Hermite Method of Approximate Particular Solutions for Solving Time-Dependent Convection-Diffusion-Reaction Problems

This article describes the development of the Hermite method of approximate particular solutions (MAPS) to solve time-dependent convection-diffusion-reaction problems. Using the Crank-Nicholson or the Adams-Moulton method, the time-dependent convection-diffusion-reaction problem is converted into time-independent convection-diffusion-reaction problems for consequent time steps. At each time step, the source term of the time-independent convection-diffusion-reaction problem is approximated by the multiquadric (MQ) particular solution of the biharmonic operator. This is inspired by the Hermite radial basis function collocation method (RBFCM) and traditional MAPS. Therefore, the resultant system matrix is symmetric. Comparisons are made for the solutions of the traditional/Hermite MAPS and RBFCM. The results demonstrate that the Hermite MAPS is the most accurate and stable one for the shape parameter. Finally, the proposed method is applied for solving a nonlinear time-dependent convection-diffusion-reaction problem.

Unilateral Problem for a Viscoelastic Beam Equation Type p-Laplacian with Strong Damping and Logarithmic Source

In this manuscript, we investigate the unilateral problem for a viscoelastic beam equation of p-Laplacian type. The competition of the strong damping versus the logarithmic source term is considered. We use the potential well theory. Taking into account the initial data is in the stability set created by the Nehari surface, we prove the existence and uniqueness of global solutions by using the penalization method and Faedo-Galerkin’s approximation.

The Structure of Multiphase Galactic Winds

We present a novel analytic framework to model the steady-state structure of multiphase galactic winds comprised of a hot, volume-filling component and a cold, clumpy component. We first derive general expressions for the structure of the hot phase for arbitrary mass, momentum, and energy source terms. Next, informed by recent simulations, we parameterize the cloud–wind mass transfer rates, which are set by the competition between turbulent mixing and radiative cooling. This enables us to cast the cloud–wind interaction as a source term for the hot phase and thereby simultaneously solve for the evolution of both phases, fully accounting for their bidirectional influence. With this model, we explore the nature of galactic winds over a broad range of conditions. We find that (i) with realistic parameter choices, we naturally produce a hot, low-density wind that transports energy while entraining a significant flux of cold clouds, (ii) mixing dominates the cold cloud acceleration and decelerates the hot wind, (iii) during mixing thermalization of relative kinetic energy provides significant heating, (iv) systems with low hot phase mass loading factors and/or star formation rates can sustain higher initial cold phase mass loading factors, but the clouds are quickly shredded, and (v) systems with large hot phase mass loading factors and/or high star formation rates cannot sustain large initial cold phase mass loading factors, but the clouds tend to grow with distance from the galaxy. Our results highlight the necessity of accounting for the multiphase structure of galactic winds, both physically and observationally, and have important implications for feedback in galactic systems.

NEOLOGISM IN ENGLISH-ARABIC TRANSLATION OF INFORMATION TECHNOLOGY TERMS

Technological advancements have aided in the expansion of a languages vocabulary through the addition of new items. Naming items can be accomplished during the translation process by constructing a diverse structure of neologisms. The purpose of this study was to analyse the results of technical term translations from English to Arabic in the field of Information Technology (IT) and to ascertain the frequency with which Arabic neologisms are published as a result of the process. Additionally, the study identified factors that influence the formation of neologisms through the translation process of translators. The study analysed data from the ProZ.com website regarding IT terms. The data were analysed by dividing the source term into a variety of neologism structures, such as derivatives, blended, compound, and acronym. The research was conducted using al-Sihabis theoretical framework for word formation, which classified word formation into two categories: Morphological Neologism, which refers to the process of word development, and Loan Neologism, which refers to the process of converting foreign language words to Arabic. The findings indicate that ProZ.com translators took one of two approaches to the formation of Arabic neologism: they either altered the original structure of the source term or preserved it as the structure of Arabic neologism. Nonetheless, 44% of the data wereconverted to compound form. While the majority of other neological structures are derived from the original structure of the source language. The structure of such neologisms is shaped by the translators translation process. Translators frequently translate data literally in order to preserve the source language neologism in its original form, according to studies. However, 25% of data were translated using descriptive and functional equivalence, while 13.1% of data were translated using the Arabization process, which converts source language terms that lack an Arabic equivalent.

Sound generation mechanism of compressible vortex reconnection

We study the sound generation mechanism of initially subsonic viscous vortex reconnection at vortex Reynolds number $Re~(\equiv \text {circulation}/\text {kinematic viscosity})=1500$ through decomposition of Lighthill's acoustic source term. The Laplacian of the kinetic energy, flexion product, enstrophy and deviation from the isentropic condition provide the dominant contributions to the acoustic source term. The overall (all time) extrema of the total source term and its dominant hydrodynamic components scale linearly with the reference Mach number $M_o$ ; the deviation from the isentropic condition shows a quadratic scaling. The significant sound arising from the flexion product occurs due to the coiling and uncoiling of the twisted vortex filaments wrapping around the bridges, when a rapid strain is induced on the filaments by the repulsion of the bridges. The spatial distributions of the various acoustic source terms reveal the importance of mutual cancellations among most of the terms; this also highlights the importance of symmetry breaking in the sound generation during reconnection. Compressibility acts to delay the start of the sequence of reconnection events, as long as shocklets, if formed, are sufficiently weak to not affect the reconnection. The delayed onset has direct ramifications for the sound generation by enhancing the velocity of the entrained jet between the vortices and increasing the spatial gradients of the acoustic source terms. Consistent with the near-field pressure, the overall maximum instantaneous sound pressure level in the far field has a quadratic dependence on $M_o$ . Thus, reconnection becomes an even more dominant sound-generating event at higher $M_o$ .