Applications of the wave packet method to resonant transmission and reflection gratings

Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive (dispersive and absorbing) media. The algorithm is based on the Hamiltonian formalism in the framework of which Maxwell's equations for passive media are shown to be equivalent to the first-order equation, $\partial \Psi/\partial t = {\cal H}\Psi$, where ${\cal H}$ is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector $\Psi$ built of the electromagnetic inductions and auxiliary matter fields describing the medium response. The initial value problem is then solved by means of a modified time leapfrog method in combination with the Fourier pseudospectral method applied on a non-uniform grid that is constructed by a change of variables and designed to enhance the sampling efficiency near medium interfaces. The algorithm is shown to be highly accurate at relatively low computational costs. An excellent agreement with previous theoretical and experimental studies of the gratings is demonstrated by numerical simulations using our algorithm. In addition, our algorithm allows one to see real time dynamics of long leaving resonant excitations of electromagnetic fields in the gratings in the entire frequency range of the initial wide band wave packet as well as formation of the reflected and transmitted wave fronts.Comment: 23 pages; 8 figures in the png forma

Evaluating the Surface Free Energy and Moisture Sensitivity of Warm Mix Asphalt Binders Using Dynamic Contact Angle

From the environmental conservation perspective, warm mix asphalt is more preferable compared to hot mix asphalt. This is because warm mix asphalt can be produced and paved in the temperature range 20–40°C lower than its equivalent hot mix asphalt. In terms of cost-effectiveness, warm mix asphalt can significantly improve the mixture workability at a lower temperature and thus reduce greenhouse gas emissions, to be environment friendly. However, the concern, which is challenging to warm mix asphalt, is its susceptibility to moisture damage due to its reduced production temperature. This may cause adhesive failure, which could eventually result in stripping of the asphalt binder from the aggregates. This research highlights the significance of Cecabase warm mix additive to lower the production temperature of warm mix asphalt and improvise the asphalt binder adhesion properties with aggregate. The binders used in the preparation of the test specimen were PG-64 and PG-76. The contact angle values were measured by using the dynamic Wilhelmy plate device. The surface free energy of Cecabase-modified binders was then computed by developing a dedicated algorithm using the C++ program. The analytical measurements such as the spreadability coefficient, work of adhesion, and compatibility ratio were used to analyze the results. The results inferred that the Cecabase improved the spreadability of the asphalt binder over limestone compared to the granite aggregate substrate. Nevertheless, the Cecabase-modified binders improved the work of adhesion. In terms of moisture sensitivity, it is also evident from the compatibility ratio indicator that, unlike granite aggregates, the limestone aggregates were less susceptible to moisture damage

A General Solution for Troesch's Problem

The homotopy perturbation method (HPM) is employed to obtain an approximate solution for the nonlinear differential equation which describes Troesch’s problem. In contrast to other reported solutions obtained by using variational iteration method, decomposition method approximation, homotopy analysis method, Laplace transform decomposition method, and HPM method, the proposed solution shows the highest degree of accuracy in the results for a remarkable wide range of values of Troesch’s parameter

Fixed-Term Homotopy

A new tool for the solution of nonlinear differential equations is presented. The Fixed-Term Homotopy (FTH) delivers a high precision representation of the nonlinear differential equation using only a few linear algebraic terms. In addition to this tool, a procedure based on Laplace-Padé to deal with the truncate power series resulting from the FTH method is also proposed. In order to assess the benefits of this proposal, two nonlinear problems are solved and compared against other semianalytic methods. The obtained results show that FTH is a power tool capable of generating highly accurate solutions compared with other methods of literature

Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

An extension of the so-called new iterative method (NIM) has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM) and the variational iteration method (VIM) reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus

Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations

A comparative study is presented about the Adomian’s decomposition method (ADM), variational iteration method (VIM), and fractional variational iteration method (FVIM) in dealing with fractional partial differential equations (FPDEs). The study outlines the significant features of the ADM and FVIM methods. It is found that FVIM is identical to ADM in certain scenarios. Numerical results from three examples demonstrate that FVIM has similar efficiency, convenience, and accuracy like ADM. Moreover, the approximate series are also part of the exact solution while not requiring the evaluation of the Adomian’s polynomials