composites

The natural fibers such as jute, coir, hemp, sisal etc. are randomly used as reinforcements for composite materials because of its various advantages such as low cost, low densities, low energy consumption over conventional fibers. In addition, they are renewable as well as biodegradable, and indeed wide varieties of fibers are locally available. In this study, glass–jute fiber reinforced polymer composite is fabricated, and the mechanical properties such as tensile, flexural and impact behavior are investigated. The materials selected for the studies were jute fiber and glass fiber as the reinforcement and epoxy resin as the matrix. The hand lay‐out technique was used to fabricate these composites. Fractured surface were comprehensively examined in scanning electron microscope (SEM) to determine the microscopic fracture mode. A numerical procedure based on the finite element method was then applied to evaluate the overall behavior of this composite using the experimentally applied load. Results showed that by incorporating the optimum amount of jute fibers, the overall strength of glass fiber reinforced composite can be increased and cost saving of more than 30% can be achieved. It can thus be inferred that jute fiber can be a very potential candidate in making of composites, especially for partial replacement of high‐cost glass fibers for low load bearing applications. Copyright © 2016 John Wiley & Sons, Ltd.