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The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of physics and engineering. The purpose of this paper is to present results on the numerical simulation for time-fractional partial differential equations arising in transonic multiphase flows, which are described by the Tricomi and the Keldysh equations of Robin functions types.

Those resulting mathematical models are solved by using the reproducing kernel method, which provide appropriate solutions in term of infinite series formula. Convergence analysis, error estimations and error bounds under some hypotheses, which provide the theoretical basis of the proposed method are also discussed.

The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are illustrated. Finally, the prospects of the gained results and the method are discussed through academic validations.

In this paper and for the first time: the authors presented results on the numerical simulation for classes of time-fractional PDEs such as those found in the transonic multiphase flows. The authors applied the reproducing kernel method systematically for the numerical solutions of time-fractional Tricomi and Keldysh equations subject to Robin functions types.

The purpose of the paper is to extend the differential quadrature method (DQM) for solving time and space fractional non-linear partial differential equations on a semi-infinite domain.

The proposed method is the combination of the Legendre polynomials and differential quadrature method. The authors derived and constructed the new operational matrices for the fractional derivatives, which are used for the solutions of non-linear time and space fractional partial differential equations.

The fractional derivative of Lagrange polynomial is a big hurdle in classical DQM. To overcome this problem, the authors represent the Lagrange polynomial in terms of shifted Legendre polynomial. They construct a transformation matrix which transforms the Lagrange polynomial into shifted Legendre polynomial of arbitrary order. Then, they obtain the new weighting coefficients matrices for space fractional derivatives by shifted Legendre polynomials and use these in conversion of a non-linear fractional partial differential equation into a system of fractional ordinary differential equations. Convergence analysis for the proposed method is also discussed.

Many engineers can use the presented method for solving their time and space fractional non-linear partial differential equation models. To the best of the authors’ knowledge, the differential quadrature method has never been extended or implemented for non-linear time and space fractional partial differential equations.

This paper aims to present a high-order scheme to approximate generalized derivative of Caputo type for μ ∈ (0,1). The scheme is used to find the numerical solution of generalized fractional advection-diffusion equation define in terms of the generalized derivative.

The Taylor expansion and the finite difference method are used for achieving the high order of convergence which is numerically demonstrated. The stability of the scheme is proved with the help of Von Neumann analysis.

Generalization of fractional derivatives using scale function and weight function is useful in modeling of many complex phenomena occurring in particle transportation. The numerical scheme provided in this paper enlarges the possibility of solving such problems.

The Taylor expansion has not been used before for the approximation of generalized derivative. The order of convergence obtained in solving generalized fractional advection-diffusion equation using the proposed scheme is higher than that of the schemes introduced earlier.

Detailed results of numerical calculations of transient, 2D incompressible flow around and in the wake of a square prism at Re = 100, 200 and 500 are presented. An implicit finite‐difference operator‐splitting method, a version of the known SIMPLEC‐like method on a staggered grid, is described. Appropriate theoretical results are presented. The method has second‐order accuracy in space, conserving mass, momentum and kinetic energy. A new modification of the multigrid method is employed to solve the elliptic pressure problem. Calculations are performed on a sequence of spatial grids with up to 401 × 321 grid points, at sequentially halved time steps to ensure grid‐independent results. Three types of flow are shown to exist at Re = 500: a steady‐state unstable flow and two which are transient, fully periodic and asymmetric about the centre line but mirror symmetric to each other. Discrete frequency spectra of drag and lift coefficients are presented.

The lack of reliable and scalable superconducting random access memory (RAM) cells is the main obstacle for full implementation of superconducting rapid single flux quantum(RSFQ) computers. This work points the methodology and the structures that shall be used in future implementation of RSFQ RAM.

A new design for RAM using two ferromagnetic strips in proximity to the superconductor in a RSFQ computer is presented (1). The concept of using a RAM RSFQ cell as a tuneable superconducting qubit is also explored.

Two basic architectures for superconducting RAM cells were developed with integration schemes in two dimensions.

The proposed RAM cells as depicted in Figures 7 and 16 offer smaller size and greater 3 scalability in comparison to other suggested schemes (4), (3), (2), (5).

Currently, the main obstacle in implementation of RSQF computer is lack of reliable RAM cell. RSQF computer shall have potential to take a large fraction of classical supercomputers, as it consumes much less power.

Computation power shall be cheaper when one uses RSQF computers for big data and computational centres. It is a matter of some time.

The publication presents the new design of superconducting RAM cell for use in RSQF computer. The numerical relaxation method is used to solve biharmonic Ginzburg–Landau equation. The analytic approach as a solution of a specified problem is given.

Information about the former and current status of many scientific journals is summarized.

Newly‐created journals (sometimes based on old ones), cessation of issues, journals incorporated into others, merged and split journals are mentioned. Information about a large number of scientific publishers (publishing houses, scientific institutions and organizations, educational institutions, societies, associations, federations, unions and companies) which make a significant contribution to printed and electronic output are noted. The web addresses of electronic libraries, information networks, search systems, databases and catalogs of natural‐scientific literature are collected.

It behoves scientists, who profess to disseminate scientific knowledge, to avail themselves of the myriad information sources on offer.

This is possibly the first attempt to embrace comprehensively and in minute detail the vast field of information on the sources of contemporary sciences and their representative bodies.

A model for impact ionisation allowing for the spatial transient is described. Ionisation rates and phonon scattering rates are adjusted to fit experimental data. To reduce some of the uncertainty, the calculated ionisation rates due to Kane are used.

Under this heading are published regularly abstracts of all Reports and Memoranda of the Aeronautical Research Council, Reports and Technical Memoranda of the United States National Advisory Committee for Aeronautics and publications of other similar Research Bodies as issued.