A novel explicit three-sub-step time integration method for wave propagation problems

A novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods.

Contrast-Independent, Partially-Explicit Time Discretizations for Nonlinear Multiscale Problems

This work continues a line of work on developing partially explicit methods for multiscale problems. In our previous works, we considered linear multiscale problems where the spatial heterogeneities are at the subgrid level and are not resolved. In these works, we have introduced contrast-independent, partially explicit time discretizations for linear equations. The contrast-independent, partially explicit time discretization divides the spatial space into two components: contrast dependent (fast) and contrast independent (slow) spaces defined via multiscale space decomposition. Following this decomposition, temporal splitting was proposed, which treats fast components implicitly and slow components explicitly. The space decomposition and temporal splitting are chosen such that they guarantees stability, and we formulated a condition for the time stepping. This condition was formulated as a condition on slow spaces. In this paper, we extend this approach to nonlinear problems. We propose a splitting approach and derive a condition that guarantees stability. This condition requires some type of contrast-independent spaces for slow components of the solution. We present numerical results and show that the proposed methods provide results similar to implicit methods with a time step that is independent of the contrast.

A Dynamic Model for the Study and Simulation of the Pantograph–Rigid Catenary Interaction with an Overlapping Span

In this paper, the authors present a mathematical and engineering model to optimally calculate the dynamic equation on the pantograph–catenary interaction when considering a rigid catenary with an overlapping span. The model starts from well-known methods adapted to the special features of rigid catenary. As a result, an algorithm for the integration of a dynamic equation based on explicit methods is provided. Moreover, from this algorithm, a reliable, efficient, and user-friendly software tool called RICATI is developed in order to approach the model to railway-based companies. The results show the usefulness of an application. such as RICATI, to check the behavior of the configuration initially established for a catenary, allowing solutions to be obtained for the problems encountered when simulating the passage of the pantograph (or pantographs), not only for the overlapping span but also for the entire catenary. That encourages us to continue future works.

Explicit Microsoft Excel Methods For Computerized System Validation

To combat CSV non-compliance, established here are cost and time effective explicit methods to verify and validate Microsoft Excel Workbooks designed to meet standards set by Australian regulatory bodies: The Therapeutic Goods Administration (TGA) and Pharmaceutical Inspection Co-operation Scheme (PIC/S).

Systematicity in Organizational Research Literature Reviews: A Framework and Assessment

In this study, we first develop a framework that presents systematicity as an encompassing orientation toward the application of explicit methods in the practice of literature reviews, informed by the principles of transparency, coverage, saturation, connectedness, universalism, and coherence. We then supplement that conceptual development with empirical insights into the reported practices of systematicity in a sample of 165 published reviews across three journals in organizational research. We finally trace implications for the future conduct of literature reviews, including the potential perils of systematicity without mindfulness.

Explicit methods for the Hasse norm principle and applications to A n and S n extensions

Let K/k be an extension of number fields. We describe theoretical results and computational methods for calculating the obstruction to the Hasse norm principle for K/k and the defect of weak approximation for the norm one torus \[R_{K/k}^1{\mathbb{G}_m}\] . We apply our techniques to give explicit and computable formulae for the obstruction to the Hasse norm principle and the defect of weak approximation when the normal closure of K/k has symmetric or alternating Galois group.