Optimal Perturbation Iteration Method for Solving Fractional Model of Damped Burgers’ Equation

The newly constructed optimal perturbation iteration procedure with Laplace transform is applied to obtain the new approximate semi-analytical solutions of the fractional type of damped Burgers’ equation. The classical damped Burgers’ equation is remodeled to fractional differential form via the Atangana–Baleanu fractional derivatives described with the help of the Mittag–Leffler function. To display the efficiency of the proposed optimal perturbation iteration technique, an extended example is deeply analyzed.This work was supported in part by the Basque Government, through project IT1207-19

Approximate analytical solutions of KdV and burgers' equations via HAM and nHAM

This article presents a comparative study of the accuracy between homotopy analysis method (HAM) and a new technique of homotopy analysis method (nHAM) for the Korteweg-de Vries (KdV) and Burgers' equations. The resulted HAM and nHAM solutions at 8th-order and 6th-order approximations are then compared with that of the exact soliton solutions of KdV and Burgers' equations, respectively. These results are shown to be in excellent agreement with the exact soliton solution. However, the result of HAM solution is ratified to be more accurate than the nHAM solution, which conforms to the existing findin

Rheology of hyaluronane solutions

Předmětem tohoto studia bylo prozkoumat reologické chování vodných roztoků vysokomolekulárního hyaluronanu. Byl studován vliv zvyšující se koncentrace biopolymeru v roztoku, která se pohybovala v rozmezí od 1 do 3 hmotnostních procent, a také vliv vzrůstající iontové síly rozpouštědla, způsobené přídavkem chloridu sodného, na viskoelasticitu a stabilitu těchto roztoků. Pro obsáhlejší popis viskoelasických vlastností roztoků byla použita, vedle běžných oscilačních měření, také metoda ceepových testů, ze které bylo možno určit důležité veličity, jako je procentuální poměr viskozní a elastické složky vzorku, rovnovážná poddajnost, viskozita při nulovém smykovém napětí a retardační čas. Ty byly následně porovnávány s výstupy z jiných typů měření, jako jsou právě oscilační a tokové křivky, nebo nesly dopňující informace důležité pro detailnější popis viskoelastických vlastností těchto roztoků. Ke studiu stability vzorků během namáhání pak byla použita metoda peak-hold, která ukázala na velmi dobou mechanickou i časovou odolnost roztoků hyaluronanu a naznačila hranice, za kterými už dochází k trvalému poškození struktury a degradaci řetězců hyaluronanu a je s němi proto potřeba při manipulaci s roztoky tohoto biopolymeru pro jejich další použití v aplikacích počítat.The objective of this work was to investigate the rheological behaviour of the highmolecular hyaluronan solutions. The influence of increasing biopolymer concentration within the range from 1 to 3% wt and the influence of ionic strength, caused by the addition of NaCl into the solvent, on viscoelasticity and stability of the samples have been studied. For further description of viscoelastic characteristics of the solutions, besides common oscillation measurements, we have also used the creep test method, from which we obtained other important characteristics, such as percentual ratio of viscous and elastic portions of the sample, equillibrium compliance, zero shear viscosity and retardation time. They were compared with the results from the other types of measurements, such as oscillation and flow curves measurements. The creep measurements results contain also some complementary information, important for more detailed description of viscoelastic properties of these solutions. For the study of the sample stability during constant mechanical strain we have used the peak-hold method. These measurements proved very good mechanical and time resistance of the HA solutions and specified the limits, beyond which we observed permanent damage of the structure and degradation of the hyaluronan chains, and which have to be taken that into account when manipulating with solutions of this biopolymer.

Generalized Stacking Fault Energy Surfaces and Dislocation Properties of Silicon: A First-Principles Theoretical Study

The generalized stacking fault (GSF) energy surfaces have received considerable attention due to their close relation to the mechanical properties of solids. We present a detailed study of the GSF energy surfaces of silicon within the framework of density functional theory. We have calculated the GSF energy surfaces for the shuffle and glide set of the (111) plane, and that of the (100) plane of silicon, paying particular attention to the effects of the relaxation of atomic coordinates. Based on the calculated GSF energy surfaces and the Peierls-Nabarro model, we obtain estimates for the dislocation profiles, core energies, Peierls energies, and the corresponding stresses for various planar dislocations of silicon.Comment: 9 figures (not included; send requests to [email protected]

The effect of parental opportunism, IJV's autonomy and tacit knowledge on IJV instability: A comparison of multi-variate regression and fuzzy-set qualitative comparative analysis

This study uses an agency theory perspective to examine how the factors that influence principal (IJV parents) and agent (IJV) relationship may affect IJV instability in China. The study proposes a framework that bridges knowledge-based theory (of tacit knowledge) and agency theory (of parental opportunism) by incorporating reactance theory (of autonomy). By comparing the empirical results of fuzzy-set qualitative comparative analysis (fsQCA) and multiple regression analysis, using a sample of 203 Chinese-foreign IJVs, the study add further evidence to growing methodological consideration regarding complexity theory. The results from multiple regressions show that parental opportunism and IJV’s autonomy has a positive effect on IJV’s instability, and that the interaction of autonomy and tacit knowledge moderates the effect of parental opportunism on IJV instability. However, fsQCA uncovers more causal paths than findings from multiple regression analysis

Asymptotic expressions for the nearest and furthest dislocations in a pile-up against a grain boundary

In 1965, Armstrong and Head (Acta Metall. 13(7):759–764, 1965) explored the problem of a pile-up of screw dislocations against a grain boundary. They used numerical methods to determine the positions of the dislocations in the pile-up and they were able to fit approximate formulae for the locations of the first and last dislocations. These formulae were used to gain insights into the Hall-Petch relationship. More recently, Voskoboinikov et al. (Phil. Mag. Lett. 87(9):669-676, 2007) used asymptotic techniques to study the equivalent problem of a pile-up of a large number of screw dislocations against a bimetallic interface.\ud \ud In this paper, we extend the work of Voskoboinikov et al. to construct systematic asymptotic expressions for the formulae proposed by Armstrong and Head. The further extension of these techniques to more general pile-ups is also outlined. As a result of this work, we show that a pile-up against a grain boundary can become equivalent to a pile-up against a locked dislocation in the case where the mismatch across the boundary is small

A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers' partial differential equation

[EN] The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods cannot capture the propagation of the uncertainty from the inputs to the model output. For some problems, such as the Burgers' equation (simplification to understand properties of the Navier¿Stokes equations), a small variation in the parameters causes nonnegligible changes in the output. Thus, suitable techniques for uncertainty quantification must be used. The generalized polynomial chaos (gPC) method has been successfully applied to compute the location of the transition layer of the steady-state solution, when a small uncertainty is incorporated into the boundary. On the contrary, the classical perturbation method does not give reliable results, due to the uncertainty magnitude of the output. We propose a modification of the perturbation method that converges and is comparable with the gPC approach in terms of efficiency and rate of convergence. The method is even applicable when the input random parameters are dependent random variables.This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI), and Fondo Europeo de Desarrollo Regional (FEDER UE) Grant MTM2017-89664-P. The author Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Calatayud, J.; Cortés, J.; Jornet, M. (2021). A modified perturbation method for mathematical models with randomness: An analysis through the steady-state solution to Burgers' partial differential equation. Mathematical Methods in the Applied Sciences. 44(15):11820-11827. https://doi.org/10.1002/mma.6420S1182011827441