Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

Overview of finite elements simulation of temperature profile to estimate properties of materials 3D-printed by laser powder-bed fusion

Laser powder bed fusion(LPBF),like many other additive manufacturing techniques,offers flexibility in design expected to become a disruption to the manufacturing industry.The current cost of LPBF process does not favor a try-anderror way of research,which makes modelling and simulation a field of superior importance in that area of engineering.In this work,various methods used to overcome challenges in modeling at different levels of approximation of LPBF process are reviewed.Recent efforts made towards a reliable and computationally effective model to simulate LPBF process using finite element(FE)codes are presented.A combination of ray-tracing technique,the solution of the radiation transfer equation and absorption measurements has been used to establish an analytical equation,which gives a more accurate approximation of laser energy deposition in powder-substrate configuration.When this new analytical energy deposition model is used in in FE simulation,with other physics carefully set,it enables us to get reliable cooling curves and melt track morphology that agree well with experimental observations.The use of more computationally effective approximation,without explicit topological changes,allows to simulate wider geometries and longer scanning time leading to many applications in real engineering world.Different applications are herein presented including:prediction of printing quality through the simulated overlapping of consecutive melt tracks,simulation of LPBF of a mixture of materials and estimation of martensite inclusion in printed steel.     

Chemometric approach to the optimisation of LC-FL and GC-MS methods for the determination of nitrite and nitrate in some biological,food and environmental samples

Gas chromatography–mass spectrometry (GC-MS) method and a liquid chromatography–fluorescence (LC-FL) detection method using experimental design and optimisation approach were improved for the quantitative determination of nitrite and nitrate in biological, food and environmental samples. The obtained recoveries of nitrite and nitrate ions from samples based on both GC-MS and LC-FL results ranged from 98.5% to 98.9% for nitrite and 97.9% to 98.4% for nitrate. The precision of these methods, as indicated by the relative standard deviations (RSDs), was within the range from 2.4% to 3.6% for nitrite and 2.5% to 3.8% for nitrate, respectively. The limits of detection of nitrite and nitrate ions from samples based on GC-MS and LC-FL results ranged from 0.01 to 0.14 ng L^?1 for nitrite and 0.02 to 0.71 ng L^?1 for nitrate, respectively. The optimised isolation procedure by central composite design was successfully applied to real samples. The results revealed that the proposed procedure combined with GC-MS and LC-FL techniques is more sensitive, reliable and selective compared to the other methods available for the precise determination of trace levels of nitrite and nitrate in biological, food and environmental samples.     

Determination of low level nitrite and nitrate in biological, food and environmental samples by gas chromatography-mass spectrometry and liquid chromatography with fluorescence detection

Gas chromatography-mass spectrometry (GC-MS) and liquid chromatography with fluorescence detection (LC-FL) methods have been proposed for the determination of low level nitrite and nitrate in biological, food and environmental samples. The methods include derivatization of aqueous nitrite with 2,3-diaminonaphthalene (DAN), enzymatic reduction of nitrate to nitrite, extraction with toluene and chromatographic analyses of highly fluorescent 2,3-naphthotriazole (NAT) derivative of nitrite by using GC-MS in selected-ion-monitoring (SIM) mode and LC-FL. Nitrite and nitrate ions in solid samples were extracted with 0.5 M aqueous NaOH by sonication. The recoveries of nitrite and nitrate ions based on GC-MS and LC-FL results were 98.40% and 98.10% and the precision of these methods, as indicated by the relative standard deviations (RSDs) were 1.00% for nitrite and 1.20% for nitrate, respectively. The limits of detection of the GC-MS in SIM mode and LC-FL methods based on S/N = 3 were 0.02 and 0.29 pg/ml for nitrite and 0.03 and 0.30 pg/ml for nitrate, respectively.     

Light charged particle emission and fission in238U+238U collisions at 1,740 MeV

Inclusive⁴He and⁴H energy spectra and heavy fragment coincidence correlations have been measured for reactions of 7.31 MeV/u²³⁸U with²³⁸U and^?197Au targets. The H/He production cross sections are in the range 15–26 mb, and their emission spectra are very similar for the two systems. The observed strong kinematic shifts with angle are reproduced in shape and magnitude by Monte Carlo simulations of particle evaporation from projectile-like and target-like fragments, indicating competition between charged particle emission and sequential fission. No evidence is found for high energy charged particle emission associated with ultra-highZ composite systems. Heavy fragment measurements indicate an abundance of quasielastic and deeply inelastic reaction fragments, as well as sequential fission of target and projectile nuclei. For²³⁸U nuclei, the fission occurs predominantly in an asymmetric mode, reminiscent of fission at low excitation energy. For²³⁸+²³⁸U reactions in the vicinity of the grazing angle, the frequency of single sequential fission (with survival of the partner fragment) is twice as large as double sequential fission in which both the target and projectile undergo fission. In²³⁸U+¹⁹⁷Au reactions, the survival probability of the heavy fragments is even greater. The surprisingly high survival probabilities of high-Z fragments imply a preponderance of very soft collisions in these very-heavy-ion reactions, at least at energies not very far over the Coulomb barrier.     

A new Taylor collocation method for nonlinear Fredholm‐Volterra integro‐differential equations

The aim of this article is to present an efficient numerical procedure for solving nonlinear integro‐differential equations. Our method depends mainly on a Taylor expansion approach. This method transforms the integro‐differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unkown Taylor coefficients. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer program written in Maple10. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Approximate renormalization group calculation of cubic crossover

The cross-over exponent for an anisotropic cubic perturbation is calculated for all n > 1 and d = 3. It is found that the isotropic fixed point is unstable for $\text{n ? 2.3}$.     

SLANT SUBMANIFOLDS OF A RIEMANNIAN PRODUCT MANIFOLD

In this article, the geometry of the slant submanifolds of a Riemannian product manifold is studied. Some necessary and sufficient conditions on slant, bi-slant and semi-slant submanifolds are given. We research fundamental properties of the distributions which are involved in definitions of semi- and bi-slant submanifolds in a Riemannian product manifold.     

Derivation of Korteweg-de Vries flow equations from the regularized long-wave (RLW) equation

We perform a multiple-time scales analysis and compatibility condition to the regularized long-wave (RLW) equation. We derive Korteweg-de Vries (KdV) flow equation in the bi-Hamiltonian form as an amplitude equation.