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In the marine ecological system, the prime role of water management and durability of an ecosystem is being played by the vegetation patches. The vegetation patches in open channels can significantly affect the flow velocity, discharge capacity and hinder energy fluxes, which ultimately helps in controlling catastrophic floods. In this study, the numerical simulation for turbulent flow properties, i.e. velocity distribution, Reynolds stresses and Turbulent Intensities (TI) near the circular vegetation patches with progressively increasing density, were performed using the computational fluid dynamics (CFD) code ANSYS FLUENT. For examination of the turbulent flow features in the presence of circular patches with variable densities, Reynolds averaged Navier-Stokes equations, and Reynolds stress model (RSM) were employed. The numerical investigation was performed in the presence of in-line emergent and submerged patches having variable vegetation density in the downstream direction. Two of the cases were investigated with three circular patches having a clear gap to patch diameter ratio of La/D = 1 (where La is the clear spacing between the vegetation patches and D is the diameter of the circular patch), and the other two cases were analyzed with two patches having a clear gap ratio of La/D = 3. The case with a clear gap ratio (La/D = 3) showed 10.6% and 153% inflation in the magnitude of longitudinal velocity at the downstream of the sparse patch (aD = 0.8) and upstream of the dense patch (aD = 3.54), respectively (where aD is the flow blockage, in which “a” represents the patch frontal area and “D” represents the patch diameter). The velocity was reduced to 94% for emergent and 99% for submerged vegetation due to successive increase in vegetation density made by introducing a middle patch which reduced the clear gap ratio (La/D = 1). For La/D = 1, the longitudinal velocities at depth z = 15cm were increased by 319% than at depth z = 6cm at the downstream of the dense patch (aD = 3.54). Whereas it was observed to 365% higher in the case of La/D = 3. The magnitude of turbulent characteristics was observed 36% higher for submerged vegetation cases having a clear gap ratio of La/D = 1. The successive increase in the patch density reduced the Reynolds stresses, turbulent kinetic energy and turbulent intensities significantly within the gap region. The major reduction in the flow velocities and turbulent properties in the gaps provides a stable environment for aquatic ecosystems nourishment and fosters sediment deposition, and supports further vegetation growth.

The variational iteration method, a powerful tool for solving nonlinear oscillators with initial conditions, has been expanded to accommodate two-point boundary conditions. In this modification, two Lagrange multipliers are introduced, and their identification process mirrors that of the conventional approach. A generalized equation is provided for a category of highly nonlinear mechanical systems, followed by three illustrative examples derived from this generalized equation. These examples serve to demonstrate the effectiveness of the method. The solutions produced by this modified approach not only show remarkable agreement with numerical results but also exhibit superior accuracy when compared to outcomes obtained through other established methods. [ABSTRACT FROM AUTHOR]

In recent decades, nano/microelectromechanical systems (N/MEMS) have garnered significant attention due to their appealing characteristics, such as compact size, batch fabrication capabilities, high reliability and low power consumption. However, these vibratory systems often present challenges, including zero conditions at the initial time, involving zero velocity and zero displacement, which complicates the solution process. Nonetheless, the theory of geometric potential offers insights into various phenomena in nanoscience and nanotechnology. In this paper, we implement the theory of geometric potential to develop an N/MEMS model. We then analyze the periodicity property of the nonlinear system using a novel method based on Sturm’s algorithm. Our analysis reveals that the model with zero initial conditions exhibits periodic solution under specific conditions on lumped parameter. Finally, we validate our findings by comparing them with numerically achieved results. [ABSTRACT FROM AUTHOR]

Physical systems frequently exhibit nonlinear behavior that remains unresolved in the majority of cases. In this study, we employ the Aboodh transform-based variational iteration method (ATVIM) to resolve the nonlinear model of a tapered beam. In order to solve the governing equation, the periodic motion is sought, and the explicit relationship between frequency and amplitude is revealed. The outcomes of the ATVIM approach are compared with those of other prevalent techniques, and a satisfactory concordance is observed between them. This study also provides an analytical approximation of the tapered beam for a detailed understanding of the effects of factors on the nonlinear frequency, which can be beneficial to researchers and engineers working on the analysis and design of structural projects [ABSTRACT FROM AUTHOR]

In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains. [ABSTRACT FROM AUTHOR]

This article discusses the variational iteration method (VIM) and its significance in solving a wide range of physical problems. The VIM does not require linearization or manipulation of nonlinear terms, making it a powerful mathematical tool. However, the identification of the Lagrange multiplier can be challenging. The article proposes a new method called the He-transform, which is a generalized integral transform that simplifies the identification of the Lagrange multiplier. This method has practical implications in various engineering fields. The authors hope that this method will attract a wide audience and be applied to solve nonlinear oscillators with generalized initial values in the future. [Extracted from the article]

Simultaneous Escape Routing (SER) is the escaping of circuit pins simultaneously from inside two or more pin arrays. This is comparatively difficult as compared to routing in a single array and has not been addressed by previous studies. The increase in pin array complexity has made the manual SER in PCBs a very inefficient and tedious task and there surely is need for the automated routing algorithms. In this work, we propose network flow based optimal algorithm that uses integer linear program to solve SER problem and area routing problem in two stages. In the first stage, pins are escaped to the boundaries of pin arrays simultaneously. These escaped pins are connected with each other in the second stage. The proposed algorithm is tested for different benchmark sizes of grids and the results show that it is not only better in terms of routability but also outperforms existing state of the art algorithms in terms of time consumption. The existing algorithms either fails to achieve higher routability or have larger time complexities, whereas the proposed algorithm achieves 99.9% routability and is also independent of grid topology and component pin arrangement, which shows the superiority of proposed algorithm over the existing algorithms.

Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations. Here we introduce a generalized integral transform, which is a generalization of the Fourier transform, Laplace transform, and other transforms, e.g., Sumudu transform, Aboodh transform, Pourreza transform, and Mohand transform, making the new transform much attractive and promising. Its basic properties are elucidated, and its applications to initial value problems and integral equations are illustrated, when coupled with the homotopy perturbation, it can be used for various non-linear problems, opening a new window for non-linear science. [ABSTRACT FROM AUTHOR]