An efficient numerical scheme for solving Hammerstein integral equation arisen in chemical phenomenon

AbstractIn Science and engineering, so many nonlinear phenomena are presented as partial differential, ordinary differential and integral equation models. So in this article, our aim is to study on Hammerstein type nonlinear integral equation μS(σ)=−RTLn[∫abPS(σ∘)exp{−ϵ(σ,σ∘)+μS(σ∘)RT}dσ∘] Where R is the gas constant, T the temperature, the term ϵ(σ,σ∘) denotes the interaction energy expression for the segments with screening charge density σ and σ∘ respectively, the molecular interaction in solvent is PS(σ) and the chemical potential of the surface segments is described by μS(σ) that should be determined. This integral equation forms the basis for the conductor-like screening model for real solvents (COSMO-RS) which is appeared in chemical phenomena. Some of numerical methods usually use techniques based on a projection in terms of some basis functions or use some quadrature formulas, and the convergence rate of these methods are usually of polynomial order with respect to N, where N represents the number of terms of the expansion or the number of points of the quadrature formula. Also, in projection methods nonlinear Hammerstein integral equation is reduced to the nonlinear algebraic equations which solving them in large scales needs high memory capacity and CPU time and because of error propagation convergence of numerical technique may be at risk. So this paper presents a powerful numerical approach based on Sinc quadrature which has exponential type convergence rate to solve conductor-like screening model for real solvents (COSMO- RS). The approach is based on preparing an iterative method to recognize the Hammerstein integral equation for the determination of the chemical potential of a surface segment as a function of screening charge density

A New Reconstruction of Variational Iteration Method and Its Application to Nonlinear Volterra Integrodifferential Equations

We reconstruct the variational iteration method that we call, parametric iteration method (PIM). The purposed method was applied for solving nonlinear Volterra integrodifferential equations (NVIDEs). The solution process is illustrated by some examples. Comparisons are made between PIM and Adomian decomposition method (ADM). Also exact solution of the 3rd example is obtained. The results show the simplicity and efficiency of PIM. Also, the convergence of this method is studied in this work

Gauge-flation and Cosmic No-Hair Conjecture

Gauge-flation, inflation from non-Abelian gauge fields, was introduced in [1,2]. In this work, we study the cosmic no-hair conjecture in gauge-flation. Starting from Bianchi-type I cosmology and through analytic and numeric studies we demonstrate that the isotropic FLRW inflation is an attractor of the dynamics of the theory and that the anisotropies are damped within a few e-folds, in accord with the cosmic no-hair conjecture.Comment: 24 pages, 18 figure

Approximate Solution of Fractional Integro-Differential Equations by Least Squares Method

In this paper, least squares approximation method is developed for solving a class of linear fractional integro-differential equations comprising Volterra and Fredhlom cases. This method is based on a polynomial of degree n to compute an approximate solution of these equations. The convergence analysis of the proposed method is proved. In addition, to show the accuracy and the efficiency of the proposed method, some examples are presented

Modified Block Pulse Functions for Numerical Solution of Stochastic Volterra Integral Equations

We present a new technique for solving numerically stochastic Volterra integral equation based on modified block pulse functions. It declares that the rate of convergence of the presented method is faster than the method based on block pulse functions. Efficiency of this method and good degree of accuracy are confirmed by a numerical example

Gauged M-flation, its UV sensitivity and Spectator Species

In this paper we study gauged M-flation, an inflationary model in which inflation is driven by three NxN scalar field matrices in the adjoint representation of U(N) gauge group. We focus our study on the gauged M-flation model which could be derived from the dynamics of a stack of D3-branes in appropriate background flux. The background inflationary dynamics is unaltered compared to the ungauged case of [arXiv:0903.1481[hep-th]], while the spectrum of "spectator species", the isocurvature modes, differs from the ungauged case. Presence of a large number of spectators, although irrelevant to the slow-roll inflationary dynamics has been argued to lower the effective UV cutoff $\Lambda$ of the theory from the Planck mass, invalidating the main advantage of M-flation in not having super-Planckian field values and unnaturally small couplings. Through a careful analysis of the spectrum of the spectators we argue that, contrary to what happens in N-flation models, M-flation is still UV safe with the modified (reduced) effective UV cutoff $\Lambda$, which we show to be of order (0.5-1)x10^{-1} M_{pl}. Moreover, we argue that the string scale in our gauged M-flation model is larger than $\Lambda$ by a factor of 10 and hence one can also neglect stringy effects. We also comment on the stability of classical inflationary paths in the gauged M-flation.Comment: 16 pages, no figures; v2: added remarks and two references; v3: JCAP versio

Issues on Generating Primordial Anisotropies at the End of Inflation

We revisit the idea of generating primordial anisotropies at the end of inflation in models of inflation with gauge fields. To be specific we consider the charged hybrid inflation model where the waterfall field is charged under a U(1) gauge field so the surface of end of inflation is controlled both by inflaton and the gauge fields. Using delta N formalism properly we find that the anisotropies generated at the end of inflation from the gauge field fluctuations are exponentially suppressed on cosmological scales. This is because the gauge field evolves exponentially during inflation while in order to generate appreciable anisotropies at the end of inflation the spectator gauge field has to be frozen and scale invariant. We argue that this is a generic feature, that is, one can not generate observable anisotropies at the end of inflation within an FRW background.Comment: V3: new references added, JCAP published versio